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By L. A. Schrider, J. A. Wasson

A method of predicting waterflood performance has been developed that combines certain facets of several previously published prediction techniques. The manner of combination has required the development and use of some new and some little-known relationships and has eliminated several of the weaker assumptions inherent in the original individual prediction methods. This approach, which was designed for computer solution, has removed the necessity of referring to plotted curves and permits the analytical prediction of water flood performance for a five-spot well pattern in either homogeneous or stratified reservoirs. The Predicted values are expressed in common oilfield units rather than in abstract or dimensionless terms. The calculation procedure has been programmed in FORTRAN IV and the entire program listing is available to potential users.* Introduction Prior to initiation of secondary recovery of oil by waterflooding, the possibilities of economic success or failure must be evaluated with the greatest practical accuracy. Although many prediction techniques are available, most, if not all, have serious limitations. In recent years, the Bureau of Mines has attempted to stimulate interest in the secondary recovery of oil from Appalachian pressure-depleted reservoirs. Waterflooding, because of its widespread acceptance and success, is the principal secondary-recovery method considered. During the life of the project, several performance prediction methods have been studied and applied. Because these methods, individually, have inherent assumptions and limi-tations, portions of some of them have been selected and combined in an effort to eliminate such shortcomings wherever possible. We believe that the resulting technique is as accurate as the necessary available data will permit and that it has several distinct advantages over previously published methods. Development of the Method The fractional flow equation developed by Buckley and Leverett' from Darcy's law is the fundamental mathematical statement describing immiscible fluid-fluid displacement in porous media. A generalized form of this relationship, whose derivation is readily available in the literature, is The formation dip, a, is usually very small in those petroleum reservoirs being considered for pattern waterflooding in the Appalachian area. Therefore. in many cases. a has an almist negligible value. In addition, Ap, the difference between the density of water and the density of oil, is relatively small. For these reasons the gravitational term may often be neglected. Capillary pressure is a function of saturation, which is in turn a function of distance from the upstream boundary of the system or the injection well. In this study it is assumed that the frontal zone of the waterflooding (or zone of capillarity) has negligible length and that only those saturations in the water-swept zone at breakthrough and later are of interest. As the distance in a waterflood pattern is comparatively large and the change in water saturation with distance is usually small, the change in capillary pressure with distance is negligible. The simplified form of the fractional flow equation is appropriate, therefore, in this application. Three variables must be considered in determining that fraction of the total fluid flow that consists of water: the viscosity ratio, saturation, and relative permeability ratio.

