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By F. D. Rosenthal, F. J. Dunkerley, G. J. Mills

Activities, free energies, and heats and entropies of mixing of liquid Pb-Zn alloys have been obtained by the electrode-potential method between 400° and 650°C. The large positive deviations observed from Raoult's law are in agreement with the phase diagram, which indicates a wide immiscibility field. A vapor-pressure method was used to extend the activity measurements to 900°C, allowing the maximum of the immiscibility gap to be estimated by thermodynamic calculation. Data on the mono-tectic and eutectic points compare favorably with previously existing work. SEVERAL long-standing methods have been in use for the study of phase diagrams from measurement of the activities of the component metals.' The use of thermodynamic analysis for interpreting equilibria data is comparatively recent, however. Such analysis is usually undertaken by first evaluating the principal thermodynamic functions as, for example, the enthalpy, entropy, and free energy of the alloy constituents. These, in turn, quite often can be correlated with the interatomic potential energies and atomistics of the system, from which a clearer understanding of the causes leading to deviations from ideal behavior is gained. The present study of liquid Pb-Zn alloys is concerned with a determination of these quantities by electrode-potential and vapor-pressure measurements, using these values in calculations involving phase equilibria and to obtain a theoretical insight into an alloy system exhibiting strong positive deviations from ideal metallic solution. A considerable portion of the previously reported work is based on thermal analysis. Supplemented by optical studies of solid alloys, these techniques have revealed the essential nature of the immiscible mixtures that are formed. It is difficult, however, using the phase-

Jan 1, 1959

US 4,185,193-Method of assaying the vicinity of a borehole for uranium ore or thorium ore. A pulsed neutron source IS operated to irradiate the earth formations with fast neutrons. A detector responds to the delayed fission neutrons emitted by the ore as a measure of ore concentration and to the delayed neutrons from oxygen-17 as a measure of the neutron output of the source. The measurement of ore concentration is corrected In accordance with the measured changes in the neutron output of the source. R L. Caldwell, assigned to Mobil Oil Corp. Jan. 22, 1980 4 pp (250-269). Filed: 5-18-78 (906,907).

Jan 1, 1982

By Harold M. Mooney

RESISTIVITY measurements for determining depth to bedrock, water table, and other geologic discontinuities have had only limited success. Many of the difficulties can be attributed to complex geology and to basic limitations of the method; current flow through a continuous medium is a diffusion phenomenon, emphasizing irregularities near the source and smoothing out those at a distance. Some of the failures, however, are due to careless field work and incompetent interpretation. A forthcoming publication1 may help to reduce difficulties of this sort. The writer here attempts to bring order into the multiplicity of interpretation methods and, to a limited extent, to evaluate them. For all methods, the field data to be interpreted consist of apparent resistivity values plotted against electrode separation, Fig. 1. The interpretation should give depths to one or more geologic horizons. Direct currents and the Wenner four-electrode configuration will be assumed, since these are widely used, although the interpretation problems remain essentially the same for other electrode configurations. Alternating currents higher than, say, 20 cycles per second introduce complications beyond the scope of this paper. Three approaches to the interpretation problem have been used. These may be called empirical, theoretical curve matching, and direct. Many techniques have been proposed, but each can be reduced to one of these approaches and to a single geologic idealization. This idealization rests on the following assumption: the earth in the limited volume of interest can be approximated by a horizontal sequence of layers, each homogeneous and isotropic in its electrical properties. This seemingly restrictive assumption has proved to have practical value, although future work should aim at removing some

