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By Spencer S. Shannon

The lanthanide elements from lanthanum (atomic number 57) to lutetium (71) plus yttrium (39) are called the rare-earth elements; scandium (21) is chemically similar to yttrium and the lanthanides, but differs in occurrence. The rare-earth metals were divided into three categories by the chemist, Berzelius, in the early 1800s; however, modern usage defines only two groups. The cerium group is named after the most abundant -element and comprises lanthanum (57), cerium (58), praseodymium (59), neodymium (60), promethium (61), samarium (62), europium (63), and gadolinium (64). Traces of natural promethium were discovered in apatite in Finland (Erametsa, 1965). The yttrium group, also named after its most abundant representative, comprises terbium (65), dysprosium (66), holmium (67), erbium (68), thulium (69), ytterbium (70), and lutetium (71). Yttrium most closely resembles holmium in chemical properties, and occurs most commonly with the heavy lanthanides. The rare-earth minerals may be divided into cerium-group, yttrium-group, or mixed-group classes. A number of rare-earth minerals contain thorium and uranium, but these are variable in content and are not essential to the composition of the minerals. In monazite, a mineral that is a principal source of rare earths, the worldwide average content of thorium oxide is 7.2 % ; however, varieties of monazite contain as little as 0.001% and as much as 31.5% thoria. Monazite is the chief ore of thorium and, until recently, thorium has been the main product; the rare-earth metals were in fact byproducts. However, because of the great demand for rare-earth metals by the petroleum refining and the iron and steel industries since the early 1970s, the roles have been reversed so that thorium is now the byproduct. Uses A 9 to 1 mixture of yttrium and thorium oxides is used for high-intensity incandescent lamps and for high-temperature-resistant windows and lenses. Yttrium oxysulfide and orthovanadate, doped with europium oxide, are used in color television tube phosphors. Yttrium, as well as cerium, praseodymium, and samarium, is alloyed with cobalt to form strong permanent magnets. It hardens magnesium alloys and retards the oxidation of iron-chromium alloys. Yttrium-iron garnets are used for transmitting low microwave frequencies. Yttrium-aluminum garnets are used as host crystals for lasers and as artificial gems. Yttria also forms strong, stable, high-temperature refractories. Gadolinium-gallium garnets are used in substrate wafers on which bubble-memory films are deposited. Rare-earth chlorides, particularly of lanthanum, neodymium, and praseodymium, are used as catalysts for petroleum cracking. Mischmetal is used for lighter flints and to improve the ductility and impact strength of iron and steel alloys. Mischmetal also reduces the fatigue resistance of magnesium and aluminum alloys. Rare-earth oxides are used for polishing glasses and lenses. Individual or specific combinations of high-purity oxides are used as additives in glass to maintain or change its color, dispersion, or refractive index. High-purity oxide combinations are also used to color tile and to opacify porcelain enamel. Rare-earth fluorides and oxides are used in carbon-arc electrodes to provide incandescent white light. Lanthanum or gadolinium oxysulfide phosphors, activated with terbium, are used as x-ray screen intensifiers. Hydrogen can be stored by sorption on lanthanum-nickel alloys (Anon., 1979). Thorium232 is bombarded with slow neutrons in breeder reactors to create fissionable thorium233 for nuclear fuel cells. The 330-MW, high-temperature gas-cooled reactor at Fort St.

Jan 1, 1983

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957

By Paul Billingsley

THE mining districts of the first and second order1 of the western United States (and borders) are those named on Fig. 1. These fall into four groups: (1) in the eastern outliers of the Rocky Mountain system; (2) in the Rocky Mountain system itself; (3) in the Great Basin; and (4) in the Sierras and Coast ranges. Of these four groups, the first three are almost entirely of Tertiary age and are within a belt of Tertiary compres-sive folding which we shall call the Rocky Mountain-Great Basin thrust arc. The backbone of this belt is shown by the line BAC. The position of the ore districts in this belt indicates a conformance to linear elements of the continental pattern. These are additional to the peripheral elements emphasized by Butler.2 NATURE OF THE THRUST ARC The thrust arc separates regions of contrasted kinds. To the east of it are flat-lying plateaus interrupted by earlier mountain folds; to the west, sunken basins, in which block-faulted ranges lie like an anchored fleet in a sea of desert wash or lava. The cross-sections are as shown in Fig. 2.

