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By I. R. Kramer

The delay time for single crystals of iron, zinc, and pre-strained aluminum was measured under conditions of high-speed deformation. The delay time of aluminum was found to be affected by the orientation of the crystal. Under the dynamic conditions employed, tile calculated "activated volume" term appears to be very small for the three metals studied. IN a previous paper,1 it was shown that under dynamic testing conditions at 78° K, there was a delayed yield in single crystals of aluminum and copper which had been cold-worked prior to testing. The experimental results also indicated that the delay-time effect was not due to the interaction of dislocations with impurity atoms or vacancies, but rather to a dislocation-dislocation interaction since aluminum which has not been prestrained shows no delay-time phenomenon. In this paper, some data are reported on the effects of orientation on the delay time of aluminum single crystals; the delay time of zinc single crystals saturated with nitrogen and the delay time of iron single crystals also were measured. EXPERIMENTAL PROCEDURE Aluminum (99.997 pct) and zinc (99.999 pct) crystals, 1/2 in. in diam and 8 in. long were grown by the Bridgman technique. The iron single crystal was supplied by Dr. R. Maddin. The zinc crystals containing nitrogen were prepared by melting high-purity zinc in a graphite crucible and the nitrogen was introduced by additions of ammonium chloride. The liquid zinc was then drawn up into glass tubes of 1/2 in. diam and allowed to solidify. The rods were cooled to room temperature before the transfer to the mold for conversion into single crystals. The orientation of all specimens was determined by the Laue' back-reflection technique, Fig. 2 and Table I. To prepare for the delay-time measurements, the crystals were cut with a fine jewelers saw and the ends carefully machined. The specimens then were electrolytic ally polished to remove the cold-worked metal, mounted in a special fixture and hand-lapped. As a final step, the crystals were annealed in evacuated tubes. Specimens of aluminum crystals, Nos. 24 and 26, were compressed 0.5 and 2 pct, respectively, in the direction of the later impact. The zinc specimens were aged at 50°C for 15 min, In the case of iron, only two specimens could be obtained. To obtain sufficient data, it was necessary to resort to a reaging treatment. After each delay-time test, the specimens were aged at 65° C for 100 min. This treatment, according to Clark,2 is sufficient to restore the original delay time. It is believed that although the specimens were plastically deformed approximately 10-4 pct, after each test the delay-time values are reliable. The delay-time measurements were made in an apparatus similar to that described previously.' Single crystals approximately 1 in. long and having a diameter of 1/2 in. were placed in a pendulum which consisted of a bar 1/2 in. in diam and 8 ft long, designed with a crystal holder to accommodate the specimen at low temperatures. The crystal was held at a position 2 ft from the front part of the pendulum. This portion of the apparatus was supported on a fine molybdenum wire. A projectile bar of the same diameter and length comprised the other portion of the apparatus. This bar was supported on

Jan 1, 1962

The Lead-Line Update held in conjunction with the 1977 SME-AIME Fall Meeting in St. Louis provided sessions on mining, mineral processing, extractive metallurgy, and economies to brief the record on the industry's activities and developments since the 1970 World Symposium on Lead and Line convened, also in St. Louis. Changes in the industry since 1970 have not been profound, notes the program committee, consisting of D. O. Rausch, F. M. Stephens, and B.C. Mariacher, cochairmen; and H. L. Clifford, S. C. Fall), and M. Snedeker. However, various environmental and conservation factors have had a direct impact on process consideration and operating practice; the result has been new mines, improved technology, and changing market opportunities. The general consensus of the participants is that the future for the Lead-zinc industry looks promising as new applications are found and new products resulting from intensive research reach the marketplace. The highlights of the HS technical papers presented at the 1977 session follows.