Jan 1, 1955

By A. W. Schlechten, R. F. Doelling

Parkes' process crusts were vacuum distilled using a shortened Pidgeon retort. Zinc was effectively removed below 800°C and recovered as a zinc sheet easily stripped from the furnace liner. Lead dasdistillationazinc required about 950°C and the resulting lead condensate tillationtended to stick to the thin metal liner. Final purity of residue is limited only by nonvolatile metals such as copper. THE successful commercial application of vacuum distillation for the removal of zinc from lead, as described by W. T. Isbell,' raises the question of whether or not a similar method can be used for other metal separations. Preliminary laboratory experiments on the vacuum distillation of Parkes' crusts by one of the authors' gave such encouraging results that it was decided to make a series of tests with large scale equipment to determine the results that might be expected in plant operation. The pilot-plant test results are reported in this paper. The great advantages of vacuum dezincing are its simplicity, the relatively low temperature of operation, and the fact that the zinc is recovered in the metallic state ready for use again in the desilveriza-tion of lead bullion. These same advantages and others would be realized from the vacuum distillation of the zinc-lead-silver crusts made in the Parkes' process. Zinc readily will distill over at temperatures of 800" to 900 °C as contrasted with the 1200°C or more used in the Faber du Faur furnace. Furthermore, the recovery of zinc as metal is practically perfect since there is no loss by oxidation or fuming. If the vacuum distillation is continued and hastened by raising the temperature to around 1000°C, the lead will distill over at an appreciable rate and deposit in a warmer zone of the condenser. This lead will contain a small amount of silver, but it can be returned to the desilverizing kettles and there is not the chance of loss that there is in disposing of the rich litharge from cupelling. The lower temperatures required will mean a saving of fuel and less wear on the equipment. One further point is that the vacuum distillation could be run on a small scale practically continuously, so as to avoid the accumulation of large amounts of silver-rich material and the need of assembling a large crew for special cupellation runs. It should be pointed out here that the final purity of the silver residue will depend on the copper or iron content of the crusts, as these and other metals with low vapor pressure will not be eliminated. The idea of treating the silver-zinc-lead crusts from the desilverization of lead bullion by vacuum distillation is not a new one, but such experiments have not been reported, as far as can be determined. In 1912, T. Turner presented a paper3 before the Institute of Metals on the vacuum distillation of brass, and a member of the audience suggested that he try his method on Parkes' crusts. In 1935, W. J. Kroll, noted for his discovery of debismuthiz-ing lead by calcium additions, published a paper' on vacuum distillation of metals and pointed out possible applications in the lead industry. Principles of Separation The successful separation of two or more metals by distillation depends upon an appreciable difference in the effective vapor pressures of the metals in the alloy to be treated. The vapor pressures of the common metals have been determined with considerable accuracy; for example, at 800°C the vapor pressures of the individual metals which are of particular interest in this paper are about .as follows: Zn, 241 mm; Pb, 0.0553 mm; and Ag, 0.0000276 mm. Unfortunately,, data are not available on the activities of the components in the ternary system Zn-Pb-Ag, but it can be estimated that on the basis of the vapor pressures of the individual metals a good separation can be made by distillation. The preliminary laboratory tests previously mentioned' supported this assumption. The pilot-plant size vacuum distilling furnace is shown in Fig. 1. It consisted of an abbreviated Pidgeon retort, 5 ft long with an ID of 8 in., heated by six silicon carbide elements placed symmetrically

Jan 1, 1952

I;. D. Godshall, Everett, Wash. (communication to the Secretary) : In Mr. Morse's interesting paper several statements occur which seem to require correction and comment. This is the more appropriate, since Mr. Morse has mentioned me by name, and has cited my "Review of the Russell Process,"* so that silence on my part might be taken as indicating an assent which I cannot give. On the first page of his paper Mr. Morse says that the " goingback " of chlorination was " the only difficulty encountered at Aspen," and adds that he has " never seen any explanation " of the cause. The plain inference is that he now fills this complete

Jan 1, 1896

By R. Dawson Hall

LONG regarded as nearly worked out, the anthracite region still shows promise of a hundred years of life, for means are being found to get bottom, top, pillar, and other coal that earlier generations disregarded as too expensive to mine. Rock drivages and, still more, machinery are making it possible to get such coal. Mechanical methods enable the owner of thin beds to mine these with profit, and the miner recognizes that he must permit the use of machinery or the inexorable laws of economics will deny him opportunity to work. E. L. Dana, Jr., well outlines this situation, which in the past year became definitely established. Stripping also is recovering, safely and inexpensively, coal that past generations regarded as too hazardous and costly for mining.

