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By E. R. Brownscombe, Francis Collins

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949

Since this paper was written, some changes have taken place, materially reducing the cost of iron-making as estimated in the text. These are chiefly reductions in the prices of ore and fuel. The charcoal used is now made in bee-hive ovens, and the price is con-

Jan 1, 1895

By J. W. Downey, A. E. Dwight, M. H. Mueller, H. Knott, R. A. Conner

Sixty new ternary equiatomic compounds are reported with a hexagonal crystal structure that is isostructural with or very similar to Fe2P, D3h-P62m. HoNiAl is a typical example, with a, = 6.9893 ± 0.0003Å, C, = 3.8204 ± 0.003Å, and c/a = 0.54 7. Three holmium atoms occupy (g): x,0,1/2 three aluminum atoms occupy (f): x,0,0; one nickel atom occupies (b): 0,0,1/2; and two nickel atoms occupy (c): 4, + , 0. The nonequivalent 1(b) and 2(c) sites give rise to two sets of unequal interatornic distances (i.e., Ho-Ni and Al-NL in the case above), which account for the prevalence of Fe2P-type tertmry compounds and the scarcity of binary examples. Unit-cell constants are presented for the sixty compounds and density measurements on the compounds HoNiAl and UFeGa confirm that three formula weights are present per unit cell. Neutron and X-ray powder diffraction intensity measurements were made on CeNiAl and HoNiAl, respectively. The atomic posiLiotml parameters in CeNiAl were determined from neutron data to be x = 0.580 5 0.001 for cerium and 0.219 5 0.001 for aluminum. An investigation of the quasibinary section between the binary compounds CeNi2 and CeA12 revealed a new ternary compound CeNiAl. The compound has a hexagonal structure and is isostructural with the prototype compound Fe2P. Additional examples discovered or confirmed in this investigation provide a total of sixty ternary compounds that are isostructural with or closely related to Fe2P. Previous investigators1'2 reported the unit-cell constants for the hexagonal compounds UFeA1, UCoAl, UIrA1, ZrNiAl, ZrNiGa, HfNiAl, and HfNiGa and the present investigation has confirmed that the compounds are isostructural with Fe2P. Independently, Steeb and petzow3 reported the same structure type for UCoAl, UIrA1, and UNiA1. However, the present results suggest a different atomic site occupancy for the component atoms in the three compounds. A detailed investigation of the relative positions of the three kinds of atoms in the compounds CeNiAl and HoNiAl will be discussed. EXPERIMENTAL PROCEDURE The equiatomic alloys were prepared from elements of 99.9+ pct purity by arc melting under a helium-argon atmosphere. After homogenization at temperatures from 700" to 900' C, a metallographic examination was performed by conventional methods, and density measurements were carried out by the immersion method in CCl4. A powder sample was prepared for diffraction studies by crushing a portion of the annealed button. X-ray diffraction patterns were obtained with a Debye-Scherrer camera, in which the annealed powder was glued to a quartz filament, and indexed with the aid of a Bunn chart. Unit-cell constants were calculated from the computer program of Mueller, Heaton, and Miller4 and d spacings were obtained by the program of Mueller, Meyer, and Simonsen.5 The intensity values were calculated from the relation I, ~ (m)(L.P.)F2 by a computer program written by Busing, Martin, and Levy.6 The absorption and temperature correction factors were neglected. An X-ray study of HoNiAl was carried out to take advantage of: large differences in atomic scattering factors for holmium and aluminum, X-ray patters free of background darkening, negligible oxidation at room temperature, and negligible weight loss in the preparation of this alloy. The neutron diffraction studies were made on a powder sample of CeNiAl contained in a -in. diam V tube and a pattern was obtained with neutrons of wavelength The neutron scattering factors employed (x 10-12 cm). In contrast to the scattering amplitude for X-rays, cesium does not have the largest cross section, however, there is a sufficient difference in the neutron scattering amplitudes to distinguish between the atomic species. The neutron transmission was high, 86 pct; therefore, absorption corrections were not necessary for the cylindrical sample. Most reflections could not be observed individually, because of the relatively large unit cell (a = 6.9756 and c = 4.0206Å) and relatively short neutron wavelength; therefore, the intensity of grouped reflections was considered. The Kennicott modification7 of the Busing-Martin-Levy program6 was employed to determine the identity of the atoms at the various lattice sites and the positional parameters. RESULTS A structure for the prototype compound Fe2P was first reported by Hendricks and Kosting;8 however, the structure was in error. The correct structure, as reported by Rundqvist and Jellinek,9 is as follows. The unit-cell constants and volumes per formula weight (V/M) are given in Table I for the sixty compounds examined in this investigation and classified as Fe2P-type compounds. The structure type was determined initially from a comparison of the unit-cell constants of HoNiAl with other known examples of this structure type1' and from the density of HoNiAl, given in Table 11. The density indicated that three formula weights comprised a unit cell, as in the prototype compound Fe2P. The assignment of the three species to lattice sites was made initially on the basis of atomic size. The large holmium atoms were assigned to the 3(g) sites that have a relatively large interatomic distance to nearest neighbor positions, the small nickel

Jan 1, 1969

By F. C. Langenberg, J. Chipman

New data on the distribution of silicon between slag and carbon-saturated iron at 1600oand 1700oC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1700°C for slags containing up to 20 pct Al2O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A1203-SiO2 slags over a range from zero pct A12O3 to saturation with A12O3, or CaO.2A12O3. The upper limit of SiO, is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently, 4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/A12O3 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al2O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al2O3 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al,O3 and of A120,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO, (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2 The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960

