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Jan 1, 1894

By C. S. Sivaramakrishnan, Manjit Singh, Rajendra Kumar

Regarding liquid nzetals structurally as a suspm-sion of clusters , having derivated solid-state coordination, in truly liquid atoms, the recently developed Kuvlar-Samarin technique of centrifuging- in liquid state enabled the determination of the cluster sizes inAl-Cu mid Pb-Sn systems. It is shown that the colutne fraction of the clusters does not exceed 9 pct and the energy of their formation in Al-Cu is about 5.5 kcal per g-atom and in Pb-Sn eutectic alloys about 25 kcal per y-atoni. STRUCTURAL investigations of liquid state have principally followed the following three courses: i) studies with X-ray, electron, or neutron diffraction; these investigations have shown that there is a certain amount of regularity in the structure of liquid metals which can be defined by a coordination number and that the structure is a derived function of that in the solid state; ii) thermodynamical investigations which are based on the concept of ideal behavior; these describe the liquid state in terms of free-energy values and other thermodynamic functions; although these investigations are of help in the study of the general effects of alloying, they do not provide any structural insight into the precise atomic distribution in liquid state; iii) measurements of surface tension and viscosity; although it is natural to expect that the viscosity is related to the structure in liquid state, these investigations have so far only provided information which can be used by the foundry technologists and has been little utilized in formulating models of the structure of liquid state. As it happens, investigators in the three groups have worked almost independently of each other and there is practically no structural correlation between the results of one group with those of another. The purpose of the present paper is to indicate that the experimentally measured parameters of these three groups of research are closely related to the structure in the liquid state. STRUCTURE OF LIQUID METALS Although atomic distribution in solid and gaseous states is rigorously known, that of the liquid state is only appreciated on the fringes. There is no universal model of atomic distribution in liquid state, but two diverse models are at present hotly contested. The first, largely expounded by ~ildebrand,' regards the liquids as condensed gas since many of their properties and much of their behavior can be adequately described by regarding them as fluids. The second mode12j3 considers that some form of near-solid as- sociation of large number of atoms exists in the liquid state. On the other hand, ~ernal' was able to predict rather precisely the radial distribution functions in liquids on the basis of statistical geometric approach which considered that liquids are "homogeneous, coherent, and essentially irregular assemblage of molecules containing no crystalline regions or holes large enough to admit another molecule". He introduced the concept of pseudonuclei in the otherwise random structure as aggregates of closely packed tetrahedra which gradually merge into irregularity and continually replace each other. To what extent the pseudonuclei can be regarded as regions of near-solid association is indefinite but Bernal suggested that the concept of pseudonuclei can be compromised with the latter model if the near-solid associations are regarded as extremely dense and not necessarily crystalline. The difficulty in projecting the structure of liquid metals arises because they exhibit duplicity of character as some of their properties are closer to those of crystalline solids and others to fluids. There is an increasing tendency to discuss the structure of liquid metals in terms of the second concept according to which the structure of liquid metals may be conceived as consisting of i) clusters of atoms where the aggregation is a close derivative of that in the crystalline state, ii) individual atoms which behave like true liquids in respect to degrees of freedom and iii) excess number of vacancies. It is noteworthy that the introduction of only 5 pct vacancies is sufficient to transform crystalline matter into the liquid state. At any instant of time thermodynamic equilibrium exists between i, ii, and iii, but the relative proportion of the clusters and random atoms is not known. That this is so can be appreciated by the fact that, when liquid metal is rapidly cooled, liquid state vacancies may condense in the form of dislocation loops and vacancies in excess of their equilibrium number in solid state. These dislocation loops have been observed in thin foils of aluminum prepared from rapid cooled aluminum. As temperature increases above melting point the number and volume fraction of clusters decrease but those of vacancies and random atoms increase. Clusters are transient in nature. In pure metals the cluster is an aggregation of the metal itself. In alloys, however, the nature of the cluster largely depends on the interaction between solvent and solute atoms. If the interaction between unlike atoms is greater than between like atoms: the clusters are then aggregates of unlike atoms. Examples of this kind of system are A1-Cu, Mg-Pb, and so forth, i.e., systems which exhibit negative departures from the Raoult's law. In systems where the interaction between unlike atoms is smaller than be-

