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By R. J. Fruehan

The oxygen activity and concentration were measured in Fe-Cr-0 melts in equilibrium with an oxide phase at 1600°C (2912°F). The activity was determined by ,use of the following solid oxide -electrolyte galvanic cell CY-Cr8,(s) I ZrOz(CaO) I Fe-CY-G(saturated)(l) The oxygen concentration decreases with increasing Cr concentration to about 270 ppm 0 at about 7pct CY and then increases gradually. The activity coefficient of oxygen (fo) decreases with increasing Cr. In melts containing up to about 20 pct Cr, log f is approximately a linear function of wt pct Cr with a slope (e q 2) of —0.037. The activity of chromium was calculated and found to exhibit a small negative deviation from Raoult's law. From the activity and solubility data for low chromium melts, the free energy of formation of chromite, FeCr204, was found to be -79.8kcal per mole where pure liquid chromium and oxygen at I wt pct in Fe are the standard states. ThE effect of chromium on the chemical behavior of dissolved oxygen in liquid iron is of great importance in controlling the deoxidation of steels containing a significant amount of chromium. Chen and chipman' equilibrated Fe-Cr melts in the presence and absence of slag with hydrogen-water vapor mixtures. They concluded that at 1595°C chromite was the oxide phase in equilibrium with Fe-Cr alloys containing less than 5.5 pct Cr while at higher chromium concentration Cr,O, was the stable phase. In the composition range 0 to 10 pct Cr they found that the interaction coefficient, was equal to -0.041. Turk-dogan,' Schenck and Steinmetz,, and pargeter4 measured egr) in a similar manner and found the value to be -0.064,-0.04, and -0.052, respectively. McLean and Be11 evaluated egr) from their data on the equilibrium of Fe-Cr-Al-0 alloys with H2/H20 mixtures and found it to be -0.058. However, McLean and Bell's value should only be considered an estimate because the effect of aluminum on the activity coefficient of oxygen is about a hundred times greater than that of chromium. Consequently, an error in the value of egl) used, which at the present time is not well-known, or an error in aluminum analysis, which is present in very small quantities, will result in a significant error in egr). Fischer et a1.6 determined the interaction coefficient (eEr) in Fe-Cr-0 melts not in equilibrium with an oxide phase and containing less than 18 wt pct Cr at 1600°C electrochemically. They determined a value of -0.031 for egr). Hilty et aL7 measured the oxygen content of Fe-Cr melts in equilibrium with an oxide phase containing up to 50 pct Cr. They found that the solubility of oxygen decreased as the chromium content increased to about 6 pct Cr and then increased gradually. They concluded that the equilibrium oxide phase was chromite below 3 pct Cr, distorted spinel from 3 to 9 pct Cr, and Cr,04 above 9 pct Cr. Adachi and lwamotoa also investigated this system, but did not find Cr30,. They X-rayed the equilibrium oxide phases and did not find the presence of Cr,O,. They also X-rayed the oxide phase extracted from a 65 pct Cr melt which was heat treated and did not find metallic chromium as would be expected if Cr3O4 were the equilibrium oxide phase as indicated by the reaction : 3Cr3O4 — 4Cr2O:, + Cr [lj It was the purpose of the present investigation to determine the effect of chromium on the activity coefficient of oxygen in Fe-Cr melts by measuring the activity and solubility of oxygen equilibrated with an oxide phase in the composition range 0.18 to 50.5 wt pct Cr at 1600°C (2912°F). The activity of oxygen in the melts was determined by use of the following galvanic cell: The relationship between the partial pressure of oxygen in equilibrium with the melt and the reversible electromotive force of the cell (E) is where 11 = 4, F is the Faraday constant, pb, is the oxygen pressure in equilibrium with the meit and is the oxygen pressure in equilibrium with Cr203 as determined from the free energy data compiled by Elliott et al? The oxide phase in equilibrium with pure chromium was assumed to be Cr If Cr30, were the equilibrium phase the activities derived would be approximately the same, since the best estimated free energy of formation of Cr,O,, if it does exist, is approximately % the free energy of formation of The activity of chromium in Fe-Cr alloys at 1600° C was also determined from the measured electromotive force. The activity of chromium (aCr) is related to the electromotive force as follows: , The oxide phase in equilibrium with pure chromium and Fe-Cr melts from 10 to 52 pct is assumed to be Cr203 so that n equals three. If future work proves the existence of Crs04 in equilibrium with Fe-Cr melts and pure chromium, the experimental results can be reevaluated using a value of $ for n in Eq. 141. A value of ^ for n will make the activities about 10 pct higher. In order for Eqs. 131 and [4J to be valid the electrolyte, ZrOa(CaO), must exhibit predominantly ionic conduction at the temperature and oxygen partial pressure of its use. Previous work1' has demonstrated that ZrOz(Ca0) is predonlinantly an ionic conductor