Jan 1, 1933

By Hugh Archbald

IT is possible to construct a simple diagram of the earnings, or the production, of the men employed at a coal mine that will show not only if the conditions tend toward contentment among the men, but if the operating distribution of the work is correct. As earnings are the greatest cause of discontent, even exceeding all the other causes, if contentment exists in the matter of earnings, the likelihood of other discontents flaring up is greatly lessened. The basis of such a diagram would be the Gaussian curve of the normal variation in human ability. Such a curve has long been recog-nized. H. L. Moore,1 in discussing the quantitative relation between wages and ability says: "It has been pointed out that industrial efficiency is dependent upon physical, mental, and moral qualities, and these qualities . . . there is good reason for regarding as being distributed according to the Gaussian law..

Jan 7, 1924

By A. P. Herring, M. Hoover, D. W. Fuerstenau

The dissolution of nickel, copper, and cobalt from five different samples of well-characterized deep sea manganese nodules was measured as a function of temperature, pH, leaching time, and particle size. Nickel, copper, and cobalt extraction each respond to these variables in a different manner. The results of this investigation indicate that copper and nickel can be selectively dissolved from iron and manganese at moderately low pH, provided the reaction is given sufficient time. A high dissolution of cobalt with dilute sulfuric acid can only be achieved from nodules that have a low iron content (<5%). The most probable rate-controlling step for copper and cobalt dissolution is diffusion through the pores of the nodules, and for nickel dissolution chemical reaction appears to be rate-controlling.

Jan 1, 1974

By F. M. Doyle-Garner, A. J. Monhemius

Hydrolytic stripping is the process whereby metal ions in a loaded solvent extractant are hydrolyzed by water, typically at 130°C to 200°C (265°F to 392°F). Equilibrium hydrolytic stripping tests were done on Versatic 10 solutions containing various metals, singly and in mixtures. Single solutions of Fe, Ni, Cu, Mg, and Mn precipitated [a]Fe2O3 Ni(OH)2 Cu2O + CuO, Mg(OH)2 and [?]Mn203 respectively, during hydrolytic stripping. Several mixtures containing iron precipitated magnetic spinel ferrites, MFe204. No other combinations formed mixed oxides. It is proposed that the mechanisms for hydrolysis and precipitation of iron in loaded Versatic solutions are similar to those for iron hydrolysis in aqueous solutions. Magnetic interactions between mixed carboxylate complexes are thought to be responsible for the homogenous nucleation of magnetic mixed oxides in preference to single oxides.

Jan 1, 1986

By Robert E. Ogilvie, Zvonimir Ban

Oxidation experiments were conducted above 600°C to investigate the oxidation products formed on the surface of MoSi2. Results are presented which indicate that minor iron impurities play a key role in the oxidation behavior of MoSi2 above 600 °C. Based on considerations of the crystal chemistry of the oxidation products, MoSi2 with rhenium and iron additions was found to be resistant to oxidation in the pesting temperature range. AS early as 1914, Honigschmidtl observed that some silicides of molybdenum exhibited high resistance to oxidation at elevated temperatures. This fact did not arouse much interest until 1950, when Kieffer and cerwenka2 examined this property in more detail. They found that Mo-Si alloys with approximately 70 pct Mo (by weight) could be heated to 1600°C in an oxidizing atmosphere without any significant damage. The surface was found to be protected by the formation of an extremely thin silica glass layer which had no tendency to spa11 during subsequent thermal cycling. In 1955, Fitzer3 discovered that even solid bodies made of MoSi2 completely oxidized within a relatively short time when exposed to the air in the temperature range from 300° to 600°C. To describe this phenomenon he proposed the name "molybdenum disilicide &apos;pest&apos; ", clearly analogous to the previously observed "tin plague" ("tin pest") which, however, arises as the result of a phase transformation. Studies performed by Fitzer and, in particular, one published recently by Berkowitz, Blackburn, and Fel-ten,&apos; comprise the most extensive research to date on the pest phenomenon in MoSi2, as far as the fundamen- tal mechanism of the process is concerned. The first of these studies revealed the existence of a crystalline phase which appeared at the surface at 750°C and dissolved in the glassy silica layer at 1150°C. The logical assumption was that this phase was some reaction product of MOO3 and SiO2. The formation of a reaction product of this type seemed probable since it had been mentioned by Glemser and Lutz6 in a paper describing their studies of molybdenum oxides; however, this assumption was later disproved.8 It is our belief that information concerning the exact nature of this crystalline phase may be important for a better understanding of both pesting and the protection mechanism. Therefore, since the only available general description of the pest phenomenon was that of Fitzer, it was decided to reproduce his experiments. These experiments established that, in addition to the "pest" and "nonpest" temperature range, an intermediate region exists between 600" and approximately 650°C. This region is characterized by the appearance of a variable amount of yellow to orange colored crystals. The electron-beam microanalyzer was used to qualitatively determine their composition. Iron and molybdenum were found to be major constituents. This result can be explained based on the following facts: 1) iron, according to literature data,* is the most common impurity in molybdenum powder, and its content can be as high as 0.25 pct; 2) technical silicon powder usually contains iron; 3) steel ball mills are often used for the crushing and grinding of MoSi2. In order to clarify the exact role of iron, it was deliberately added to a stoichiometric mixture of molybdenum and silicon. The observed results corroborated the previous experiment, proving that iron (probably as some silicide phase) concentrates along the grain boundaries. I) EXPERIMENTAL PROCEDURE A) Oxidation of MoSi2 with Iron Additions. 1) Specimen Preparation. Specimens were prepared by both