Jan 1, 1969

By Irving B. Cadoff, Ernest Levine

The crack formation and propagation in the single -phase Cu-4 pct Ag alloys were studied. The alloys were loaded in mercury to various stress levels, the mercury was removed, and the specimen examined for cracks. Cracks were found to develop below the fracture stress; the frequency of such cracks increased with increasing stress level. Some cracks were nmpropagative. Fracture in mercury was found to occur by the link-up of cracks formed at various stress levels rather than by the growth and propagation of a single crack. If the mercury environment is removed prior to a critical amount of crack formation, then continued loading results in ductile fracture. The appearance of the cracks at selected grain boundaries is related to the relative orientation of the boundaries, as are the propaga-tive characteristics of the crack. The mercury interaction appears to be one of lowering the strength of the metal-metal bonds in the high-stress area of the grain boundary. GRIFFITH'S microcrack theory1 proposed a critical crack size above which a crack in an elastic material grows with decreasing energy at a stress of From his theory it was proposed that the presence of a liquid tends to lower the surface energy of the microcrack faces2 leading to a decrease in the critical crack size necessary for spontaneous fracture propagation. stroh3 proposed that the stress concentration at a grain boundary due to pile-up may initiate a microcrack at the grain boundary. petch4 and Stroh5 evaluated the stress distribution at the head of a pile-up in a polycrystal-line material and deduced that the critical crack size and hence of is dependent on the grain size. Experimental verification of this dependence was found by petch6 for hydrogen embrittlement of steel. Studies in stress-corrosion cracking7 have provided a picture of fracture which shows that initial separations occur in a scattered, independent fashion in regions of high tensile stress. A minimum or threshold stress is necessary to produce a sufficient stress concentration to initiate frac- ture. These separations join up to form a crack. The extension of fracture is largely discontinuous and consists of a joining up of cracks. In recent worka evidence of this scattered crack network was found in a Cu-Ag alloy embrittled by mercury. For the Cu alloy-Hg couple, the crack path has also been found to be dependent on the orientation of adjacent grains, and with the addition of zinc to mercury a reduction in embrittlement along with a change in fracture morphology was found.9 In this present study, a mercury-dewetting method was used to observe crack initiation and fracture morphology when a Cu-4 pct Ag alloy is deformed in mercury and Hg-Zn solutions. PROCEDURE Specimens of Cu-4 pct Ag were prepared as in previous crack-path studies.' The specimens were heated at 770°C for 24 hr and water-quenched Tension tests using a table-model Instron were carried out in mercury and in various concentrations of Hg-Zn. Loading was in steps up to the fracture stress, with the load being removed and the specimen examined for surface cracks at each step. The specimens were dewetted after each load to permit examination of the surface structure and rewetted prior to continued loading. The specimens were wetted by electro polish ing in phosphoric acid, rinsing in alcohol, and then immersing in a pool of mercury. Dewetting was accomplished by flame heating the specimen for 30 sec in a vacuum. Some surface contamination was found, but not enough to obscure crack configurations and grain boundaries. RESULTS Fracture Characteristics in Mercury. Fig. 1 is a stress-strain curve showing the progressive step-wise loading of the specimen. As may be seen from the graph, the first position stopped at a is at a stress 5000 psi below the expected fracture stress of 25,000 psi. Examination of the specimen after removal of mercury showed only one crack. The appearance of this crack at a stress far below the fracture stress of this alloy in mercury did not affect the stress-strain curve in any manner. The specimen was then recoated with mercury and deformation was continued (curve b, Fig. 1) raising the stress by 4000 psi, and the same procedure re~eated. The initial crack was located and appeared as in Fig. 2 (crack lb). In this figure the crack is

Jan 1, 1964

By F. W. Smith

Within the Northern Pennine Orefield, England, intersections of fluorite veins are generally richest in ore, and their recognition enables investigation of the ore potential of the intersecting bodies. A method, based on routine analysis of fluorite for yttrium, has been used with success in mines of the district to predict the location of intersections in partially developed fluorite-bearing ore bodies. This short note is intended as a brief introduction; the details of United Kingdom applications are to be published at a later date. Geology The Northern Pennine Orefield is the second largest fluorspar-producing region in Britain. The associated minerals galena, sphalerite, chalcopyrite, barite, and witherite have all been extensively worked in the past but, with the exception of a single barytes mine, all of these operations are now abandoned. Galena alone is recovered as a byproduct of fluorspar beneficiation. At the present time two companies are producing about 38,000 tpy of fluorspar from high grade vein ore bodies, and a number of concerns are actively prospecting in old lead workings. The mineralization is localized in veins and replacement flats within favorable lithologies in an alternating limestone, sandstone, shale sequence. Since the thickness of individual beds is not great (generally less than 20 m), vein bodies tend to be ribbon-shaped, with length greatly exceeding width and height (Dunham). They thus present difficult exploration targets for conventional diamond drilling techniques. Ore grade varies greatly along the veins, which can change rapidly in character from mineral stained fault gouge to massive mineral bodies up to 10 m in width. It has been known for a very long time that the richer ore bodies tend to be associated with vein intersections in favorable beds. It is assumed that vein fissure intersections provided vertical channelways through which hot ore-bearing brines were able to ascend from deeper cavities in the sequence. Thus investigation of intersections at other horizons generally yields further ore bodies. Technique The relative concentration of yttrium in fluorite is a good indicator, in the North Pennines, of the direction of flow of mineralizing fluids. In all of the ore bodies so far studied in detail in this region, the concentration of yttrium increases markedly in the direction of vein intersections that are believed to have acted as feeder zones to the remainder of the bodies. The reason for this relationship is probably connected with the degradation of soluble rare earths-fluoride complexes by the changes in various physicochemical parameters of the hydrothermal fluids as they entered the ore body cavities from the feeder zones. The simultaneous release of free fluoride ions also contributed to the increased ore values in these intersection zones. Yttrium values in fluorite taken from a longitudinal traverse of the western ore body, Redburn mine, Rookhope, are plotted in [Fig. 1.] The position of a major vein branch and three cross veins are clearly indicated by yttrium maxima. The cross veins themselves contain up to 2.5 m of low grade fluorspar ore. The exact positions of B and C were unknown previous to the geochemical survey. Similar results have been obtained for several other veins and ore bodies in the area. Clean fluorspar was collected as bulk samples from within 300 mm of the vein wall and, since the vein infilling is simple, with mineral growth from the walls inward, analyses of the samples are considered comparable along the length of the ore body. A number of samples taken from the center of the vein show a

