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By Malcolm T. Hepworth

RECENT interest in thermoelectric devices has been directed toward studies of the properties of thermoelectric materials of semiconducting solid compounds with little attention given to ionic and semiconducting liquids such as aqueous solutions, fused salts, and mattes. One type of thermoelectric system is the thermocell: a nonisothermal galvanic cell with two identical electrodes at different temperatures connected by an electrolyte bridge. An electromotive force, v, is generated which is a function of the electrode reactions and the properties of the electrolyte according to the Eastman' equation: where S* is the entropy change of the system arising from the electrode reactions and by heat transferred by ion migration and by thermal conduction. The quantity nF is the product of equivalents passed and Faraday's constant. A value of S* of 23.06 cal per "C is equivalent to 1 mv-Faraday per "C. The symbol, a, is used for dV/dT in analog to the See-beck coefficient of solid-state thermoelements. de Bethune2 has calculated the temperature coefficients of the electromotive force of a large number of nonisothermal aqueous cells from measurements on the nonisothermal temperature coefficients of the standard hydrogen electrode, combined with data on the isothermal temperature coefficients of half-cells tabulated in the literature. Values of these coefficients (a) in de Bethune's compilation ranged up to 3 mv per C. In particular he reported a value of +2.059 mv per "C at 25'C for the cell: Fe (aqueous, unit activity) (aqueous, unit activity) written for the hot-electrode reaction. The positive sign indicates that the hot electrode is positive (an "n-type thermocell"). In analog to a solid-state p-n system, it would be possible to couple two thermocells together to form a system in which the figure of merit could be calculated by adding the temperature coefficients according to the relationship described by offee:' where a is the Seebeck coefficient in volts per "C, p is the specific resistivity in ohm-cm, and K is the thermal conductivity in watts per cm "C. Even though ionic systems have rather high electrical resistivities compared with semiconducting and metallic systems, it was felt that a preliminary study of one ionic system should be made to establish some basis for evaluating the possibility of a p-n thermocell for energy conversion. Accordingly the Fe", Fe"' system was studied as a possible component for a p-n system. A glass system was constructed consisting of two vertical water-jacketed tubes connected by a horizontal tube, Fig. 1. Platinum-black electrodes 1 cm by 1 cm in dimension were inserted in each vertical tube with thermometers to register the electrode-compartment temperatures. The temperature of the electrode compartments was controlled by circulating water from thermostatted baths around the electrode compartments. The electromotive force of the cell was then read by a potentiometer for zero current as a function of the temperature of the hotter electrode. Current output of the cell for varying external loads was also measured. The cell resistance was measured by means of a bridge circuit with 10,000 cps signal and oscilloscope. Resistance measurements were converted to specific resistivity by calibrating the cell with a solution of known conductivity.

Jan 1, 1965

By J. M. Weehuizen

Complete details are given of the drilling method by which two shafts were sunk at the new Beatm'x mine of Staatsmijnen in the Netherlands. The nature of the rock strata in the Dutch mining district determined choice of the drilling rather than the freezing method. Data for each step and details of the equipment used are given in the illustrations. Staatsmijnen was founded in 1902 with government financial backing, but it is run as a private enterprise, on a commercial basis, with the normal fiscal obligations. The company now has four mines in operation with annual outputs amounting to 7 1/2 million tons of coal. In 1952 it was determined that a new mine—the Beatrix—would be opened. Details of the shaft-sinking operation are described in this paper. SHAFT LOCATION The coal-bearing carboniferous rock in the Dutch mining district is overlain almost completely by soft water-bearing strata, which at the site of the new shafts are about 1600 ft thick. The sinking of the new shafts through this soft water-bearing overburden (Fig. 1) is a costly and time-consuming affair. From the two availaible sinking methods: 1) Poetsch's well known freezing method or 2) the drilling method of Honigmann-de Vooys, the latter was preferred, not only because of its relative cheapness, under the prevailing conditions, but primarily because by using the drilling process, a special type of shaft lining of steel, concrete, and bitumen could be used. The new shafts, located 330 ft apart, have an inner diameter of 18 ft, 4 1/2 in. The boreholes, which have a diameter of 25 ft and which were drilled through nearly 1600 ft of overburden and some 100 ft of carboniferous, each contain more than 29,000 cu yd—by far the largest in the world. DRILLING METHOD The drilling method is based on the use of mud-flush—a thin mixture of clay and water—to keep the borehole filled during the entire drilling period and during insertion of the lining (Fig. 2). The pressure of the mudflush against the borehole wall is greater than that of the water in the surrounding