Jan 1, 1967

By T. K. Perkins, L. E. Bartlett

Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenonema This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young&apos;s moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy me generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. INTRODUCTION The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface). In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young&apos;s Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50-12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry.1 An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith6 has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1.

By L. C. Armstrong

Twice in the past two years and in two widely separated localities—ane near Williamsville, Mo., and the other in the Allard Lake district of Quebec— the Contract Drilling Division of the Longyear Company has experienced perplexing difficulties in drilling granitoid igneous rocks. The rocks in both places are characterized by appreciable amounts of feldspar intimately inter-grown with quartz particles of microscopic dimensions. The disappointingly slow rate of advance and the exceptionally high bortz loss, obtaining during the life of these two projects, are ascribed largely to the resistance to abrasion of these two minerals when arranged in this intergrown pattern. Whether all intergrowth-bearing igneous rocks would offer extraordinary resistance to bit progress cannot be stated with assurance on the strength of these experiences alone. More data on diamond drilling this sort of material in a number of localities are needed before any generalizations can be made safely. It should be pointed out that the lack of time and funds made it impossible for the writer, or other persons interested in correlating the details of bit histories with the kinds of rocks drilled, to be present during the performance of the contracts. However, the records kept in the normal course of drilling are deemed complete enough to be reportworthy. This information is presented here together with the findings made in studies of the rocks involved, with the thought that it may attract the comments of others who may have encountered similar refractory drilling conditions. A pooling of knowledge on the problem would be of material aid in devising more efficient cutting tools and procedures for penetrating this kind of rock. Drilling Blastholes in the Williamsville Granite Due to the unsatisfactory perform- ance of pneumatic percussion drills in boring blastholes on a construction contract near Williamsville, Mo., tests were made with a diamond drill. The poor progress achieved and the excessive loss of diamonds, however, soon led to the abandonment of these trials. The diamonds, in all of the bits tried, lost their cutting edges and acquired a polish after being in service for distances ranging from a few inches to a few feet. Coring bits containing surface-set, whole-stone bortz in a tungsten powder matrix were employed. The cost assignable to bortz wear averaged $7.17 per foot. This item of expense is several times the amount normally expended in diamond drilling in firm, unfractured, granitic rocks. Diamond-impregnated, tungsten carbide bits also were used without success. The diamond wear was at the rate of $0.98 per foot, but the diamond chips became too polished for further duty in less than a foot of drilling. The Williamsville granite is pink and medium-grained. In the hand specimen, it has a fresh, sound appearance; it is seemingly composed almost entirely of interlocking grains of feldspar and quartz and has no discernible features suggesting a greater durability than is usually found in rocks with this composition and texture. Microscopic examination, however, reveals a predominance of feldspar grains with more or less regularly distributed and sharply angular masses of quartz (see Fig 1). The pattern assumed by the two minerals in this mode of occurrence is referred to as a "graphic intergrowth," as it bears some resemblance to the cuneiform characters of ancient Persian writing. The other principal constituents are quartz-free feldspars (microcline and orthoclase) and quartz. All of these constituents are in nearly equidimensional grains, ranging up to about 3 mm in length. There are also