Jan 1, 1970

By C. T. Liu, J. Gurland

The deformation behavior in tension of spheroidized carbon steels was studied at room temperature as a function of carbon content, 0.065 to 1.46 wt Pct, and carbide particle size, 0.88 to 2.77 p. It was found that the Hall-Petch strength-grain size relation is directly applicable to the yield and flow stresses of the two lower-carbon steels , 0.065 and 0.30 pct C. The strength data for the medium- and high-carbon steels, 0.55 to 1.46 pct C, also satisfied the Hall-Petch relation, provided that these data are based upon the particle spacing. Beyond 4 pct strain, the flow stress data of all the steels studied could be represented by the same Hall-Petch relation with dinerent spacings for grain boundary and particle strengthening. The behavior of the higher-carbon steels was consistent with the postulated formation of a dislocation cell network during processing and initial deformation (up to 4 pct strain). The cell size was assumed to be equal to the planar particle spacing. The true stress at the ultimate tensile strength was also found to be a function of the particle spacing. At a given temperature and strain rate, the yield and flow stresses of carbon steels depend on the type and dimensions of the microstructure. Starting with the work of Gensamer et al. in 1942,' experimental studies on pearlitic and spheroidized carbon steels revealed that the strength of steels is a function of two main parameters: the ferrite grain size2'3 and the carbide particle spacing;1'4'5 on this basis, two different strengthening mechanisms have been developed to apply to steels of low and high carbon contents, respectively. In polycrystalline iron and mild steels the grain boundaries are regarded as the major structural barriers to slip. The relation between strength and grain size is generally represented by the Hall-Petch equation which is based on a linear proportionality between strength and the inverse square root of the average grain size.2'3y677 However, Gensamer et al.' and Roberts et related the yield strength of medium -and high-carbon steels to the carbide particle spacing alone, and they found a linear relation between the logarithm of the mean free path in the ferrite and the yield strength in both spheroidized and pearlitic steels. By means of the electron microscope, Turkalo and LOW' extended the study to finer structures; they concluded that the logarithmic relation is not valid for the entire range of microstructures unless grain boundaries are also included in the measurement of the mean free path. For the specific case of spheroidized steels, Ansell and aenel' found that the yield strength data,4'5 when plotted as a function of mean free path, fit the Hall-Petch equation; however, T'ysong found that the same data fit the 0rowanl0 relation if a planar inter-particle spacing is used. Recently Kossowsky and ~rown" studied the strength of prestrained spheroidized steels, 0.48 and 0.95 pct C, and concluded that the strength due to the carbide dispersions varies linearly with the reciprocal of the square root of the mean free path between carbide particles and dislocation networks. Such networks were first observed by Turkalo." The conclusion common to all these studies is that the available slip distance in the ferrite is the most important variable in determining strendh. Previous work on carbon steels is restricted to limited composition and strain ranges. The mechanism which governs the flow properties is not clearly understood, and, in particular, little is known about the composition dependence of the transition between grain boundary strengthening and particle hardening. The purpose of the present work is to investigate the strengthening mechanism in spheroidized steels over a wide range of carbon content, 0.065 to 1.46 wt pct, and plastic strain, yielding to necking. The spheroidized structure was chosen because of its relative simplicity and the relative ease of control and measurement of the structural parameters. The experimental work is limited to tensile testing at room temperature at constant extension rate. The effects of the carbide particles on the fracture behavior of spheroidized steels are discussed elsewhere.13 EXPERIMENTAL PROCEDURE Eight different grades of vacuum-cast carbon steels were supplied in the form of forged and rolled plate by the Applied Research Laboratory of the U.S. Steel Corp. The compositions furnished with these steels are given in Table I; the carbon content ranges from 0.065 to 1.46 wt pct, or from 1.0 to 22.3 vol pct of carbide. The steel plates were cut transversely into rods a little larger than the test specimens, 1 in. gage length, i in. diam. The rods were austenitized in air (enriched with CO by a consumable carbon-rich muffle) at 50° C above theA, orA., temperature for 2 hr and then quenched in oil with vigorous stirring. The as-quenched rods were tempered in two stages in order to obtain the desired distributions and sizes of carbide particles. The rods were first tempered at 460° C for 10 hr and then at 700" C for periods ranging from 4 hr to 3 days, in vacuum. After final machining, all specimens were vacuum-annealed again at 650°C for 1 hr in order to relieve residual stresses. The tension tests were carried out in two steps. The initial part of the load-strain curve, up to about 2 pct strain, was determined on a Riehle testing machine with an extensometer of small strain range, 4 pct strain, in order to obtain the yield and initial flow piopertiesi As soon as the first part of the test was finished, the specimen was placed in an Instron testing machine equipped with a strain gage extensometer with a maximum strain range of 50 pct. The load-strain curve to fracture was