Jan 11, 1977

By John K. Hammes

INTRODUCTION This introductory paper presents a description and definition of what the finance function is and what it specifically means for the mining industry. In its simplest terms, finance is, "management of money matters". As an area within the discipline of business administration it draws heavily on the related fields of economics and accounting, and to a lesser extent on marketing and production. MINING FINANCE DEFINED In preparing to write about what finance means to the mining industry, I asked a number of mining people the question, "What does mining finance mean to you?" Most responded that mining finance was "How a company borrowed money for mine development", and perhaps half those questioned included "raising equity" in the definition. It is not surprising that the mining industry concept of finance is the providing of funds needed for the objectives of the business, for that was once a view shared by authorities in the field of business administration. Further, it is certainly the area where much of the emphasis has been placed in the past ten to fifteen years as the industry struggled with the development of more remote and more refractory or lower-grade orebodies while profitability and internal cash flow were below expectations. No wonder project finance became such a popular topic. Twenty years ago it is probable that the emphasis would have been on mine valuation, for that subject was the area of finance then most often examined in industry publications. Papers concerning the pros and cons of payback, internal rate of return, and discounted cash flow appeared regularly. Let's examine the following situations, each the result of a financial decision: - Funding the exploration program in a developing country was accomplished by buying the next six-months budget needs in local currency. One week later the currency devalued 30 percent. If the purchase had been delayed or the local currency borrowed short term, a substantial saving would have been made in funding the program. - A major mining company borrows heavily to finance both expansion of its primary mining business and its entry into several new industry segments. When markets for all of the commodities it produces turn down for a prolonged period, there is concern over the adequacy of cashflow to cover debt service in addition to other company needs. The company's financial officers, however, had arranged very large committed credit facilities from numerous financial institutions which assured the availability of funds for several years. This enabled the company to implement a strategy to conserve cash, sell assets and survive until conditions improved. Further, short term suppliers of credit also were comfortable with the assurance that longer term credit was there to support them. -A medium size mining company financed several mines independently with limited obligations on the part of the parent company. The company decided to refinance the operations under one agreement. More flexible terms, lower interest cost and a longer tenor financing were achieved in return for assuming the risk as a direct obligor. - The exploration and development group of a large mining company proposes to develop a new mine in a country in which the company does not presently operate. When the investment is rejected they are advised that one reason was that the reinvestment assumption inherent in the discounted

Jan 1, 1985

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

By Wing L. Lew

LEAD, silver, and zinc, in quantities of economic importance are found in the Aguilar ore. The lead occurs as galena and the zinc as sphalerite and marmatite. The silver occurrence is more complex. Pyrargyrite and proustite have been identified only occasionally. Galena is silver-bearing and so are the various other sulphides, though to a lesser degree. The principal nonsulphide gangue minerals include calcite, quartz, wollastonite, rhodonite, and various calcium, aluminum, and iron silicates. A typical analysis of, the ore is: Pb, 11.2; Zn, 12.3; Fe, 4.4; Mn, 2.2; Cu, 0.15; S, 11.2; CaO. 7.6; "Insoluble," 50.1 percent; and Ag 263 g per ton. Crushing is done in three stages. The primary crusher at the mine is set to deliver about a 5-in. product. The crushed ore is then transported to the secondary crushing plant by a 3-km cableway where the general practice is to hold the product of the first Symons to about 1 in., and of the second Symons to about 1/2 in. When the ore is soft and rich the product of the first Symons is by-passed directly to the ball-mill bins. Dust control in the secondary crushing plant is effected by enclosing the dust-emanating sources and exhausting the enclosures with a Clarage No. 18 fan driven at 1300 rpm by a 20-hp motor. Use is also made of spray water at one or two critical places. Every effort is made to keep the air free from visible dust. Dust counts taken at the working places show dust concentrations of less than six million particles ner cu ft. The composition

