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By David R. Poirier

Activity data of carbon as a function of both temperature and composition throughout the stable austenite range is correlated by mearts of an equation derived from a quasi-chemical model. The carbon activity data of austmite for temperatures between 800° and 1200°C are utilized in conjunction with the activity of carbon calculated for the y solidus using the activity of carbon in liquid iron and published austenite-liquid equilibria. The results agree very well with Chip-man's correlation; however, a small difference in the activity of carbon in the high-temperature range of the austenite field is evident. Excellent agreement is found for the heat of solution of graphite in infinitely dilute austenite; from this study the value is 10,550 cal as compared with Chipman's value of 10,680 cal. AS part of a program to study microsegregation in dendritic solidification of ternary Fe-C-Cr alloys, it was desirable to be able to describe the equilibria between austenite and liquid iron in Fe-C-Cr alloys. In this regard, it was necessary to correlate existing data on the activity of carbon in Fe-C austenite as a function of both temperature and composition. At that time, Chipman's analysis1 of the thermodynamics of binary Fe-C austenite was not available. It will be shown that this study and Chipman's study agree rather well throughout the stable austenite range of temperature and composition; however, some small differences appear at temperatures greater than the eutectic temperature. Benz and Elliott 2 presented isoactivity lines for austenite superimposed on their revised Fe-C phase diagram. Using an expression from Darken and Gury 3 representing Smith's4 activity data between 800" and 1000°C, they found that the activities extrapolated above 1000°C to the solidus did not agree with the activities determined from the corresponding liquidus compositions. It is the purpose of the following argument to reconcile carbon activity data of austenite with the activity in liquid Fe-C alloys as determined by Rist and Chipman. 5 In addition, a simple analytical expression is sought for computational convenience. ACTIVITY DATA OF CARBON IN ZRON Fig. 1 shows the activity of carbon in Fe-C austenite as determined by Smith, 4 Schenck and Kaiser, 6 Scheil et a1.,7 and Bungardt et al.' The lines are merely drawn to separate the data into the respective isotherms. These data are inadequate to determine the activity of carbon at temperatures greater than 1200°C. The activity coefficient in Fe-C liquid alloys was assumed by Rist and chipmans to obey the following

Jan 1, 1969

By J. W. Rutter, K. T. Aust

Competitive growth of recrystallized grains into striated single crystals of zone-refined lead produced preferred orientations of the coincidence type after annealing at 175°C, but not at 300°C. This preferred orientation development was found to result from the higher mobility and lower energy of large -angle coincidence boundaries compared to large-angle noncoincidence boundaries. These mobility and energy difference provide a useful basis for explaining many cases of preferred orientation observed in annealed metals. DURING a study1 of the mobility of grain boundaries in zone refined lead, it was observed that the temperature dependence of the grain boundary migration rate is smaller for large-angle, coincidence-type grain boundaries than for large-angle noncoincidence ("random") boundaries. This observation is illustrated schematically in Fig. 1, which shows log rate of grain boundary migration vs reciprocal absolute temperature for two large-angle boundaries. The upper curve refers to a coincidence-type boundary of the sort discussed by Kronberg and Wilson.2 While the mobilities of these two boundaries are similar at 300°C, the coincidence-type boundary has a greater mobility, by a factor of about: four, at 175°C than does the noncoincidence boundary illustrated in the lower curve. The observation described above suggested a simple experiment for testing the role of grain boundary mobility in the development of preferred orientation in annealed, high-purity lead. On the basis of this observation, it would be expected that if a large number of grains of different orientations are growing competitively, and if relative grain boundary mobility is a controlling factor, then the specimen procluced by boundary migration will contain crystals having random orientations if annealing is done at 300°C, while preferred orientations of

Jan 1, 1962

By Herbert Banks Johnson

DURING the past 10 or 12 years very little information has been made generally available concerning the commercial possibilities of separating materials by means of static electricity; and yet during that same period important improvements have been made in various branches of the science of electricity, which, when taken together, and applied to electrostatic separation, have resulted in important improvements in that art as well. For example, much improvement has been made in high-voltage electrical equipment such as full-wave vacuum-tube rectification and improved mechanical rectification. Great strides have likewise been made in the development of insulators for high-voltage work, not only in the materials used but also in the design of the insulators themselves. Again, in another field, the development of air-conditioning equipment has improved the technique of controlling the surface condition, through drying or humidifying, of the various materials that are passed through the electrostatic separator. In many authoritative publications and textbooks, the electrostatic separation process is declared to require a balance far too sensitive for general commercial application. For example, one publication1 in the past has referred to an unfavorable effect on the process caused by varying atmospheric conditions such as humidity. Some2 have even gone so far as to state that sunlight and shadows may seriously affect the separating efficiency of the process. Such statements may have been true in the early development of the art, when the source of static electricity was derived from a friction disk machine, such as the Wimshurst. The Blake Mosher equipment and the work of Huff in applying motor- generator sets, transformers and mechanical rectification overcame much of this kind of objection to the commercial application of the electrostatic separating process. Another objection made periodically is that it is generally considered necessary to feed the particles into the electrostatic field in a stream that

Jan 1, 1938

W. Morton Webb, Germiston, Transvaal, South Africa (communication to the Secretary*):—The experience of Mr. Boeh-mer in the Leadville district and his reputation as an engineer assure the interest of anything he may write on the ore-bodies of that district; and all engineers who have operated in Leadville will agree that the theory of the origin of the Leadville deposits, as given by Mr. Emmons in his famous monograph, does not adequately explain the genesis of all the deposits. The solutiou of the problem does not, however, appear to be quite so simple as Mr. Boehmer would make it; and the advance pamphlet issued by the U. S. Geological Survey, pending the completion of the main report, shows that there is still much ground for controversy. No doubt the later eruptive0 had a greater influence on the deposition of the ore-bodies than was thought at the time of the first investigation by the Survey; but it has always appeared to me that the influence exerted by these dikes mas more in the nature of a physical than a chemical one. The weight of evidence in recent years is mostly in the direction of ascension rather than lateral secretion; and one of the strongest evidences is the fact that most of the ore-bodies lie under one of the comparatively impervious layers which help to make up the structure of these hills.

