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By A. M. Sarem

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady - state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two - phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-pbase relative permeability as it does in two-phase flow. INTRODUCTION In the light of increasing demand for three-phase relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis 1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between I/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression for determining the outflow face saturation from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. PROPOSED METHOD The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three - phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Jan 1, 1967

By Harry M. Mikami

Chromite is the only ore mineral of metallic chromium and chromium compounds and chemicals. Because of this fact, chromite and chrome ore are used synonymously in trade literature. In commercial market quotations, chrome ore is the term commonly used. Chromite per se, because of properties imparted by its chromium content, is used in refractories and in special purpose molding sands for metal casting. There are many other minerals containing some, generally minor, amounts of chromium, but none are commercial sources of the element (Thayer, 1956). Chromium and chromite have many diverse uses that, directly and indirectly, critically affect vast segments of our modern industrial system. Most important are probably the metallurgical applications wherein chromium is a component of heat-, abrasion-, corrosion-and oxidation-resistant and high-strength alloys of many types. Stainless steels are the largest volume category of chrome-bearing alloys. Chromium chemicals are used in leather tanning, in pigments, dyes and mordants, printing, chemical process industries, photography, pharmaceuticals, metal plating, pure chromium metal production, and for many other purposes. Chromite is a necessary constituent in basic refractories indispensable for the production of steel, copper, cement, and glass. Under present conditions, the US and North America, with the possible exception of Cuba, have no commercial ore reserves. There are chromite deposits, as will be described, but they would be used only under highly abnormal conditions if all outside sources were cut off for an extended period. All chromite used in the US is imported from the eastern hemisphere in which are contained the principal world reserves. The main suppliers in 1980 were the Republic of South Africa (43%), the USSR (21% ), the Philippines (12%), Albania (11 %), Turkey (8%), and others (5%). The strategic nature of chromite is obvious. End Uses-Grades and Specifications As noted before, the three principal uses for chromite are metallurgical, refractories, and chemical with a fourth minor use as foundry molding sand. For metallurgical applications chrome ore is first reduced in electric carbon arc furnaces to various types of ferrochromium alloys. There are high, medium, and low carbon ferrochromiums with carbon ranging from 0.01 up to 10%. Chromium itself ranges from 50 to 73 %. Ferrosilicon chromium and ferrochromium-silicon grades have chromium from 33 to 67% and silicon from 3 to about 48%. Since iron is reduced with chromium, the Cr:Fe ratio of the ore will determine the ultimate grade of the ferrochromium whereas carbon and silicon can be controlled during processing. MgO, A12O3, CaO, and excess SiO2, are removed in slag. A small amount of pure chromium metal is prepared by alumino-thermic and electrolytic processes from essentially iron-free chrome components that have been made via the chemical route. The higher grades of ferrochromium with chromium in the 66 to 73% range can only be made from ores with not only high chromium content, but low iron, i.e., high Cr:Fe ratio. These ores, conventionally termed metallurgical grade, have Cr2O3 contents of 45 to 56% with Cr: Fe ratios of 2.5 to 4.3. A standard composition is generally 48% Cr2O3 and 3:1 Cr:Fe ratio. Very high grade ores are often blended with lower grades even with the high iron chemical grade. For some ferrochromiums, additions of high alumina refractory grade are used as slag conditioners to facilitate smelting while still contributing chromium values. A lower grade ferrochromium, the high carbon charge chrome, has become the predominant grade in use today for making chromium-bearing steel alloys. This

Jan 1, 1983

By Rollin E. Hook, Attwell M. Adair

The yield and fracture behavior of recrystallized chromiztm have been studied in order to gain an understanding of the recrystallization embrittlement-rheotropic recovery phenomenon. The duc tile-brittle tensile transition temperature of recrystallized chromium was found to vary from 225 ° to -80°C as the ratio of specimen diameter/mean planar grain size decreased. The applicability of this observation to other bcc metals is briefly discussed. Brittle fracture in recrystallized chromium was found to be initiated predominately from intercrystalline rupture nuclei. Single crystals exhibit a high degree of ductility at 23 "C. The experimental data indicate that grain boundaries play a significant part in the yield and fracture behavim. Pres training significantly reduces the transition temperature, and high temperature aging does not result in re-embrittle-ment until complete recovery or re crystallization occurs. SEVERAL theories have been used to explain the recrystallization embrittlement-rheotropic recovery phenomenon in chromium. Wain, Henderson, and ohnstone' propose a Cottrell dislocation locking mechanism due to nitrogen, and Weaver and Gross and weaver 3 propose a strain-induced precipitation mechanism involving a chromium nitride precipitate. The researches of many investigators seem to leave little doubt that brittleness in chromium is promoted by interstitial impurities. Smith and seybolt4 have shown that the ductile-brittle transition temperature is lowered as the interstitial content is reduced. weaver3 provides evidence for a 150°C reduction in the tensile transition temperature as the nitrogen content is reduced from 20 to 5 ppm. Maykuth and affee' have suggested that the amount and orientation of grain boundary impurities may be responsible for the brittle nature of recrystallized chromium. This suggestion was based on their findings that wrought iodide chromium possessing a fiberous grain structure is ductile in tension at room temperature while a recrystallized grain structure is completely brittle. Previous investigations have not studied this phenomenon sufficiently to determine its cause. Perhaps this has been largely due to previous experimental findings that brittle fracture observed in chromium has been almost entirely transgranular.' In addition McNeil and imb,' who investigated coarse-grained as-cast chromium, describe the point of initiation of fracture as cleavage, close to the (100) plane, near or at grain bound-daries, or at included particles or voids. However, Hook, Adair, and ipsitt found that fracture in coarse-grained recrystallized chromium is initiated by intergranular rupture and then propagates nearly entirely by cleavage. This result, together with their finding that room temperature ductility in bending is observed for single crystals and coarse-grained polycrystalline specimens for which the number of grains through the specimen diameter is small, suggests that grain boundaries may play an important role in the brittle behavior of chromium. The recrystallization embrittlement problem can be resolved into two questions. These are, whether the controlling mechanism is predominately one of crack initiation or crack propagation, and whether brittle fracture is initiated predominately by slip or twin induced intergranular rupture or by cleavage. The following research was designed to study the role of grain boundaries on the brittle fracture of chromium in an effort to resolve these questions. EXPERIMENTAL PROCEDURES, RESULTS, AND DISCUSSION General Procedure. All tensile specimens (except 0.04 in. diam wires) were prepared from 1/4 in. diam swaged rod fabricated from one ingot. Details of fabrication are given elewhere. The results of impurity analysis for the swaged rod and for the