Jan 1, 1968

By AUGUSTUS J. MONKS, Norman L. Weiss

THE Santa Barbara Unit of the Compania Minera Asarco, of which the San Diego mill is a part, is in the Parral District of southern Chihuahua. Although the concentration of sulfide ores has been practised in Santa Barbara since 1900, the San Diego mill, completed in 1921, was the first plant in northern Mexico to attempt the treatment of oxidized lead ores. From the milling point of view the many ores that have been treated at San Diego are very similar, the differences among them being rather of degree than type. Since 1921 the number of ores from different sources treated simultaneously has varied from four to eleven; in no case have any distinctive characteristics warranted the separate treatment of any of these. The zone of oxidation, source of the ores milled at San Diego, extends to a depth of 300 to 400 ft. below the surface. These ores carry more gold and less silver, lead, copper, and zinc than the underlying sulfide ores; the gangue minerals appear comparatively unchanged by oxidation and leaching. Lead occurs in diverse minerals, chiefly in cerussite, galena, and angle-site, the proportion of the lead in galena varying considerably in the different mines. An average of the feed to the mill would show the following approximate distribution of the lead content:

Jan 1, 1930

By Hiroshi Kato, Shin’ichi Nagashima, Hiroshi Takechi

The preferred orientations detleloped during cold rolling, annealing, and hot rolling of low-carbon steel sheets have been investigated by means of an inverse pole figure technique. And X-ray line profile meas-urerrlents were made for the study of the factor which causes the textural changes between cold-rolled and recrystallized sheets. From ND (sheet normal divection) and RD (rolling direction) inverse Pole figures tlze axis detisity change with increasing cold reduction was measured and the Preferred orientations were analyzed. These results can be explained by crystal rotation due to slip during rolling deformation. The ND axis density change during annealing of cold-rollitig sheets is contrary to the change observed in the case of rolling. It was found that the orientation dependency of stored strain energy resulting from cold rolling apparently corresponds to the textural changes during recrystallization. The texture in hot-rolled sheets was found to be influenced by finishing tenlperatltre. In a sheet kol-rolled below the Ar, temperature a significant differernce in texture between the surface and central layers was obtained, the former having {hkl}(111} and {110 )(uvw) orientations and the latter having {pqr}( 110) orientation. A large number of investigations1 6 have been made on the textures of iron and low-carbon steel sheets, and, since it was shown7 13 that preferred orientations are closely related to deep drawability of steel sheets, studies14" 7 on the influence of production processes upon textures have been made from the standpoint of industrial interest. Generally, the textures in low-carbon steel sheets have several components of preferred orientations, but the overlapping of poles makes it difficult to analyze texture quantitatively from pole figures. On the other hand, an inverse pole figure directly expresses quantitative values of components of preferred orientations as the density of a certain sample axis with respect to the crystallite coordinates. Such a texture representation is desirable for a study of deep drawability. The purpose of the present work is to use both inverse and conventional pole figures, with emphasis on the former, to clar~fy the textural changes ~n low-carbon steel sheets by the production processes of hot rolling, cold rolling, and annealing. And the factor causing the textural changes during annealing is studied using an X-ray diffraction line profile technique. EXPERIMENTAL PROCEDURE Sheet specimens for study of cold rolling and annealing textures were taken from a hot-rolled strip of rimmed steel 2.7 mm thick. The chemical composition is shown in Table I. Although the study of cold-rolling textures requires a suitable material with random orientation, it is difficult to produce a perfect random one. But the used specimens, obtained from the hot-rolled strip with a finishing temperature higher than Ar3, were nearly random, such as shown in Fig. 15. These were cold-rolled to various reductions by a 4-high rolling mill with 150-mm-diam work rolls and 300-mm-diam backup rolls. The influence of hot-rolling conditions such as finishing and coiling temperatures on textures of hot-rolled strips was studied. The chemical compositions of these hot coils are given in Table I1 and the hot-rolling conditions are given in Table 111. inverse Pole ~i~ure -~easurement. Two methods for determining inverse pole figures with high precision have been proposed. The first, by Jetter et a1.,18 consists of obtaining mean densities of divided regions in a unit stereographic triangle by solving simultaneous linear equations to approximate the integral relation between conventional and inverse pole figures. The second, proposed by ~oe'~-'~ and Bunge,22'23 consists of determining an expanded series of spherical surface harmonics which express axis densities from several sets of pole distribution data. Both methods require laborious numerical calculations which make them unsuitable for practical use. However, the axis densities of the locations corresponding to low Miller indices in a unit stereographic triangle can be obtained