Jan 1, 1975

By Thomas Fraser, Alvaro Abreu

The work described in this paper was carried out under the sponsorship of the Foreign Economics Administration and in cooperation with the Departamento Nacional da Produggo Mineral, Rio de Janeiro. The project was undertaken to obtain complete data on the variations in washability of coal to be used for coke manufacture in the steel industry and to determine the economy of preliminary hand-sorting operations. The coal-producing industry of Brazil is in that pioneering stage in which operating practices and methods are just being developed. Increased wartime demand for fuel, coincident with a drastic curtailment of foreign supplies due to lack of shipping facilities, has put a tremendous pressure on the national industry to furnish more coal. Under this incentive, production facilities are being -expanded- and new methods of operation are being tested. Such changes are being developed both by improvement of existing methods that originated in the field and by adaptation and modification of methods introduced from the United States and Europe. These mining conditions and mining practices in Brazil are typical of what the American mining engineer will find in many instances when he goes pioneering into the developing coal fields of the Southern Hemisphere. The producing coal fields of Brazil are all in the southern states of that country. The coal measures are in a band roughly paralleling the coast and extending in a generally southwesterly direction from northern Sao Paulo through the states of Paraná, Santa Catarina and Rio Grande do Sul to near the Uruguayan border in the vicinity of Bajé. The accompanying map1 (Fig. I) shows the general location of these fields and also the principal routes of movement of both national and imported coal in a late pre-war year (1940). Statistical data on production by states up to that year are given in Table I. Rio Grande do Sul is still the largest producer among the coal states; but wartime

Jan 1, 1947

By Alvaro Abreu, Thomas Fraser

The work described in this paper was carried out under the sponsorship of the Foreign Economics Administration and in cooperation with the Departamento Nacional da Produggo Mineral, Rio de Janeiro. The project was undertaken to obtain complete data on the variations in washability of coal to be used for coke manufacture in the steel industry and to determine the economy of preliminary hand-sorting operations. The coal-producing industry of Brazil is in that pioneering stage in which operating practices and methods are just being developed. Increased wartime demand for fuel, coincident with a drastic curtailment of foreign supplies due to lack of shipping facilities, has put a tremendous pressure on the national industry to furnish more coal. Under this incentive, production facilities are being -expanded- and new methods of operation are being tested. Such changes are being developed both by improvement of existing methods that originated in the field and by adaptation and modification of methods introduced from the United States and Europe. These mining conditions and mining practices in Brazil are typical of what the American mining engineer will find in many instances when he goes pioneering into the developing coal fields of the Southern Hemisphere. The producing coal fields of Brazil are all in the southern states of that country. The coal measures are in a band roughly paralleling the coast and extending in a generally southwesterly direction from northern Sao Paulo through the states of Paraná, Santa Catarina and Rio Grande do Sul to near the Uruguayan border in the vicinity of Bajé. The accompanying map1 (Fig. I) shows the general location of these fields and also the principal routes of movement of both national and imported coal in a late pre-war year (1940). Statistical data on production by states up to that year are given in Table I. Rio Grande do Sul is still the largest producer among the coal states; but wartime