Jan 1, 1963

By M. Muskat, M. O. Taylor

Theoretical calculations have been made on the performance to be expected of gas-drive reservoirs for various characteristics of the oil and gas and the producing rock. Such performante has been expressed graphically as curves for the reservoir pressure and gas-oil ratios of the production as functions of the cumulative oil recovery. The latter has been expressed in terms of percentage of pore space of the reservoir rock. Such curves automatically give values for the ultimate physical recovery, if the latter is interpreted as the recovery obtained when the reservoir pressure has declined to atmospheric, or to any other pressure chosen as defining the state of practical complete depletion. Calculations of these pressure and gas-oil ratio histories have been made for conditions in which the oil viscosity, the gas solubility and shrinkage, the size of an overlying gas cap, if present, the permeability-saturation characteristics of the rock, and the amount of connate water, have been individually varied, The results serve to show the extent to which the ultimate recoveries are sensitive to the important physical parameters characterizing the oil reservoir. As is to be expected, the ultimate recoveries are found to decrease with increasing oil viscosity. Because of the predominant effect of the oil shrinkage associated with the liberation of the gas in solution, the ultimate recovery will decrease with increasing gas solubility. Increasing gas-cap volumes lead to higher recoveries, although the contribution made by the gas-cap gas is small as compared with the oil expulsion by the equivalent amount of solution gas. As a whole, the oil recovery when expressed in percentage of the pore space is not very sensitive to the details of the permeability-saturation relationship. However, if the rocks possess an equilibrium free-gas saturation, the rise in gas-oil ratio will be retarded, and the 'ultimate recovery somewhat increased' The oil shrinkage associated with the liberation of the dissolved gas also leads to the result that as long as the connate water is immobile and the permeability ratio curve for the rock is a function only of the total liquid saturation, the stock-tank oil recovery will be less for a sand containing no connate water than for One with an Original water content as high as 3' per cent. The space voidage in the former case will be somewhat greater, but the effect of oil shrinkage will lead to smaller values for the equivalent stock-tank recovery. These calculations also give data showing how the productivity indexes for the producing wells will vary during the reservoir history. Because of decreasing Permeability to the oil and increasing oil viscosity, the productivity index will fall continuously as Production proceeds, and may finally reach values as low as 10 per cent of the initial productivity index. Introduction In a previous paper1 was developed the basic theory for the prediction of the production histories of gas-drive reservoirs. The data required for the application of this theory included the characteristics of the petroleum fluids, such as the viscosity of the Oil and gas phases, the solubility of the gas in the oil, and the oil shrinkage— all expressed as functions of the reservoir pressure—and the permeability-saturation characteristics of the producing rock, as

Jan 1, 1946

By M. Muskat, M. O. Taylor

Theoretical calculations have been made on the performance to be expected of gas-drive reservoirs for various characteristics of the oil and gas and the producing rock. Such performante has been expressed graphically as curves for the reservoir pressure and gas-oil ratios of the production as functions of the cumulative oil recovery. The latter has been expressed in terms of percentage of pore space of the reservoir rock. Such curves automatically give values for the ultimate physical recovery, if the latter is interpreted as the recovery obtained when the reservoir pressure has declined to atmospheric, or to any other pressure chosen as defining the state of practical complete depletion. Calculations of these pressure and gas-oil ratio histories have been made for conditions in which the oil viscosity, the gas solubility and shrinkage, the size of an overlying gas cap, if present, the permeability-saturation characteristics of the rock, and the amount of connate water, have been individually varied, The results serve to show the extent to which the ultimate recoveries are sensitive to the important physical parameters characterizing the oil reservoir. As is to be expected, the ultimate recoveries are found to decrease with increasing oil viscosity. Because of the predominant effect of the oil shrinkage associated with the liberation of the gas in solution, the ultimate recovery will decrease with increasing gas solubility. Increasing gas-cap volumes lead to higher recoveries, although the contribution made by the gas-cap gas is small as compared with the oil expulsion by the equivalent amount of solution gas. As a whole, the oil recovery when expressed in percentage of the pore space is not very sensitive to the details of the permeability-saturation relationship. However, if the rocks possess an equilibrium free-gas saturation, the rise in gas-oil ratio will be retarded, and the 'ultimate recovery somewhat increased' The oil shrinkage associated with the liberation of the dissolved gas also leads to the result that as long as the connate water is immobile and the permeability ratio curve for the rock is a function only of the total liquid saturation, the stock-tank oil recovery will be less for a sand containing no connate water than for One with an Original water content as high as 3' per cent. The space voidage in the former case will be somewhat greater, but the effect of oil shrinkage will lead to smaller values for the equivalent stock-tank recovery. These calculations also give data showing how the productivity indexes for the producing wells will vary during the reservoir history. Because of decreasing Permeability to the oil and increasing oil viscosity, the productivity index will fall continuously as Production proceeds, and may finally reach values as low as 10 per cent of the initial productivity index. Introduction In a previous paper1 was developed the basic theory for the prediction of the production histories of gas-drive reservoirs. The data required for the application of this theory included the characteristics of the petroleum fluids, such as the viscosity of the Oil and gas phases, the solubility of the gas in the oil, and the oil shrinkage— all expressed as functions of the reservoir pressure—and the permeability-saturation characteristics of the producing rock, as