By Juptner von Jonstorff

A discussion of the paper by Messrs. Jüptner von Jonstorff, Blair, Dillner and Stead, read by title at the Lake Superior meeting, but presented first at the New York meeting of the Iron and Steel Institute (October, 1904), and here published under a mutual agreement between the two Institutes. Correspondence. MR. R. HAMILTON (Glengarnock) wrote to say that it was known for many years, that unless certain precautions were taken in dissolving the sample, there was a liability to obtain a solution from which the ammonium-molybdate solution would not precipitate the whole of the phosphorus. In 1877 Blair and Finkiner independently attributed this interference to the presence of carbonaceous matter in the solution, derived from the action of acids on the combined carbon of the metal, and they directed that the solution should be prepared in such a manner as to destroy these carbonaceous compounds. This was practically effected by evaporating the acid solution to dryness and roasting the residue. Adolf Tamm, in 1884, accentuated the same view. There are methods founded on the above-mentioned observations which leave nothing to be desired in point of accuracy, but the evaporation to dryness with subsequent roasting and re-solution consumes much time, besides the minor inconvenience caused by large amounts of acid fumes. In 1888 P. W. Shinier suggested that the incomplete precipitation of phosphorus was due to incomplete oxidation of -.the phosphorus, and proposed to render all the phosphorus precipitable by oxidizing the solution with potassium permanganate, etc. Experiments were made to test the accuracy of this view (details will be found in the Journal of the Society of Chemical Industry, vol. x., p. 904), and the results obtained seem to-prove that it is the correct one. It was first proved that carbonaceous matter in solution did not prevent the precipitation of properly oxidized phosphorus

Mar 1, 1905

By E. T. Turkdogan

The activity of sulfur was determined as a function of composition of ferrous sulfide by equilibrating with hydrogen sulfide-hydrogen gas mixtures at 670° , 800°, and 900". The present results supplement the available data over the composition range from 36.6 to 39.5 pct S. The X-ray lattice spacing measurements made are in accord with the available data and indicate that the limiting composition FeSl.008 may be taken for the iron-iron sulfide equilibrium. The growth rate of ferrous sulfide on iron was measured by reacting iron strips or blocks in hydrogen sulfide-hydrogen gas mixtures. Owing to the slow approach to equilibrium between the gas phase and the surface of the sulfide layer, The sulfidation experiments were carried out for several days. It is shown that the growth rate ullimately proceeds in accordance wilh the parabolic rate law. From the parabolic rate constants and the thermodynamic data on iron sulfide the self-difiusivity and chemical diffusivity of iron in ferrous bisulfide are evalualed. The self-diffusivity of iron thus derived zs found to increase with increasing sulfur content. THE ferrous sulfide known as "pyrrhotite" is a non-stoichiometric phase having a wide composition range from about 50 to about 58 or 60 at. pct, depending on the sulfur activity. RosenQvistl studied the thermodynamics of this phase over wide ranges of temperature and composition. Hauffe and Rahmel' and Meussner and ~irchenall~ studied the parabolic rate of sulfidation of iron in sulfur vapor. By using markers, these investigators showed that the iron cations were the predominant diffusing species in iron sulfide. This is confirmed decisively by the self-diffusivity measurements of condit4 who showed that the self-diffusivity of sulfur in ferrous sulfide is several orders of magnitude lower than the self-diffusivity of iron. Although much has been learned from these studies about the Fe-S system, further research on this subject was considered desirable for better understanding of the physical chemistry of iron sulfide. This work was confined to the study of the kinetics of sulfidation of iron in hydrogen sulfide-hydrogen gas mixtures. The results of this study are given in two consecutive parts. Part I, the present paper, is on the parabolic rate of sulfidation of iron and the diffusivity of iron in ferrous sulfide. The second paper, Part 11, is on the kinetics of the surface reaction between hydrogen sulfide and ferrous sulfide. EXPERIMENTAL Three types of experiments were carried out: i) equilibration of ferrous sulfide with gas of known E. T. TURKDOGAN, member AIME, is Manager,Chemical Metallurgy Division, Edgar C. Bain Laboratory for Fundamental Research, U. S. Steel Corp., Research Center, Monroeville, Pa. Manuscript submitted March 6. 1968. ISD sulfur potential; ii) X-ray studies of ferrous sulfide; and iii) measurements of the parabolic rate of sulfidation of iron. Equilibrium Studies. About 1 g of iron powder or foil. contained in a small recrystallized alumina crucible ind suspended from a calibrated silica spring, was reacted with a hydrogen sulfide-hydrogen mixture of known ratio until no further change in weight was observed. %hen the gas composition was changed and the new state of equilibrium was established after several hours of reaction time. The composition of the sulfide was obtained from the initial weight of the sample and the weight after equilibration. X-Ray Studies. The lattice parameters of some of the equilibrated samples were determined using the General Electric XRD-5 diffractometer with a cobalt tube (no filter) set at 40 kv apd 10 ma; the CoK, radiation was taken as 1.79020A. Observed 220 and 311 diffraction peaks of silicon served as an internal comparison standard to correct for possible misalignment of the goniometer. The lattice parameters of the sulfide phase were calculated from the corrected Bragg angles of the 110 and 102 peaks. Rate Studies. In the initial experiments attempts were made to measure the parabolic rate of sulfidation by measuring the gain in weight of a thin iron strip, -0.05 cm thick, suspended from a silica spring in the reacting atmosphere. The preliminary experiments showed that this technique was not reliable for the measurement of the parabolic growth rate of the iron sulfide layer. In the subsequent experiments the data on growth rate were obtained by measuring, on a microscope stage, change in the thickness of the sample after reaction for a specified time in a hydrogen sulfide-hydrogen mixture of known sulfur activity. For each reaction time a new sample was used. Precision-machined iron blocks, 0.5 by 2 by 5 cu cm, were de-greased and annealed in hydrogen for several hours prior to the sulfidation rate measurements. The experiments were carried out at 670°, 800°, and 900°C in gas mixtures having the ratios, and 1.0 for periods of times from a few hours up to 8 days. Apparatus and Materials. A vertical globar tube furnace with a 3-in.-long uniform temperature zone was used. The glass tube fittings were fused on the zircon reaction tube, 1.5 in. diam. The temperature was measured with a Pt-10 pct Rh/Pt thermocouple placed in the hot zone of the furnace inside the reaction tube (an alumina thermocouple sheath was used). A separate thermocouple was used for the temperature controller which maintained the furnace temperature constant within about 2°C. Anhydrous liquid hydrogen sulfide and oxygen-free dry hydrogen from gas tanks were used in preparing the gas mixtures by the constant head capillary flow-meters. In all cases volume flow rate was 1000 cu cm per min at stp, corresponding to a linear velocity of about 6 cm per sec at 800°C; under these conditions