Jan 1, 1947

By J. H. Swislzer

TWO-LIQUID miscibility gaps have been found to exist in both the CaO-SiO, system above 1705 and the Cr,03 system above 2200"c. Glasser and 0sborn3 studied the extension of these miscibility gaps into the Ca0-Si0,-Crz03 ternary system and reported that the two-liquid region is not present at temperatures below the monotectic temperature of 1705°C in the CaO-SiO, system. The present authors, in connection with other work on surface-tension measurements and foam stabilities in the same ternary system,4 observed that the miscibility gap exists at temperatures as low as 1600°C. A brief experimental study was devoted to deter- mining tie-line positions in the two-phase region. The technique used was to obtain a separation of phases at 1600°C, then to quench-in the high-temperature phases and obtain a chemical analysis of each phase. It was necessary to take special precautions in obtaining a phase separation because of a tendency toward emulsification of the two liquids. The procedure followed is described in the schematic drawing in Fig. 1. A small platinum crucible containing several pinholes on its sides was placed inside a larger platinum crucible. An excess of Crz03 was placed in the outer crucible, together with a prefused binary CaO-Si02 mixture, and the Cr203 was allowed to diffuse through the pinholes and saturate the same binary CaO-SiOl mixture in the smaller crucible. After equilibration at 1600°C, the inner crucible contained only the lighter liquid (liquid A) saturated with Cr203. The outer crucible contained layers of both liquids. Experimental data were obtained by analyzing the entire contents of the inner crucible and only the bottom layer of the larger crucible (liquid B). The upper layer of the outer crucible was not suitable for chemical-analysis purposes because dispersions of the second phase sometimes were found in the samples. The technique is described in more detail in Ref. 4. The same method was used by Grieveson and urkdoan' to study a miscibility gap in sulfate-ferrite melts, where the liquids were difficult to separate because of similarities in density. In addition to the phase-separation experiments, a few others were conducted to obtain information

Jan 1, 1964

By D. Walton, B. Chalmers

A preferred orientation is known to occur frequently in the columnar zone of castings. This has been attributed to a preferred direction of growth. However, no satisfactory mechanism was proposed by which the preferred direction of growth led to the preferred orientation. The purpose of this work has been to establish this mechanism. It has been found that in general the observed preferred orientations only develop when the preferred directions of growth reveal themselves by dendritic growth. A mechanism based on this premise is found to be in agreement with the experimental data obtained in the course of this work. WHEN a liquid metal is allowed to solidify in a mold, it usually freezes in three stages, distinguished from each other by the size and shape of the grains. The first zone to freeze (the chill zone near the mold wall) consists of relatively fine grains that are equiaxed in shape and random in orientation. The next zone consists of crystals that are elongated in the direction of heat flow, i.e., normal to mold wall. These crystals are much larger in cross section than the crystals of the chill zone and have a very strongly preferred orientation. This is the columnar zone. The final zone, which is absent in very pure metals, is again equiaxed and randomly oriented, but usually has a much coarser grain size than the chill zone. The purpose of this study is to describe and account for the crystal size and orientation in the columnar zone. The occurrence of a preferred orientation in the columnar zone is well known, and in 1940, Greninger' suggested that it is apparently related to dendritic growth although at that time the only data were for metals with the face-centered-cubic structure. Table I shows that the direction of dendritic growth and the crystal axis that follows the heat flow direction coincide in all cases so far studied. The term "dendritic growth" is used here to represent the branched type of morphology that is characteristic of growth into supercooled melts.' In addition to the supercooling which is necessary before nucleation will occur at the mold wall, the necessary supercooling for continued dendritic growth can be provided in a mold by heat flow into the already formed solid at an interface whose Liquidus temperature is depressed by an accumula-

Jan 1, 1960

By P. Gordon, A. S. Iyer

IN a paper on the mechanical behavior of heat-treated steel, N. H. Polakowski' put forward arguments to the effect that the stored energy resulting from the deformation of metals should be reduced during the inital stages of subsequent deformation carried out under conditions which produce work softening. At the time (1957) the only energy measurements available as indirect evidence on this point were the results of M. M. Degtyarev,2 some of which Polakowski reproduced in his Fig. 6, and which are again reproduced here in Fig. 1. The solid lines in the upper part of Fig. 1 are Degtyarev's, the dashed Lines Polakowski's prediction of the true trend of the stored energy in copper samples pre-strained in tension and then given various amounts of subsequent compression. The accuracy of this prediction has been borne out by some experiments carried out on American Smelting and Refining Co. copper (99.999' percent Cu) by the present authors. Bars of this copper about 0.4 in. in diam and 12 in. long were prepared by vacuum melting and casting, followed by cold forging and swaging in several stages of about 40 pct reduction in area with intermediate recrystallization anneals. After the final anneal one bar was deformed in tension to 30 pct elongation; the gage length was then cut into several samples which were given axial compressions of various amounts. The hardness of