Jan 1, 1946

By W. B. Mather

A RKANSAS is not only a geologist's paradise, but Ait is also particularly fortunate in possessing a wide variety of mineral resources. The future mineral production and mineral industry of Arkansas, like the other states in Mid-America, will probably depend to a large degree on efforts to increase the exploitation of the non-metalliferous deposits of the state. The term nonmetalliferous, as used in this paper, embraces all types of mineral deposits, except fuels, water, and those deposits from which, after bene-ficiation, metals are ultimately derived. For example, bauxite is the ore of aluminum, but a considerable portion of the bauxite mined eventually is employed in the production of nonmetallic alumina, an important oxide in the abrasive and ceramic industries. The bulk of the production, however, becomes metallic aluminum and therefore this type of mineral resource is considered metalliferous and is omitted from this paper. Arkansas' nonmetalliferous deposits are of many different types, too numerous to discuss in detail in a single paper; therefore, only their salient features are presented. Many types of deposits such as limestone, glass sand, novaculite, shale, and sandstone are exposed over wide areas, providing inexhaustible reserves. Other types of deposits, such as barite and tripoli, contain large reserves which certainly are not unlimited. Still other types of deposits, such as celestite, kaolin, and vermiculite, appear to occur in small isolated deposits containing relatively small reserves. Of course, all of Arkansas' nonmetalliferous deposits probably have not as yet been recognized, nor have all of the known deposits been prospected, tested, and evaluated. Various types of deposits are too low grade or too limited in extent to be profit- ably produced by today's standards. In the case of other deposits, the known uses are few in number, thus acting as a retarder to their development. Due to anticipated technologic advancements, the future demands of industry are not expected always to be the same as they are today, and therefore idle deposits or those of current limited production may readily become the important revenue producers of the future. The types of nonmetalliferous deposits discussed here include: clays, shales, and slates; silica deposits including glass sand, novaculite, tripoli, sandstone, chert, and quartz crystals; limestone and dolomite; barite; gypsum; celestite; nepheline syenite; green-sand; phosphate; vermiculite; fuller's earth; ben-tonite; diamonds; sand, and gravel. The location of the various types of deposits are presented on the accompanying map (fig. 1). Symbols indicate the general area of occurrence. Many deposits, such as limestone, shale, novaculite, and so on, are represented by formations which could only be properly shown on a geological map. In these instances only active deposits or those of exceptional merit are indicated by symbols on the map. A general northeast-southwest line divides the interior highland from the Gulf Coastal and Mississippi Alluvial Plains of south and east Arkansas. The data presented in this paper are only a surnmary of a portion of a more comprehensive survey and study of the natural resources of the entire state.' The study was sponsored and underwritten by the Arkansas Power and Light Co., Little Rock, as a public service to the state and its residents. Permission to present some of the data and conclusions resulting from the survey is gratefully acknowledged. Table I, prepared by the Arkansas Geological Survey from state severance tax records, presents the annual production secured from Arkansas nonmetalliferous mineral deposits. Clays, Shales, and Slates Clays: It is realized that each method of classifying clays is prone to criticism. In this paper, Arkansas' clays of potential value are arbitrarily

Jan 1, 1951

By W. B. Mather

A RKANSAS is not only a geologist's paradise, but Ait is also particularly fortunate in possessing a wide variety of mineral resources. The future mineral production and mineral industry of Arkansas, like the other states in Mid-America, will probably depend to a large degree on efforts to increase the exploitation of the non-metalliferous deposits of the state. The term nonmetalliferous, as used in this paper, embraces all types of mineral deposits, except fuels, water, and those deposits from which, after bene-ficiation, metals are ultimately derived. For example, bauxite is the ore of aluminum, but a considerable portion of the bauxite mined eventually is employed in the production of nonmetallic alumina, an important oxide in the abrasive and ceramic industries. The bulk of the production, however, becomes metallic aluminum and therefore this type of mineral resource is considered metalliferous and is omitted from this paper. Arkansas' nonmetalliferous deposits are of many different types, too numerous to discuss in detail in a single paper; therefore, only their salient features are presented. Many types of deposits such as limestone, glass sand, novaculite, shale, and sandstone are exposed over wide areas, providing inexhaustible reserves. Other types of deposits, such as barite and tripoli, contain large reserves which certainly are not unlimited. Still other types of deposits, such as celestite, kaolin, and vermiculite, appear to occur in small isolated deposits containing relatively small reserves. Of course, all of Arkansas' nonmetalliferous deposits probably have not as yet been recognized, nor have all of the known deposits been prospected, tested, and evaluated. Various types of deposits are too low grade or too limited in extent to be profit- ably produced by today's standards. In the case of other deposits, the known uses are few in number, thus acting as a retarder to their development. Due to anticipated technologic advancements, the future demands of industry are not expected always to be the same as they are today, and therefore idle deposits or those of current limited production may readily become the important revenue producers of the future. The types of nonmetalliferous deposits discussed here include: clays, shales, and slates; silica deposits including glass sand, novaculite, tripoli, sandstone, chert, and quartz crystals; limestone and dolomite; barite; gypsum; celestite; nepheline syenite; green-sand; phosphate; vermiculite; fuller's earth; ben-tonite; diamonds; sand, and gravel. The location of the various types of deposits are presented on the accompanying map (fig. 1). Symbols indicate the general area of occurrence. Many deposits, such as limestone, shale, novaculite, and so on, are represented by formations which could only be properly shown on a geological map. In these instances only active deposits or those of exceptional merit are indicated by symbols on the map. A general northeast-southwest line divides the interior highland from the Gulf Coastal and Mississippi Alluvial Plains of south and east Arkansas. The data presented in this paper are only a surnmary of a portion of a more comprehensive survey and study of the natural resources of the entire state.' The study was sponsored and underwritten by the Arkansas Power and Light Co., Little Rock, as a public service to the state and its residents. Permission to present some of the data and conclusions resulting from the survey is gratefully acknowledged. Table I, prepared by the Arkansas Geological Survey from state severance tax records, presents the annual production secured from Arkansas nonmetalliferous mineral deposits. Clays, Shales, and Slates Clays: It is realized that each method of classifying clays is prone to criticism. In this paper, Arkansas' clays of potential value are arbitrarily