Jan 1, 1935

By M. E. Nicholson

The solid solubility of boron in iron has been determined by saturating iron with respect to FeyB at several temperatures from 870° to 1135 C. In alpha iron the maximum solubility was found to be 0.002 pct B and in gamma iron the solubility varied from 0.001 pct at 915°C to 0.020 pct B at 1165OC. The eutectic and peritectoid temperatures were found to be 1165° and 911 °C respectively and the gamma iron solidus was located approximately at 0.020 pct B. RECENT investigations of boron-treated steels', ' indicate that the solubility of boron in austenite is of the order of 0.003 pct at 900°C. This has led to the general belief that the solubility of boron in a and r iron is considerably less than that indicated by Wever and Muller." Therefore the solid solubilities of boron in a and r iron have been re-determined. The eutectic and peritectoid temperatures were also remeasured and the r-iron solidus was studied in some detail.* In 1929 Wever and Miiller investigated the phase equilibria of Fe-B alloys. Fig. 1 shows the solid solubility region of the Fe-B diagram based on their investigation. They found that boron lowered the A, transformation temperature to 1381 °C where saturated 6 solid solution "which must contain about 0.15 pct B" and "r solid solution containing about 0.10 pct B" are in equilibrium with liquid containing 1.9 pct B. At the eutectic temperature of 1174"C, 7 solid solution was found to contain "about 0.15 pct B." A peritectoid relation was found to exist between a and y iron with an invariant temperature at 915 "C, where the boron solubility in 7 iron was "about 0.10 pct B" and the solid solubility in a iron "did not exceed 0.15 pct B." Although most of their

Jan 1, 1955

By John Lamont, Walter Crafts

The principle formulated by Grossmannl for calculating hardenability of steel by multiplying the ideal diameter of "pure" iron-carbon alloys by factors for grain size and alloying elements has been confirmed on many steels and has proved useful in designing substitute alloy steels. Grossmann found that the typical behavior of the multiplying factors was to increase directly in proportion to the amount of the alloy present in a steel. However, the multiplying factor for the effect of silicon on hardenability was found by Grossmann to increase to a lesser degree as the amount of silicon was increased. In view of the increasing use of silicon in heat-treating steels, the effect of silicon on hardenability is becoming more important. Calculation of the hardenability of high-silicon steels made at the Union Carbide and Carbon Research Laboratories, Inc., indicated that the multiplying factor for silicon increased directly in proportion to the amount of silicon present. A more extended study of high-silicon steels covering fairly wide ranges of grain size, carbon, manganese, and aluminum has confirmed that up to 2 per cent silicon the multiplying factor is directly proportional to the silicon content. Manganese and aluminum factors have also been! determined. The results of the study offer strong confirmation of the general validity of Grossmann's multiplying principle. Testing Procedure Steels on which the study of the effect of silicon on hardenability was based were made in high-frequency induction furnaces using Armco iron and standard alloying materials. The ingots were forged to bars, and sections were normalized prior to machining Jominy hardenability test specimens. The Jominy test was carried out under standard conditions.2 The depth of hardness penetration for determination of ideal diameter at "half hardness" was taken at the hardness level indicated in Fig. 29 in Grossmann's paper by the solid line for 50 per cent martensite in plain carbon steel. The depth of penetration of hardness on the Jominy specimen was converted to ideal diameter by the relation given in Fig. 28 of Grossmann's paper. Chemical analysis was determined on a sample taken adjacent to the Jominy specimen. Aluminum was determined as "acid-soluble aluminum" rather than as total aluminum, as it is probably more representative of the aluminum that is effective as an alloying agent. In addition to the elements nominally present in the steels, analyses were made for residual phosphorus, sulphur, nickel, copper, molybdenum and chromium on one heat of those made with the same materials during the same period. Actual grain size was determined by microscopic examination of small samples quenched in water after receiving the same thermal cycle as the Jominy hardenability specimens. Chemical analyses, heat-treatment, grain size, and hardenability are shown in Table I representing three ranges of composition.