Jan 1, 1960

By K. G. Davis, P. Fryzuk

WEINBERG,' in an investigation of solute distributions along unidirectionally solidified rods of dilute silver in tin alloys, concluded that, for rods of 2 mm diameter or larger, a very high degree of convective mixing takes place in the melt ahead of the advancing interface. Suggested causes for this mixing were (1) thermal convection, (2) convective currents set up by changes in fluid density associated with concentration gradients, and (3) currents set up by changes in volume during freezing. Evidence was presented that causes (2) and (3) were not primarily responsible for solute mixing. Further, convective mixing took place in horizontal rods with temperature gradients as low as 6°C per cm, putting doubt on the importance of thermal convection. In the present work, convective mixing is examined in melts with known initial solute distributions. The absence of a moving solid-liquid interface eliminates convection caused by volume changes on solidification. In the first experiment, three silica tubes 2 mm in diameter and approximately 20 cm long were filled with an alloy of 100 ppm Ag in tin (99.999 pct purity), placed adjacent to one another in a horizontal furnace, and solidified from one end at 1 cm per hr. A110, a Y emitter, was used as tracer. A few centimeters at the start of the rod were left un-melted, to determine the initial concentration Go. After solidification was complete, one sample was removed. The hot furnace was then brought back to

Jan 1, 1965

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

By L. S. Darken

The manufacture and treatment of metals comprises operations whose effectiveness depends in large measure upon diffusion phenomena. The significance of such phenomena has, for a few simple cases, long been understood, but in more complex cases it has not been adequately recognized. This paper presents a mathematical analysis of some of the cases in which diffusion leads to the formation of a new phase within the metal, and this analysis provides a basis for interpreting quantitatively many apparently diverse experimental observations recorded in the literature, some of which are outlined in the following pages. OBservt1ons Recorded in Literature An outstanding instance is the general type of phenomenon in which diffusion of an element into an alloy is followed by a phase change, which most frequently is a reaction (precipitation) of the diffusing element with one or more components of the alloy to form a compound. Thus in certain alloys heated in contact with oxygen not only the usual oxide scale appears but, in addition, beneath the surface, a well-defined zone in which free oxide particles are dispersed with notabIe uniformity. This zone, commonly referred to as the subscale or zone of internal oxidation, is remarkable in that the visible boundary between it and the unaltered metal is usually sharp. Such a subscale, which appears to have been recognized first in oxidized copper alloys, has been described and studied by C. S. Smith,l by Rhines,2 and by Rhines, Johnson and Anderson;3 but it appears also in other alloys when they are exposed to conditions that bring about the precipitation of some compound, not necessarily an oxide. Another clear case of this same kind is the diffusion of carbon into a steel containing an element such as molybdenum, chromium, vanadium or tungsten, whose carbide is less soluble in iron than iron carbide, the result being that some part of that element is precipitated as a dispersed carbide. A similar phenomenon may occur on the welding of two alloys each of which contains one of a pair of elements that react to form a compound or a new phase of any sort. But in addition to the precipitation of a compound formed from the diffusing element, other effects may result merely from the presence of the diffusing element. For instance, if homogeneous austenite, nearly saturated with respect to carbon, is heated in contact with silicon in the absence of oxygen, one would expect to find, behind the several iron-silicon phases analogous to a scale, a zone of austenite containing dispersed carbide, because of the fact that silicon decreases the solubility of carbon in iron. As still another example, oxidation of an alloy may result in diffusion toward the surface of one or more of the constituents; for instance, during oxidation of a steel containing an element such as "copper, which is less prone to oxidation than iron, there is a notable enrichment of copper just beneath the scale-metal interface. AS an example of a yet more