Jan 1, 1969

By Philip D. Wilson

IT has been my privilege to read the article prepared by R. S. Dean entitled "Production of Alumina from Low-Grade Domestic Materials" which appears on another page of this issue. Dr. Dean should be congratulated on the preparation of such an erudite and scholarly dissertation on bauxite and on the work which the Bureau of Mines has been doing in connection with the development of processes to use low-grade domestic materials.

Jan 1, 1943

By AIME AIME

HOLDING the annual dinner-dance of the Institute at the Waldorf-Astoria had become such a tradition that there was widespread regret when it became known that the demolition of the building to make way for a huge office structure would perforce bring to an end the long and enjoyable series of gatherings our Institute had held there. This year the . Commodore was the place at which it was held and the commuters on the New York Central and the New Haven railroad systems, at least, found it a more convenient place for them. Except for the famous "Hoover" dinner, which will probably set a mark for all time, it was the largest dinner the Institute held, 1000 being present, and it taxed the facilities of the hotel to the utmost.

Jan 1, 1930

By Thomas R. Couzens

Jan 1, 1985

By Roscoe W. Stensrud

Marcona Mining Company operations are located 500 kilometers south of Lima, Peru, on the Pacific Coast, at approximately 15º-22' latitude south and 75º-11' longitude west. The terrain is sandy rolling hills ranging from sea level at the coast and rising sharply (escarpment) to an elevation of 800 meters at the mine area. The climate is arid and windy with a moderate year-round temperature, ideal for a year-round mining operation. San Juan, a new and modern community of 14,000 inhabitants and developed by Marcona, houses the working forces and their families.