Jan 1, 1969

By R. W. Raymond

ALL history testifies that the mineral resources of a region have furnished both the impulse for its first development by man, and the foundation for its subsequent occupation by civilized and prosperous communities. In the pre-historic ages, the hunters, fishers, shepherds and gardeners of the world may have wandered or tarried without regard to the attractions of the mineral deposits which they could not utilize, and therefore did not value. But with the rise of civilization, as expressed in manufactures and commerce, the national value of such deposits began to be realized. Barbarous and remote tribes, possessing the sources of such supplies, won recognition in trade long before they could attain it through any other means. Thus, the North American Indians of Lake Superior exchanged their native copper for the mica of North Carolina; the ships of Tyre sailed all the way to Spain for lead and to Britain for tin; and the fleets of Solomon brought gold from Tarshish. In more modern times it has been chiefly the precious metals that have stimulated exploration and conquest. The inherent qualities and the traditional value of gold and silver sufficiently explain this historic fact, the continued existence and potency of which is evidenced, even in our own times, by the occasional rush of eager adventurers to new districts where gold and silver have been discovered. The history of North and South America has been peculiarly influenced by this factor. It was the prospect of obtaining gold and silver that led the Spanish adventurers to the shores of America, and the conquests of Mexico by Cortez and of Peru by Pizarro were inspired by the stories of the wealth of the Aztecs and the

Mar 1, 1909

By Jonas Svensson

A new method is described for the production of cold-bonded pellets using a hydraulic binder, such as portland cement. Large-scale pilot-plant tests have proved that self-fluxing pellets of high reducibility and good handling strength can be made by the method. Blast-furnace trials have shown that the pellets are an acceptable burden material, comparable with self-fluxing sinter or heat-hardened pellets. Economic factors of commercial-scale production are discussed. The Grangcold Pellet Process—for which patents have been applied or already granted in a number of coun-tries—uses a hydraulic adhesive such as portland cement, slag cements, pozzolanic cements, etc., for the production of cold-bonded pellets. The idea of using a hydraulic binder for the agglomeration of iron-ore fines is not new. Portland cement was proposed as an adhesive for cold-bonded iron-ore briquettes in patents granted more than 50 years ago.' In a report on the briquetting of iron-ore fines, published in Stahl und Eisen in 1959; it is stated that briquettes bonded with portland cement are used on a small scale at an ironwork in Germany. According to the report, the briquettes showed excellent strength in the blast furnace although their general use was made impossible because they required a long hardening time, during which they are sticky, soft, and difficult to store and handle. The Grangcold Pellet Process has overcome this particular disadvantage by mixing the balls with a suitable amount of the balling concentrate before storing them. The pellets are embedded in the concentrated during storing in such a way that they are isolated from each other and thus prevented from sticking together to form clusters. Thanks to the embedding concentrate, the pellets are subjected to a more or less uniform pressure from all sides which does not deform them. Thus, the mixture can be stored in a stockpile or in a bin until the pellets have hardened sufficiently. The concentrate is separated from the pellets by means of screening. The concentrate is returned to the balling operation and the pellets are either shipped to the blast furnace or stored for final hardening. The binder preferred for the Grangcold Pellett Process is portland-cement clinker, ground without the admixture of gypsum in order to avoid sulfur in the pellets as far as possible. Usually a 10% binder content is used. Two-thirds of the portland-cement clinker consist of lime and the rest is silica, alumina, and ferric oxide. Thus, self-fluxing or overbasic pellets are produced with this binder if the amount of silica in the concentrate used does not exceed 4%. The Grangcold Pellet Process was developed by the mineral Processing Laboratory of the Granges Co. Work started in 1963 with batch-scale tests. In 1966, a small pilot plant was put into operation in which 1800 tons of pellets were produced using 10% of rapid-hardening portland cement as a binder. Favorable results from a blast-furnace test with this batch led to the decision to erect a larger pilot plant which went into production in the summer of 1967. Since then, approximately 100,000 tons of cold-bonded pellets have been produced, mostly with 10% gypsum-free portland cement as a binder. Several full-scale blast-furnace trials have been performed with the pellets. The results of the trials indicate that the Grangcold pellets constitute a satisfactory blast-furnace feed. An industrial plant for the production of Grangcold pellets with a rated capacity of 1.5 million tpy is now under construction at the Granges Co.'s mine at Grangesberg. The plant will come into operation in the summer of 1970. Results from Laboratory Work Pellets made from iron-ore concentrate bonded with portland cement harden slowly and their handling is very critical until they have hardened enough to loose their stickiness. It is therefore especially important to study the progress of the hardening action and the factors influencing it. This is best achieved by investigating the relationship between the compressive strength of the cement-bonded pellets and the curing time under varied conditions. The general course of this relation-