Jan 1, 1961

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K' to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K', at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962

By H. H. Dreissen, F. J. Fontein

The operating principle of the classifying cyclone has been described often but some special aspects of the cyclone receive further clarification here. In addition, several uses of the classifiers are summarized and made clear by means of practical examples. In coal and ore washeries, the washing cyclone is widely used for the separation by specific gravity of sizes up to about 12 mm. This application has lately been extended to the separation by specific gravity of particles up to about 50 mm. This use makes special demands on the construction and wear resistance of the cyclone. The sieve bend, a development of the Dutch State Mines which is less well known than the hydrocy-clone, is dealt with at some length. The sieve bend is an apparatus designed for wet screening. Attention is given to the variables influencing the performance of the sieve bend. Hydrocyclones are now so widely applied that it would be difficult to find an industry not, directly or indirectly, using them or knowing how to use them since publications on this subject abound.1-3,5,9-11,13-15 However, because of the large number of variables influencing the operation of classifying cyclones, it is not entirely possible to calculate the results of this type of cyclone. Therefore, a number of lesser known variables will be discussed here along with some special applications of the classifying cyclone. FACTORS INFLUENCING CYCLONE CLASSIFICATION Shape of Particles: The shape of particles may cause a much coarser classification than the one expected, considering the sieve analysis and the cyclone dimensions chosen. This was clearly shown by feeding a mixture of spheres and disks in water into a cyclone. The spheres were 0.36 mm diam and the disks, 3 mm diam and 0.03 mm thick. These dimensions were chosen in order that the disks and spheres might have the same rates of fall under gravity. Both spheres and disks had a specific gravity of 1.05. The results obtained with these particles in a cyclone are summarized in Table I. Test No. 2 shows that the catch of spheres was

Jan 1, 1963

By S. A. Hovanessian

The method of characteristics which reduces the Buckley-Leverett mnlineur, partial differential equation to two first-order, linear differential equations is applied to the solution of a waterffood recovery problem for multiple lines of producing wells and one line of injection wells. The application of the method is described by a numerical example, and a brief theoretical background is given. From the results of this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple sets of producing wells. INTRODUCTION In this paper, the method of characteristics is applied to the solution of a waterflood recovery problem with multiple lines of producing wells and one line of injection wells. The application of the method to this type of recovery problem considerably simplifies the procedure of obtaining a numerical solution. It differs from the method described by Kern1 because it eliminates the need for integration in obtaining saturation fronts. In addition, the saturation history at any location within the field is obtained from a single diagram (time vs distance with saturation as a parameter)'. The paper includes a brief theory of the method of characteristics and its application to the solution of oil recovery problems. A numerical example is worked out, and the cumulative oil recovery-vs-time curve for a system with multiple sets of producing wells is obtained. This curve is then compared with the recovery curve of a system with only one set of producing wells. From this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple lines of producing wells. However, the recovery time is considerably longer for multiple sets of producing wells.

By E. Northcott, I. M. LeBaron

Before describing the electrostatic processing of feldspar, it might be well to review some of the basic definitions and terminology of feldspars. The feldspar minerals constitute a group of alumino-silicates of potassium, sodium, and calcium. Barium feldspar sometimes occurs naturally but is very rare. Hardness varies between 6 and 6.5 and specific gravity between 2.5 and 2.8. Color is generally white or pale shades of red, yellow, or green. The approximate chemical composition of the principal feldspars is given in Table I. The albite (sodium aluminum silicate) and an-

Jan 1, 1959

By E. Northcott, F. N. Oberg

By electrostatic separation, course Florida pebble phosphate, too lou-grade to find a ready market, can be upgraded to a satisfactory saleable product. Pebble running from 60 pct bone phosphate of time may be upgraded to 73 to 77 pct BPL depending on the mineralogical. structure of the pebble and the nature of the silica innpurity. High-grade concentrates from Florida pebble phosphate deposits have long been recovered by wet methods. When work was begun in the field, only the coarse pebble (generally +1 mm) was re- covered. In the 1920's a froth flotation process was developed to separate quartz from the finer phosphate fractions, but this method proved unsatisfactory for treating the intermediate fraction (—1 mm +35 mesh). Consequently various other processes were adapted, including agglomerate tabling and spiral separation of reagentized feed. Today the three processes are used—washing and screening for coarse pebble, tabling or spiraling for intermediate sizes, and flotation for —35 mesh material.