Jan 1, 1943

By John Lamont, Walter Crafts

The principle formulated by Grossmannl for calculating hardenability of steel by multiplying the ideal diameter of "pure" iron-carbon alloys by factors for grain size and alloying elements has been confirmed on many steels and has proved useful in designing substitute alloy steels. Grossmann found that the typical behavior of the multiplying factors was to increase directly in proportion to the amount of the alloy present in a steel. However, the multiplying factor for the effect of silicon on hardenability was found by Grossmann to increase to a lesser degree as the amount of silicon was increased. In view of the increasing use of silicon in heat-treating steels, the effect of silicon on hardenability is becoming more important. Calculation of the hardenability of high-silicon steels made at the Union Carbide and Carbon Research Laboratories, Inc., indicated that the multiplying factor for silicon increased directly in proportion to the amount of silicon present. A more extended study of high-silicon steels covering fairly wide ranges of grain size, carbon, manganese, and aluminum has confirmed that up to 2 per cent silicon the multiplying factor is directly proportional to the silicon content. Manganese and aluminum factors have also been! determined. The results of the study offer strong confirmation of the general validity of Grossmann's multiplying principle. Testing Procedure Steels on which the study of the effect of silicon on hardenability was based were made in high-frequency induction furnaces using Armco iron and standard alloying materials. The ingots were forged to bars, and sections were normalized prior to machining Jominy hardenability test specimens. The Jominy test was carried out under standard conditions.2 The depth of hardness penetration for determination of ideal diameter at "half hardness" was taken at the hardness level indicated in Fig. 29 in Grossmann's paper by the solid line for 50 per cent martensite in plain carbon steel. The depth of penetration of hardness on the Jominy specimen was converted to ideal diameter by the relation given in Fig. 28 of Grossmann's paper. Chemical analysis was determined on a sample taken adjacent to the Jominy specimen. Aluminum was determined as "acid-soluble aluminum" rather than as total aluminum, as it is probably more representative of the aluminum that is effective as an alloying agent. In addition to the elements nominally present in the steels, analyses were made for residual phosphorus, sulphur, nickel, copper, molybdenum and chromium on one heat of those made with the same materials during the same period. Actual grain size was determined by microscopic examination of small samples quenched in water after receiving the same thermal cycle as the Jominy hardenability specimens. Chemical analyses, heat-treatment, grain size, and hardenability are shown in Table I representing three ranges of composition.

Jan 1, 1943

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By John L. Lamont, Walter Crafts

THE principle formulated by Grossmann1 for calculating hardenability of steel by multiplying the ideal diameter of "pure" iron-carbon alloys by factors for grain size and alloying elements has been confirmed on many steels and has proved useful in designing substitute alloy steels. Grossmann found that the typical behavior of the multiplying factors was to increase directly in proportion to the amount of the alloy present in a steel. However, the multiplying factor for the effect of silicon on hardenability was found by Grossmann to increase to a lesser degree as the amount of silicon was increased. In view of the in¬creasing use of silicon in heat-treating steels, the effect of silicon on hardenability is becoming more important. Calculation of the hardenability of high-silicon steels made at the Union Carbide and Carbon Research Laboratories, Inc., indicated that the multiplying factor for silicon increased directly in proportion to the amount of silicon present. A more extended study of high-silicon steels covering fairly wide ranges of grain size, carbon, manganese, and aluminum has confirmed that up to 2 per cent silicon the multiplying factor is directly proportional to the silicon content. Manganese and aluminum factors have also been determined. The results of the study offer strong confirmation of the general validity of Grossmann's multiplying principle. TESTING PROCEDURE Steels on which the study of the effect of silicon on hardenability was based were made in high-frequency induction furnaces using Armco iron and standard alloying materials. The ingots were forged to bars, and sections were normalized prior to machining Jominy hardenability test specimens. The Jominy test was carried out under standard conditions.2 The depth of hardness penetration for determination of ideal diameter at "half hardness" was taken at the hardness level indicated in Fig. 20 in Grossmann's paper by the solid line for 50 per cent martensite in plain carbon steel. The depth of penetration of hardness on the Jominy specimen was converted to ideal diameter by the relation given in Fig. 28 of Grossmann's paper. Chemical analysis was determined on a sample taken adjacent to the Jominy specimen. Aluminum was determined as "acid-soluble aluminum" rather than as total aluminum, as it is probably more representative of the aluminum that is effective as an alloying agent. In addition to the elements nominally present in the steels, analyses were made for residual phosphorus, sulphur, nickel, copper, molybdenum and chromium on one heat of those made with the same materials during the same period. Actual grain size was determined by microscopic examination of small samples quenched in water after receiving the same thermal cycle as the Jominy hardenability specimens. Chemical analyses, heat-treatment, grain size, and hardenability are shown in Table I representing three ranges of composition.