Jan 1, 1951

By George P. Chapman

Mica is a platy mineral occurring in a variety of complex hydrous aluminosilicate forms with differing chemical composition and physical properties. Principal minerals in the mica group include: Muscovite-potassium mica (colorless or pale green/ ruby) Phlogopite-magnesium mica (dark brown or amber) Biotite-magnesium-iron mica (black or dark green) Lepidolite-lithium mica (lilac) Selected properties are given in Table 1. Muscovite is most important commercially with phlogopite of lesser use. The laminated structure of mica enables it to be split into very thin films which are transparent and tough as well as having outstanding dielectric and insulating properties. Commercially, mica is used in a number of forms (Chowdbury, 1941; Rajgarhia, 1951; Skow, 1962). Sheet mica consists of flat sheets mined from naturally occurring books of mica, free from defects and capable of being punched or stamped into required shapes. Sheet mica is separately classified into blocks, films, or splittings according to thickness. Built-up mica, or micanite, is made by arranging overlapping splittings in layers , cemented with a binder and pressed together at high temperature. Reconstituted mica, or mica paper, is made by depositing fine flakes of high-quality scrap mica in a continuous film impregnated with binder. Scrap and flake mica are normally unsuitable in quality or size for making sheet mica. Originally the term scrap mica referred to the waste byproduct of mining and fabricating sheet mica, and distinct uses were developed for this material. Subsequently it became economically feasible to mine lower quality mica for these uses, and the term flake mica was introduced. Although the two terms are still used somewhat synonymously, it is considered better, at least in the United States, to use the term flake mica in referring to mica mined for uses other than as sheet mica; and to restrict the term scrap mica to mica mined for or with sheet mica, but which will not meet the specifications. Synthetic mica, such as fluorophlogopite, is produced by slow crystallization of a melted blend of pure raw materials. Mineralogy In the true sense the term mica does not relate to, a particular mineral, but to a group or family of minerals of similar chemical composition and to some extent similar physical properties. These minerals are predominantly potassium aluminum silicates with varying amounts of magnesium, iron, and lithium. The precise formulas and isomorphic relationships of the various group members have been studied, but general agreement has not been reached (Grimshaw, 1971; Hurlbut, 1952; Skow, 1962). The general formula describing the chemical composition of micas is [X2Y4-6Z8020(OH, F)4, where X is mainly K, Na, or Ca; Y is mainly Al, Mg, or Fe; Z is mainly Si or Al (Deer, et al., 1962).] These minerals have an internal structure of the layered lattice type where the silicon atoms are in the center of a tetrahedral grouping of oxygen atoms. The groups are linked together in a single plane by three oxygen atoms that lie within the common plane. Each of these oxygen atoms is shared by two tetrahedra. These linked tetrahedral groups, when continually extended, produce a hexagonal network within the plane. This internal structure of the mica has been used to explain the ex-

Jan 1, 1983

By John R. Keith

Lead and zinc contents of elm, maple, and oak trees and of soils in which the trees grew were determined in samples from the Upper Mississippi Valley mining district, and from an area outside but contiguous to the district. The lead and zinc analyses of plant materials served to differentiate the mineralized and nonminer-alized areas. Stems contained about two times as much lead and about two to five times as much zinc as did leaves taken from the same stems. Lead and zinc analyses of all soil horizons could be used to differentiate between the two areas. Soils at most sample sites in the mineralized district seemed to be more reliable than plants for geochemical prospecting and are a more practical sampling medium. Soil samples from areas with thick loess cover, however, failed to indicate the presence of mineralized bodies whereas tree samples from the same sites contained anomalous amounts of lead and zinc. It is suggested that in areas of thick loess cover, plant samples could be used in prospecting for lead and zinc. The important part that plants play in the cycling of elements through the soil horizons is well-known. The concentration of elements in the upper soil horizons by the action of plants has been called the Goldschmidt enrichment principle.' The fact that plant species vary greatly in their ability to concentrate particular elements in their tissues is also well-known.' Agricultural literature has dealt extensively with relationships of the major nutritive elements in soils and plants3 The extent, however, to which plant actions cycle the minor nutritive and the nonmetabolic elements in the soil has not been adequately investigated. Lead is non-nutritive and toxic to plants, whereas zinc is a micronutrient in low, but toxic in high, concentrations.4 This report presents the results of a biogeochemical study concerned with the amounts of lead and zinc in some plants and soils that occurred both within and adjacent to the Upper Mississippi Valley lead-zinc district. Field work for this study was done in the summers of 1961 and 1962. SAMPLE TARGETS AND CHEMICAL ANALYSES Geologic and physiographic descriptions of' the district have been made by Heyl 5 and several other authors in a series of U.S. Geological Survey (USGS) reports and quadrangle maps.6-I Sedimentary rocks, mostly dolomite, limestone, shale, and sandstone, of Cambrian, Ordovician, and Silurian age predominate in the area. Mineral deposits are of the vein and cavity-fill type; the principal ore minerals are galena and sphalerite. Vegetation of the area was characterized by Curtis1 6 as southern hardwood forest interspersed with patches of oak savanna and prairie. Plant genera typical of the eastern United States Temperate Zone, including ash, cherry, dogwood, elm, hackberry, hickory, maple, oak, and other woody and herbaceous genera, are present. The natural vegetation has been greatly modified by agricultural, logging, and mining operations. The species of the original flora are present, but not in their former relative abundance. Soils of this district belong, for the most part, to the Brunizem and Gray-Brown Podzolic great soil groups. The Brunizems are the soils developed under prairie vegetation.'' The Gray-Brown Podzolics are the soils developed under deciduous forests,18 They are derived from both bedrock and from loess parent materials, and