Jan 1, 1950

By D. K. Bose, C. K. Gupta, K. U. Nair

A new approach to processing an indigenously available low grade molysulfide concentrate by chlorination with elemental chlorine in presence of oxygen is reported. Recovery of nickel and copper values associated with the sulfide concentrate by suitably treating the residue obtained after chlorination is also reported. In the chlorination process, a gaseous mixture of chlorine and oxygen in the volume ratio bf 2:5 has been passed at 1.66 x 10- 5 m3/s for 1800 s over a 0.01 kg batch of molysulfide concentrate at a temperature of 573°K. Most of the molybdenum has been volatilized as molybdenum oxychloride which has subsequently been extracted in water. The molybdenum value from the aqueous solution has been recovered in the form of calcium molybdate (CaO.MoO3) by treatment with calcium chloride (CaCI2). In an alternative processing scheme, the molybdenum rich solution has been treated with an oxidizing agent (K2S20f.J) and allowed to boil to recover a major portion of the molybdenum value in the form of molybdic oxide (MOOS). The spent charge obtained after molysulfide chlorination has been mixed with about 1 wt % sodium chloride and heated at 773K under an oxygen atmosphere. The reacted mass has been water-leached to yield a nickel-copper bearing solution with limited iron. The process liquor appears to be well suited for further processing by known hydrometallurgical recovery processes for nickel and copper. In the conventional process of molybdenum extraction, the molysulfide concentrate (-59% Mo) is first subjected to roasting to produce molybdic oxide. The oxide is then further processed in sequential steps involving vacuum distillation, ammonia leaching, and calcination to higher purity prior to hydrogen reduction to metal. In India there is at present some small tonnage production of molysulfide concentrate from a byproduct recovery plant of the M/s. Uranium Corp. of India Ltd. (M/s UCIL), Bihar. Efforts are being made at this laboratory to process the low grade fraction of the concentrate which contains sulfides of copper, nickel, and iron; quartz; and chlorites. Here, the conventional routes involving roasting and vacuum distillation appear unsuitable to produce an acceptable quality of molybdic oxide at high recoveries. Formation during roasting molybdates of some of the impurities present in the sulfide concentrate make subsequent vacuum distillation less efficient. In view of these problems, in earlier work reported from this laboratory the low grade concentrate has been processed hydrometallurgically to P. produce calcium molybdate. Starting from this molybdenum intermediate, processes have also been developed for the production of molybdenum and ferromolybdenum. Chlorination as an alternative to roasting for metal sulfides has been drawing considerable interest. The high reactivity of chlorine, the relatively low temperature of operation, the suitability of application to low grade resources, the convenience of recovering sulfur in non-polluting form, and the purity of chlorides which are separated by distillation all favor chlorination. In recent years, considerable work has been reported on the chlorination of common metal sulfides. In the field of molybdenum extraction from its sulfide resource, use of chlorination technology has been rather limited. Senderoff and Labrie3 were the first to chlorinate molysulfide concentrate with elemental chlorine at about 823°K to molybdenum pentachloride for use in the electrolytic preparation of molybdenum. The only other reported work, by Haver, Uchida and Wong, involved reaction between molysulfide and chlorine at 673°K to recover sulfur. The reaction products were, however, identified as molybdenum pentachloride and sulfur monochloride.

Jan 1, 1979

By O. B. Bennett

WHEN diamond drilling was introduced in the Rhokana mines in 1939 it was used principally for pillar removal and for completion of the upper portions of shrinkage stopes which were being affected by increasing pressure. This method of drilling long blastholes proved so successful that it was extended gradually to cover stoping, pillar recovery, and hanging cave work. By 1949 virtually all the production of Mindola and Nkana was being obtained by this method. At the present time 87,500 ft are drilled each month by the 80 diamond drills in daily operation. Responsibility for control and issue of diamond drilling equipment and crowns, as well as tabulation of all performance figures, was taken over by a specially formed Roto drill department, which also investigated the problems encountered with this new method. To assist this department a fully equipped test chamber, Fig. 1, was established underground where performances of various types of machines and equipment could be studied under conditions as nearly uniform as possible.

