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By Raymond B. Ladoo, C. A. Stokes

Bruce C. Netschert—It is unfortunate that the authors of this paper consider it necessary to begin with an expression of concern over possible false interpretations of the word "economics." In their preoccupation with the definition of economics, they have adopted a definition of mineral economics which is, to say the least, unduly narrow. Just as the broad field of economics is not confined to a study of the profitability of business concerns, but includes the problems of production, distribution, and consumption as they pertain to society as a whole; so an inclusive definition of mineral economics should not be confined to the determination of the profitability of mineral-producing and processing enterprises, but should include the significance of the unique characteristics of mineral resources as raw materials for the use of society. Such features as the exhaustibility and localized, haphazard occurrence of deposits, the existence of a secondary (scrap) supply, and the increasing cost of operation during the life of a mining enterprise are obviously factors which concern those businesses which are producing mineral raw materials, since they partially determine the profitability of such enterprises. They are also of concern to society as a whole, however, as characteristics of one of the basic elements of the economic system. In the last analysis, the contribution which mineral economics can make as a means of determining and guiding social policy with respect to the production and utilization of mineral resources is perhaps more important than its use as a basis for determining the cost accounting procedure of individual firms. The list of "economic factors peculiar to the industrial minerals" which the authors present is in reality an application of such a broad definition of mineral economics. An inconsistency appears, however, in the inclusion of items 8 and 9 in the list. As this writer sees it, the point in question is: What influences do the characteristics of industrial minerals have on the characteristics and operating procedures of industrial mineral enterprises which are not present in the metallic mineral field? In answering this question with items 8 and 9, Messrs. Ladoo and Stokes do not recognize that there are two distinct types of differences between the two fields of enterprise. There are, on the one hand, important basic economic distinctions due to inherent economic characteristics of industrial minerals which do not pertain to metallic minerals. On the other hand are those characteristics of the industrial mineral enterprises peculiar to them alone, but which are superficial and temporary, in that they may be changed or eliminated at the discretion of the managers of those enterprises. The lack of adequate research and development in industrial mineral production, processing, and marketing (item 8) is not due to an inherent characteristic of industrial minerals. It is true that one may perhaps describe the field of industrial mineral enterprise in terms of such a deficiency, just as one could, until recently, point to a similar lack of research and development in the coal industry; but unless it can be shown that the deficiency has been wholly or partially due to the very nature of industrial minerals themselves it is not an "economic factor peculiar to the industrial minerals" but a temporary characteristic peculiar to the industry. In the writer's opinion, the authors have not demonstrated that the former relationship exists. Similarly, item 9, the "influence of technologic developments," is also not inherently peculiar to industrial minerals. Nowhere in the discussion of this item do the authors mention anything that is not equally applicable to the field of metallic minerals. This is not meant to imply that the specific technologic developments which the authors list are of equal significance in both fields. It does mean that such a statement as, "technological advances together with new consuming areas to provide markets make deposits commercially valuable which once were of no interest" cannot be considered as an argument that technological developments have significance in the field of industrial minerals alone. In considering the problem of stockpiling, the authors note that the stockpiling of nonstrategic materials might be desirable if future wartime needs could exceed domestic production capacity, but dismiss this as hardly adequate to justify such stockpiling. The problem, however, can be stated in broader economic terms, i.e., the real costs (as distinguished from the money costs) of prewar versus wartime production. In other words, it might well be that the labor and capital required to produce a given amount of a certain mineral raw material could be used more efficiently in another industry. In such a case it is obviously advantageous to stockpile the material in prewar times rather than forego the benefits of additional production in another line of endeavor during wartime under conditions which demand the optimum use of all resources, including manpower and capital. To the writer's knowl-