Jan 1, 1959

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

By J. van Lookeren

In the case of a reservoir where the oil underlies a large gas cap and overlies bottom water, production can be inzproved considerably if wells are perforated below the water-oil contact rather than opposite the oil-bearing section. The theoretical arguments for this improvement, which in some cases may be tenfold, are supported by experimental evidence. INTRODUCTION Reservoirs frequently consist of one sand body containing an oil layer underlying a thick, gas-bearing section and overlying bottom water (Fig. 1). Wells in such reservoirs are customarily opened up opposite the oil-bearing interval or, rather, opposite the lower part of this interval (Fig. 2). More often than not, it is inefficient or prohibited to blow off large quantities of gas with the oil. This im-psses a severe limitation on the drawdown, which results in low oil-production rates. Because of the small difference in specific gravity between oil and water, the latter will easily cone upwards, so that the production of water together with the oil is not prevented by this completion method. In such a situation wells should be opened deeper, in the originally water-bearing zone. The gas can be shut off by not perforating over the upper part of the interval (Fig. 3) or by a tubing hung close to the bottom of the interval (Fig. 4). Initially much water will be produced, but when steady-state conditions have been established (as depicted in Figs. 3 and 4) larger drawdowns are permissible than in a conventionally completed well, and correspondingly higher oil-production rates will result. Water cuts are only slightly higher because of the small effect of gravity on the water-oil flow distribution. CALCULATIONS The ratio of improvement has been estimated by means of approximate calculations. The completion depicted in Fig. 4 is the most convenient basis for these calculations. By postulating that vertical flow gradients can be disregarded, the Appendix shows that the well-known Dupuit formula can be obtained except for some complication due to the presence of two fluids rather than one. The Appendix makes the reasonable assumption that, for suitable boundary conditions, the oil layer occupies a constant fraction of the total fluid height throughout the reservoir. The oil- and water-production rates can thus be related to the liquid levels in the borehole as follows:

Jan 1, 1966

By W. A. Hockings, D. W. Fuerstenau, A. L. Mular

This paper briefly describes a simple air pycno-meter and its use for rapid determination of the composition of mixtures of solid particles. Research on such problems as the pelletizing of solids, the mixing of solid particles, and the comminution of mixtures can be simplified by means of this analytical tool. THEORY OF OPERATION Liquid pycnometers1 are commonly employed to measure volumes. These devices are time consuming and sometimes give inconsistent results. The liquid used in the pycnometer may have an undesired influence on the material to be measured; moreover, complete displacement of air by the liquid is seldom

Jan 1, 1963

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By A. S. Odeh

During the last few years, several authors1-6 have advanced mathematical solutions, both exact and approximate, to the pressure behavior of a well producing from a region bounded by a circular discontinuity. The most recent solutions were reported by Carter, and by Bixel and van Poollen. Varter solved the appropriate equations analytically. Bixel and van Poollen reported a numerical solution and provided correlation charts for the interpretation of flow tests; their method uses an overlay technique and is valid for wide ranges of mobility and storage capacity ratios. The mobility ratio is defined as the ratio between k/p of the two zones, and the capacity ratio is defined as the ratio between $c of the two zones. We have developed independently an analytic solution, programmed for the CDC 1604, that agreed with Carter's.'1 The same differential equation, assumptions, boundary, and initial conditions were used. We ran 30 drawdowns and 30 buildups of a unit capacity ratio and of varied mobility ratios. We also varied the radial distances to the discontinuity, and the radii of drainage. We examined the results and obtained correlations that were simple to apply and useful in flow test interpretation. The results and the correlations reported here in graphical form allow the determination of the mobility of the two zones and the radial distance to the discontinuity. They eliminate the need to fit field data to a curve as is required in the overlay technique.6 Thus, the advantages of the present correlations are that they require less effort and they provide a unique answer. They also provide guidelines for selecting the parts of the flow test plot to be used in the interpretations. Moreover, the results obtained from the programmed analytic solution define the time intervals where the approximate solution reported by Hurstl and discussed by Larkin2 are applicable. Normal buildup and drawdown plots resulted in an early straight line, a long transition zone and a late (second) straight line. However, the second straight line will not occur if the drainage radius is not at least 10 times the radial distance to the discontinuity. The mobility of the imer and outer zones can be calculated from the slopes of the first and second straight lines, respectively, by the normal methods of the flow test analysis. We found that the radial distance to the discontinuity may be determined from the abscissa value for the point of intersection of the extensions of the two straight lines. Results similar to some of these were reported by Adams et aL7 The approximate solution compared favorably with the exact one during the first and second straight-line periods. However, during the transition zone, deviation occurred between the two solutions. Discussion of Figures Figs. 1 through 7 summarize the results of this investigation. On Figs. 3 through 7 there appears the equation of each respective plot. In this paper the mobility ratio M is defined as klp2/kzpl, where subscripts 1 and 2 refer respectively to the inner and outer zones, and dimensionless time = t, = 6.32 X In the investigation, M ranged from 0.25 to 50;