Jan 12, 1954

By Rossiter W. Raymond

The manufacture of ferromanganese in the blast furnace having been the subject of considerable attention in the Institute, I beg to put on record a contribution to the discussion from a quarter hitherto not directly represented, namely, the St. Louis furnaces, near Marseilles in France, belonging to a company of which M. Jordan, a member of the Institute, is Managing Director. These furnaces commenced in 1862 to manufacture specular pig (fontes facettes) containing from three to six per cent. of manganese. In 1864 the regular production of spiegeleisen (fontes miroitantes), containing seven to ten per cent. of manganese, was inaugurated. At that time the Rhine was the only locality of this manufacture, and the Bessemer works of England and France obtained from Gernlany all their spiegel. From 1864 to the present time, the St. Louis furnaces have been advancing steadily the percentage of manganese in their product. From ferromanganese of thirty per cent. they had arrived, about two years ago, at a product containing seventy to seventy-five per cent., and for some time past they have been turning out what, as M. Jordan remarks, may fairly be Termed fonte de manganese, or manganese pig, instead of iron, since the percentage of iron it contains is not more than 8.5, while the percentage of manganese is 85, or ten times as great. This very high grade material has a peculiar appearance, entirely different from that of ordinary cast iron or spiegel. It is granular, and steely gray in color. The following analyses, communicated to the Sociètè des Ingenieurs Civils, by M. Jordan, show the composition of various products of the St. Louis furnaces:

Jan 1, 1879

By V. N. Burnhart

After eight years of testing and development, the E. J. Longyear Co. has adapted the wire- line core barrel to small diameter drillholes. Field performance indicates that the apparatus for the BX hole will be an important supplement to the conventional techniques used in the diamond core drilling industry. Higher core recovery, faster drilling progress, and reduced diamond costs will provide substantial savings to the user of coring equipment. The wire-line principle is not new, having been successfully applied to the large-diameter holes of the petroleum industry. But scaling the practices of core recovery in oil well drilling down to the small BX hole presented a number of problems. The technique, difficult even for large holes, was complicated by the exacting limitations of the small diameter in which durable and foolproof mechanisms would be required to operate. Since the maximum benefits could be realized from this sys- tem in holes 1000 ft and deeper or in holes in badly fractured ground, the drill string would have to be able to withstand heavy stresses. Most vital to the success of the idea was the development of a positive latching mechanism to assure proper positioning of the inner tube of the core barrel when the tube is dropped into place. Lastly, little was to be gained from the wire-line method without diamond bits that would give optimum penetration rates and a long service life in the drillhole.

Jun 1, 1955

By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick&apos;s Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??&apos;i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff&apos;s approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author&apos;s derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author&apos;s Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick&apos;s First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire&apos;s approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire&apos;s description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

By Albert S. Trube

Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of reservoir fluids well in advance of more accurate laboratory data. One such factor is the isothermal coefficient of expansion of an undersaturated hydrocarbon liquid which may be contained in a particular reservoir. This coefficient, or liquid "compressibility", has often been assumed to be relatively insensitive and nearly constant. Although this assumption may be nearly correct in the case of high specific gravity liquids, it cannot apply in the case of medium to low specific gravity liquids. Any treatment of the nature of liquid compressibilities must give consideration to the variable nature of the isothermal expansion coefficient and the fact that it can be both pressure sensitive and temperature sensitive. The isothermal coefficient of expansion, or compressibility, of a substance is defined as -c = 1/V (?V/?p)T......(1) The value of Eq. 1 may be approximated for a finite pressure change by using the well-known relation, c = V1 - V1/Ve (p2-p1), ........(2) in which p1 > p1 and V2 > V2 and V1 + V2/2. The instantaneous compressibility may also be estimated from the slope of a curve on which log V is plotted vs pa. In this instance, it has been shown that c = In V1/V2/p2-p1 ...........(3) Eq. 3 may be used for variable compressibilities by plot-ting V vs p on semi-log paper. In this case, the instan-taneous or point compressibility is c = 2.303 m.......... . (4) in which m is the slope of the curve at a point in log cycles per psi. ISOTHERMAL COMPRESSIBILITY OF UNDERSATURATED LIQUID In the case of gases, the compressibility has been defined by Muskat&apos; and others as Co = 1/p - ?z/z?p ..........(5) This was later generalized through application of the theorem of corresponding states&apos; to co = 1/pr - (?z/z?pr) T8 ........(6) in which c, is defined as the pseudo-reduced compres-sibility and is numerically equal to (c.p,) and the sign is arbitrarily changed for mathematical convenience. Eq. 6 is general and applies to gases and liquids. In the case of liquids, c. = c1,pe, but if Eq. 6 is used, values of z and ?z/?p, must be determined for the liquid in question. The difficulty of obtaining accurate values of ?z/?p,, particularly in the region where T, is approaching 1.00, was pointed out in the previous paper&apos;. This method of approach is unreliable for extension into computations of liquid compressibilities. On the other hand, c, can also be defined as follows: - Cr = 1/Vr (?Vr/?pr) Tr ......(7) and from which, Cr = 1/pr (?pr/?pr) Tr .....(8) In accordance with the theorem of corresponding states, Vr = V/Vr, p, = p/pr and pr = p/pr. Ref. 2 pro-vides an excellent source of reduced density, reduced pressure and reduced temperature data for a wide variety of fluids. For the purpose of this investigation, the set of fluids2 having ze = 0.27 was chosen because it in-cludes most of the heavier hydrocarbons usually found in those complex mixtures loosely defined as "reservoir oils". Data on undersaturated liquids in Ref. 2 were rearranged to conform with Eq. 8. To simplify the computation of cr, the isothermal p, data were plotted vs the log of pr, in which case for any straight line or tangent cr = 1/M pr pr .....(9)