Jan 1, 1951

By Raymond B. Ladoo, C. A. Stokes

Bruce C. Netschert—It is unfortunate that the authors of this paper consider it necessary to begin with an expression of concern over possible false interpretations of the word "economics." In their preoccupation with the definition of economics, they have adopted a definition of mineral economics which is, to say the least, unduly narrow. Just as the broad field of economics is not confined to a study of the profitability of business concerns, but includes the problems of production, distribution, and consumption as they pertain to society as a whole; so an inclusive definition of mineral economics should not be confined to the determination of the profitability of mineral-producing and processing enterprises, but should include the significance of the unique characteristics of mineral resources as raw materials for the use of society. Such features as the exhaustibility and localized, haphazard occurrence of deposits, the existence of a secondary (scrap) supply, and the increasing cost of operation during the life of a mining enterprise are obviously factors which concern those businesses which are producing mineral raw materials, since they partially determine the profitability of such enterprises. They are also of concern to society as a whole, however, as characteristics of one of the basic elements of the economic system. In the last analysis, the contribution which mineral economics can make as a means of determining and guiding social policy with respect to the production and utilization of mineral resources is perhaps more important than its use as a basis for determining the cost accounting procedure of individual firms. The list of "economic factors peculiar to the industrial minerals" which the authors present is in reality an application of such a broad definition of mineral economics. An inconsistency appears, however, in the inclusion of items 8 and 9 in the list. As this writer sees it, the point in question is: What influences do the characteristics of industrial minerals have on the characteristics and operating procedures of industrial mineral enterprises which are not present in the metallic mineral field? In answering this question with items 8 and 9, Messrs. Ladoo and Stokes do not recognize that there are two distinct types of differences between the two fields of enterprise. There are, on the one hand, important basic economic distinctions due to inherent economic characteristics of industrial minerals which do not pertain to metallic minerals. On the other hand are those characteristics of the industrial mineral enterprises peculiar to them alone, but which are superficial and temporary, in that they may be changed or eliminated at the discretion of the managers of those enterprises. The lack of adequate research and development in industrial mineral production, processing, and marketing (item 8) is not due to an inherent characteristic of industrial minerals. It is true that one may perhaps describe the field of industrial mineral enterprise in terms of such a deficiency, just as one could, until recently, point to a similar lack of research and development in the coal industry; but unless it can be shown that the deficiency has been wholly or partially due to the very nature of industrial minerals themselves it is not an "economic factor peculiar to the industrial minerals" but a temporary characteristic peculiar to the industry. In the writer's opinion, the authors have not demonstrated that the former relationship exists. Similarly, item 9, the "influence of technologic developments," is also not inherently peculiar to industrial minerals. Nowhere in the discussion of this item do the authors mention anything that is not equally applicable to the field of metallic minerals. This is not meant to imply that the specific technologic developments which the authors list are of equal significance in both fields. It does mean that such a statement as, "technological advances together with new consuming areas to provide markets make deposits commercially valuable which once were of no interest" cannot be considered as an argument that technological developments have significance in the field of industrial minerals alone. In considering the problem of stockpiling, the authors note that the stockpiling of nonstrategic materials might be desirable if future wartime needs could exceed domestic production capacity, but dismiss this as hardly adequate to justify such stockpiling. The problem, however, can be stated in broader economic terms, i.e., the real costs (as distinguished from the money costs) of prewar versus wartime production. In other words, it might well be that the labor and capital required to produce a given amount of a certain mineral raw material could be used more efficiently in another industry. In such a case it is obviously advantageous to stockpile the material in prewar times rather than forego the benefits of additional production in another line of endeavor during wartime under conditions which demand the optimum use of all resources, including manpower and capital. To the writer's knowl-

Jan 1, 1951

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By L. B. Gittinger

Sulfur is a nonmetallic element widely distributed in nature. It constitutes 0.06% of the earth's crust but only a very small portion occurs in sufficiently concentrated amounts to justify mining. Sulfur occurs in practically all animal and plant life. It constitutes approximately 0.09% of the elements in the oceans; it has been found in meteorites. Sulfur was known and used by man before recorded history. The American Chemical Society approved spelling for the element is sulfur. The English spelling sulphur is used commercially in the United States. In ancient times, sulfur was called brimstone, literally "burning stone." Today the term brimstone is used interchangeably with the term elemental sulfur. Sulfur is found naturally in the elemental form in subsurface deposits associated with gypsum and anhydrite in salt domes and sedimentary formations in evaporite basins and in solfatara-type deposits associated with volcanoes and mineral springs. Sulfur occurs also in molecular combination in ferrous sulfides (pyrites and pyrrhotite) and nonferrous sulfides (copper, lead, zinc, and nickel), and in mineral sulfates (gypsum and anhydrite); as hydrogen sulfide contaminant in natural gas; as organic compounds in crude oil and tar sands; and as pyrite and organic compounds in coal and oil shales. Sulfur resources are abundant and exist throughout the world but the extent to which they can be classified as reserves is greatly circumscribed by prevailing prices and technology. Estimates of world sulfur reserves are compiled by the U.S. Bureau of Mines. A compilation of reserves by area and source of sulfur published in 1970 and presented here as [Table 1] totaled 2.47 billion tons (Lewis, 1970). The effect of the decline in prices which has occurred since the earlier estimate is dramatically illustrated by the 1972 estimate of the U.S. Dept. of the Interior which shows world sulfur reserves of only 1.2 billion tons (Anon., 1972d). Sulfur is produced commercially from one or more sources in nearly 70 countries of the world. World production of sulfur in all forms totaled 41.6 million tons in 1971. (Sulfur statistics given in this chapter are long tons.) Native deposits, sulfides and oil and gas contributed, respectively, 31, 41, and 25% of world production (Table 2). Of the sulfur produced from native deposits, salt domes accounted for 54% and evaporite basin deposits, 44%. Volcanic deposits are of little significance except for local consumption. The past two decades have seen important shifts in the world's sulfur sources. In 1950, native deposits and sulfides each supplied about one-half of the world's production. During the 1950s, sulfur recovered from oil and natural gas grew rapidly, representing about 10% of the total by 1960. Since then, the petroleum industry has continued to increase its relative importance as a source of sulfur, representing more than 30% at 1972 year-end. Sulfur is generally classified as elemental or nonelemental for statistical purposes. Elemental sulfur is sulfur produced in the pure, uncombined form. It includes production from native deposits, as well as that recovered in the elemental form from oil and natural gas or other sulfur-bearing materials. When produced from other than native deposits, it is generally referred to as recovered elemental sulfur. Nonelemental sulfur is that which is utilized commercially in molecular combination with other elements, such as sulfides or sulfates. Elemental sulfur is being produced from salt dome deposits in the Gulf Coast region of the United States and the Isthmus of Tehuantepec in Mexico, and from evaporite basin deposits in west Texas, Poland, Sicily,