Jan 1, 1947

By D. K. Das, P. A. Beck, S. P. Rideout

IN a previous publication1 1200°C isothermal phase diagram sections were given for the Cr-CO-Ni, Cr-Co-Fe, Cr-Co-Mo, and Cr-Ni-Mo ternary systems, in which the a phase formed narrow, elongated solid solution fields. The present investigation is concerned with the 1200°C isothermal sections of the Co-Ni-Mo, Co-Fe-Mo, and Ni-Fe-Mo ternary systems. A prominent feature of these systems is the presence of narrow, elongated µ phase fields. The crystal structure of the phase designated as µ both here and in the previous publication1 was determined by Arnfelt and Westgren.2 For the (CO, W)µ phase, named by them Co,W, (and also frequently designated as a), these authors found that the crystal system is hexagonal-rhombohedra1 and the space group is D53d — R3,. Westgren and Mag-neli3 later found that isomorphous phases exist in the Fe-W and the Fe-Mo systems (these phases are often referred to as < and E, respectively). Henglein and Kohsok4 stated that the phase described by them as Co7Mo,; (otherwise frequently designated as c) is also isomorphous with the above three. The Co-Fe-Mo system was investigated at 1300°C by Koester and Tonn,5 who found a continuous series of solid solutions between (Co, MO)µ and (Fe, MO)µ Koester6 also indicated similar uninterrupted solid solutions in the Ni-Fe-Mo system. However, since the Ni-Mo binary system does not have a phase isomorphous with F, Koester&apos;s diagram is expected to be erroneous. No data appear to be available in the literature concerning the Co-Ni-Mo system. The face-centered cubic (austenitic) solid solut,ions of iron, nickel, and cobalt, which are quite extensive in all three systems at 1200°C, are here designated as the a phase. The body-centered cubic (ferritic) solid solutions, based on iron, are designated in this report as the ? phase, in conformity with the nomenclature used previously.&apos; Experimental Procedure The alloys were prepared by vacuum induction melting in zirconia and alumina crucibles. The lot analyses for the metals used have been given.&apos; The number of alloys prepared was 46 for the Co-Ni-Mo system, 65 for the Co-Fe-Mo system, and 113 for the Ni-Fe-Mo system. The compositions of these alloys were selected with due regard to maximum usefulness in locating phase boundaries. The alloy specimens were annealed at 1200°C in an atmosphere of purified 92 pct helium and 8 pct hydrogen mixture. Alloys consisting almost entirely of the face-centered cubic austenitic a phase, or of the body-centered cubic ferritic c phase were double-forged with intermediate annealing. The double-forged specimens were then final annealed for 90 hr at 1200 °C and quenched in cold water. Alloys containing considerable amounts of any of the other phases could not be forged. Such specimens were annealed for 150 hr at 1200°C and quenched. Microscopic specimens of all alloys were prepared by mechanical polishing, in many cases followed by electrolytic polishing. Description of the polishing and etching procedures used and tabulation of the intended compositions of the alloys prepared are being published in two N.A.C.A. Technical Notes.7,8 , Many of the alloys were analyzed chemically and, in general, the results are in excellent agreement with the intended compositions. X-ray diffraction samples were prepared by filing or crushing homogenized alloy specimens and by reannealing the obtained powders in evacuated and sealed quartz tubes. After annealing for 30 min at 1200°C the tubes were quenched into cold water. X-ray diffraction patterns were made with unfiltered chromium radiation at 30 kv, using an asymmetrical focusing camera of high dispersion. X-ray diffraction and microscopic methods were used jointly to identify the phases present in each specimen. The amounts of the phases in each alloy were estimated microscopically. The phase boundaries were located by the disappearing phase method. The results were used to construct 1200°C isothermal sections for the three ternary phase diagrams. The accuracy of the location of the phase boundaries determined in this manner is estimated to approximately ±1 pct of each component. The portion of the three phase diagrams lying between the µ, P, and 6 phases on the one hand, and the molybdenum corner on the other, has not been investigated. Recently Metcalfe reported0 a high temperature allotropic form of cobalt on the basis of dilatometric results and of cooling curves. In the present work no attempt was made to search for the new phase in the cobalt corner of the Co-Fe-Mo and Co-Ni-Mo systems. No alloy was prepared with more than 80 pct Co; the alloys used were intended to locate the boundary of the a phase saturated with cL. The microstructures of the quenched a alloys near the cobalt COrner gave no suggestion of an in-suppressible transformation On quenching. The location of the boundaries of the a + ? two-phase fields in the Fe-Ni-Mo and Fe-CO-MO systems was determined entirely by the microscopic method. The face-centered cubic a alloys near the ? field transform partially or wholly into the body-centered cubic ? phase on quenching from 1200°C to room temperature. The ? formed in this manner has an