Jan 1, 1970

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By G. G. Priest, B. E. Morgan

The production of oil and gas from wells is often seriously hindered by the compaction of solids in the perforations during the perforating process. To realize the full productive capacity of a well, it is necessary either to remove the plugging material from the perforations or to perforate in a manner which does not cause plugging of the perforations. The latter method can be accomplished by having a non-plugging fluid in the casing at the time the well is perforated. This paper describes the results of laboratory tests, perforating tests, and experimental field tests which demonstrate that certain emulsions serve effectively as non-plugging perforating fluids. The principal components of these emulsions are two liquids: an aqueous phase consisting of a solution of either sodium chloride or calcium chloride, and an oil phase consisting of diesel oil, tetrachloroethylene, or a combination of both. Small amounts of other agents which serve to stubilize the emulsions, to reduce the fluid loss, and to inhibit corrosion are also present. The density of the emulsions is controllable within the range of 7.5 to 12.5 lb/gal; no insoluble solids are present, the filtration rate is low, and the thermal stability is satisfactory at temperatures as high as 200°F. The corrosion of steel by these emulsions is negligible. Tests conducted under conditions which simulate the temperature and the pressure in an actual well demonstrate that these emulsions fulfill the requirements of a non-plugging perforating fluid. In addition, lirnited field experience furnishes evidence that these emulsions remain in position after they are spotted, that they are retained in the casing after the perforations are made, and that they are easily removed from the perforations when the well is opened for production. When the pressure in the borehole is greater than the formation pressure at the time a well is perforated, plugging of the perforations can be avoided by spotting an emulsion adjacent the interval to be perforated. This procedure should eliminate low well productivity caused by plugging the perforations. INTRODUCTION Nature of Problem The most widely used method for the completion of oil and gas wells is to set and cement casing through productive horizons, and then to obtain production by gun-perforating the section of casing opposite the desired interval. This method is gen- erally successful and it was thought at one time that those failures which did occur were due to insufficient penetration by the perforator. Despite recent improvements in perforators which assure ample penetration, unsatisfactory fluid production continues to be a problem. Evidently, the trouble comes from some other source. Recent results obtained by Allen and Worzel1 demonstrated that low fluid productivity may be caused by the perforating process and/or by the fluid in the wellbore at the time of shooting. They found that perforations are often completely plugged by debris from the perforator, pulverized sand from the formation, and compacted solids from the drilling mud when the pressure in the wellbore is greater than the pressure in the formation at the time of perforation. In some cases a differential pressure in excess of 400 psi was required to initiate flow into the well through these plugged perforations. The plugging of perforations by solids not only causes low productivity from wells, but it creates simultaneously other problems in the production of oil and gas. For example, when most of the perforations are plugged, high rates of flow must occur through the few perforations that are open. The resulting high pressure drop may cause production

Jan 1, 1958

By L. R. Page, J. J. Norton

EFFECTIVE methods for determining grade and reserves of pegmatites in advance of mining have been developed in recent years. When intensive work began on the economic geology of pegmatites during the early years of World War 11, it was widely believed that grade and reserves could be estimated only in a most general way. The literature indicated that not all pegmatite deposits are unpredictable, but statements emphasizing unpredictability and irregularity seem to have been more widely accepted. Many standard references reflect the prevailing opinion that minerals: are unsystematic in their occurrence in pegmatites. Pegmatites have been described as "notorious for their irregular structure," and minerals within pegmatites as "irregularly distributed." "irregularly disseminated," of "erratic occurrence," "proverbially erratic in distribution," "characterized by extreme irregularity in ... size and distribution of the essential minerals, and variety and proportion of the accessory minerals," and "spotty.'"" Over many years, however, geologic techniques have been applied with increasing success to economic analysis of pegmatites. Investigations, chiefly since 1939, have shown that mineral distribution and structure of pegmatites are largely systematic and that detailed geologic study can be used to predict the size and shape of mineral deposits in pegmatites. Because the writers are most familiar with the pegmatites of the Black Hills, S. D., examples cited are from that area." Pegmatites mined in other dis- * All examples are described more cornpletely elsewhere.: tricts are similar to those in the Black Hills," and the techniques described here have been applied by geologists and engineers working in other districts. In actual practice few pegmatite mine operators attempt to make accurate estimates of grade and reserves in advance of mining. Many deposits are too small for mining except on a very small scale; few pegmatite mines have more than ten employes. Hence there is little systematic preparation for mining, and the capital outlay may be so small that only a general knowledge of reserves is necessary. Technical personnel are rarely employed by pegmatite mine operators to make such estimates. In the future, however, as capital outlay becomes larger, estimates of grade and reserves will have to be more accurate. Geologic Aspects of Determining Grade and Reserves Estimating grade and reserves requires that the type of pegmatite, the size and shape, and the internal structure be determined by detailed geologic mapping and careful mineralogic study. The wide variations in the texture and distribution of minerals within many pegmatite deposits make a thorough geologic study of this kind necessary before it is possible to decide what sampling methods should be used to determine mineral content or grade. Types of Pegmatites: The first step in economic appraisal of a pegmatite is to determine the min-eralogical and structural type. In general, pegmatites may be classified into two groups: 1) those in which component minerals are more or less evenly distributed throughout the entire body and show relatively minor variations in texture, and 2) those in which component minerals have been segregated into units with recognizable differences in texture, mineralogy. or both. Johnston" has classified these types of pegmatites as homogeneous and heterogeneous, respectively. Cameron et al.10 have used the terms ~inzoned and zoned for similar types. The difference between the homogeneous and heterogeneous types is of great commercial importance. Homogeneous pegmatites can seldom be mined where the products are concentrated by the hand methods now commonly used, but they have been mined in a few places where a milling process has