Jan 1, 1975

By Jack L. Taylor

Single crystals of tungsten grown from powder -metallurgy swaged rod by high-temperative annealing were deformed in tetzsion at temperatures from 2500 to 5000 OF. Orientation of specittzen tensile axis, strained ratrix, and defortnation bands was determined optically by reflections from {110} etch pits. Slip traces meve analyzed and slip directiorz determined. Results indicate that {110}(111) , {112){111}. and {123}{111} type slip occur in tungsten over the terpe,atuve rutge investigated. Slip is orientation-dependent occuvring on tCuzt cowzbitzation oj slip plane and direction which has the highest critical resolved shear stvess. Overshooting appears to be a general occurrence between 2500' and 5000°F. Dejornatiotz bands show rotation in a directiorz opposite to the yotation of tire tensile axis. DEFORMATION in bcc metals has been reviewed by Maddin and Chen,' Keh and eissman,' and most recently by Nabarro, Basinski, and olt. From these reviews it is apparent that some disagreement exists concerning the crystallography of plastic deformation in bcc metals. There is evidence of noncrystallo-graphic slip, the crystal slipping on or near a noncrys-tallographic plane in the (111) zone for which the resolved shear stress is greatest. There is also evidence to indicate that crystallographic slip occurs in the planes of the same zone. On the other hand, there is agreement that the close-packed direction ( 111) is the slip direction in bcc metals. Further, in pure bcc metals4 and alloys the operative crystallographic slip systems are strongly dependent on temperature. Both crystallographic and noncrystallographic slip have been reportede8 in tungsten, a group VIA bcc metal. The number of slip families which operate in the case of crystallographic slip, however, has been in question. The earliest study by oucher' of single-crystal tungsten tested at temperatures of 1800 to 5000°F led to the conclusion that only {112)( 111) type slip operated. Raymond and eumann recently reached the same conclusion studying deformation by rolling of plasma-flame single crystals at 1800°F; however, only [loo] and [110] orientations were studied. Work at high temperatures by Leber and Pughs on tungsten and Chen and Maddin9 on molybdenum suggests that conjugate slip on nonparallel (110) planes may account for the slip on (112) and (123) planes found by others working with bcc metals. The present paper presents evidence of three families or modes of slip in tungsten in the temperature EXPERIMENTAL PROCEDURE Material. Standard microtensile specimens, 0.160 in. diam by 0.640 in. gage length, were ground from commercial powder-metallurgy swaged tungsten rod, type MK. Specimens were heated for 10 min at 5150°F or 6 hr at 5400°F in vacuum of 1 x 105 Torr or less to produce single crystals. At the lower temperature an average of two out of seven specimens heated in a group developed single crystals throughout the specimen length as shown in Fig. 1, the rest remaining wholly poly crystalline. At the higher temperature, three or four out of seven specimens became single crystal. Other than to note that Laue X-ray photographs generally showed sharp, well-defined spots, no attempt was made to assess crystal perfection or measure dislocation density. Two tungsten single crystals grown from the melt by the plasma-arc process were also used for this study.

Jan 1, 1967

By W. Ivanick, Frank W. Glaser

ORDERING reactions of Fe-Si compositions in the a region have been mentioned in a number of review articles.7-8 However, little is known in regard to the critical temperature, T at which this transformation takes place. Greiner and Stoughton,' in a study of the constitution of iron-rich Fe-Si alloys below 800°C, placed the onset of order at a composition of about 4 to 5 wt pct (7.5 to 9.5 atomic pct) Si. They observed that at this composition the ductility and strength begin to decrease sharply and brittleness develops. During X-ray studies they observed only the appearance of superlattice lines for compositions containing 12.5 atomic pct Si. More recent X-ray diffraction studies- etected the appearance of superstructure lines (corresponding to the calculated positions of [Ill] and [ZOO] reflections) for alloys containing 9.5 atomic pct. This fact confirms Greiner and Stoughton's original hypothesis in regard to the onset of order at compositions containing about 7.5 to 9.5 atomic pct Si. The physical properties.of Fe-Si alloys containing more than 10 atomic pct Si have been studied only to a limited extent. Their extreme brittleness and difficulties of sample preparation render them of little industrial use in comparison with alloys in the 0 to 10 atomic pct Si range. The properties of Fe-Si alloys reported to date are mostly properties measured at room temperature on ordered compositions It appears that because of experimental difficulties fully disordered alloys could not be produced in the critical composition ranges and their properties could therefore not be reported. In Figs. la, lb, and lc, a summary of physical properties of Fe-Si alloys, measured during recent investigations of the influence of silicon additions to iron, is presented. No mention of determination of the critical temperature, T for disorder could be found in the literature. The following is an account of work done in an attempt to: 1) produce the disordered state of various Fe-Si alloys and establish the critical temperature, T for disordering, and 2) compare the electrical and thermal conductivity characteristics of the ordered and disordered phases as functions of composition. Materials, Preparation of Test Samples, and Testing Methods Fe-Si alloys with high silicon contents (about 10 atomic pct) are usually prepared using powder metallurgy techniques. This method insures accurate compositions and high purity through the use of protective atmospheres during solid state diffusion alloying of the mixed powders."" Iron and silicon powders were mixed in the desired proportions, cold or hot pressed, and then homogenized at 1150°C for periods ranging from 6 to 12 hr under a protective getter and in a hydrogen atmosphere. Fully homogenized samples were quenched in water from various and successively higher temperatures to establish the critical temperature for disorder. Temperatures were determined using Pt—Pt-Rh thermocouples in contact with the test samples. Test bars were approximately 0.6x1.25x7.5 cm. Electrical measurements were made at room temperature by determining the potential drop over a 1.5 cm span for a current of 10 amp. Densities of the samples were determined by immersion. High temperature electrical resistivities were measured using previously described techniques.'" Specific heat conductivity up to 200°C was measured by heating one end of the test bar and water-cooling the other; heat conductivity was then obtained by subtracting the rate at which heat entered the water from the