Jan 1, 1953

Jan 1, 1918

By R. E. HORE, J. B. Tyrrell

IN the vicinity of Kirkland Lake, northern Ontario, several gold mines are producing, and three are at present being operated very profitably. At these three mines and on the adjoining properties east and west of them there have been important developments during the past year, and additional equipment has been installed to permit a large increase in output. At the end of 1924 the total production amounted to $13,688,600. For the year 1926 the production is estimated at about $19,000,000, and during 1926 the output should be much greater than that of 1925. The mines which are being operated most profitably and are producing a large part of the ore now being milled are the Wright-Hargreaves, Lake Shore and Teck-Hughes. Others which have contributed smaller amounts are the Tough-Oakes-Burnside and the Kirk- land Lake Gold mines.

Jan 1, 1926

By A. CHESTER BEATTY

SO much has been written about African, and particularly about Northern Rhodesian, copper during the past two years that I feel safe in assuming that you are familiar with the general background of the Rhodesian picture. Therefore, I will confine myself to certain of the high lights in connection with the history, geology, development, ore reserves, and contemplated mining methods in this relatively new and highly important copper field., Unlike most of the other great orebodies of the world, the Roan Antelope mine was not discovered by the hoof of a starving prospector&apos;s faithful burro; nor even, as its name might suggest, by a well-placed kick of protest from an antelope stumbling over a malachite outcrop. Late in 1905 an English prospector named Collier, traveling in the N&apos;Dola district, came upon some natives using a green powder for medicinal purposes. Closer examination of the powder revealed that it &apos; was ground-up malachite. Collier endeavored to persuade the natives to tell him where they obtained this medicine, but&apos; for a long time without success, because of the general feeling among the natives that they did not wish to reveal the resources of their land to the white. Finally however, - he persuaded- brie &apos;of-the elders to at" least take &apos;him part way toward, the- place where the malachite was supposed to occur. The bid took him, to a point on the lower regions of the Luanshya river and there left him with the instructions that if he followed the stream up toward its.

Jan 1, 1931

By C. E. Abbott

THE Birmingham district, Alabama, is distinctive in the proximity to one another of its deposits of iron ore, coal and flux. These three basic requisites for the making of iron and steel are found within a radius of 10 miles. Both dolomite and limestone are produced, the former for blast-furnace flux and the latter for basic open-hearth operations. The Tennessee Coal, Iron and Railroad Co., a subsidiary of the United States Steel Corporation, operates a limestone mine at Muscoda, near Bessemer, 12 miles southwest of Birmingham, served by its own railroad transportation system. The mine has a capacity of 130 tons per hour. Average analyses of a recent month&apos;s production are as follows: Fe2O3 Si02 A12O3 CAC03 MGCO Lump, per cent 0.51 0.22 98.63 0.14 Crushed and washed, percent 0.70 0.26 98.36 0.18 Lump stone, 2 1/2 to 7 1/2 in., is used in open-hearth operations at Fairfield Steel Works. Fine crushed and washed stone, 1 ¼ to 0.063 in., is calcined at the, lime-burning plant and used for lime charges at the Ensley open hearths.