Jan 1, 1969

By H. S. Cannon, F. N. Rhines

IT. H. Hausner( Sylvunia Electric Products Inc., Bay-side, N. Y.)—The results reported by the authors are interesting because they contribute some information on the principles of sintering and also because of a certain practical value for the manufacture of powder . metallurgical parts in production. Pressed powder compacts are frequently sintered in a boat in several layers so that the lower layers are actually sintered under the weight of the upper layers and, therefore, are frequently deformed. The authors gave information on this deformation process by determining the effect of the load on the density. The experimental setup of the authors, however, has a disadvantage—that the sintering occurred in a cylindrical container so that the deformation was stopped in the direction of the diameter. The authors should have rather called this a study of hot-pressing than of sintering. I want to call the attention of the authors and others interested in sintering under load to the experimental work described by Dawihl and Rix.' These authors sintered cylindrical compacts under a lengthwise ten-sional load of 0 to 25 g and found that the shrinkage in length and diameter changes considerably with the load, but that the volume shrinkage is affected very little by the load. H. S. Cannon (authors' reply)—We wish to thank Dr. Hausner for calling attention to the experimental work of Dawihl and Rix. The fact that they found volume shrinkage little affected by varying tensional loads during sintering seems to support the contention that the forces due to loading are equivalent to and additive to the forces which cause densification. This contention is the basis of our comparison of sintering and creep.

Jan 1, 1952

By F. T. Selleck, H. H. Reamer, B. H. Sage

An experimental investigation was made of the effect of temperature upon the three-phase pressure associated with the propane-water and propene-water systems when hydrates were present. In addition, the characteristics of the propane-propene-water system were established over a limited range of ternperatureo under conditions such that hydrate was formed. The hydrate phase for this system may he a solid solution and the distribution of propane and propene in it is similar to that found in the coexisting hvdrocarhon liquid phase. INTRODUCTION A knowledge of the characteristics of hydrates of the hydrocarborrs encountered in industrial practice is of importance in connection with the design of process equipment. Villardl.1,2 carried out early studies of hydrates, and de Forcrand1 con-sidered the more probable compositions of the hydrates of hydrocarbons. Hammerschnid1 presented information about the propane-water and the isobutane-water systems. Scheffer5 studied the hydrate of hydrogen sulfide in detail, and de For-crand reported on the hydrates of krypton, argon, and xenon.1 Roberts and co-workers1,2 determined the nature of the hydrates formed in the methane-water and ethane-water systems. Carson and Katz10 studied the methane-propane-water, methane-pentane-water, and the methane-hexane-water systems in the four-phase region. The results of this rather extensive investigation indicated that the paraffinic hydrates formed solid solutions. The experimental evidence now available does not Support the existence of hydrates of the pentanes-antl-heavier hydrocarhons but it cannot be stated with certainty that such hydrates are not formed. Stackelherg. 11,12,13 made extensive studies of the crystal structure of paraffinic hydrate; by means of x-ray techniques and found that hydrates poses; a definite structure and composition. The existence of such a Structure does not preclude the firmation of Solid solutions of hydrates in aqueous systems containing two or more hydro-carbon~. Wilcox, Carson and Katz" reviewrd the information on the hydrates of importance in the processing of natural gas and presented data concerning their formation from natural gas. Kobayashi and Katz1' made studies at high pressure of the Hydrate of methane. and Unruh and Katz"' investigated hy-drates in mixtures of carbon rlioxide and methane. Frost and Deaton contributed to the knowledge of the composition of the paraffinic hydrates The irregularities in the experimental results were several times the expected uncertainties. This experience confirms the behavior encountered by other investigators indicating that hydrates tend to occlude water during their formation, thus rendering difficult the direct measoremeut of their composition. Miller and Strong2 investigated a number. of paraffinic hydrates from the standpoint of their possible application to (, the industrial storage of gas. Powel1 studied the effect of solutes upon the decomposition temperature of paraffin hydrates. Marked lowering of the decomposition temperature at a given pressure may he obtained by the use of such additive agents as ethylene glycol, urea. and sodium chloride. APPARATUS AND METHODS Two method* were here employed to study the behavior of hydrates. The first involved a glass capillary within which the hydrocarbons and water were confined over mercury. The second made use of a double-ended weighing bomb technique." The glass capillary equipment has been described elsewhere.'" A schematic drawing of it is presented in Fig. 1, where the arrangement of the agitator and mercury reservoir is shown in some detail. The lower part of the glass capillary, D, was enlarged to afford space within which the fluids used in the investigation could he stored at low pressures after their introduction through the valve. G. The temperature of the capillary was controlled by the circulation of a hydrocarbon oil of low viscosity from the agitated bath, B, through the vacuum jacketed column. C. The pump, A, was employed for the circulation of this oil. A relatively clear view of the capillary tube, D, was obtained through the vacuum jacket. Mercury was introduced into the lower part of the vessel, E, from