Jan 11, 1968

By D. J. Rose, W. M. Armstrong, A. C. D. Chaklader

The wetiability of single crystals of MgO by specimens of vacuum-cast iron was studied using the sessile drop technique in vacuo at 1550ºC. Formation of FeO at the liquid-vapor interface caused the contact angle (6) to decrease from 117 to 65 deg during the first minute. After cooling, all specimens possessed a peculiar annular interfacial deposit of Fe,O,. Within the annulus the interface showed no sign of chemical attack. Chemical reaction occurred where the iron was alloyed with Ti, V, Cr, Nb(Cb), Ta, cmd Zr. Vnriation of 6 with alloy concentration was studied. Although vanadium md chromium improved the wettability of MgO by iron, the effect of Zr, Ti, Nb, and Ta was indeterminable because the 8 derived from sessile drop considerations was that of the metal against a restrictive peripheral volume of liquid oxide wetting the substrate. INTEREST in the nature of metal-ceramic interactions has been stimulated by progressive development of metal-ceramic combinations. One of the more valuable methods used for bond investigation is the sessile drop technique. Recent attempts to improve wettability through solute additions to the drop have revealed that the solute may a) react with the oxide creating new compounds at the solid-liquid interface, b) adsorb at the interface in a monolayer formation, or c) distribute throughout the drop uniformly causing no wettability variation. This work, part m in a series1,2 of investigations of interface reactions between metals and ceramics, embraces a study of the Fe-MgO system. MgO possesses a large negative free energy of formation (-173 kcal per g mole 0, at 1550ºC) compared to FeO at this temperature (-73 kcal per g mole 02). Hence the electronegativity difference between the drop and substrate allows selection from an extensive group of metal solutes with intermediate electronegativity differences that would, in the absence of chemical reactions, be expected to adsorb pre- ferentially at the solid-liquid interface. However, the high oxygen pressure of MgO in vacuo creates an oxidation environment which influences the solute behavior. Recent studies of the Fe-MgO systemJ74 have been restricted by chemical reactions that obscured observations. In view of the current interest in liquid-phase sintering of metal-ceramic combinations under partial oxidizing conditions,5 a more comprehensive study of the Fe-MgO system seemed beneficial. EXPERIMENTAL PROCEDURE 1) Specimen Preparation. Optical-grade MgO single crystals and Ferrovac vacuum-cast iron were used in all experiments. A spectrographic analysis of the iron indicated 0.008 C, 0.05 V, 0.005 Mo, 0.01 Ti, 0.002 S, 0.01 Cr, 0.001 Mg, 0.01 Si, 0.003 A1 (wt pct). The MgO crystals were cleaved along (100) planes into plates approximately 20 by 20 by 1 mm. Following annealing in vactto at 1100°C for 3 hr, surface irregularities were removed by a chemical etch in phosphoric acid at 100°C. The iron rod was machined into small cylinders approximately 0.250 in. in diam and length and these were carefully cleaned in organic and acidic solutions to remove surface impurities. All specimens were weighed to the nearest 0.1 mg. 2) Apparatus. The apparatus described in detail by previous authors1,2 was modified for this work. A Polaroid Land Camera was incorporated into the optical system so that drop measurements at ten-second intervals after melting were possible with ultra-high-speed self-develop ing film. 3) Procedure. The iron cylinders were placed upright on the MgO plates and positioned in the molybdenum susceptor. After furnace assembly the system was pumped down to a vacuum of 1 µ and flushed with H2 at 800°C. The system was again evacuated to 5 x 10-5 mm of mercury and the temperature raised to 1550°C within 2 min. The molten drops were photographed at appropriate time intervals. TWO min after melting the iron vapor pressure caused gas discharge, or corona, within the tube. The specimens were then slowly cooled to room temperature, sectioned and examined metallographi-cally. X-ray identification of interfacial reaction products was attempted by the powder diffraction technique. Alloying elements (Ti, V, Cr, Zr, Ta, Nb) were added to the iron in various concentrations up

Jan 1, 1963

By T. V. Moore

IN many of the important problems of the petroleum engineer, it is necessary to know accurately the laws governing the flow of gas and liquid mixtures in vertical' pipes. Although much work has been done along these lines, no satisfactory solution to the problem has been found. A good theoretical discussion of the energy balance in a gas¬lift has been published-by Versluys.1 One of the most important factors affecting the efficiency of the flow of oil and gas mixtures is slippage, and in most of the experimental work that has been done no provision has been made for the measurement of this quantity. As Versluys pointed out, since there is no method now known to estimate it from the data usually taken; slippage must be determined empirically. This paper presents the results of some work carried on to, measure slippage in short experimental gas-lifts. As shown herein, slippage can be easily calculated in a vertical pipe carrying a mixture of oil and gas if the fractions of the pipe occupied by liquid and gas respectively are known. In this work, the fraction of the pipe occupied by the liquid was measured under a wide variety of conditions and the relationship between this fraction and other quantities, which are easily measured in ordinary work, was determined. It was hoped that the quantitative relationship obtained from this work could be used-for making accurate calculations in flowing or gas-lift wells, but unfortunately it did not check satisfactorily when applied to actual wells. Apparently flow in long flow pipes is mote efficient than in the short ones used for the experimental work. Nevertheless, it is felt that the data themselves are of interest; that the method of attack may be of value in future work and that the relationship derived between slip and the relative velocities is a contribution toward the solution of the gas-lift problem.