Jan 1, 1943

By J. B. Cheatham

An analysis of indexing is given for an idealized plastic rock. Indexing refers to chipping from a bit tooth to a previously formed crater. A method is indicated for computing the dependence of chip size and shape as well as force on the tooth for various tooth shapes as a function of crater configuration and distance to the previous crater. Pressure on the tooth is found to vary with depth of penetration after a critical depth has been reached. Damp sand model experiments indicate that simple solutions using linear and logarithmic spiral slip-line fields for Coulomb plastic materials give reasonable approximations to the failure patterns. Both idealized roller cone bits and fixed blade or drag bits are considered, and methods are presented for approximating the force on the bit and the chip volume when the rock is subjected to sufficiently high pressure to behave plastically. One of the primary objectives of drilling research investigations is to develop theoretical equations which can be used to predict the behavior of rock under drilling loading conditions. Since rocks usually fail in a brittle manner at atmospheric conditions, much current research is directed to studies of the brittle failure of rock under the action of drilling too1s. 1,2 The results of triaxial test on rocks indicate that both rock strength and ductility increase at high confining pressures.3 Recent results from single bit-tooth indentation experiments on dry rocks indicate that the transition from brittle to ductile failure under a bit tooth can occur at pressures sufficiently low to be of interest in oil well drilling.4 Single bit tooth experiments and analyses are not directly applicable to the drilling process since one of the important facets in drilling is the interaction between a bit-tooth and the previously formed crater. This interaction is referred to as indexing.' The purpose of the present paper is to indicate how plasticity theory can be applied to the analysis of indexing for plastic rock. Drag bit or fixed-blade drilling is considered and a discussion is given of the drilling action of an idealized roller cone bit. Results of simple experimental studies using a damp sand model are given as a method of visualizing the failure patterns in rocks under high confining pressures. These results are compared with plasticity theory using simple solutions based on linear and logarithmic spiral slip-lines. Discontinuous stress fields are proposed for drag bit drilling based upon the soil mechanics analysis of Shields. SINGLE BIT TOOTH RESULTS Single bit tooth indentation experiments using dry rocks under pressures from 0 to 5000 psi have indicated a correlation between the shape of a force-displacement curve and the nature of the rock failure beneath the tool.4 Continuous linear curves are in-

Jan 1, 1965

air-lift and equipped with tapered tubing of proper design, we would have a gas input consumption of about 2500 cu. ft. per bbl., which at 3 to 4c. per 1000 cu. ft. would be 7 1/2 to l0c, per bbl., and there would be very infrequent loss of production due to stoppages. It has been demonstrated that with efficient design of air-gas lift, the production of wells can be increased much beyond that obtained with the former type of air-lift employed; also that small wells can be operated by air-lift with tapered tubing at a cost that places this method in competition with beam pumps in many fields. The next step in conservation that the writer expects to have an opportunity to demonstrate is that of restoring the pressure in a pool and producing by air-gas lift all of the oil possible to lift economically. This combined operation is probably the method toward which we shall eventually be working in recovering the maximum quantity of oil from pools where the oil is recovered through bore holes. General Discussion on the Air-gas Lift H. P. Porter, Tulsa, 0kla.—The papers presented at this meeting contain a great amount of valuable information. Wonderful progress has been shown in the development of air and gas-lifts. There has been nearly everything brought out that touches upon the subject. The real point that is lacking is exact knowledge of the velocity with in the flow column which will produce the best effect—that is the thing we must know more about. Velocity in Gas-lift Flow In other lines of industry the matter of velocity of fluids in pipe lines has been well analyzed and there are known laws by which to calculate velocity of flow; for instance, in irrigation work large pumps are designed with intake pipos to employ an intake velocity of 4 ft. per scc. By reduced cross-sect'ion the velocity is increased rapidly as it enters the pump and the discharge rate is at 12 ft. per src., which in turn is reduced in the discharge column to 4 ft. per sec. Crushed coal, grain and granular material is found to be best conveyed by air when a pneumatic conveyor is employed at 100 ft. per sec. As in the design of a pumping plant or a pneumatic conveyor, the velocity at the lower end of the column in the flowing well must be controlled within certain limits for best results. Mr. Griswold, I believe, stated that they had velocity as low as 15 it. per scc. and from that up to 78 ft. per sec. Mr. Pierce and Mr. Lewis showed an ideal flow column showing how the velocity increased as the fluid was carried up the column, hut did not give any figures as to the velocity. It would be well to take that sort of a diagram to establish an ideal velocity at the lower or intake end, and then calculate the velocity from expansion of the gas as it goes up. It may be that the, ideal intake velocity would vary, depending on the depth of the well, the quantity of liquid to be handled or the pressure which it may be desired to hold. The subject is one that might be worth much research.