Jan 1, 1942

By L. S. Darken

The manufacture and treatment of metals comprises operations whose effectiveness depends in large measure upon diffusion phenomena. The significance of such phenomena has, for a few simple cases, long been understood, but in more complex cases it has not been adequately recognized. This paper presents a mathematical analysis of some of the cases in which diffusion leads to the formation of a new phase within the metal, and this analysis provides a basis for interpreting quantitatively many apparently diverse experimental observations recorded in the literature, some of which are outlined in the following pages. OBservt1ons Recorded in Literature An outstanding instance is the general type of phenomenon in which diffusion of an element into an alloy is followed by a phase change, which most frequently is a reaction (precipitation) of the diffusing element with one or more components of the alloy to form a compound. Thus in certain alloys heated in contact with oxygen not only the usual oxide scale appears but, in addition, beneath the surface, a well-defined zone in which free oxide particles are dispersed with notabIe uniformity. This zone, commonly referred to as the subscale or zone of internal oxidation, is remarkable in that the visible boundary between it and the unaltered metal is usually sharp. Such a subscale, which appears to have been recognized first in oxidized copper alloys, has been described and studied by C. S. Smith,l by Rhines,2 and by Rhines, Johnson and Anderson;3 but it appears also in other alloys when they are exposed to conditions that bring about the precipitation of some compound, not necessarily an oxide. Another clear case of this same kind is the diffusion of carbon into a steel containing an element such as molybdenum, chromium, vanadium or tungsten, whose carbide is less soluble in iron than iron carbide, the result being that some part of that element is precipitated as a dispersed carbide. A similar phenomenon may occur on the welding of two alloys each of which contains one of a pair of elements that react to form a compound or a new phase of any sort. But in addition to the precipitation of a compound formed from the diffusing element, other effects may result merely from the presence of the diffusing element. For instance, if homogeneous austenite, nearly saturated with respect to carbon, is heated in contact with silicon in the absence of oxygen, one would expect to find, behind the several iron-silicon phases analogous to a scale, a zone of austenite containing dispersed carbide, because of the fact that silicon decreases the solubility of carbon in iron. As still another example, oxidation of an alloy may result in diffusion toward the surface of one or more of the constituents; for instance, during oxidation of a steel containing an element such as "copper, which is less prone to oxidation than iron, there is a notable enrichment of copper just beneath the scale-metal interface. AS an example of a yet more

Jan 1, 1942

By F. M. Lewis, E. C. Johnson

Used as a classifier in a plant expanding capacity or changing to closed-circuit operation, the liquid-solid cyclone offers the advantage of being adaptable to existing conditions. This paper presents the costs involved and experience gained from operating a unit of this kind. BY now application of the liquid-solid cyclone to various classification problems in the chemical and metallurgical fields is more or less familiar. A less publicized application receiving wider consideration as time goes on is its use as a classifier in closed-circuit grinding operations. This paper presents the costs involved and the experience gained from operating a unit of this kind. In May 1951 the Tennessee Copper Co. installed in its London mill at Copperhill, Tenn., a liquid-solid cyclone in closed circuit with a 6x12-ft ball mill. The circuit in which this cyclone is used is the regrind or secondary grinding circuit of a copper flotation plant. Originally it consisted of a 7x1-ft conical ball mill in closed circuit with a bowl classifier. Changes made in the primary grinding circuit of the mill necessitated a regrind circuit of greater capacity. The bulk concentrate to be ground was raised from 900 or 1000 tpd to 1200 or 1300 tpd, and to accommodate this increase a 6x12-ft ball mill which had been in the primary grinding circuit was moved into the regrind circuit. When this was done it was found that the classifier was too small to give efficient operation. Space in the plant was at a premium, and since use of the cyclone offered considerable economy the installation shown in Figs. 1-3 was made. The unit installed is a 24-in. diam cyclone classifier with a 20" cone angle. Diameter of the vortex finder is 8 in., the feed entrance area 20 sq. in. Maximum diameter of the adjustable apex valve is 6 in. and minimum diameter approximately 3.5 in. To refer again to Figs. 1 and 2, the cyclone* is mounted motor. It is charged with 18 tons of 1-in. balls. The overflow, or fines, passes by gravity directly to the copper flotation plant. The ball mill discharge and the new feed combine in a sump from which they are sent to the cone by an 8x6 SRL pump at a rate of 497 gpm. Pressure at the cyclone is 5 psi. For reasons dictated by the nature of the ore treated, particularly the bonding of fine grains of chalcopyrite to pyrrhotite, the froth from the second cell of the copper rougher circuit is returned to the regrind mill. This flow, which somewhat complicates the standard closed-circuit calculation, is seen in Fig. 1 to be 156 tpd of solids. This combines with the cyclone classifier underflow to constitute the ball mill feed. The requirement of the regrind product is that it be 77 to 80 pct —200 mesh. The liquid-solids cyclone operating in conjunction with the 6x12-ft mill adequately met this requirement. Of primary importance is the fact that this arrangement provided sufficient classification capacity to replace the undersized classifier and was capable of building up a circulating load to 87 pct, large enough to give an efficient grind. In this instance the circulating load is taken as the ratio of sands to new feed. Any comparison of performance between this liquid-solid cyclone and the replaced classifier would of course be unfair, since the bowl classifier was