Jan 1, 1970

By F. W. Schaller

TETRAGONALITY is an important aspect of the models of transformation, strengthening, and tempering of ferrous martensite. When the c/a

Jan 1, 1963

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates (or sodium-free compounds) are required for certain end uses, but in general, nonsodium borates are used only where borax is not avail- able. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of about a million tons of B2O3. Leadership in supplying borates has shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates. In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, Calif., is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, Calif., the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "lo-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7- lOH2O. In addition to ship- ping all major refined borate products from Boron, the company ships semiprocessed ore concentrates to treatment plants elsewhere.

Jan 1, 1975

By W. H. Bassett

In considering the effects of reducing gases on hot solid copper the following conclusions have been reached. (1) Depth of deoxidation of copper heated in reducing gas is greater the smaller the amount of cuprous oxide originally present in the copper, the range studied being from 0.015 to 0.136 per cent. oxygen. It is suggested that the reason for this difference in depth of deoxidation is that, when the copper is low in cuprous oxide, the reducing gas is diluted less by the gas that is formed in the reaction than when the copper is high in cuprous oxide; and the greater the concentration of the reducing gas the deeper the deoxidation. (2) The rate of deoxidation is much mire rapid at the beginning of exposure than at the end, a condition especially noticeable at temperatures around 900° C.; that is, deoxidation is retarded as the depth penetrated by the reducing gas increases. (3) Within the accuracy of the experiments arsenic in copper up to 0.5 per cent. has no tendency to increase or decrease the action of a reducing gas on the cuprous oxide present in the copper. IN 1912 pieces of 0.365-in. hard copper rod 1/2 in. long were heated in a porcelain tube in an electric furnace, while illuminating gas was passed through. An approximate analysis of this gas is: FIG. 1.-EFFECT OF TIME AND TEMPERATURE ON DEOXIDATION RATE OF 0.365-IN. COPPER BY ILLUMINATING GAS; COPPER PLUS SILVER, 99.983 PER CENT. Hydrogen 38 per cent., carbon monoxide 30 per cent., illuminants 13 per cent., methane 10 per cent., ethane 3 per cent., carbon dioxide 3 per cent., nitrogen 2 per cent., oxygen 0.4 per cent. After heating for various lengths of time at various temperatures, samples were quenched

Jan 1, 1926

By A. G. Rozner

TRANSVERSE rupture tests have been commonly used in mechanical investigations of brittle materials. The specimens are simple, easy to prepare, and loading presents no difficulty. Owing to the complexity of stress distribution in bending1 one can determine stresses rigorously only for the elastic range. The bend-test results, however, are at times converted into tensile-strength data, determined as maximum fiber stress. The assumption is made that for small plastic deformations the linear stress-strain relation applies. This problem was experimentally investigated by Bach3 who tested cast iron in bending and in tension and found that the maximum fiber strength obtained in bending exceeded the experimental tensile strength by a factor depending on the geometry of the tested piece. The factor varied from 1.57 for a rectangular cross section to 2.12 for a circular cross section of the tested beam. Since this work was carried out 60 years ago, the cast iron used could be expected to have been highly brittle, thus the extent of plastic deformation prior to fracture very small. We have therefore carried out a number of tests on magnesium-modified cast iron with an average elongation of -5 pct. It was hoped that the data obtained from the tests would serve as a guideline for comparing data obtained in tension and bending for brittle materials. Mechanical properties were measured at room temperature on an Instron tensile machine at a crosshead speed of 0.05 in. per min. The three-point bend test employed cylindrical bars 0.20 in. in diameter with a 1.0-in. span. For the tensile test, cylindrical tensile specimens with a gage length of 0.85 in. and a diameter of 0.160 in. were used. Results are summarized in Table I. From Table I one can see that fracture strength