Jan 1, 1957

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By Gerald Edmunds

Castings of pure metals and many alloys usually have a coarse-grained structure characterized by long columnar grains throughout the main body of the casting. Frequently, the surface exhibits finer, sometimes nearly equiaxed grains, and such grains may also compose other parts of the casting. This paper deals .primarily with determinations of the grain-orientation textures of the columnar and surface grains of polycrystalline zinc castings. It includes some results upon a cadmium casting and a magnesium casting. A hypothesis is developed to account for the observations on columnar grains and to use as a basis for predicting orientations in other cast metals. A general description of the position of the columnar grains in castings is that their long axes are approximately parallel to the direction of the thermal gradient during crystallization. Thus, in cylindrical castings the columnar grain axes tend to be radial, and in large flat castings where most of the cooling is through one or both of the large mold surfaces they tend to be perpendicular to the mold surfaces. At the edges and corners the direction of heat flow and therefore the position of the grains is more cornplex. Actually observation shows that even in castings made in flat molds the cooling seems to be somewhat irregular, since columnar grains tend to emanate from certain areas of the cooling surface, indicating that thermal contact was better there than in neighboring areas. The nucleus from which a columnar grain grows may be so oriented that its direction of maximum growth rate does not coincide with the direction of the thermal gradient. In this case the long axis of the grain probably assumes an intermediate position. Notwithstanding these minor irregularities, the situation does exist that the long axes of the columnar grains are generally disposed approximately perpendicular to the mold surface. Schmid and Wassermanl and Nix and Schmid2 have determined the orientation texture of columnar grains in castings of several cubic, tetragonal, hexagonal close-packed and rhombohedra1 metals. For zinc and cadmium, they report the basal plane to be parallel to the columnar grain axes, with no preference for any particular direction in this plane to coincide with the grain axes. This texture, termed a ring fiber texture,3 is uncommon in metals; zinc and cadmium are the only ones reported to exhibit it. Generally, it is stated, a simpler texture exists in which a principal, though not necessarily the most closely packed, crystallographic direction is parallel to the direction of heat flow. In cast magnesium (also hexagonal close packed) they report a digonal axis I, [100] direction, parallel to the direction of heat flow. The writer is not aware of any other orientation-texture determinations on cast polycrystalline hexagonal metals. In view of the observations reported in the present paper it is of interest also to note that Nix and Schmid stated that a

Jan 1, 1941

By Gerald Edmunds

Castings of pure metals and many alloys usually have a coarse-grained structure characterized by long columnar grains throughout the main body of the casting. Frequently, the surface exhibits finer, sometimes nearly equiaxed grains, and such grains may also compose other parts of the casting. This paper deals .primarily with determinations of the grain-orientation textures of the columnar and surface grains of polycrystalline zinc castings. It includes some results upon a cadmium casting and a magnesium casting. A hypothesis is developed to account for the observations on columnar grains and to use as a basis for predicting orientations in other cast metals. A general description of the position of the columnar grains in castings is that their long axes are approximately parallel to the direction of the thermal gradient during crystallization. Thus, in cylindrical castings the columnar grain axes tend to be radial, and in large flat castings where most of the cooling is through one or both of the large mold surfaces they tend to be perpendicular to the mold surfaces. At the edges and corners the direction of heat flow and therefore the position of the grains is more cornplex. Actually observation shows that even in castings made in flat molds the cooling seems to be somewhat irregular, since columnar grains tend to emanate from certain areas of the cooling surface, indicating that thermal contact was better there than in neighboring areas. The nucleus from which a columnar grain grows may be so oriented that its direction of maximum growth rate does not coincide with the direction of the thermal gradient. In this case the long axis of the grain probably assumes an intermediate position. Notwithstanding these minor irregularities, the situation does exist that the long axes of the columnar grains are generally disposed approximately perpendicular to the mold surface. Schmid and Wassermanl and Nix and Schmid2 have determined the orientation texture of columnar grains in castings of several cubic, tetragonal, hexagonal close-packed and rhombohedra1 metals. For zinc and cadmium, they report the basal plane to be parallel to the columnar grain axes, with no preference for any particular direction in this plane to coincide with the grain axes. This texture, termed a ring fiber texture,3 is uncommon in metals; zinc and cadmium are the only ones reported to exhibit it. Generally, it is stated, a simpler texture exists in which a principal, though not necessarily the most closely packed, crystallographic direction is parallel to the direction of heat flow. In cast magnesium (also hexagonal close packed) they report a digonal axis I, [100] direction, parallel to the direction of heat flow. The writer is not aware of any other orientation-texture determinations on cast polycrystalline hexagonal metals. In view of the observations reported in the present paper it is of interest also to note that Nix and Schmid stated that a