Jan 1, 1971

By Carl E. Swartz

ALTHOUGH a number of articles appeared during the war advocating the use of cadmium in lead-tin solders, very little information of value can be found in the literature regarding the properties of solders containing cadmium. In most of the published articles the cadmium seems to have been considered merely as a partial substitute for tin in a tin-lead alloy rather than as an essential constituent of a ternary alloy. The primary object of the substitution of cadmium for tin was to lessen the amount of tin required, at a time when the latter was scarce and high-priced, and thus to produce a cheaper solder. While this object was accomplished, the new properties resulting from a change from a binary lead-tin alloy to a ternary lead-tin-cadmium alloy were not given proper consideration in many cases. For the past few years, the American Smelting & Refining Co. has been marketing a very considerable amount of cadmium in the form of lead-tin-cadmium alloys for use as solders for certain special purposes, and the successful use of these solders suggested that if more extensive knowledge were available concerning the properties of lead-tin-cadmium alloys of various compositions their field of usefulness might be materially extended. The investigation described in the present paper was undertaken to obtain this information and, by means of tests under conditions approaching those of practical use, to determine the suitability of cadmium solders for various purposes. CHARACTERISTICS AND REQUIREMENTS OF SOLDERS IN GENERAL General Physical Properties.-When cast into bars, solder should present a smooth and bright appearance free from oxide inclusions and bubbles. Ductility should be as great as possible without sacrificing tensile strength, and vice versa. Hardness and specific gravity are not of any great importance. Melting Characteristics.-The melting or solidification range is important. This statement applies both to the extent of the range and to the actual temperature at which complete solidification occurs. A rather narrow solidification range is desirable in soft solders in order that solidification may take place quickly. The solder should have high fluidity at temperatures only slightly above its melting range. For a

Jan 1, 1928

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

The present paper records a chapter in the history of the development of an electrolytic manganese industry in the United States.l A relatively large pilot plant at Boulder City, Nev., for the production of electrolytic manganese was conceived as part of the national defense program to make this country independent of foreign importation of manganese ore. The first authorization, in November 1940, however, was for a plant of only several hundred pounds capacity. Improvements in process and subsequent additions to some sections authorized by subsequent appropriations have enabled the plant to produce as much as 2000 lb. of manganese a day for substantial periods of time. Since in pilot-plant operation frequent changes are made in the flowsheet, the electrolytic manganese plant was constructed so that equipment could be rearranged with a minimum of expense and time. Several different kinds of the various ¦ types of equipment were installed for many of the operations, so that the one most suitable for the process might be chosen. Pilot-plant operations were begun in November 1941 and have been continuous except for brief shutdowns for installation of new equipment. More than one-half million pounds of manganese have been produced. The improvements in process, selection of equipment, and operational procedure developed are recorded here. Development of the Process The work of early investigators on the electrolysis of manganese solutions has been reviewed by Shelton. Until the method of continuous production of manganese by electrolysis was perfected by SheltonZm4 and coworkers, no practical procedure had been devised. The method as originally developed by the Bureau of Mines will be described here only briefly. The manganese dioxide ore was reduced in a rotating kiln-type furnace at 650°C. in an atmosphere of "city" gas. The calcine was leached with spent electrolyte and enough sulphuric acid to produce a neutral leach solutioil containing 2 5 grams manganese per liter as manganese sulphate and zoo grams per liter of ammonium sulphate. Arsenic was removed from the solution by the addition of 0.0j gram iron per liter as ferrous sulphate followed by oxidation with manganese dioxide, and aeration, which precipitated the iron as ferric hydroxide. The solution, free from iron

Jan 1, 1944

By CARL B. SNYDER

PERHAPS the most extraordinary thing about business, the trade and production of the country as a whole, is its amazing continuity and growth, its momentum and energy. It goes on year after year, growing steadily, almost without breaks, in spite of every kind of disturbance. We have been grossly deceived into the idea that business is highly variable. We have taken a few things like pig iron, and the like, constructional activity broadly, and imagined that these are a trustworthy measure of trade. Actually they are the worst that we could find. They do not apply to more than 10 per cent or, at the most, possibly 15 per cent of the total of the country's industrial activity. The other 85 or 90 per cent, or even more, goes on growing surely and steadily just like the growth of population and the steady advance in technique, invention, discovery, and improved methods of production Let me give you what seems to me one of the most remarkable examples of this amazing momentum and regularity. You know that 90 per cent or more of the business of the country is done 'by means of checks. About seven-eighths of the total of all checks drawn are reported regularly every week in the newspapers. Let us follow these reports from week to week, just as they come, and plot them up against the correspond- ing weeks of last year, and the year before, and the gear before that, as far back as you would like to go. Take especially the figures for 140 selected cities out- side of New York.