Jan 1, 1952

By J. E. Berry

AII evaluation is made of the acoustic velocity log for measurement of formation porosity. Plots of field-observer1 velocities vs core-measured porosities of sandstones and limestotnes with inter intergranular porosity show that the velocity log gives a useful measure of porotity, in agreement with published data. A new method of plotting electrical and velocity log data makes it easier to recognize hydrocarbon-water coritnct~ from log darn and to make serni-quantitative estinlates of hydrocarbon saturation. Two examples of this interpretation technique are given. This paper also discusses the various factors that affect acoustic velocity and shows how corrections can be made for some of these factors. INTRODUCTION Although the continuous velocity log was developed primarily as an aid to seismic interpretation, it is finding widespread use for measurement of porosity. The purpose of this paper is to evaluate this use of the log. Results are presented for the velocity-porosity relationship in many sandstones and one limestone. Practical applications of porosity values derived from the velocity log to improve interpretation of electrical surveys are presented. Various parameters which affect velocity in porous media are considered. Porosity, composition, cementa-tion, pressure difference (overburden pressure minus fluid pressure), fluid saturation, and wellability are discussed. Some of the ideas are opinions based on general considerations of well logging problems while others are supported by published data and our own observations. Major conclusions from these studies arc given in the body of the paper and detailed discussions of some of the various factors affecting porosity are given in the Appendix. POROSITY Sandstones The primary factor affecting the velocity of sound in porous media is porosity. Wyllie, et al,1 have reported a time average equation for the relationship between velocity and porosity.* This has found considerable acceptance in the industry. Other relationships between velocity and porosity have been proposed, none of which are entirely satisfactory. It is doubtful that any one relationship will completely describe all situations. We have tried an empirical relationship based on correlating log velocities with core-measured porosities. Measured porosities were averaged over a depth interval equal to the spacing used in recording the velocity logs. The depth range for the information used was from 2,000 to 12,000 ft. Velocity measurements were normalized for the effects of depth and overburden pressure. A detailed discussion of the basis for this normalization is given in the Appendix. The change is usually insignificant and when working with individual formations it can be neglected. All velocity measurements were normalized to a depth of 10,000 ft. The velocity-porosity data for sandstones in Fig. 1 came from 20 wells scattered throughout the Mid-Continent and Gulf Coast areas. The scatter of the data points is attributed to three causes: 1. There is no theoretical basis for expecting an exact velocity vs porosity relationship and it is not possible to correct precisely for the effects of such factors as impurities, grain shape, manner of cementation, etc. Some of these factors are discussed in the Appendix. 2. Porosities measured by core analysis are not necessarily representative of what the velocity log "sees". 3. Inaccuracies appear in the velocity log reading. This is particularly true of velocities from one-receiver logging tools.*" A linear-time curve (time-average equation) is plotted in Fig. 1 along with the best straight line through the points. Velocities used for the linear-time curves were 19,500 ft/sec for the matrix velocity (zero porosity) and 5,500 ft/sec for fluid velocity. For clean sandstones with velocities greater than 10,000 ft/sec, there is little difference between the velocity-porosity and the time-porosity curves. Both curves are well within the scatter of data points. The data points in Fig. 1 were restricted primarily to clean sandstones, using the SP and/or gamma-ray logs as clues to the lithology. Where a lithologic de-

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG's ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid' have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey' presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,

By J. M. Locke

BRÜCKNER's revolving cylinders for roasting ores, etc., are now used at a number of the mills in Colorado and New Mexico, for the purpose of roasting and chloridizing silver ores, with highly satisfactory results, even from those cylinders of small size, erected before the many improvements of recent date. As examples of the larger improved cylinders, reference can be made to those erected at the Tennessee Reduction Works, Silver City, Grant County, New Mexico, and those which were built, in 1871, at the celebrated Caribou Silver Mill and Mines, Colorado, a mining enterprise which has proved so satisfactory as to have been lately sold to a Holland company for an enormous amount. These cylinders, as now constructed by Messrs. Lane & Bodley, of Cincinnati,, Ohio, are shown in Plate III, in which Fig. 1 is an elevation in perspective, Fig. 2 a longitudinal, and Fig. 3 a trans¬verse section. Fig. 4 is a sketch of a mill, with Brückner's cylinder. The exterior of the cylinder is a shell of boiler iron, 12 feet long by 5 feet 6 inches in diameter. The ends are partially closed with similar material, leaving in the centre a circular opening about 2 feet in diameter, bounded by a flange projecting several inches.. Upon one side is placed an opening closed by a hinged door. Upon the outside of the cylinder are bolted three bands, as shown in Fig. 1, in which the section of the first is square, and that of the third semi¬circular; the second, or middle band, is a strong spur gear. Passing through the cylinder are six pipes parallel to one another, in a plane at an angle of 15° to the axis of the cylinder; these pipes also lie in this plane at an angle of from 30° to 35° to the longitudinal, axis of the plane, as shown in Fig. 2, where the internal arrangement of the cylinder is seen, a perforated diaphragm being formed through part of the cylinder by means of perforated plates placed between