Jan 1, 1931

By C. S. Witherell

THE first feature that strikes one when considering the use of air enriched with oxygen in pyrochemical processes is the conservation of Enriched Air FIG. 1.-TEMPERATURES THEORETICALLY OBTAINABLE BY BURNING PURE AMOR¬PHOUS CARBON IN AN ATMOSPHERE COMPOSED OF AIR ENRICHED WITH OXYGEN, PRODUCING GAS CONTAINING CO. heat due to the partial elimination of the inert heat-carrier nitrogen, as set forth in the report of the committee. The second feature, which

Jan 11, 1924

By Leon W. Dupuy

Many articles have been written describing peculiar and particular types of drilling. Little correlation has been made between the character of ground to be drilled and sampled and the type of drilling most desirable for procuring satisfactory samples. In development work, the engineer and metallurgist often desire the recovery of a sample in as physically natural a condition as possible, particularly when the sample must provide material for process tests as well as chemical and physical analyses. This paper describes the results of experimentation in drilling unconsolidated materials carrying titanium minerals in the Magnet Cove area, Ark. The drilling was most difficult in that the ground varied much in consistency, and it was vitally necessary to recover a physically natural sample. Ordinary churn drilling recovered a sample that could be analyzed chemically, but the sample was not in its natural state. The problem was successfully solved by utilizing and further developing methods used in the oil and clay industries.

Jan 1, 1949

By J. C. Smock

The magnetic and polaric properties of magnetite, or magnetic iron ore: are fundamental facts in magnetism. The disturbing erect of this mineral upon the magnettic needle in land surveying must have been very early observed. The difficulties arising from this source are still almost insurmountable in making accurate surveys in districts where this ore occurs to any extent, either as a rock

By J. Tarwater

The torsional testing of cylindrical medium-carbon steel specimens, heat treated to a high strength level, revealed a stress-strain relationship that was dependent on the direction of torsional plastic pre-strain. This Bauschinger effect was observed in prestrained specimens both with and without subsequent elevated-temperature strain aging. Yield stresses in strain-aged specimens exceeded those of simply prestrained specimens and the difference in stress was greater when the prestrain direction opposed the test direction. This behavior is discussed in terms of the classical dislocation pile-up using Cottrell's equation, A plastically prestrained strain-hardenable member, loaded in a direction opposite to the direction of prestrain, produces a stress-strain relationship differing appreciably from the curve representing reloading in the prestrain direction. This phenomenon, referred to as the Bauschinger effect, will be discussed in terms of the stress differences ob- served at a specified strain. The effect, dating back to the 1880's, was first attributed to grain boundary stresses. When later work revealed that the effect was also present in single crystals, revised theories attributed the diminished applied reverse stress to assistance from internal long-range stresses. These stresses have been associated with dislocation pile-ups or with dislocation arrays having analogous stress patterns. The stress patterns are subject to alteration by interaction with interstitial solute atoms and acceleration of the interaction may be accomplished with elevated-temperature strain aging. As discussed herein, the interaction showed a directional effect with regard to the applied stresses necessary for small plastic strains. Aside from the rigorous Bauschinger stress-strai relationship, which compares prestrained members, it is interesting to compare the stress-strain curve of a member being prestrained with that of a prestrained member being reverse loaded. For small strains which are a fraction of the prestrain deformation, the applied stresses of the reverse reloaded member are smaller. However, as the reverse strain approaches the prestrain value, the stresses approach equivalence. It has been reported1 that the stress required to return a prestrained specimen to its initial "zero" position generally exceeds the prestrain stress because of the work hardening occurring on potential slip systems during prestrain.

Jan 1, 1963

By F. Lynwood Garrison

The future of the Witwatersrand depends upon the possibility of mining and milling profitably the large tonnage of relatively low-grade gold ores known to exist in that area. The problem must be solved if the existence of the gold-mining industry in South Africa is to be saved and continue. To show that this disaster may be avoided, or at least postponed for another decade or longer, the following official statement is of interest: "There is a fairly large area of possible orebody on the East Rand of whose value and depth from the surface we have some though not very accurate knowledge. There is a far larger area south of the Central Rand which probably carries much payable ore, but at depths that at present appear too great to mine. Finally, there is a narrow strip of country over 100 miles in length stretching south from the Rand to Klerksdorp and beyond, which may contain large ore-bodies. The Witwatersrand rocks outcrop over portions of this ground and in places conglomerates occur in it that carry small bodies of payable ore. There is reason to believe that conglomerates of the Witwatersrand system exist over all this strip, though they are for the most part covered by later sediments. It seems probable also that there are large blocks of payable reef in this belt, at any rate in the area that lies close to the present western limit of the developed mines. The structure in this neighborhood is however very complicated and to prove the orebodies will be both difficult and costly." Ores in the Witwatersrand It should be explained in this connection that the conglomerates mentioned here were originally old gravel beds now consolidated into bedded sedimentary rocks, very hard because strongly cemented with secondary silica. The gold exists in this cement and is rarely found in the pebbles composing the rock or bed called locally reef. It is important to realize that these gold deposits are beds; not veins as generally understood by mining engineers and geologists. In addition to these low-grade ore reserves we have also to consider the ore left behind in the old stopes of the upper levels near the surface,