Jan 1, 1936

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1&apos;2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By M. F. Goudge, R. V. Tomkins

Sodium sulfate is an important chemical raw material that is being used in ever increasing quantities in modem industry. It comes on the market mainly in three forms: (1) Salt cake (Na2SO4), a relatively crude form of the anhydrous salt containing up to 3 pct impurities, and comprising about three-quarters of the North American production; (2) anhydrous sodium sulfate (Na2SO4), a refined form containing less than 0.3 pct impurities; (3) Glauber&apos;s salt, the decahydrate (Na2SO4.10H2O) containing 55.9 pct water of crystallization. Competing with salt cake from natural sources is byproduct salt cake from a number of industrial operations. For instance there is Mannheim cake resulting from the manufacture of hydrochloric acid by the reaction of salt (NaCl) and sulfuric acid in Mannheim furnaces; rayon cake, a high-quality product, resulting from the process of making rayon by the viscose process; chrome cake from the processing of sodium chromate to dichromate; phenol cake from the manufacture of phenol; also byproduct sodium sulfate resulting from the conversion of lithium sulfate to lithium carbonate; from the processing of sodium tetraborate to boric acid; from converting sodium formate to formic acid; and in the manufacture of cellophane. Sodium sulfate is also obtained as a byproduct in the manufacture of isosebasic acid. In addition strong competition has resulted from imports of byproduct salt cake from the chemical industries of a number of highly industrialized European countries. However in recent years due to technological changes the output of byproduct salt cake is rapidly diminishing and the natural deposits are becoming the most important source of sodium sulfate used in North America. For instance, the production of hydrochloric acid in Mannheim plants has become obsolete and thus the greatest single source of byproduct salt cake will disappear. Also viscose rayon is meeting strong competition from nylon and other synthetic fibers and production of byproduct salt cake from this source may do little more than remain at the present level. These factors together with increasing demand for sodium sulfate point to increased production from natural sources. In 1958, 36 pct of the total United States production was derived from natural sources and in addition 97,000 short tons was imported so that over 40 pct of the total consumption was supplied by natural sources whereas in 1953 the proportion was only 24 pct. The rapid growth in production is shown in Table 1. Principal Sodium Sulfate Minerals There are many minerals in which sodium sulfate is a constituent but those of commercial importance at the present time, and consisting wholly of sodium sulfate in either the hydrous or anhydrous states, are mirabilite and thenardite. Minerals of potential importance but consisting in part of compounds other than sodium sulfate are glauberite in which sodium sulfate is combined with calcium sulfate, and blödite in which sodium sulfate is combined with magnesium sulfate. Mirabilite (Na2SO4.10H2O) the decahydrate, consists of 24.8 pct SO3, 19.3 pct Na2O, and 55.9 pct H20. It is a colorless to opaque, soft, water-soluble mineral with a slightly bitter taste. It has a hardness of less than 2 and a specific gravity of 1.48. It forms long needle-

Jan 1, 1960

US 4,189,461-Hydrometallurgical extraction of values from a sulfide ore of copper, silver, nickel, cobalt, molybdenum or zinc Ore is leached in a first stage with an aqueous nitric acid leach liquor and In a second stage the preleached mineral is oxidized with nitrogen dioxide to enable the metal values to be solubilized. The second-stage leach liquor is routed to the first stage, while first-stage liquor is subjected to electrolysis or other treatment for values This patent is a continuation- in-part of US Patent No. 4,132,758, dated Jan 2, 1979. R E Lueders and T C Franiewicz, assigned to Kennecott Copper Corp Feb. 19, 1980. 8 pp. (423-27). Filed. 2-23-78 (880,552). (Drawing below)

Jan 1, 1982

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy&apos;s law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By C. N. Kravig

STANDARD raises at Homestake are 150 ft long. Raises of more than 150 ft, driven with the use of a cage and hoist, are considered long raises- some have been driven more than 900 ft. Long raises have eliminated the need for access drifts on each level when transfer and ventilation raises are driven. These timbered cage raises, 7x9 ft in cross section, include a rock compartment and a combination cage, pipe, and manway compartment. To prevent excessive weight on the timbers, 10x10-in. bearing beams are cemented into hitches cut in the rock at 150-ft intervals. The beams also hold back timber movement caused by daily drawing of rock through the rock compartment.