Jan 1, 1957

By K. K. Kershner, W. A. Calhoun, C. W. Funk

Future resources of aluminum may require the utilization of low grade ores to provide a more permanent protection for the nation. Aluminum minerals such as cloy, shale, and high iron laterites may become important sources. An evaluation of reserves is given. New laboratory results are reported on the Vereinigte desilication process. THIS report on future resources of aluminum metal emphasizes the necessity for investigating utilization of low grade potential ores to provide more permanent protection for the nation. Partial or complete interruption of the importation of high grade aluminum ores must be given consideration. Ultimately, aluminum minerals such as clay, shale, and high iron laterites may become the principal sources of aluminum. The development of extractive processes for treating these low grade materials is a step in long-range national preparedness that should receive more attention. In formulating such processes, the application of beneficiation methods for the purpose of classifying the several types of minerals before subjecting each type to the more expensive extractive procedures should be considered, and a careful survey of the basic factors of power sources, transportation facilities, and sources of raw material should be made. Domestic Bauxite Resources Of the domestic supply of current, treatable-grade bauxite, 95 pct comes from Arkansas. The present reserve of Arkansas bauxite suitable for metal production, including abrasive-grade, Bayer-grade, and modified Bayer-grade ores, is 34,000,000 tons. The total reserve of bauxite of all grades is approximately 75,000,000 tons. Reserves are estimated on a mined and dried basis. Data available to the Bureau of Mines in 1948 to 1949 were used in preparing Table I, which shows a breakdown by grades of bauxite for about a half of the reserves of the state. The modified Bayer ore, 10,555,500 long dry tons, is based on a cutoff of 8 to 15 pct silica. The sub- marginal 10,074,700 long dry tons is assumed to contain more than 40 pct gibbsite, more than 15 pct silica, and less than 32 pct available alumina. A considerable amount of this low grade material was consumed in 1949 and 1950. Additional tonnages of bauxitic and kaolinitic clays are indicated by the Bureau of Mines drilling project.' Applying a 50 pct factor to arrive at long tons mined and dried, the results of this project are approximately 31,500,000 tons kaolinitic clay at +35 pct Al²O3 and 11,800,000 tons kaolinitic clay at 20 to 35 pct A1,0,. Total reserves of kaolinitic clays are probably quite extensive—several times the reserves shown in the Bureau's work. Total reserves of bauxitic and high iron clays from the drilling program and previously established figures are 63,980,000 tons. The mineral dressing methods,' the lime-sinter process, he lime-sinter modification of the Pederson process," the lime-soda sinter process,"-' and the Alcoa combination processa. have been described in the literature and will not be elaborated upon here. The less familiar Vereinigte Aluminium-Werke process used by the Germans during World War 11 may require some amplification. It was used to bene-ficiate boehmite ores containing 12 to 18 pct silica for a feed to the European Bayer process. Ore was

Jan 1, 1952

By William E. Galloway, Gary E. Smith, Christopher D. Henry

INTRODUCTION Studies relating to the Oakville aquifer as presented in this report and by Henry et al. (this volume), are part of a larger , comprehensive examination of regional and local stratigraphic, hydro- geologic, and geochemical parameters within the Oakville Formation recently completed by the Bureau of Economic Geology. The Oakville serves both as a major Gulf Coast aquifer and an important uranium host (Fig. 1). Regional and local controls on hydrodynamics and hydrochemistry have important implications for hydrochemical exploration, the establishment of premining baseline parameters, and the design of post mining restoration procedures. Investigations of the Oakville Formation were de- signed for the purpose of determining the response of the aquifer to uranium extraction and were funded by the U.S. Environmental Protection Agency under grant numbers R-805357-01 and R-805357-02. Physical Stratigraphy Physical stratigraphic analysis shows that the Oakville Sandstone, a lithostratigraphic unit deposited by a major coastal-plain f luvial system, consists of five mappable, component depositional elements (Figs. 2 and 3). Each major component element is the product of one or more rivers traversing the Miocene coastal plain. In turn, each river possessed a unique sediment load, discharge characteristics, and source terrane. Consequently, each element exhibits distinguishing geometric and compositional parameters that potentially influence the flux and hydrochemical evolution of contained ground waters (Galloway, Henry, and Smith, in preparation). The Oakvil le Sandstone, as mapped and interpreted as a lithostratigraphic unit in the study area, corresponds closely to the Jasper aquifer system, an equally well-defined Gulf Coastal Plain hydrogeologic unit (Baker, 1978). Principal surrounding hydrogeologic units include the underlying Catahoula confining system, the Jasper aquifer system itself, and the overlying Burkeville confining system (lower Fleming mudstones). The Evangeline aquifer system includes much of the Fleming Formation. The Jasper aquifer system is bounded above and below by relatively less transmissive, finer grained confining systems, although absolute transmissivity varies greatly within both the Jasper and confining units. Lithostratigraphic and hydrogeologic boundaries coincide almost exactly within the Hebbronville flu- vial axis (Fig. 3). Correspondence of geologic and hydrostratigraphic boundaries is good within the George West axis; farther to the northeast the correlation of the Jasper aquifer with units mapped as Oakville Formation diverges to varying degrees. A complete analysis of these trends and a study of the depositional facies comprising the Oakvillle are included in Galloway, Henry, and Smith (in preparation). REGIONAL HYDROGEOLOGY The stratigraphic, compositional, and structural framework of the Oakville Formation and the mosaic of interrelated depositional facies that are combined in this framework play a key role in defining the hydrogeology of the Oakville. Furthermore, a combination of climate and hydrogeology, as well as past and present socioeconomic conditions, has determined water and land use patterns within the region of Oakville outcrop. Utilization of Oakville Ground Water Stratigraphic control for determining which wells produce ground water from the Oakville aquifer was established by preparing structural and isopach maps of the Oakville Formation using regional electric log cross sections. Surface elevation and screened interval data (or total well depth, if open-hole completion techniques were used) from each water well, combined with the stratigraphic data, allowed accurate assessment of the producing aquifer for individual wells. Information on well and screen depths, water levels, and usage of water from