Jan 1, 1941

Jan 1, 1892

By Glenn S. Wyman

CHUQUICAMATA, located in northern Chile in the Province of Antofagasta, is on the western slope of the Andes at an elevation of 9500 ft. Because of its position on the eastern edge of the Atacama Desert, the climate is extremely arid with practically no precipitation, either rain or snow. All primary blasting in the open-pit mine at Chuquicamata is done by the churn drill, blasthole method. Since 1915, when the first tonnages of importance were removed from the open pit, there have been many changes in the blasting practice, but no clear-cut rules of method and procedure have been devised for application to the mine as a whole. One general fact stands out: both the ore and waste rock at Chuquicamata are difficult to break satisfactorily for the most efficient operation of power shovels. Numerous experiments have been made in an effort to improve the breakage and thereby increase the shovel efficiency. Holes of different diameter have been drilled, the length of toe and spacing of holes have been varied, and several types of explosives have been used. Early blasting was done by the tunnel method. The banks were high, generally 30 m, requiring the use of large charges of black powder, detonated by electric blasting caps. Large tonnages were broken at comparatively low cost, but the method left such a large proportion of oversize material for secondary blasting that satisfactory shovel operation was practically impossible. Railroad-type steam and electric shovels then in service proved unequal to the task of efficiently handling the large proportion of oversize material produced. The clean-up of high banks proved to be dangerous and expensive as large quantities of explosive were consumed in dressing these banks, and from time to time the shovels were damaged by rock slides. As early as 1923 the high benches were divided, and a standard height of 12 m was selected for the development of new benches. The recently acquired Bucyrus-Erie 550-B shovel, with its greater radius of operation compared to the Bucyrus-Erie 320-B formerly used for bench development, allowed the bench height to be increased to 16 m. Churn drill, blasthole shooting proved to be successful, and tunnel blasts were limited to certain locations where development existed or natural ground conditions made the method more attractive than the use of churn drill holes. Liquid oxygen explosive and black powder were used along with dynamite of various grades in blast-hole loading up to early 1937. Liquid oxygen and black powder were discontinued because they were more difficult to handle due to their sensitivity to fire or sparks in the extremely dry climate. At present ammonium nitrate dynamite is favored because of its superior handling qualities and its adaptability to the dry condition found in 90 pct of the mine. In wet holes, which are found only in the lowest bench of the pit and account for the remaining 10 pct of the ground to be broken, Nitramon in 8x24-in. cans, or ammonium nitrate dynamite packed in 8x24-in. paper cartridges, is being used. This latter explosive, which is protected by a special antiwetting agent that makes the cartridges resistant to water for about 24 hr, currently is considered the best available for the work and is preferred over Nitramon. Early churn drill hole shots detonated by electric blasting caps, one in each hole, gave trouble because of misfires caused by the improper balance of resistance in the electrical circuits. Primarily, it was of vital importance to effect an absolute balance of resistance in these circuits, the undertaking and completion of which invariably caused delays in the shooting schedule. Misfires resulting from the improper balance of electrical circuits, or from any other cause, were extremely hazardous, since holes had to be unloaded or fired by the insertion of another detonator. The advent of cordeau, later followed by primacord, corrected this particular difficulty and therefore reduced the possibility of missed holes. After much experimentation, the blasting practice evolved into single row, multihole shots, with the holes spaced 4.5 to 5 m center to center in a row 7.5 to 8 m back from the toe. Sucti shots were fired from either end by electric blasting caps attached to the main trunk lines of cordeau or primacord. The detonating speed of cordeau or primacord gave the practical effect of firing all holes instantaneously. Double row and multirow blasts, fired instantaneously with cordeau or primacord, proved to be unsatisfactory in the type of rock found at Chuquica-

Jan 1, 1953

ARTICLE I Name and Object Sec. 1. This Division shall be known as the Institute of Metals Division of the American Institute of Mining and Metallurgical Engineers. Sec. 2. The object of the Division shall be to furnish a medium of cooperation between those interested in the field of physical metallurgy; that is, the nature, structure, alloying, fabrication, heat treatment, properties and uses of metals; to represent the AIME insofar as physical metallurgy is concerned, within the rights given in AIME Bylaw, Article XI, Sec. 2, and not inconsistent with the Constitution and Bylaws of the AIME; to hold meetings for the discussion of physical metallurgy; to stimulate the writing, publication, presentation and discussion of papers of high quality on physical metallurgy; to accept or reject papers for presentation before meetings of the Division. ARTICLE II Members Sec. 1. Any member of the AIME of any class and in good standing may become a member of this Division upon registering in writing a desire to do so, but without additional dues. Sec. 2. Any member not in good standing in the AIME shall forfeit his privileges in the Division. ARTICLE III Funds Sec. 1. The expenditure of the funds received by the Division shall be authorized by the Executive Committee of the Division. ARTICLE IV Meetings Sec. 1. The Division shall meet at the same time and place as the annual meeting of the AIME, and at such other times and places as may be determined by the Executive Committee subject to the approval of the Board of Directors of the AIME. Sec. 2. The annual business meeting shall be held within a few days before or after the annual business meeting of the AIME. Sec. 3. At a meeting of the Division, for which notice has been sent to the members of the Division through the regular mail or by publication in the Journal of Metals at least one month in advance, a business meeting may be convened by order of the Executive Committee and any routine business transacted not inconsistent with these Bylaws or with the Constitution or Bylaws of the AIME. Sec. 4. For the transaction of business, the presence of a quorum of not less than 25 members of the Division shall be necessary. ARTICLE V Officers and Government Sec. 1. The officers of the Division shall consist of a Chairman, a Senior Vice-Chairman, a Vice-Chair -man, a Secretary and a Treasurer. The office of Secretary and Treasurer may be combined in one person, if desired by the Executive Committee. Sec. 2. The government of the affairs of the Division shall rest in an Executive Committee, insofar as is consistent with the Bylaws of the Division and the Constitution and Bylaws of the AIME. Sec. 3. The Executive Committee shall consist of the Chairman, Senior Vice-Chairman, Vice-Chairman, past Chairman, Secretary, and nine members, all of whom shall be nominated and elected as provided hereafter in Article VII. Sec. 4. The Chairman, Senior Vice-Chairman and Vice-Chairman shall serve for one year each, or until their successors are elected. Each member of the Executive Committee shall serve three years. The Chairman shall remain a voting member of the Executive Committee for one year after his term as Chairman. Sec. 5. The Treasurer of the Division shall be invited to meet with the Executive Committee, but without ex-officio right to vote. He shall be appointed annually by the Executive Committee, from the membership of the Executive Committee or otherwise. Sec. 6. The annual term of office for officers of the Division shall start at the close of the Annual Meeting of the Institute and shall terminate at the close of the next Annual Meeting. ARTICLE VI Committees Sec. 1. There shall be standing committees as follows: Programs Committee. Finance Committee, Membership Committee, Annual Lecture Committee, Technical Publications Committee, Mathewson Gold Medal Committee, Nominating Committee, Education Committee and such other Committees as the Executive Committee may authorize. Sec. 2. It shall be the duty of the Programs Committee to secure the presentation of papers of appropriate character at meetings of the Division. Sec. 3. It shall be the duty of the Finance Committee to inquire into and examine the financial condition of the Division and to consider proper means of increasing its revenue and limiting its expenses. The Finance Committee shall audit the accounts of the Division and report to the Executive Committee prior to the Annual Meeting of the Division. It shall render a budget to the Executive Committee estimating receipts and expenses for the ensuing year so that action can be taken on same at the first meeting following the Annual Meeting.