Jan 1, 1929

By J. H. Polhems, R. B. Brackin, D. B. Grove

THE heavy media separation process plays an outstanding role in the concentration of 4000 tons of zinc ore per day at the Mascot mill of the American Zinc Co. of Tennessee. Of the total tonnage, 72 pct is treated in the heavy media separation plant to reject 56 pct of the ore as a coarse tailing, which has a ready market. Concentrates from this separation are beneficiated further by jigging and flotation. Approximately 25 pct of the total zinc concentrate production is made in the jig mill. Jig tailings are ground and pumped to the flotation circuit where the balance of the production is made. Fig. 1 shows a generalized flowsheet of the mill. The Mascot ore is a lead-free, honey-colored sphalerite in dolomitic limestone, with lesser amounts of chert and some pyrite. A mineralogical analysis is given in Table I. After 10 years of successful operation with galena medium and treatment of nearly 10,000,000 tons of ore, a decision to convert to ferrosilicon was made early in 1948 because of the increasing price of galena and consequent high operating costs. The conversion was made on Nov. 6, 1948, and the results obtained since that time have shown remarkable improvement over those made with galena. The Table I. Mineralogical Analysis of Mill Feed, Pct Calcium carbonate 49.5 Magnesium carbonate 35.2 Iron oxide and aluminum oxide 1.5 Zinc sulphide 4.5 Insoluble 9.3 100.0 Table II. Comparative Data, Galena and Ferrosilicon Ferro- Diner-Gelenaa siliconb ence Operating costs per ton milled, ct. 21.21 9.12 12.09 Medium consumption per ton milled, lb 0.80c 0.15 0.65 Reagent consumption per ton milled, lb 0.45 0.02 0.43 Tailing assay, pct Zn 0.310 0.297 0.013 Concentrate. oct Zn 12.08 10.33 1.75 Heavy medla ieparatlon recovery. pct 89.38 90.22 0.84 Mill feed rate, tons per hr 153 166 13 Heavy mesa separation feed rate. tons per hr 100 10 0 Tons milled per heavy media separation man shift 350 620 270 Mill feed to coarse tailings, pct 51.0 56.7 5.7 Lost mill time, pct 5.6 5.0 0.6 Power consumption, kw-hr per ton 2.06 1.92 0.14 a 1947. " First 6 months of 1950. c Net consumption after deducting credit for reclaimed waste galena. Consumption of new galena was 1.320 lb per ton milled. For entire life of galena operation, a credit of 40 pct of the value of the new galena added was realized from the sale of waste galena. comparisons given in this report cover the first 6 months of 1950 as representing the ferrosilicon operation, and the year 1947 as representing the galena operation. This was the last full year in which galena was used exclusively and is representative of the best work done during the 10 years of operation with this medium. After only 2 years' operating experience, with ferrosilicon and treatment of 1,807,585 tons many advantages have been revealed and are summarized in Table 11. Development Prior to the introduction of the heavy media process, all the mill feed was crushed through 5/8 in. and treated by jigging. A finished tailing assaying 0.66 pct Zn was made on rougher bull jigs, and cleaner jig tailings were ground for treatment by flotation. The first test work on the sink-and-float method of mineral beneficiation was carried out at Mascot in 1935, using a 3-ft cone and galena medium for batch tests. The following year a 6-ft cone was installed for pilot-plant work. This unit became a part of the mill circuit on March 1, 1936, and handled a gradually increasing tonnage in the next 2 years as the process developed to the point where it could treat all the + 3/8-in. material in the mill feed. Coarse jigging was then discontinued on March 1, 1939, and all coarse tailings have been made by the heavy media separation plant since that time. Feed Preparation: The original feed preparation plant consisted of a drag washer followed by two 4x10-ft Allis-Chalmers washing screens. A surge bin and two additional 5x12-ft AC washing screens were added in 1943. Use of primary and secondary washing screens was found essential to provide the cleanest possible feed for the cone and thereby avoid excessive contamination of the galena medium. Improved washing was obtained by replacing the drag washer with a 7x20-ft Allis-Chalmers scrubber, shown in Fig. 2, which has been in service since May 1944. Throughout the life of the galena operation, delivery of extremely muddy ore to the mill overloaded the medium cleaning system, and it frequently was necessary to cut off the feed and clean the medium for several hours until its normal viscosity had been re-established. The cleaning circuit