Jan 1, 1955

By A. Bentzen, S. S. Wong, W. K. Fletcher, B. J. Price, A. J. Sinclair

One hundred eleven pyrite samples from three porphyry-type deposits in the Canadian Cordillera were analyzed (many in duplicate) by AA spectrophotometry for Co, Ni, Cu, Pb, Zn and Mn. All elements have density distributions that are lognormal or combinations of lognormal populations. Co and Ni in pyrites show zonal patterns that relate generally to mineralogical zones in the porphyry systems, particularly if contoured as the Co/Ni ratio. High Cu and Mn values in pyrites also correlate with Cu-rich mineralogical zones. Other elements studied appear less regular in their distribution patterns, although Pb and Zn highs in pyrite seem to occur sporadically near the margins of porphyry systems. These data considered with two other studies permit construction of an empirical model for the distribution of certain minor elements of pyrites from porphyry systems of the calc-alkalic suite. In particular cases pyrite geochemistry shows potential as an exploration tool to aid in target definition for detailed exploration.

Jan 1, 1978

By J. Brett, S. Friedman

A study of the diffusion of nickel into both fibrous and recrystallized 0.065-in.-diam silica-alumina doped tungsten wire at 1200°C has been conducted. The diffusion profiles were determined by chemical dissolulion of successive circumferential layers and spectro-photometric determination of nickel in the etchant. It was shown that the diffusion of nickel into tungsten is markedly structure-sensitive. No significant amount of nickel could be introduced at 1200°C into tungsten which had first been recrystallized at temperatures of 2300°C, leading to an upper limit estimate for the bulk diffusivity of nickel in tungsten of 10-11 sq cm per sec at 1200°C. However, nickel did diffuse into initially fibrous wires, caused re crystallization, and was alsays present at the advancing recrystallization front. The accumulation of nickel in an initially fibrous region ceases when the recrystallization front arrives. The characteristics of the resulting diffusion profiles are explained in terms of the relation between diffusion processes and micro structural changes. WHILE it is well-known that the presence of nickel and certain other metals causes low-temperature recrystallization of the cold-worked fibrous structure of doped tungsten,''' the character of the phenomenon is not well understood. Recently it was shown that the recrystallization reaction can be induced at low temperatures by the presence of solid nickel on the surface of doped wire, but not by exposure to nickel vapors.3 Once recrystallization was initiated, a continued source of nickel was required for propagation of the recrystallization front. The phenomenon appeared to be a complicated solid-state reaction since, in addition to the change in structure of the tungsten from fibrous to equiaxed grains, diffusion of nickel from the surface into the recrystallized and fibrous structures was occurring with possible chemical reaction between nickel and tungsten at the surface and interaction of nickel with the dopants which ordinarily stabilize the fibrous structure within the wire. The objective of the present work was to study the diffusion of nickel into fibrous and recrystallized tungsten structures in order to clarify the relationship of the diffusion process to nickel-induced recrystallization. Studies of interdiffusion in the Ni-W system4"7 have been principally concerned with the mobility of tungsten in nickel. Information on diffusion of nickel in tungsten is meager, and there seem to be no studies of the mobility of nickel in tungsten which elucidate the structural aspects of the phenomenon. The present experiments were designed to determine the diffusivity of nickel at 1200°C in fibrous tungsten, in large-grained tungsten prerecrystallized at high tem- perature, and in tungsten recrystallized at 1200°C due to the presence of nickel. Although the concentration profiles were determined in these experiments, unexpected changes in boundary conditions or complex diffusion paths complicated the analysis of these profiles so that the interpretation could not be readily expressed in terms of simple diffusivities. EXPERIMENTAL PROCEDURE The experiments were conducted on Sylvania 0.065-in.-diam silica-alumina doped commercial tungsten wire, hereafter designated as ordinary doped wire. A special lot of 0.065-in.-diam silica-alumina doped low-nickel wire was also used. Impurity analyses of the wire are given in Table I. The experimental design is shown in Fig. 1. All heat treatments were conducted in vacuum. Two groups of ordinary doped wire were prepared for diffusion with nickel. One group in the as-received (fibrous) condition was elec-tropolished, nickel-plated, and annealed at 1200°C for 20 and 40 hr, or was exposed to nickel vapor at 1200°C for 20 and 40 hr. The second group was recrystallized to an equiaxed grain structure at 2300°C for 3 hr, electropolished, nickel-plated, or exposed to nickel vapor for anneals at 1200°C for 20 and 40 hr.