Jan 1, 1953

By P. Marier, T. R. lngraham

The kinetics of the sulfation of MnO,, MnzO3, and Mn3O4 in SO,, SO3, and O, mixtures was examined and the descending order of sulfation rates at temperatures near 400°C was found to be Mn,O3 > MnO, > Mn3O4. The respective activation energies for the thermal decomposition of MnO, and Mn,O, are 39 and 47 kcal. At 900°C, the thernzal decomposition of MnSO, to MnzO3 is slower than that to Mn3O4. The respective activation energies are 62 and 51 kcal, respectitely. MANGANESE is used to improve the hot workability of steel in the proportions of approximately 13.5 Ib of ferromanganese per ton of steel produced. This requirement accounts for about 95 pct of its large industrial market in North America. The remaining 5 pct is used in the battery and chemical industries. In most North American ores, the percentage of manganese and the manganese-to-iron ratio are not suitable for the direct production of ferromanganese. Hence, most of the North American requirements for manganese are satisfied by importing ore. Typically, many of the studies done on native low-grade manganese resources have been directed toward the production of ore substittes" and the recovery of manganese from open-hearth slags.3 Of the wide variety of processes which have been proposed, the most popular involve compounds in the Mn-S-O system. The thermodynamic properties of manganese and its compounds were reviewed by ah' in 1960 and, more recently, lngrahams discussed the thermodynamics of some of the reactions involved in the Mn-S-O system at normal roasting temperatures. The conditions for producing manganese sulfide during the reduction roasting of manganese sulfate are discussed by Fuller and Edlund.9 A novel scheme was proposed recently by zimmerley7 for utilizing waste sulfur dioxide from stack gases to recover the manganese from ocean-mined manganese nodules. Very little of the work published on manganese compounds has been related to reaction rates. Singleton et 1.' studied the rates of reaction on the MnO-C and Mn7C3-3MnO systems and observed linear and parabolic kinetics respectively in the systems. Tatievskaya et a1.' studied the low-temperature reduction of Mn&, MnO,, and Mn& in HZ and CO, and reported activation energies in the range 1628 kcal. In this paper, the rates of some of the decomposition and formation reactions involving MnSO4, MnOz, MnzO3, and Mn3O4 will be examined after the conditions for the thermodynamic stability of the individual compounds have been designated. CONDITIONS FOR STABILITY OF MnSO4, MnOz, MnZO3, AND Mn3O4 The areas of stability for h'hSO4, MnOz, MnzO3, and h3O4 were established from the data of Mah4 and Ingrahams and are shown in the predominance area diagram,10 logpq- logpsq, in Fig. 1. The diagram is drawn for two temperatures, 700°K, solid lines, and 1100°K, dotted lines. The sketch for the lower temperature includes the conditions likely to prevail in the Zimmerley patent7 when manganese nodules react with sulfur dioxide and that for the higher temperature indicates the conditions for recovering MnzO3 or Mn3O4 from MnSO4 during a roasting reaction. From the fact that the boundary between the areas of stability of MnOz and hSO4 at 700°K is parallel to the abscissa, it is evident that MnOz and SO2 should react together to produce MnSO4, irrespective of the oxygen pressure in the system. If the source of sulfur for sulfation were from waste flue gases, it is likely that the oxygen content of the gas stream would be more than sufficient to oxidize any MnsO4 to MnzO3, 107 atm of O2 required, or even to convert any Mnz03 to MnOz, 0.02 atm OZ required, prior to sulfation. At 1100°K, the diagram indicates that MnSO4 may be converted directly to either MnzO3 of Mn3O4, depending upon the prevailing partial pressure of oxygen. When the gas stream contains more than 1 pct Oz, logpq = -2, only MnzO3 would be recovered from an experiment done under equilibrium conditions. At oxygen partial pressures of less than 1 pct, one would expect to bring about a reversible exchange between MnSO4 and Mn3O4 by appropriate adjustment of the partial pressure of SOZ. These various reactions will be described in the subsequent kinetic experiments.