Jan 1, 1928

By R. L. Perrine

This paper presents results obtained by consider ation of unstable miscible displacement within a porous medium as a quasi-turbulent displacement process, that is, a process characterized by fluctuations around a simpler, mean flow behavior. The instability usually results from the miscible displacing fluid having a viscosity lower than that of the displaced fluid. Such instability is evidenced in suitable experiments by the presence of viscous fingering. A unified theoretical relationship applicable to both stable and unstable displacement is derived. Parameters in the theory are obtained by empirical means. Although the theory describes an idealized conceptual model, agreement with experiment is quite reasonable up to moderately adverse viscosity ratios, such as 17:1. INTRODUCTION Many experimental studies of miscible displacement in porous media have been conducted with prediction of reservoir displacement efficiency as the ultimate objective. Most such studies have utilized lower displacing than displaced fluid viscosity, scaled to potential reservoir fluid pairs. Theoretical approaches have been largely limited to unit viscosity ratios, however, in spite of the necessity for an understanding of the mechanism of the unstable, adverse viscosity ratio displacement process. An obvious reason is the difficulty of describing in mathematical form the viscous fingering characteristic of these conditions. Observation of experiments conducted with dyed fluids in transparent systems suggests an analogy between unstable miscible displacement and turbulent flow in a pipe. In both cases there are fluctuations around a simpler, mean flow behavior. An important difference is that flow behavior of interest in the porous medium is entirely transient, contained within a transition zone between displacing and displaced fluids. Transient behavior complicates description in that coefficients in the equations become variables rather than constants. In the study reported here, the analogy with turbulent flow has been used in treating unstable miscible displacement as a quasi-turbulent displacement process. The purpose has been to derive, even if restricted to an idealized conceptual model, a unified theoretical relationship applicable to both stable and unstable displacement. A relationship meeting these specifications up to moderately adverse viscosity ratios, such as 17:1, is presented. One fluctuation parameter in the theory and dispersion coefficients are obtained by empirical means. The idealized theory is compared with experimental results. UNSTABLE MISCIBLE DISPLACEMENT AS QUASI-TURBULENT DARCY FLOW The miscible displacement of one fluid by another within a porous medium is considered in this study. Flow conditions are such that Darcy's law is applicable. It is further assumed that, by the stability criterion proposed by perrine,1 initial flow conditions lie well within the regime of instability. Thus substantial viscous fingering is assured. We wish to show how this flow regime can be represented as quasi-turbulent. That is, the Reynolds number for the established flow conditions is below that for inertial or turbulent flow within a porous medium, and lies within the regime for which Darcy's law is valid. Yet flow behavior can be described as the combination of some relatively simple average result, and characteristic fluctuations that are superimposed on the simpler behavior. Stated another way, flow behavior includes the movement of layers of fluids with different velocities past or over one another. Such descriptions are characteristic of turbulent pipe flow. The fluctuations in the present case are a direct consequence of the local viscous fingering which accompanies the unstable displacement process. Should displacement become stable, fluctuations would die out. It is of particular importance to note that fluctuations such as these can interact in a way that contributes to material transport by the basic flow. The basic transport equations required for engineering calculations must be modified to reflect this fact.