Jan 1, 1931

By Charles R. Simcoe

It was pointed out in a recent paper'g that the initial flow stress of as-quenched martensite is very low even in an alloy steel with an M, well above room temperature. It was also shown that the high ultimate tensile strength resulted from a very high rate of work

Jan 1, 1967

By T. KIRKE ROSE

A Discussion of the paper by H. O. Hofman and M. G. Magnuson, read at the Lake Superior meeting, September, 1904. (British Columbia Meeting, July, 1905.) T. KIRKE ROSE, London, Eng. (communication to the Secretary*`) :-The authors have shown that, under certain conditions, the rate of dissolution of gold by chlorine and bromine is re¬duced by the addition of 10 per cent. of silver to the gold, and that the action is almost stopped when the silver amounts to 30 or 40 per cent. of the alloy. Even if full recognition is given to the practical way in which the work was done, how¬ever, it is to be regretted that Prof. Hofman and Mr. Magnuson did not determine the temperature at which the experiments were carried out. From the details given it may be inferred that the temperature was raised by chemical action by about 20° C. when 21 g. of sulphuric acid were added, and that the mixture was then slowly cooled down during the experiment. When bromine or very weak chlorine solutions were used, there could not have been any perceptible heating action. As the action of both chlorine and bromine is aided by heat, it follows that the stronger solutions of chlorine were given an unfair advantage over the weaker solutions and over bromine. If the temperature had been the same in each case, I do not think that the conclusions given oil p. 432 of the Bi-Monthly Bulletin, March, 1905, 1 would have been found to be justified. (This is speaking generally. In barrel-treatment the conditions are similar to those in the experiments.) The superior speed of bromine as compared with chlorine at equivalent strengths is not yet disproved, and the differences noted between strong and weak solutions of chlorine may have been largely a function of the temperature. Moreover, the authors used somewhat coarse particles of gold

Sep 1, 1905

By Charles H. Fulton

IT is assumed that the word "college" for the present purpose signifies technical school or technical department of a college or university. About ten or fifteen years ago, and more recently in some instances the contact between the technical school and the industry, as represented by the operating companies, was very limited. The school made no effort to place its graduates in the industry and the graduate's first position was obtained by his own or his friends' efforts; the friend often was a professor. The industries, or the operating companies, seemingly had little interest in the training of the technical graduates they employed or in seeking to discover their personal characteristics and fitness for the work. In the public mind there was little relation between technical training and industry. Such training was in the field of education; industry was in the field of business; and the interrelationship was not a matter of common knowledge or concern.

Jan 1, 1929

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'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 Simon D. Strauss

The world appetite for minerals in the, third quarter of this century grew at a higher rate than had been anticipated. To illustrate, consider the experience of four, commodities. Excluding the Communist bloc, sometimes referred to as the centrally planned economies, demand for aluminum increased at a compound rate of 8.6% between 1950 and 1975,; copper rose by 4.4%; iron ore by 5.5%; and tin, the laggard in the group, by 2%. Except for tin, the figures are substantially greater than growth rates anticipated in 1950 in the Paley Commission report and other studies. The growth rate was not evenly distributed in geographical areas. Professor Wilfred Malenbaum of the University of Pennsylvania did an interesting study breaking these figures down as among three principal sources of demand -- the United States, other industrialized nations (which he referred to as the "rich lands"), and the developing world (which he referred to as the "poor lands").

Jan 1, 1982