Jan 1, 1980

By Hsun Hu

Direct observations were made on the recrystalli-zntion of a cold-rolled (110) [001] crystal of 3 pct Si-Fe by annealing thin sections of the specimen inside the electron microscope during examination. Subgrain formation, presumably by polygonization, occurs rapidly, followed by a slow increase in the subgrain size before recrystallization can be detected. No migration of the subgrain boundaries was observed, and the formation of recrystallization nuclei by coalescence of subgrains is suggested. Re-c~ystallization characteristics of various texture components were individually examined. AS reported in a previous paper: orientations of the various deformation texture components in a 70 pct cold-rolled (110) [0011 crystal of 3 pct Si-Fe were completely confirmed by transmission electron diffraction patterns taken at various areas of the specimen. These orientations can be summarized as follows: Over most areas of the deformed crystal (111) planes are parallel to the surface. These areas correspond to either $- the two main defor: mation textures, the (111) [112] or the (111) [112].2-5 Within a few areas, (100) planes parallel to the surface are frequently found. These areas represent the minor deformation texture component, the (100) [Oll] type, which is derived from rotated Neumann bands.2'4'5 Only in very rare instances are (110) planes found parallel to the surface. This orientation corresponds to the very weak texture component of the (110) [001] type. In a pole figure, this (110) [0011 orientation is located within the orientation spread between the two main (111) [1121 type textures. Usually the electron diffraction patterns taken at various areas of the specimen are very simple ones, i.e., for any one area the pattern consists only of sharply defined spots of a single orientation. In some areas, however, more or less continuous rings of weaker intensities are superimposed on a simple pattern, indicating the presence of a wide range of additional orientations. In order to understand in detail the recrystallization of this cold-worked crystal, the recrywtallization characteristics of each of the various deformation texture components must be examined. This can best be done by using a high-temperature stage and transmission electron microscopy techniques, whereby small areas corresponding to the various texture components can be selected individually for examination. The present paper presents results obtained by this method. MATERIAL AND METHOD Specimens were prepared from a previously studied1 single crystal of a commercial grade 3 pct Si-Fe alloy with an initial orientation (110) [00l], cold-rolled 70 pct from 0.014 in. to 0.004 in. in thickness. Thin foils were prepared by electrolytic polishing as described in the earlier paper.' Specimens of this thin foil were then mounted in a high temperature stage similar to the one designed by Whelan.6 A direct current was used as the heating source. The temperature of the heating grid was calibrated by means of a Pt vs Pt-10 pct Rh thermocouple in a vacuum chamber (0.01 to 0.02µHg). Maximum variation within the temperature range of 250o to 000°C was about ± 25°C. After the desired areas were selected for examination, the specimen was heated to a low temperature for some time while the selected area was constantly watched. When no further change in structure and orientation could be observed, a higher temperature was applied. Photomicrographs and diffraction patterns were taken from time to time during examination, with the heater temporarily turned off* while the photographs were

Jan 1, 1962

By H. K. Najarian

This paper describes recent development work on the Wheaton-Najarian Vacuum Condenser for Zinc at Josephtown Zinc Smelter, wherein, to dissipate the heat of condensation, the "airlift" action of gases bubbling through the molten zinc in the condenser is utilized to circulate the zinc through an outside "cooling well" and cooling it continuously. AN earlier paper1 gave an account of initial development of the Wheaton-Najarian Vacuum Zinc Condenser at the Josephtown Zinc Smelter of the author's company. This paper is a progress report of further development work over the years directed toward improving the efficiency and increasing the capacity of the condenser. In this type of zinc condenser, zinc vapor with accompanying noncondensable gases from electro-thermic zinc smelting furnaces is passed upwardly through a mass of molten zinc confined in a refractory-lined U-tube. The zinc vapor condenses in the molten zinc and the noncondensable gases are drawn out of the condenser by suction applied over the surface of the molten zinc. The heat of condensation of zinc, amounting roughly to 1000 Btu per lb of zinc condensed, is absorbed by the molten zinc and, in turn, is dissipated continuously to keep the temperature of molten zinc in a range to permit effective condensation. At the time of publication of our first paper, we had at Josephtown Smelter five units of 69-in.-bore metal furnaces and one larger metal furnace having 96-in. bore. Each 69-in. metal furnace had a condenser with 22-ft overall length. The 96-in.-bore furnace had a condenser with overall length of 31 ft. Condensers were of circular cross section, with corrugated steel outer shell and carborundum lining. Diameter of these condensers was 32 in. inside the refractory lining. Molten metal in the con- denser was kept cool by spraying cold water on the outside of the condenser shell. Under good operating conditions, 22-ft condensers produced some 12 tons of metal per day; and the 31-ft condenser, about 22 tons. When the furnaces produced zinc vapor at higher rates, invariably the condenser temperature would rise to levels where excessive blue powder would form and accumulation of accretions in the condenser would be accelerated. We found that, with the system of cooling in use, we had to provide heat-exchange surface of some 150 sq ft to condense 1000 lb of metal per hr with reasonable efficiency. The wall of the condensers was made up of 5/8-in.-thick corrugated-steel shell having next to it several layers of mica and inner refractory lining of special carborundum shapes to fit the corrugation in the steel shell, and having a minimum thickness of about 2 in. Relatively low rate of heat transfer through the thick condenser wall and slow internal circulation of the molten zinc limited the rate of heat exchange between hot metal within the condenser and the cold water flowing over the outer steel shell. The thickness of the condenser wall was about minimum that we considered suitable for continuous operation. As we learned to operate the electrothermic furnaces with higher power input, producing zinc vapor at higher rates, it became apparent that we needed condensers having larger heat-exchange surfaces. Our 96-in.-bore furnace had 6 single-phase power circuits with transformers rated at 500 kva each and normally good for power input of 3000 kw.