Jan 6, 1957

By L. J. Dijkstra, R. J. Sladek

IN earlier work the effect of manganese on the general behavior of nitrogen in iron was the subject of a careful examination by Fast.&apos; Part of the investigation was made, in collaboration with one of the present authors (L.J.D.), by using the internal friction method. This technique, which has been described elsewhere,&apos; showed some significant changes in the properties of Fe-N alloys by the addition of a small amount of manganese namely: 1—Under standard conditions the maximum of the nitrogen peak in pure iron appears around 20 °C and the half width is about 27 °C. By addition of 0.5 atomic pct Mn a general broadening of the internal friction peak occurs. The half width is increased by about 9°C. Moreover, a shift of the maximum of about 5°C toward a higher temperature takes place, Fig. 2. 2—The precipitation of nitrogen from the supersaturated solution, measured, e.g., at 200 °C, was inhibited by the addition of the amount of manganese given in effect 1. The broadening of the nitrogen peak was confirmed in more recent work3 on samples which were prepared from Westinghouse Puron iron. The effect of manganese on the rate of precipitation, however, was much less striking than in the earlier work&apos; based on Philips high purity iron. Theory To explain the first change in properties just referred to, effect 1, the following two assumptions were made:&apos; First, every manganese atom in sub-stitutional solid solution creates around it six interstices located between an iron and a manganese atom, as is evident from Fig. 1. These interstices, conveniently called Fe-Mn interstices, have for nitrogen a free energy level which is AG* lower than the normal Fe-Fe interstices between two iron atoms. For such low concentrations of manganese as 0.5 atomic pct, the possibility that two manganese atoms will be nearest neighbors can be disregarded. Second, it is assumed that in addition to the normal relaxation time TFe at least one new relaxation time, Mn, Fe, enters in the phenomena which is associated with the elementary diffusion jumps between a Fe-Mn interstice and an adjacent Fe-Fe interstice. Fig. 1 gives schematically the free energy for a nitrogen atom as a function of its position along the line ABC. A tentative analysis of the nitrogen peak in a 0.5 pct Fe-Mn alloy based on these assumptions has been made in Fig. 2. The dotted curve with a maximum at 22°C is caused by jumps between Fe-Fe interstices, the dotted curve with maximum at 32°C by jumps between an Fe-Mn and an Fe-Fe interstice. The two effects added together give the dash-dot internal friction curve for the alloy. In the following these two components will be referred to as the normal peak at 22°C and the abnormal one. (The small secondary peak at

Jan 1, 1954

By Morris Muskat

TEe method of R. W. Moore&apos; for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

By Morris Muskat

TEe method of R. W. Moore&apos; for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period April 1 to 15. William B. McKinley, New York, N. Y Collier Cobb, Chapel Hill, N. C. C. W. Goodale, Butte, Mont. E. P. Fleming, Guayacan, Chile. D. C. Brown, San Luis Potosi, Mex. Albert Sauveur, Cambridge, Mass. W. H. Rettie, Yonkers, N. Y. H. M. La Follette, La Follette, Tenn. Mark B. Kerr, San Francisco, Cal. E. Fleming L&apos;Engle, New York, N. Y. H. W. Turner, San Francisco, Cal. H. Garlichs, St. Louis, Mo. Frank M. Leland, Mackay, Idaho. Henry Hay, London, England. Sir Robert Hadfield, London, Eng. Edward J. Way announces that his agreement as consulting engineer in South Africa for the Anglo-French Exploration Co., Ltd., having terminated, he will engage in professional consulting work with headquarters at 135 Cullinan Buildings, Simmonds St., Johannesburg, South Africa.

Jan 5, 1914