Jan 1, 1874

By G. Wranglen

On account of the possibility of isolating carbides in steel it is generally assumed that the electrode potential of iron carbide is more noble than that of ferrite.1,2,3,4,5 Differences from 0.032 V1 to 0.4 V4 have been recorded. However, it is important to realize that the more noble behavior of cementite in relation to ferrite is not an issue of thermodynamics but of reaction kinetics. Theoretically, cementite is less noble than ferrite, which is a direct consequence of its thermo-dynamic instability. With the value ?F°298 = +4700 cal per mol for the free energy of formation of cementite6 it is easily calculated that the electrode

Jan 1, 1950

[Trans. No. Place Date Vol. Page 1, Wilkes-Barre, Pa.* .... May, '71.. 1 3 2. Bethlehem, Pa Aug., '71.. 1 10 3 Troy, N. Y Nov.,'71.. 1 13 4. Philadelphia, Pa Feb., '72.. 1 17 6. New York, N. Y •.... May, '72.. 1 20 6. Pittsburgh, Pa..:.Oct., '72.. 1 25 7. Boston, Mass Feb., '73.. 1 28 8 Philadelphia, Pa.' May, '73.. 2 3 9. Easton, a Oct., '73.. 2 7 10. New York, N. Y Feb., '74.. 2 11 11. St. Louis, Mo.* May, '74.. 3 3 12. Hazleton. Pa Oct.. '74.. 38 13. New Haven, Conn Feb., '75.. 3 15 14. Dover, N. J.' May, '75.. 4 3 16. Cleveland, 0 Oct., '75.. 4 9] [ ]

Jan 1, 1925

By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By G. J. Heuer, J. N. Dew, G. C. Clark

The effect on well behavior of partial permeability barriers, changes in producing rates and well spacings have been calculated through use of a radial, unsteady-state, two-phase-flow mathematical model. This model allows for variations in permeabilities and porosities with distance from the wellbore. The numerical methods necessary to solve the problem require use of a highspeed digital computer, in this case an IBM 704. In each instance, pressure and saturation gradients, gas-oil ratios and recoveries around a well producing by solution-gas drive have been calculated as a function of time and distance from the wellbore. Comparisons are made to show the effect of changes in producing rate and of varying permeability near the wellbore and out in the formation on the production and pressure history of the well. The effect of different well spacings on producing rate and ultimate recovery is considered. Although the mathematical description of the reservoir is simplified in comparison to an actual reservoir, the results do give some insight into the difficult problem of spacing and proration in a heterogeneous solution-gas-drive reservoir. Results show that for the cases considered spacing has little effect on ultimate recovery and that permeability barriers removed from the well decrease producing rate for a period of time but have only a small effect on ultimate production. INTRODUCTION The effect of spacing and producing rate on the production characteristics and ultimate recovery of a well producing by the solution-gas-drive mechanism have been topics of interest to the oil industry for many years and the subject of many hearings before state regulatory bodies. The problem is very complicated because of the difficulty of simulating in the laboratory a reservoir producing by the solution-gas-drive mechanism under anything like normal field conditions. This paper gives the initial results of a study aimed at determining the effect of these factors on production from reservoirs simulated by a mathematical model. Two-phase, unsteady-state equations are used to calculate pressures, saturations, and rates of oil and gas flow as a function of time and distance from the wellbore. The model is radial, and reservoir properties may be varied with distance from the wellbore. A decrease in permeability at a given distance results in a low-permeability ring concentric with the wellbore through which all the fluids from more distant portions of the reservoir must flow. The current mathematical model allows for variation of permeability, porosity and saturations as a function of distance from the well. Any desired drainage radius for the well may be selected. Drainage radii of 745 and 1,053 ft, which correspond to 40- and 80-acre spacing, were chosen for the calculations which follow. A large amount of the input data has been held constant. No investigation was made into the effect of changes in fluid properties and relative permeability characteristics on oil and gas production behavior. Fluid properties and relative permeabilities are essentially those of the White Mesa portion of the Greater Aneth area in southeastern Utah. A recently concluded hearing before the Utah Oil and Gas Conservation Commission to determine spacing for the field aroused interest in the possible effect of permeability constrictions located some distance from the well on production and recovery. This interest stimulated the present study. In this paper, no attempt has been made to simulate any field production characteristics exactly. Only the solution-gas-drive mechanism has been investigated, and production by liquid expansion has not been considered. This investigation is exploratory in nature but does give some insight into the problems of spacing and proration in a solution-gas-drive field having permeability variations. THE MATHEMATICAL MODEL The mathematical model is similar to that proposed by West, Garvin and Sheldon.' Approximately the same techniques have been used in arriving at a solution. The equations are nonlinear, partial differential equations which have been known for some time. The particular equations used for this study neglect the effects of capillary pressure and gravitational forces. The advent of modern digital computing equipment has made their solution practical. Basically, the method solves for pressure, saturations, and oil and gas flow rates as a function of distance and time. In our model, distance to the