Jan 1, 1959

By Thomas W. Wälde

BACKGROUND Foreign investment has been a major factor in bringing about the substantial mining industries of Chile, Peru, Bolivia, Venezuela, Brasil and Guyana. But economic nationalism and sentiment against foreiqn domination of vital national industries grew in the 1960s and most major mining projects were transferred into state owner ship. Among the state mining enterprises formed were CODELCO - Chile, MINERO-PERU/ CENTRCMIN - Peru, CCMIBOL - Bolivia (in 1952), Hierro-PERU, GUY-BAU/BIDCO - Guyana, etc. New investment during that time was discouraged because it was subject to the restrictive conditions of the investment regulations of the Andean-Pact, a grouping of Chile, Bolivia, Peru, Ecuador, Venezuela and Colombia. The philisophy was that mineral resources were to be developed exclusively by national enterprises. Essential foreign inputs had to be acquired "depackaged" as separate purchases of equipment and technical assistance services. As a result of the worldwide economic recession which hit the mining industries in 1980-1982, many projects that were viable in 1970 were not developed by the new state enterprises due to lack of capital, managerial and technical abilities and due to problems with marketing. As a consequence of the long-term decline of metal prices, governments experienced difficulty in getting investment organized through national or foreign enterprises and have had to face up to the trade-offs between national control and active mineral development. A change has since taken place in governmental policies. The 1981 Peruvian mining law, the 1982 mining law of Uruguay, the 1979/1980 mineral promotion laws of Argentina, all witness the gradual shifting of emphasis from restriction to promotion. The investment rules of the Andean Pact have been progressively softened through national regulation and today are more or less irrelevant. Nationalizations and forced renegotiations have not occurred in the last few years. Countries have gone to great lengths (without much success) to re-attract foreign investment on terms that accommodate the political sensitivities of the South American countries and the practical requirements of investors and financiers. For this analysis, three contracts have been selected which reflect this accommodation in three South American countries, where miner a1 production plays a major role in the national economy. These con tracts reflect both the attitudes and traditions of the individual countries, but also mark the shift in mineral investment policies that has taken place. EL INDIO AGREEMENT The 1977 investment agreement between Chile and St. Joe Minerals marked a dramatic relationship between Chile and foreign mining investor s. In Chile, mining of copper has played a major role in the country's history. Large scale copper mining was initiated and developed by Kennecott and Anaconda. The nationalization of these two companies under the Allende government in July 1971 started a wave of nationalizations of foreign-held mining and petroleum operations since then in many parts of the world. The military government supported the new Chilean state mining companies ((30DELCO and ENMI) , but it also attempted to accelerate mineral development by prom ting foreign private investment, thus reversing the nationalistic policies followed by the Allende and the preceding Frei government. The new policy by the military government is expressed in Decreto-Ley 600 (1974) which governs foreign investment in Chile. Decreto-Ley 600 is

Jan 1, 1985

By A. Berghezan, E. Bull Simonsen

A simple and general method is described for melting and zone refining refractory metals by induction heating on a specially shaped water-cooled copper crucible. The crucible is the essential part of the apparatus and is placed horizontally. It consists of either a copper plate, or a flattened tube, or of several parallel small diameter tubes all water cooled. The charge lies on the crucible, or whenever possible, is suspended above it. This assembly goes into a transparent quartz tube and the whole is passed through the coil of a radio frequency generator. Vaarious atmospheres can be used. No contamination is detected from the copper crucible. purification is obtained both by selective evaporation of impurities and by zone refining. METHODS of melting and refining relatively large ingots of all reactive and refractory metals as well as some semiconductor materials have been developed in this laboratory during the past several years using induction heating and cold crucibles. These methods are simple and permit the use of a variety of starting materials in preparing ingots of suitable shapes. Among these methods, two are of particular interest. One deals only with the problem of melting without contamination. In this method the induction coil has a specially designed shape and acts simultaneously as heating element and crucible. The second goes one step further, being designed for both melting and further purification of the refractory metals. The aim of this paper is to describe the second method which is of more general interest and of greater applicability to metallurgical problems. A) THE PRINCIPLE OF THE MELTING AND PURIFICATION METHOD As originally proposed by one of us1 the method consists of heating a charge of any refractory metal or semiconductor material to the melting point on a water-cooled copper crucible by passing both the charge and the crucible through the induction coil of a radiofrequency generator. Although both are subjected to the same induction field, one achieves the melting of a refractory metal on a copper crucible even when the refractory metal has a melting point of more than 2000°C above that of the crucible. This seemingly "odd" method works effectively for the following reasons. Because of its high electrical and thermal conductivity as compared with the material being melted, copper can be used as the crucible and kept at a low temperature while the material is heated by induction to its melting point. With water Silver and other highly conducting materials can also be used. If a nonconducting material is contemplated, e.g. SiO or a high polymer, a very thin wall should provide efficient cooling. cooling through ducts in the crucible its temperature can be kept between 40" to 70°C; thus its electrical resistivity is kept low, while the resistivity of the charge increases rapidly as its temperature is increased. B) APPARATUS The crucible is the essential part of the apparatus. It has been designed in various shapes depending on the atmosphere used, whether vacuum or an inert gas or hydrogen. In all crucible designs an effort was made to reduce its volume to "nothing but the cooling water" in order to avoid shielding the ingot from the induction field. In practice it is either a

Jan 1, 1962

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.