By O. K. Riegger, L. H. Van Vlack

The median angle of relatively few two-dimensional observations provides a satisfactory value for dihedral angle determinations. Those data that contain bimodal or non-equilibriated dihedral angle distributions are readily detected. THIS paper is concerned with a statistical simplification for determining dihedral angles in solids. Microstructures are partially controlled by relative energies of interphase boundaries and grain boundaries. smith1 has shown rather conclusively that such boundaries may be equilibrated to give a vectorial balance at grain and phase edges. Thus if an accurate measurement is made of the dihedral angle associated with grain and phase edges, an accurate calculation of the relative energies may also be made. The accurate measurement is difficult because the dihedral angle involves two planes in three dimensions, and only a two-dimensional cut through the dihedral angle is usually observed. Such a two-dimensional cut is statistically random provided there is no preselection or orientation. Harker and parker2 have shown that the mode of the frequency distribution of observed angles is within 5 deg of the true angle if the true dihedral angle is 120 deg. smith1 had calculations made to show that the same generalization could apply to dihedral angles of 30, 60, 90, and 150 deg. This procedure of requiring the determination of the statistical mode is time consuming because experience has shown that more than 200 angle observations are necessary before the mode is clearly indicated. It is possible to determine the dihedral angle with equal accuracy with only 25 angle observations if the median angle is used in place of the mode angle. Use is made of Harker and parker's2 basic equation tan =2 sin x cos

Jan 1, 1961

By Richard B. Reese, George R. St. Pierre, Robert A. Rapp

The vapor pressures of pure iron and pure chromium have been measured using a Knudsen cell coupled with a mass spectrometer. The experimental results agree well with some previously reported data; heats of sublimation and vaporization have been calculated. From vapor pressure rr~easurernents, the activities of iron and chromium in their binary alloys have been determined for NcY = 0.10 to 0.65 over a 1400" to 1700~ temperature range. The activity of chromium in the liquid alloys was found to exhibit positive deviation from ideal behavior when referred to solid chromium as the standard state; however, for the activity of chromium referred to nonequilibrium undercooled liquid chromium as standard state, the activity behavior is almost ideal. ALTHOUGH the Fe-Cr system is important as the basic system of alloy steels, the thermodynamic properties of this system have not been thoroughly investigated at elevated temperatures. In view of the potential practical applications of such data as well as their contribution to alloy theory, further study of the Fe-Cr system was undertaken. In addition, further development of experimental techniques for equilibrium measurements at high temperature is required. The present research involved an application of the Knudsen effusion method in conjunction with a time-of-flight mass spectrometer. Belton and ~ruehan' have measured the activities in Fe-Ni and Fe-Co alloys by a similar method. Speiser, Johnston, and lackbburn' have determined the vapor pressure of pure solid chromium between 1283" and 1561°K by a Langmuir free evaporation technique. The vapor pressure of chromium was described by the expression: over the temperature range 1283" to 1561°K. McCabe, Hudson, and paxton3 have measured the vapor pressures of pure iron and pure chromium by the Knudsen cell technique around 1500°K. The vapor pressure and heat of sublimation at O°K, AH,", for pure chromium agreed within experimental error with the measurements of Speiser et al. at 1200°C. Kubaschewski and HeYmer~ determined the vapor pressure of pure solid chromium in the temperature range 1170" to 1400°C by the Knudsen effusion technique combined with a radioactive tracer analysis of crS1. Their results agreed with the work of previous investigators. Edwards, Johnston, and Ditmars5 have measured the vapor pressure of pure solid iron by the Langmuir technique between 1356" and 1519°K. The vapor pressure of solid iron in the temperature range studied was given by: The data of McCabe, Hudson, and paxton3 on the vapor pressure of pure iron around 1500°K by the Knudsen effusion technique were in good agreement with those obtained by Edwards et a~.~ Hultgren, Orr, Anderson, and Kelley give the selected values for the AH: of pure iron and pure chromium as 98,990 *200 and 94,340 * 500 cal per mole, respectively. These values are the average values determined in the several investigations by different methods. The Fe-Cr phase diagram7 is shown in Fig. 1. Previous determinations of activities in this system have been carried out by several investigators, but most of the work has been done on solid alloys. Using a Knudsen effusion method with cr5', Kubaschewski and Heymer4 reported that the Fe-Cr system exhibits positive deviation from the ideal behavior for compositions ranging from NCr = 0.0398 to 0.699 at 1170"