By T. L. Joseph

A study is made of the amount of solution loss necessary to maintain the reducing power of the gas stream in the blast furnace. Curves are presented to show the effect of solution loss, moisture in the blast, and carbon dioxide from the flux on the nitrogen in the THE blast furnace process is based upon the counter flow of gases and solids. As CO, N, and H, flow upward from the combustion zones, oxygen is acquired from the descending charge. In the reduction of iron ore, a portion of CO is converted to CO, and similarly a portion of H, is converted to water vapor. The inert N,, from the air used in combustion, passes through the furnace with little change. Its concentration is, however, decreased by reactions such as direct reduction and solution loss which increase the volume of CO in the gas stream; Similarly the evolution of C02 from the limestone also dilutes the nitrogen. he purpose of this paper is to illustrate an idealized and simplified method of studying furnace processes by following changes in the gas phase between the tuyeres and the stock line. A more specific objective is to evaluate the effect of solution loss upon the CO/CO, ratio in that region of the furnace in which FeO is reduced to metallic iron. This last stage of reduction requires relatively high CO/CO, ratios to exceed the equilibrium requirements. Solution loss or the reaction of COZ with C to produce CO has a pronounced effect upon the ratio of the carbon gases and is necessary to maintain the reducing power of the gas stream if the consumption of coke is low. It will be explained later that indirect reduction followed by solution loss is stoichiometri-cally equivalent to direct reduction. Calculations will be made to show how the composition of the gas in the region of the mantle varies with coke consumption and with different amounts of solution loss. Such calculations show the condi- tions under which gasification of C with oxygen in the charge is needed to maintain the reducing power of the gas. Equilibrium conditions for FeO and the carbon gases will be used to establish a minimum CO/CO, ratio below which reduction will not proceed. The manner in which carbon is gasified in the furnace, at the tuyeres with oxygen in the air or above the tuyeres with oxygen from the charge, will be a basic feature of all calculations. It is hoped that greater interest in the use of top gas as a means of following furnace reactions will be aroused by the calculations and generalized curves which are presented. Bosh Gas Equations Subject to some alteration by the amount of moisture in the blast and by direct reduction, the gas leaving the combustion zones of a blast furnace has a definite composition. Because a relatively small amount of oxygen is acquired from the charge in the bosh and in the crucible, the products of combustion undergo little change until they enter the shaft. Bosh gas is, therefore, essentially the products of combustion of carbon in a deep fuel bed with air. The relative weights and volumes of reacting materials are expressed by the equation: 2~ + 0? + 3.76N, = 2C0 $ 3.76NZ [I] Air Bosh Gas -air = 79% N? = 3.76) 21% 02 Starting with a known mass of C consumed largely by air, Eq 1, but partly by water vapor, Eq 2, the volume and C + H2O = CO $ H? [21 composition of the bosh gas can be calculated and subsequent changes followed as reactions take place at various elevations in the furnace. As shown in