Jan 1, 1952

By J. F. Tavernelli, L. F. Coffin

The deformation and fracture characteristics of eight metals subjected to fully reversed cyclic strain ranging from 0.2 to 50 pct were investigated at room temperature. Strain-hardening characteristics unique to the interna1 structure of a particular metal were found. Complete removal of the strain-hardening effects resulting from prior deformation was brought about by subsequent cyclic strain. Further support for the validity of the inverse relationship between the plastic strain range and the square root of the number of cycles for failure is given. THE resistance of materials to cyclic plastic strain is of interest both from a fundamental and practical point of view. It is now a well-accepted fact that fatigue failure in metals is a consequence of the localized slip deformation which occurs within the individual crystals of metal.'-' Hence the failure process should be strongly dependent upon the magnitude of the gross cyclic plastic deformation of the metal under conditions where this is a measurable quantity. Therefore, an experimental investigation of metals in which the cyclic plastic strain is the independent variable should shed new light on some of the basic aspects of the problem. From the practical point of view, there are many uses for information relating to the cyclic strain resistance of metals. One is the case of thermal stress fatigue where fatigue failure can occur as a consequence of a com- paratively few cycles of thermally induced mechanical deformation. Another is the mechanical working of metals where large cyclic strains are employed. In recent years several publications have appeared relating to the cyclic-strain resistance of metals,8-11 dealing mostly with the fracture aspects where the temperature is cycled simultaneously with the mechanical strain. Some work has been reported on the cyclic-strain resistance of metals at constant temperature, again oriented more toward the fracture aspects of the problem than the deformation aspects. 12-16 The present research investigation was undertaken to obtain information regarding the deformation characteristics of several metals whose structure-property relationships were simple and straightforward under conditions of both cyclic and monotonic strain. It has been shown for example that under cyclic-strain conditions some materials will strain harden, while other materials, particularly cold-worked structures, strain soften and these effects required further clarification.8,17-19 It was also de-

Jan 1, 1960

By A. Lubinski, J. L. Logan, W. S. Althouse

A4ost gas twells and flowing oil wells are completed and treated through a string of tubing and a packer. Changes in temperature and in pressure inside or outside the tubing will: (I) if free motion of the tubing inside the packer is permitted, increase or decrease the length of the rubing; or (2) if free motion is prevented, induce forces in the tubing and on the packer. If pressure inside the tubing is greater than outside, the tubing may buckle helically even in the presence of a packer-to-tubing tension. The tubing will always buckle, and much more severely, if free motion is permitted. The buckling may be prevented by pulling the tubing in sufficient tension. The prediction of these forces and tubing movement has here to fore been based upon calculations that did not inciude helical buckling. This paper preseitts means with which these length or force changes can be calculated while taking into account the effect of helical buckling. To avoid damaging formations, failure of remedial operations, or damage to the tubing or packer, application is made to practical problems involving calculations of the required length of seals, amount of sluckoff or tension, and prevention of permanent corkscrewing. INTRODUCTION Leakage of a packer may result in costly failures of such operations as squeeze cementing, hydraulic fracturing, etc. To avoid such failures, the authors are often asked questions pertaining to the length of necessary seals, the amount of necessary slackoff, etc. Published work' does not take into account helical buckling of tubing. Investigation of helical buckling was prompted by the fact that allowance must be made for this phenomenon in order to provide relevant answers. In the past, theoretical work on helical buckling was confined to conditions for which such buckling does not The mathematical treatment of behavior in a buckled condition, given in the Appendix, is novel. Assumptions upon which this investigation is based are listed and discussed in a special section. The following are a few of the many kinds of problems which may be solved with this paper. 1. Consider a packer in which tubing may move. Such movement will occur after pressures and temperature are changed. The paper provides means for: (a) calculating the amount of such movement and, therefore. the required length of seals; and (b) calculating the necessary amount of initial slackoff, for which there is no danger of unsealing the packer, if the length of seals is given. Such calculations, as well as those which follow, tully take into account the fact that part of the movement ib due to elastic helical buckling of the lower part of the string. This buckling may occur even in tubing under tension. Insufficient initial slackoff for a given length of seals, or insufficient length of seals for a given slackoff, may result in costly failures. A field case of such a failure will be given further in this paper. 2. In the case in which tubing cannot move in the packer, changes of pressure and temperature result in tubing-to-packer forces and forces in the tubing above the packer, both of which may be calculated. This knowledge is important because, if these forces are too large, the) could damage the packer or the tubing. 3. For wells in which wireline tools are to be run through the tubing, the paper provides means to keep the tubing from buckling, thereby permitting free passage of tools. 4. In deep wells, mainly in the presence of large casing, tubing may become "corkscrewed", i.e., take a permanent helical set. A field case is described further in the text. Using this paper, one may calculate in advance conditions under which permanent corkscrewing would occur, and then take preventive steps. HELICAL BUCKLING Consider a string of tubing, freely suspended in the absence of any fluid inside casing, as shown in Fig. I(a). Now consider an upward force F applied at the lower end of this tubing. This force compresses the string; and if the compression is large enough (which is always the case in actual problems), the lower portion of the string will buckle into a helix, as shown in Fig. 1 (b). The lower end of the tubing is subjected to a compression F. This compression decreases with the distance from the bottom and becomes nil (neither compression nor ten-