Jan 1, 1969

By G. P. Chatterjee

HARDNESS is one of the most common properties of metals and alloys but is one of the most difficult to define or express in terms of the fundamental units. In the Brinell or Vicker's hardness test, the hardness number N is defined as N = L/A where L is the load in kilograms and A is the area in mm'. This does not necessarily imply that a pressure of N kilograms per mm2 actually acts on the specimen.' It is essential that for a true comparison of hardness values the angle of indentation be kept constant,' a which is not done in the Brinell test. For this and other reasons, the Brinell hardness value is not based on a satisfactory physical concept.' The concept of hardness based on the work done per unit volume of indentation3-6 offers a simple and scientific definition. An attempt has been made here to develop this concept (at constant angle) and to compare the values so obtained with the Bhn for different metals and alloys. In Fig. 1 a vertical load L is applied to a compara- tively hard ball of diameter D creating an indentation of diameter 6 and depth h on the specimen S. The work done, W, is then given by W = So Ldh. [I] Since L is not independent of h, Honda and Takahasip and Matsumura" assumed different functions leading to equations which do not apply equallye to a wide variety of metals and alloys. A better relation is obtained from Meyer's Law L = ad" [2] where A and n are constants depending on the nature of the material but independent of the ball diameter D. From Fig. 1 it is obvious that h = R(l — cosq) and d = 2R sin 8.

Jan 1, 1957

By Edmond S. Miksch

The morphology and growth rate of ice grown in supercooled water are markedly affected by convection of the water. A dendritic ice sheet with water flowing past the dendrite tip exhibits deflection of the dendrite spine toward the upstream direction, accelerated growth of secondary spines on the upstream side, and suppression 01" secondaries on the downstream side. Flow causes a thin disk to become corrugated, the corrugations being parallel to the flow. Flow causes an increase in the growth rate of the ice. IF a small seed of ice is placed in slightly supercooled water, it grows initially as a disk with the axis of the disk parallel to the c axis of the ice crystal.' It appears that growth in the c direction is inhibited, while growth occurs with equal facility in all directions in the basal plane. It appears that growth rate as a function of interface temperature is very nearly equal for all directions similarly oriented relative to the c axis. Subsequent to the discoid growth, branching occurs and dendrites develop. The primary dendrite spines grow parallel to the six equivalent a axes of the crystal. Secondary, and in some cases, tertiary spines also grow in these directions. The highly anisotropic: dendritic growth indicates that there must be some finite difference of growth rate for different directions in the basal plane. These differences must be quite small, however, since if they were large, the discoid mode would not occur. Hence, it was expected that the dendrite growth direction could be deflected from the crystallographic direction by perturbation of the thermal field at the dendrite tip. Experiments were done in which perturbation of the thermal field was accomplished by causing the supercooled water to flow past the dendrite tip. The flow direction was perpendicular to the c axis of the crystal, and was perpendicular to the primary spine of the unperturbed crystal. Supercooled water was supplied by a 15 cm cubical copper box, which was refrigerated and insulated so it could cool water to temperatures down to —2oC, and maintain the temperature constant to O.l°C for the duration of a run. A lucite channel of rectangular cross-section, 12 by 24 mm, was mounted horizontally in the box, with one end open so water could flow into it, and the other end leading out through the wall of the box to a length of tubing leading: to an orifice plate 123 cm below. cnunMn s MIKSCH, MemberAiMe, formerly Research Associate, Research Associate, Fig. l(b)—Vertical section of apparatus A horizontal cross-section is shown in Fig. l(a), and a vertical section is shown in Fig. l(b). Means for observing the ice are shown in Fig. l(a). Collimated light passes through the ice sheet and forms an image on the ground glass screen. A lucite box containing dry air was employed to prevent condensation. Ice of the desired orientation was provided by the seed holder shown in Fig. l(b). This device was made of lucite, and had a reservoir in which ice could be frozen by placing it in a freezer. This reservoir com-unicated with the outside only through a narrow gap between two sheets of lucite. The seed holder (after ice had been washed off its exterior) was immersed in the tank of supercooled water, the narrow gap terminating in a slot in the top of the flow channel. Ice growing through a thin water layer in the gap between the two sheets of lucite was oriented so its c axis was perpendicular to the sheets. This orientation is an application of a growth phenomenon2 which causes ice growing along a smooth solid surface in supercooled water to orient itself so its c axis is normal to the surface. After the ice grew into the channel, further orientation was necessary, since the direction of the a axis

Jan 1, 1970

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using