Jan 1, 1969

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-' because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:' J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.' As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA' and CC' define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970

By D. J. Carney, J. Chipman, N. J. Grant

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some remaining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By Ernest Kirkendall

The amount of research done in the last fen years on the subject of diffusion in solid metals is significant of the importance of this problem. To review the literature dealing with diffusion is unnecessary here. Deschl in 1912 reviewed the work that had been done on diffusion in solids and gave a bibliography of the literature published before that time. Mehl's paper in 19362 is an excellent review of diffusion in metals and contains a large bibliography. Of importance also for it? review and bibliography is an article by 14. I. Krynitsky.~ While considerable material lias appeared in the literature on diffusion in brass, the amount of information is not great compared to that pertaining to some of the other alloys. Most of the information published is of a qualitative nature; that which is quantitative varies considerably. Thus the quantitative determination of the rates of diffusion of copper and zinc in alpha brass by a new method appeared worth while. In the present investigation the rate of diffusion of zinc in approximately the same composition alpha brass has been determined :it three temperatures. Procedure The method used consisted of plating copper on a beta brass, heating it, to allow diffusion to take place, and measuring the concentration of copper by determining the lattice constant of the alloy. This method is unique in that it uses a beta brass of such a composition that at the tem perature at which diffusion takes place the beta brass is saturated wit11 copper. Thus, while the beta brass supplies thc zinc, no diffusion takes

Jan 1, 1939

By Ernest Kirkendall

The amount of research done in the last fen years on the subject of diffusion in solid metals is significant of the importance of this problem. To review the literature dealing with diffusion is unnecessary here. Deschl in 1912 reviewed the work that had been done on diffusion in solids and gave a bibliography of the literature published before that time. Mehl's paper in 19362 is an excellent review of diffusion in metals and contains a large bibliography. Of importance also for it? review and bibliography is an article by 14. I. Krynitsky.~ While considerable material lias appeared in the literature on diffusion in brass, the amount of information is not great compared to that pertaining to some of the other alloys. Most of the information published is of a qualitative nature; that which is quantitative varies considerably. Thus the quantitative determination of the rates of diffusion of copper and zinc in alpha brass by a new method appeared worth while. In the present investigation the rate of diffusion of zinc in approximately the same composition alpha brass has been determined :it three temperatures. Procedure The method used consisted of plating copper on a beta brass, heating it, to allow diffusion to take place, and measuring the concentration of copper by determining the lattice constant of the alloy. This method is unique in that it uses a beta brass of such a composition that at the tem perature at which diffusion takes place the beta brass is saturated wit11 copper. Thus, while the beta brass supplies thc zinc, no diffusion takes

Jan 1, 1939