By David A. Sterling, Roger C. Malan

The Atomic Energy Commission is investigating the distribution of uranium and thorium in the Precambrian of the western United States and the relationship of time-space-facies patterns of uranium and thorium enrichment in the Precambrian, to the major resources of umanium in Mesozoic and Cenozoic continental clastic sediments. The results of preliminary studies in the southwestern. United States are summarized. Approximately 50% of the uranium resource of the Free World is in deposits of Precambrian age, principally in lower Proterozoic conglomerates in Canada and South Africa (Uranium Resources, Joint Report, ENEA and IAEA, 1967). Most of the uranium resource of the United States is in Mesozoic and Cenozoic continental clastic sedimentary rocks that fill intracratonic basins. The Atomic Energy Commission (AEC) is investigating the distribution of uranium and thorium in the Precambrian of the western United States and the relationship of time-space-facies patterns of uranium and thorium enrichment in the Precambrian to the major resources of uranium in the Mesozoic and Ce-nozoic host sedimentary rocks. This paper summarizes the results of preliminary studies of the Precambrian in the southwestern United States including New Mexico, Arizona, southern Nevada, and southern California (Fig. 1). The host rock provenances for the major uranium resources in epigenetic deposits of Mesozoic and Ce-nozoic age in the western United States were in areas of extensive Precambrian exposure along the eastern margin of the Phanerozoic geosynclinal belt (Fig. 2). Mesozoic continental clastic sediments in the Colorado Plateau contain about two-thirds of the uranium resource of the United States. These sediments formed from detritus derived from the Mogollon highland in the southwestern United States where the Precambrian was extensively exposed1-1 (Fig. 2). A genetic relationship may exist between this provenance and the major uranium deposits of the Colorado Plateau. The Pre- cambrian might be equally important in the genesis of uranium deposits whether the most important process in the formation of these deposits was the leaching of low-order intrinsic amounts of uranium from Precam-brian granite or from Mesozoic pyroclastics derived from syntexis of the Precambrian basement rocks.' Precambrian Geochronology of the Southwestern United States The Precambrian geochronology of the southwestern United States is in an early stage of systematic study. Until recently, the only basis of correlation was through inconclusive field relationships. However, with the increased use of isotopic age dating, new data are becoming available for correlating regional and local events. As yet, there is no undisputed evidence of ages greater than 1.8 billion years (by) old in the southwestern United States. However, most geologists who have studied the region agree that volcanism and marine sedimentation of predominately eugeosynclinal facies took place in a northeasterly trending geosyn-cline prior to 1.7 by."' Because of insufficient evidence for a pregeosynclinal continental crust, some researchers believe the geosyncline may have developed on oceanic crust.' However, sediments metamorphosed to 1.7 by-old felsic paragneisses in the Panamint Range, California," and southeastward into southern Nevada are believed to have had a nearby continental provenance. The three Precambrian disturbances that are recognized in the southwestern United States are 1.6 to 1.8 by, about 1.4 by, and about 1.1 by-old (Fig. 3). In addition to plutonism, these disturbances are characterized by predominately lower-grade metamorphism. In this report, lower-grade metamorphic rocks include argillite, phyllite, slate, mica schist, and gneiss with relic sedimentary textures. Higher-grade metamorphic rocks, in this report, are recrystallized beyond megascopic recognition of the original rock type. Principal

Jan 1, 1971

By Dwight L. Sawyer

IF it had not been for the testimony of former Secretary of the Interior, Harold L. Ickes, before the Senatorial investigating committee the public would have heard little about the Federal Government's suit against California for the ownership of the tidelands. The Ickes-Pauley dispute brought to public attention that the California tideland oil deposits are the last remaining large Federal oil reserves. Ickes contends that these tideland oil deposits belong to the nation for the benefit of all the people of all the states and not solely to the State of California. Ickes also accused California oil man Ed Pauley of offering to give $330; 000 to the Democratic party fund if Ickes would drop the Federal Government's suit against the State of California for the ownership of said tidelands. The tidelands may be considered as the land bordering the coast line between mean high tide and outward under the ocean for a distance of a marine league, or about three statute miles. This strip of land along the coast of southern California contains large oil deposits which have a present and future prospective value of several billion dollars.

Jan 1, 1947

By J. L. Lehman, J. D. Sudbury, J. E. Landers, W. D. Greathouse

A full scale field experiment on cathodic protection of casing answers questions concerning (1) the proper criteria for determining current requirments, (2) the amount of protection provided by different currents, and (3) the transfer of current at the base of the surface pipe. Three dry holes in the Trico pool in Rooks County, Kans., were selected for cathodic protection tests. The three holes were in an area where casing failures opposite the Dakota water sand often accur in less than a year. Examination of the electric togs showed the wells to be similar to other wells in the field where casing in four of seven producing wells has failed. The three holes were cleaned out and cased with 75 joints of new 51/2-in. 14-tb J-55. Each joint was visually inspected and marked before it as run. The casing was bull plugged and floated in the hole 50 that the inside might remain dry and free of excessive attack. Also, if a leak occurred, a pressure increase could be observed on gawge at the surface. Extensive testing was done, including potential profiles, log current-potentid curves and electrode measurements from both surface and downhole connections. Based on these data, a current of 12 amps was applied to one well and 4 amps to mother. The third well was left to corrode. During the two-year period when the casing was in the ground, [he applied current was checked weekly, and reference electrode measurements were made about every two months. Three sets of casing potential profi1e.c were run. When the three strings were pulled, each joint was examined for type of scale formed, presence of sulfate-reducing bacteria, extent of corrosion nttnck and pit depth. Since the pipe was new when run, quantitative determination of the protection provided by current was possible. This is the first concrete field evidence to help resolve the many arguments about the proper method for selecting adequate current for cathodic protection of oilwell (-using. INTRODUCTION A casing string is run when a well is drilled. This pipe is supposed to protect this valuable "hole in the ground" for the life of the well. Often the casing does not last the life of the well; it is with these casing failures that this work is concerned. The cost of repairing a casing failure varies from field to field—from as much as a $30,000 per leak average in California to $5,000 per leak in Kansas. Additional costs other than actual repairs are also important. These include formation damage, lost production, etc. Casing damage caused by internal corrosion is important in some areas. Treatment normally consists of flushing inhibitor down the annulus, but further research is being done on control measures. The test described in this paper is concerned only with external corrosion. The problem of casing failure from external attack has appeared in several areas including western Kansas, California, Montana, Wyoming, Texas, Arkansas and Mississippi. Cathodic protection is currently being used in an attempt to control external corrosion. From reports in the NACE there are thousands of wells currently under cathodic protection. The quantity of current being applied ranges from 27 amps on some deep California wells to a few tenths of an amp being supplied from magnesium anodes on wells in Texas and Kansas. Considerable field and laboratory effort1,9,5,6 was exented on the problem of cathodic prctection of casing, and it became fairly obvious that this method could be used to protect wells. Early workers showed that current applied to a well distributed itself over the length of the casing and was not concentrated on the upper few hundred feet. Basic cathodic protection theory had shown that corrosion attack could be stopped by applying sufficient current. The problem resolved itself, then, into one of trying to decide just how much current was necessary. Various criteria were utilized in installing the many existing cathodic protection installations. These methods included the following. 1. Applying sufficient current to remove the anodic slope as shown by the potential profile." 7. Applying enough current to maintain all areas of the casing at a pipe-to-soil potential of .85 v.' 3. Applying the current indicated by a log current-potential (or E log I) curve." 4. Supplying the current necessary to shift the pipe to-soil potential .3 v." 5. Applying 2 or 3 milliamps of current per sq ft of casing."