Jan 1, 1969

By T. A. Read, M. S. Wechsler, D. S. Lieberman

A theoretical analysis of the austenite-martensite transformation is presented which predicts the habit plane, orientation relationships, and macroscopic distortions from a knowledge only of the crystal structures of the initial and final phases. THIS paper presents a new theory of the formation of martensite. This theory makes possible the calculation of the austenite planes on which the martensite plates form, the orientation relationship between the austenite and martensite crystal axes, and the macroscopic distortions which are observed. The only input data needed are the crystal structures and lattice parameters of the austenite and martensite. Considerable effort has been devoted over the past thirty years to the development of an understanding of the crystallographic features of martensite reactions. Much of this work has been done on steels and iron-nickel alloys, for which a great deal of data has been accumulated concerning the shape and orientation of the martensite plates, the relative orientations of the austenite and martensite crystal axes, and the observable distortions which result from transformation. These observations are reviewed in refs. 1, 2, and 3. The first major step toward an understanding of these phenomena was made in 1924 by Bain,' who showed that the a body-centered cubic structure can be produced from the 7 face-centered cubic structure by a contraction of about 17 pct in the direction of one of the austenite cube axes and an expansion of 12 pct in all directions perpendicular to it. Since that time, most of the efforts at further interpretation have been made by investigators who have worked from the phenomenological data, incorporating some of the information from the lattice properties, and have sought an analysis into likely deformations which would produce the observed results."- "11 but the three most recent papers on the subject have already been reviewed in some detail." Machlin and Cohenl0 measured the components of the distortion matrix and verified that the habit plane is a plane of zero distortion and rotation for the (259) case. They showed that the measured distortion matrix, when applied to the parent lattice, does not yield the product lattice and hence some inhomogeneous distortion must occur. Frank,u working from the lattice properties and taking some clues from the observations, considered the correspondence of close-packed rows and planes in the austenite and martensite. He predicted substantially the observed lattice relationship and habit plane for certain steels which have a (225) habit. Geisler12 suggested that there is a natural tendency for the habit plane to be a (111) and postulated certain slip processes to account for the fact that the experimentally observed habit plane is irrational and deviates from the assumed one. The present work differs from previous treatments of martensite formation in that it permits calculation of all the major manifestations of the process. Habit plane indices, orientation relationships, and observable distortions are all calculated from a knowledge of the crystal structures of the initial and final phases alone. The calculations contain no adjustable parameters. The agreement found between calculated results and the observations reported in the literature constitutes powerful evidence in favor of the mechanism of martensite formation proposed. The theory is applicable to systems other than steel (as is discussed later in this paper) which exhibit a diffusionless phase change but because of the wide-spread interest in the austenite-martensite transformation, particular attention will be given to the iron-base alloys. For other systems which undergo a similar face-centered cubic to face-centered tetragonal transformation, the mathematical treatment is identical with that presented here. Hence the theory successfully describes the transformation in the indium-thallium alloy.'" Homogeneous Transformation to Martensite The distortion which any homogeneously transforming volume of austenite undergoes in order to become martensite is shown in Fig. 1, as was first suggested by Bain.' (This distortion will hereafter be referred to as the "Bain distortion.") This specification of a contraction along one cube axis ;ombined with an expansion in all directions perpendicular to this axis describes what is properly called the "pure" distortion associated with this transformation. The distinction between a "pure" and an "impure" distortion plays an important part in the discussion which follows. A "pure" distortion is characterized by the existence of at least one set of orthogonal axes fixed in the body which are not rotated by the distortion. (These are called the "principal axes" of the distortion.) No such set of axes exists in the case of an "impure" distortion. On the other hand, an impure distortion can always be represented as the result of a pure distortion combined with the rotation of the specimen as a rigid body. For a given impure distortion the corresponding pure distortion

Jan 1, 1954

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats' technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats' technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given' by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

By R. M. Waterstrat

The phases occurring in the V-Mn system were studied by means of X-yay diffraction and metallo-paphic techniques, using are-melted alloy specimens annealed in the temperature range 800° to 1150°C and quenched. The bcc solid solution extends at 1250°C all the way from vanadium to 6-manganese. Below 1050°C the a-phase is formed, and the terminal a-manganese phase is stabilized up to about 900°C by vanadium in solid solution. IN the only previous general survey of the V-Mn system Cornelius, Bungardt and Schiedtl reported the existence of three intermediate phases corresponding to the approximate compositions VMn,, VMn, and V5Mn. The phase VMn8 has recently been identified as a o phase2 but the alloy VMn was found to have a bcc structure2 corresponding apparently to the vanadium solid solution rather than to the large cubic unit cell reported by Cornelius et al. 1 Subsequent work by Rostoker and Yamamoto3 has shown that the vanadium-base bcc solid solution extends to at least 15 pct Mn at 900°C. An alloy corresponding to the composition VMn, was examined by Elliott,4 who reported that the as-cast sample as well as samples annealed at 1200o and 1300°C had bcc structures, but that annealing at 1000°, 800") and 600°C produced two phases. One of these phases was apparently the bcc solid solution and the other resembled the o phase structure. Hellawell and Hume-Rothery5 established the phase relationships in manganese-rich alloys above 1000°C, and showed that the o phase in this system is replaced by the 6 Mn (bcc) solid solution at temperatures above 1050°C. These results suggest that a continuous bcc solid solution may exist above 1050°C between vanadium and 6 Mn. The present investigation was undertaken in order to develop more complete information in regard to this system. EXPERIMENTAL METHODS The alloys used in the present work were prepared by arc-melting electrolytic manganese having a minimum purity of 99.9 pct and vanadium lumps with a purity of 99.7 pct. The major impurities present in these metals were carbon, nitrogen, and oxygen and this would account for the small percentage of nonmetallic inclusions observed metal-lographically. The arc-melting was at first performed under a helium atmosphere and it was necessary to keep the melting times as short as possible in order to minimize the loss of manganese by vaporization. It was later found that the evaporation of manganese was considerably reduced when the melting was done under argon atmosphere. The final composition of each alloy was calculated by assuming that the total weight loss during melting was due to evaporation of manganese. Compositions which were calculated in this manner agreed reasonably well with the results of chemical analysis, as shown in Table I. Spectrographic analysis revealed the presence of contamination by tungsten, but in no case was the percentage of tungsten greater then 0.4 at. pct. The specimens were in each case broken in half and the fractured section was examined visually and microscopically for evidence of inhomogeneity. Each specimen was homogenized at temperatures near l100°C, as shown in Table I. After this treatment most specimens consisted of large columnar grains of the bcc vanadium solid solution. The etchant used in most of the metallographic work consisted of 20 pct nitric acid, 20 pct hydro-flouric acid, and 60 pct glycerine. It was found that this etchant would clearly delineate the phases present in these alloys although it does not produce any striking contrast between the phases. For certain manganese-rich alloys, a 1 pct aqueous solution of nitric acid was used. This etchant gave a brown color to the a-manganese phase, whereas the o phase was virtually unattacked and appeared very light as shown in Fig. 1. The etchants used by Cornelius et a1.l were found to produce spurious effects in some of these alloys. In particular, the vanadium-rich alloys etched in hot sulfuric acid often appeared to consist of two phases when both X-ray diffraction and etching with the glycerine-acid mixture indicated the presence of single phase bcc solid solution. A few percent of what appears to be an oxide or nitride phase was found at the grain boundaries and in the interior of the grains, especially in the vanadium-rich alloys. All alloys were annealed in sealed silica tubes containing 1 atm of pure argon and these tubes were then quenched in cold water. Although some manganese loss occurred during annealing, the loss seemed to be confined to the surface of the speci-