Jan 1, 1952

By H. E. Cline

Mechanical properties of the eutectic between CoAl and cobalt were measured over a range of- temnperatures and strain rates for a variety of microstructures produced by directional solidification and by thermo-mechanical processing. Directional solidification led to rodlike, lamellar, and irregular microstructures. The unusually high volume fraction of the cobalt-rich rods and the lurge spacing of the rods were explained by the phase diagram. The hot-worked structure consisted of fibers of COAL in a cobalt-rich matrix. The roonl- tevlperature strength of the uvrought material increased with decreasing grain size but the 1000°C strength decreased with decreasing pain size. At high temperatures the directionally solidified tnaterial was stronger and less strain-rate-sensitice than the hot-rolled material. The fine-grained hot-worked ma-terial became superplastic at high temperatures, with tensile elongations greater than 850 pct, while at root temperature this material was ductile and impact-resistant because of the ductile matrix. Fracture occurred in the directionally solidified material at elevated temperatures by inter phase separation and at roorn temperature by cracks in the intermetallic phase. Growth of these cracks was impeded by the ductile cobalt-rich phase. It was found that the CoAl intermetallic remains ordered at elevated temperatures. DIRECTIONAL solidification of eutectic alloys has been used to produce structures consisting of parallel rods or lamellae. Although the spacing of the phases depends on the growth rate, it has been observed to be of the order of 1 µ in many eutectics. A strong intermetallic phase has been used to reinforce a ductile matrix in the rod eutectic A1-Al3Ni and the lamellar eutectic Al-Al2cu.1 The microstructure of the eutectics A1-A13Ni and A1-A12Cu remained aligned after samples of these alloys were exposed to temperatures just below their melting points for long times. Stability of the microstructure at elevated temperatures makes directionally solidified eutectics a candidate for high-temperature applications. Recently Thompson4 has developed the Ni-NiMo eutectic containing 40 pct NiMo lamellae, giving a tensile strength superior to nickel-base superalloys. Unfortunately, this eutectic oxidizes rapidly at elevated temperatures. By mechanically processing a two-phase structure, one may reach strengths as high as 700,000 psi, as demonstrated by drawn pearlite.5 In this case the strengthening mechanism was thought to be related to the fine substructure formed during deformation.5 However, a heavily worked structure may recrystallize and coarsen at elevated temperatures. Some worked eutectics such as Al-Al2Cu,6 Pb-Sn,7 and Sn-Bi7 have shown unusually large elongations in tension when tested at elevated temperatures. This phenomenon of large extension, called "superplasticity", was related to the fine grain size of wrought two-phase alloys at elevated temperatures. A mode of deformation of "superplastic" material has been shown to be grain boundary sliding,' which has also been observed during creep of polycrystalline materials.9 The Co-A1 system was chosen for this investigation after examining the phase diagrams of binary eutectics." The high melting point of 1400°C, the aluminum content which was expected to give oxidation resistance, and the properties of the intermetallic CoAl were the chief factors influencing this choice. This eutectic consists of a mixture of the intermetallic CoAl and a cobalt-rich solid solution. The intermetallic CoAl has a large range of solubility and a CsCl structure." From the similarity between CoAl and NiAl one would expect CoAl to be ordered at elevated temperatures; however, specific heat measurements" show a transition at 800°C. West-brookL2 has measured the hot hardness of CoAl and found a rapid decrease in hardness above 600°C. The tensile properties and stress rupture properties of as-cast CoAl-Co eutectic were measured by Ashbrook and wallace13 who report a room-temperature tensile elongation of less than 1 pct. I) EXPERIMENTAL A) Sample Preparation. Experimental materials were prepared by directional solidification, by hot working, and by powder processing. The starting materials were electrolytic 99.9 pct pure cobalt and 99.99 pct pure aluminum. 1) Directional Solidification. A vertical Bridgman apparatus heated by induction was used to directionally solidify cylindrical ingots $ in. in diam and 5 in. long. The apparatus was first evacuated and then an argon atmosphere was introduced to retard evaporation. The ingots were contained in an alumina crucible inside a graphite susceptor that rested on a movable water-cooled base. The base was lowered out of the induction coil at a constant rate. Eight of the ingots were solidified using a drive rate of 2.5 cm per hr, two of the ingots at 1.2 cm per hr, and one ingot at 10 cm per hr. The eutectic composition Co 10 wt pct A1 was used in all but one ingot which had the composition of the stoichiometric CoAl intermetallic, Co 32 wt pct Al. 2) Mechanical Processing. At 1000°C the eutectic Co 10 wt pct A1 is a mixture of an intermetallic phase, Co 21 wt pct Al, and a cobalt-rich phase, Co 5 wt pct Al.10 These phases differ from the stoichiometric CO 32 wt pct A1 and pure cobalt because of the large solubility of this eutectic at elevated temperatures." Four rectangular slab ingots, 4 by 1 by 12 in. high, of Co 10 wt pct Al, Co 5 wt pct Al, Co 21 wt pct Al, and Co 32 wt pct A1 were cast for hot rolling. The cobalt was first vacuum-melted, H2-treated for 20 min,