By Alex Boozenny

The results of potential measurements between 1) a titaniurn electrode in NaCl-TiCl, melts and a graphite-cizlorine reference electrode and 2) a titanium electrode in NaC1-Nu "melts and a graphite-chlorine reference electrode show that the following relationship expresses the equilibrium relationship between the TiCl, and the dissolved metallic sodium concentrations, expressed in mole fraction units, in dilute NaCl welts at 850°C. The results of potential measurenments between a graphite electrode in NaCl-TiCl, melts that were saturated with TiCl, and a graphite-chlorine reference electrode, when combined with the standard free energy data given in literature, gave the following expression for the equilibrium relationship between the TiCl, and TiCl, concentrations, expressed in mole fraction units, in dilute NaCl melts at 850°C. These relationships are for melts in equilibrium with pure titanium. In impure systems, less sodiurn and more TiCI, can be copresent with a given concentration of TiCl,. AFTER 10 years of existence, the titanium metal industry still relies on the original Kroll and the sodium reduction processes for the only important means of converting titanium-bearing ores to titanium metal via production of titanium tetrachloride as an intermediate. Through years of modification and development these two processes have evolved to a point where any further major economic advances in the field of titanium metal production must be achieved through implementation of processes which are distinct departures from simple magnesium or sodium reduction of titanium tetrachloride. Concurrently with the refinement of the Kroll and sodium reduction processes, industries and government have sponsored research and development in the field of producing titanium by electrolysis of oxides,' carbides,' and halides3'4 in fused salt media. However, the incomplete understanding of the physical chemistry of fused salt systems has in many cases hindered the development of promising new titanium production processes to the point where they will have a clear advantage over the processes presently employed. Fortunately the volume of information on fused salt physical and electrochemistry is increasing at an accelerating pace. The first approaches tbward investigating the electrochemical behavior of fused salt systems have been the measurements of equilibrium potentials of metals immersed in melts containing their halides.' Some work on the kinetics of fused salt electrochemical processes has been reported.'09" Some descriptions of the structural composition of fused salt systems are also available. The work described herein is a continuation of the study of metal electrode potentials in fused salts. Specifically, this contribution to the growing store of fused salt chemistry information presents a description of the equilibrium relationships between the concentrations of titanium dichloride, titanium trichloride, and metallic sodium in fused sodium chloride. The investigation of the titanium dichloride-titanium trichloride equilibrium relationships is not completely new. Kellog and Krye and Melgren and opie15 have presented the results of chemical analysis of salts containing titanium chlorides. Flengas and lngrahaml' have published the results of an investigation of these equilibrium relationships obtained by measurement of electrode potentials in a fused NaCl-KC1 mixture. The investigation described herein differed from that of Flengas and Ingraham principally in the use of straight NaCl as the solvent in place of the more costly and more difficult to purify mixture. This investigation was conducted in three parts. First, the equilibrium potentials of titanium in sodium chloride containing known concentrations of titanium dichloride were measured. A graphite-chlorine electrode was employed as reference. Second, the equilibrium potentials of titanium immersed in sodium chloride containing known concentrations of elemental sodium were measured. Third, the equilibrium potentials of graphite immersed in titanium tetrachloride-saturated sodium chloride containing known concentrations of titanium trichloride were measured. The results of these three related investigations are presented in the above order. The results are combined with the thermodynamic properties of titanium chlorides and sodium chloride, obtained from literature, to give the titanium dichloride-titanium trichloride-elemental sodium equilibrium concentration relationships. In the test, whenever a melt contains titanium chlorides in predominantly divalent form, the melt

Jan 1, 1962

By P. K. Koh, H. A. Lewis, H. F. Graff

New data on the distribution of silicon between slag and carbon-saturated iron at 1600Oand 1700OC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1'700°C for slags containing up to 20 pct A12O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A12O3-SiO, slags over a range from zero pct Al2O3 to saturation with Al2O3, or CaO.2Al2O3. The upper limit of SiO2 is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/Al203 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al,O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al0 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al2O3 and of Al20,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO2 (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2. The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960