Jan 1, 1958

By J. P. Norris, W. T. Pettijohn

The Mufulira Copper Mine, Ltd., is in Northern Rhodesia, ten miles from the Belgian Congo border, and is one of the group of four operating mines comprising the Northern Rhodesian Copperbelt. The ore deposits at Mufulira are on the limb of a large syncline striking NW.-SE. and dipping NE. at about 45 deg towards the Congo border. The host rocks are well-consolidated, highly-silicified, felspathic quarzites of the lower part of the pre-Cambrian Séries des Mines of the Katanga. The ore rocks are underlain, unconformably, by the older "Muva Series," in this case hard, green, metamorphosed quarzites. There are three superimposed orebodies, the first, or upper, orebody averaging 40-ft true thickness with a strike length of about 5000 ft, the second, or middle, orebody of about 50-ft true thickness with a strike length of about 6000 ft, and the third or lower orebody of around 60-ft true thickness with a strike length of 8000 ft. The orebodies are separated by varying widths of waste, or very low-grade ore, from a few feet up to 50 ft. The middle and lower orebodies are so close together for a strike length of 3000 ft that they are mined as one orebody. In all, the mineralized zone is about 200 ft in true thickness.

Jan 6, 1950

By Thomas E. Howard

Recently, the mining community has begun to move toward a more prominent place in the structure of American society. Extensive press coverage of our energy problems during the past year or two has led to an increasing awareness on the part of the public of the vital role that mining must play if today&apos;s standard of living is to be maintained. It appears that mining may be emerging from a status generally characterized in the public mind as an esoteric, dirty, man-killing, land- scape-despoiling endeavor, to a new stature that may eventually become as respectable as agriculture. To be sure, we are still being criticized, as has been the lot of miners since the time of Agricola. In fact, the clamor has never been louder. Nevertheless, the public, in increasing numbers, is beginning to know it needs us. But we cannot be complacent. Our improving stature brings along with it increasing responsibility. The mineral industry will be expected to produce mineral raw materials and fuels in ever larger amounts and sell them at reasonable prices, in the face of rising labor costs, decreasing labor availability, chacging labor attitudes, increasingly stringent environmental regulation, stricter health and safety standards, and a deteriorating geo-political climate.

Jan 6, 1975

By G. S. Hume

RECENT developments in the Turner Valley gas and oil field, 40 mi. southwest of Calgary, Alberta, have indicated a large producing crude-oil area. Drilling be¬gan in Turner Valley in 1913 but no major developments took place until the fall of 1924, when Royalite No. 4 well at a depth of 3740 ft. in the upper part of the Paleozoic (Mississippian) limestone obtained a production - of 20,000 M cu. ft. of gas with a content of about one imperial gallon of naphtha (73° A.P.I.) per M cu. ft. This well produced as much as 600 bbl. of naphtha per day, and until abandonment in 1934 produced 911,313 bbl., which together with the gas sold was valued at about $5,000.000.

Jan 1, 1937

By T. A. Pollard, C. R. Sandberg, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler&apos;, and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl&apos; have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By C. R. Sandberg, T. A. Pollard, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler&apos;, and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl&apos; have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949