Jan 1, 1968

By J. J. Scott

This investigation utilizes three dimensional photo-elastic techniques to determine the stress distributions in the pillars and the roof of a room and pillar mine model. Castolite plastic was used for the construction of the model in which a stress pattern was developed by the stress freezing process. Analysis of the stress pattern was accomplished by observation of points in slices from the model with a polariscope and solving the data thus obtained by the shear-difference method. Slices through the centerline, edge of pillar and centerline of span were investigated. The results of this work provide information on the overall stress distribution in points of stress concentration in compression, shear and tension, show relative magnitude of stress throughout the model and indicate directions of the most important stress values. A generalized roof bolt pattern is developed for room and pillar mines based on the stress distribution. A digital computer was used in the reduction of data and proved to be extremely useful for investigation of this type. Underground excavations disturb the equilibrium of the earth's crust and a core of fracture, or altered stress distributions exists around the openings. This fact is well known by mining operators and investigators in the rock mechanics field. Analysis of the stress distribution in the areas around mine workings is a most difficult problem and one which has no simple and direct solution. Some of the approaches used by investigators in attempts to study stress distribution around mine openings involve mathematical analysis, photoelastic techniques, statistical analysis, model studies on brittle materials and observation of fracture patterns. Models involving imbedded strain gauges, gelatin models using imbedded strings to show internal movement, and many other unique laboratory techniques are employed. Work is also being done in mining operations where load cells, strain gauges, photostress material, convergence plugs, dynamic plugs, etc., are used to measure strain which can in turn be used to obtain stress. Some of these devices measure strain from which stress may be derived. All approaches to the solution of stress distribution are hampered by the fact that the earth is not a homogeneous, isotropic and elastic media. Geologic faults, fractures, bedding planes, vugs, variations in material composition, variations in grain size and structure, etc., make it extremely difficult to obtain results which can be universally applied to mining operations. The purpose of this investigation will be to demonstrate the use of three-dimensional photoelastic techniques to obtain the stress distribution in the pillars and roof of a room and pillar mining operation. This method utilizes full analysis of interior points, and thus it may be that small tensile or shear stresses found in the investigation will prove to be of greater significance than the more obvious points of stress concentration found by two-dimensional techniques. A digital computer was employed to simplify and to shorten the time necessary to obtain final results. Application of the computer to problems of this type may enable future investigators to attempt more elaborate analyses than have been previously considered feasible. THEORY Three Dimensional Stress Analysis-Shear Difference Solution:' Photoelastic studies are based on the fact that an optically isotropic transparent solid becomes optically anisotropic when subjected to forced deformation; the degree of optical anisotropy being proportional to the deformation of the material. There are two fundamental laws which govern photoelasticity: 1) Light is polarized in the directions of the principal stress axes, and is transmitted only on planes of principal stress. 2) The difference in principal stresses is proportional to the difference in the indices of refraction along the planes of principal stress. One method used in three-dimensional photoelastic work is to examine a slice of the object by normal incidence and oblique incidence. In normal incidence,

Jan 1, 1964

Institute of Metals Division Iron and Steel Division Extractive Metallurgy Division Council A W Thornton (ISD), Chairman, R W Shearman, Secretary, C S Barrett (IMD), J C Kinnear, Jr (EMD), John Chipman (ISD), J S Smart, Jr (IMD), A W Schlechten (EMD), M E Volin (MED), D S Eppelsheimer (MIED) Journal of Metals Editorial Advisory Committee J S Smart, Jr, Chairman, W A Dean, J J Golden,T D Jones, Evan Just, J C Kinnear, Jr, M Tenenbaum Pacific Northwest Regional Conference E R Marble, General Chairman, Marshall Huntting, Assistant General Chairman, W C Douglass, Mining Chairman, H C Hughes, Mining Chairman for British Columbia, W C Douglass, Mining Chair¬man for United States, Paul Billingsley, Geology Chairman, W D Nesbeitt, Miner¬als Beneficiation Chairman, H D Kelley, Industrial Minerals Chairman, J G Johnston, Metals Chairman, Lloyd Banning, Iron and Steel Chairman, W G Rouillard, Extractive Metallurgy Chairman, E C Roberts, Physical Metallurgy Chairman, D A Pifer, Mineral Industry Education Chairman, Frederick Brien, General Arrangements Chairman Metals Branch Membership Committee C M Squarcy, Chairman, R C Cole, Harold Mar¬golin, M E Nickel, S K Scovil Bylaws Committee A W Thornton, Chairman, W R Hibbard, Jr, J S Smart, Jr (IMD), John Chipman, T S Washburn (ISD), T D Jones, J D Sullivan (EMD)

Jan 1, 1956

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division Council R R McNaughton, Chairman (EMD), Ernest O Kirkendall, Secretary, J H Scaff, (IMD), Morris Cohen, (IMD), T J McLoughlin, (ISD), J S Marsh, (ISD), P T Stroup, (EMD), R D Parks, (MED), D S Eppelsheimer, (MIED) Journal of Metals Editorial Advisory Committee J S Smart, Jr, Chairman, W A Dean, T D Jones, Evan Just, J C Kinnear, Jr, J S Marsh, M Tenenbaum Pacific Northwest Regional Meeting F X Cappa, General Chairman, W W Wiltschko, Chairman (Metals Branch), Program Chairmen H E Lee (EMD), S E Maddigan (IMD), G R Heffernan (ISD), L C Richards (Ind Min Div), James Bell (Finance Committee), Ed Vestica (Registration), Donald Johnson (Special Events)

Jan 1, 1954

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