Jan 1, 1965

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By E. P. Abrahamson II

The effect of transition elements which form binary solid solution upon the recrystallization temperature of zirconium has been investigated. All additions raised the recrystallization temperature. A correlation is obtained between the logarithm of the rate of change of recrystallization temperature with atomic percent solute and the free atom ground state electron configuration of the solute element. ThE work of Abrahamson, et al., on dilute binary solid-solution alloys indicated a correlation between the free-atom ground state electron configuration of the solute and either the brittle-ductile transition or recrystallization temperature. These studies were carried out on bcc base materials. The implication is that the outer s and d electrons of the solute are the prime determinant of the absolute rate of change of recrystallization or transition temperature. Furthermore, the limit of linearity has been shown to be a function of solute electron configuration for recrystallization in iron and vanadium. To date no Complete systematic recrystallization study of dilute binary zirconium base alloys has been made. It is the purpose of this study to note whether the change in solvent structure from bcc to hcp will influence the correlation. It was also desired to learn more of the role of the electron configuration of the solvent on recrystallization temperature. PROCEDURE All alloys were made using 99.87 pct Zr with 0.01 Cr, 0.04 Fe, 0.006 Hf, 0.003 Mg, 0.003 Mn, 0.003 N, and 0.080 0 (132 BHN). The solute elements were 99.9 pct pure. According to the published binary phase diagrams6 and metallographic examinations at X750, all alloys used were solid solutions. The alloys were arc melted and remelted six times in the form of cubic 200-g buttons under an argon atmosphere. They were then hot pressed at 950°C to 0.450 in., upset pressed to 0.350 in., and annealed at 800°C for 1 hr. The specimens were then Blanchard ground to 0.250 in., removing 0.050 in. from each side. The grain size of the material at this stage was found to be 8000 100 grains per sq mm. The specimens were then cold rolled to 0.130 in. and cold pressed to 0.125 in., yielding 50 1 pct cold work. All alloys were then chemically analyzed for the principal addition. The interstitial contents remained at the values of the starting material when checked on random alloy specimens. The rolled sheet was cut into 6.75 by 0.25-in. lengths and heat treated in a gradient furnace for 1 hr. The gradient was 250o to 900°C over the 6-in. length, recorded continuously by six thermocouples resting on each specimen. Control was 3oC, accomplished at the hot end. The recrystallization temperature was determined metallographically using polarized light. The criterion chosen was the point on the specimen showing the first recrystallized grain at a constant magnification, X200. Specimens were repeated, and the agreement was found to be 3°C. RESULTS Three different pure zirconium specimens were tested, and the recrystallization temperature was

Jan 1, 1962

By H. F. Silliman, Daniel R. Hull, Earl W. Palmer

THE brass-rolling industry has not had a great deal of experience with antimony in its product. There have been some recent excursions with antimony as a corrosion inhibitor in tubes, but in sheet brass it has been regarded with apprehension and generally avoided. This is not to say that [ ] contaminations have never occurred, and probably a great many brass mill men have had their own ideas on the effect of such contamination. Our own views were based upon certain experiences some years ago with strip castings that split lengthwise in the early stages of rolling. The nature of this splitting is shown in Fig. I, from a photograph taken in 1922 as a record of 20 bars of 65-35 common brass made with an antimonial brand of copper. These bars were cast 6 ¾ in. wide by 1 in. thick by 45 in. long. In the first pass through the rolls, 19 of the 20 split lengthwise throughout their length, while each half curved outward in a wide arc as it emerged from the rolls. [ ] In those days, if splitting was not a frequent occurrence, it was not unfamiliar. One can recall periods of short duration when large amounts of common brass would behave in this way. There was nothing imaginary about these spells. The affected metal would split lengthwise in the breaking rolls, and no maneuvering of mill practice made any difference. The condition would descend like a plague, demoralize the mill for several days, and disappear. It is doubtful if anyone knew the cause-however many explanations may have been current. In 1921 a quantity of split brass was traced to the use of fired small-arms

Jan 1, 1943

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963