Jan 1, 1962

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10' to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969

By H. M. Cyr, T. F. Steele, C. W. Siller

The development of a new metallurgical roasting device is described. It consists of a refractory column into which air is injected at various levels, forming several superimposed fluidized beds with no supporting grates. When pelleted zinc sulphide concentrates are charged, the roasted product needs no further sintering before reduction to metal. WHEN a gas such as air is blown upward with increasing velocities through a loose mass of solid particles, marked changes in the physical behavior of the particles are noted. At first, when the velocity of the gas is insufficient to support any of the solid, the mass constitutes a "fixed bed." As the gas velocity increases until the pressure drop through the bed approaches the effective weight of the bed per unit area, the bed expands until the solid particles are supported by the air rather than by the lower particles. Some vibration of the particles becomes apparent, but little mixing occurs. This condition is called a "quiescent fluid bed." A further increase in gas velocity imparts more separation and more motion to the individual particles until a condition of turbulence is reached. This "turbulent fluid bed" resembles a rapidly boiling liquid with the characteristic highly agitated diffuse surface and many small eruptions of the boiling mass. Different degrees of turbulence can be generated and all produce excellent mixing. The final stage occurs when the gas velocity becomes so great as to create a "dispersed suspension." Here no surface of the mass is defined and the gas carries solid particles out of their original positions. These changing conditions of fluidization have been studied carefully and pertinent nomenclature standardized by a committee of the American Institute of Chemical Engineers.' Many mathematical analyses2-3 have been made of the forces acting in a fluid bed. These analyses are invaluable, especially for the design of column sizes and selection of equipment. However, in a metallurgical process involving solids of many sizes with changing densities, varying temperatures, and changing gas compositions within the bed, calculations based on theory become approximate. Optimum operating conditions then are best determined experimentally. Many applications have been made of the principles of fluid-bed action by mechanical, chemical, and metallurgical engineers. Especially when good con- tact between reacting solids and gases is desired, very effective results are obtained from fluid beds. They permit excellent temperature control and uniformity throughout a mass of solids in fluid action. Heat transfer to walls and any coolers is high, and fast reaction rates are attained because the solid surfaces are continuously swept clean. The main disadvantages of fluid-bed operations are the danger of short-circuiting in a single bed, danger of incipient sintering which stops action, the necessity of avoiding large changes in particle size or density during roasting, and dust losses when particles of the charge are carried out with exit gases. In the metallurgical field the roasting of sulphide ores to form oxides and sulphur dioxide appears to combine several operating conditions which can be achieved to advantage in a fluid bed. Roasting involves a solid-gas reaction where a high reaction rate is necessary for high capacity, where good temperature control is important in order to prevent sintering, where good heat transfer is needed, and where the density of the solids, when changing from sulphides to oxides, is not largely changed. Short-circuiting, however, constitutes a major problem when a single fluid bed is used. Because of the turbulence of the bed, an entering particle may be in the region of the discharge before it is roasted. Hence, to attain a satisfactorily low sulphur in the calcine, a long average residence time with correspondingly low capacity is required. The solution to this difficulty is the use of multiple stages, which in the conventional fluid-bed design requires separate hearths with feed and discharge mechanisms for each stage. A further practical difficulty in fluid-bed roasting of flotation zinc concentrates is their fine particle size which makes a true fluid action without excessive carry-over of dust very difficult to attain, especially when the large air volumes necessary for high capacity are used. A New Design After considerable experimentation in the laboratory and on a semipilot-plant scale, a new method and equipment for roasting were devised which provided a unique solution to these problems. A detailed account of this development appears in the patent literature," and many of the variations of this development reported herein are the subject of

Jan 1, 1955