Jan 1, 1911

By M. A. Childers

Recent work with controlled laboratory tests.' field experience and a new analytical approach indicate that casing centralization, pipe movement and relative rheological properties between the mud and cement (yield point and density) are the three controlling factors in successfu1 primary cementing of dual casing. Turbulent flow has been demonstrated to be unnecessary under the severe displace ment conditions of parallel dual strings of casing. Simultaneous reciprocation of dual casing in directionally drilled boreholes is highly dependent on centralization and on the rapid initiation of pipe movement once the casing has been run to total depth. Successful cementing of 30 out of 32 dual, 3%-in casing wells substantiated these conclusions. A review of 15 dual, 3 1/2-in. casing wells completed prior to the adoption of these principles disclosed only one success. Mathematical and graphical techniques permit the engineer to analyze and anticipate the success or failure of a cementing operation. Standoff, mud displacement and reciprocation can be analyzed mathematically and planned in deep, directional or straight boreholes by review of annular geometry, relative rheological properties between the mud and cement, and forces caused by caring weight, functional drag and differential sticking. Introduction The objective in primary cementing is to displace the drilling fluid with cement that will bond to the formation and casing to prevent communication through the annulus. The predominant cause of failure appears to be channels of gelled mud that remain in the annulus after cementing.1 '* Past investigations have noted many procedures that could improve the displacement process.2-' These procedures include centralization, chemical preflushes, mechanical mud cake removers, controlled flow rates in certain regimes, pipe movement an1 control of mud and cement properties. Not until recently have the effects of many of these procedures been isolated so that their individual importance could be determined. In a recent paper,' a comprehensive and analytical laboratory study of various factors controlling the displacement process concluded that there are three major factors in obtaining complete mud displacement by the cement slurry. 1. Good relative rheological properties between the mud and cement. The cement should be heavier and have a yield point and plastic viscosity higher than the mud being displaced. Buoyancy forces often can dominate the displacement process. 2. High degree of standoff or centralization. The more centered the casing, the greater the likelihood of complete mud displacement and removal. 3. Pipe movement obtained by rotation or reciprocation. Often unfavorable rheological properties between the mud and cement, and poor standoff can be compensated by pipe movement. This work demonstrates the compatibility of the latter concepts with field results extended to the more severe dual casing displacement process. Early Experience With Dual 3'/t-In. Primary Cementing Early slim casing completions in the West Delta Block 73 field, offshore Louisiana, included 17 dual 3%-in., 3 single 3% -in. and 1 dual 2% -in. casing installations. Table I provides data on these earlier wells. Usually, common Class A cement was placed across the pay zone and 12 percent gel cement was placed to a height of 500 ft above the highest productive sand. Centralizers (6%-in. OD maximum expansion) were placed two or three per joint on both casing strings from total depth through the completion intervals and at least one per joint for the remainder of the cement sheath. A number of techniques and procedures were attempted to improve cementing success. Casing was run simultaneously or separately with a number of mud conditioning and circulating techniques. Mechanical aids such as cement bonders, slmiding sleeves, turbulizers and various sizes and strengths of centralizers were used. Common and gel cements were mixed with fresh or sea water with a number of different additives to control retardation and dispersion. Cements were thinned and mixed at high rates to try to induce turbulent flow in the annulus. On one well the "slow flow" method was used." Perforating was accomplished with a jet orienting gun. Unsuccessful cement jobs were indicated by production of extraneous fluids or by pressure communication between zones. On test, five wells flowed water, four flowed sand and six had pressure communication with the other string or the 10%-in. casing. A total of 25 remedial squeeze ce-

Jan 1, 1969

By Donald L. Katz, Leo B. Bicher

A correlation is presented for predicting the viscosities of light paraffin hydrocarbon mixtures such as natural gases for temperatures from o° to 4o0°F. and for pressures fro1 atmospheric to I0,000 lb. per sq. in. The correlation is based on the viscosity data for the methane-propane system and requires only a knowledge of the molecular weight of the naturaI gas. The viscosities of natural gases reported in the literature up to 2500 lb. were reproduced by the correlation with an average deviation of 5.8 per cent. Introduction The viscosity of a natural gas is required whenever calculations are made of the pressure drop that occurs while the gas flows through pipes or porous media. Methods of predicting the viscosities of gases at the present operating pressures are not available. This paper presents a simple method of predicting the viscosity of a natural gas in the single-phase region from its molecular weight, temperature, and pressure. Viscosity oF Methane-propane Mixtures The viscosity of methane, propane, and four of their binary mixtures, 20,40, 60, and 80 mol per cent, have been determined for pressures from 400 to 5000 lb. per sq. in. and temperatures from 77" to 437 F., with an experimental accuracy of 3.2 per cent.2 The apparatus used in the investigation was a modification of that employed in previous studiesaJ4 on the viscosity of normal paraffin hydrocarbons. It consists of a viscosimeter of the rolling-ball, inclined-tube type,5>k7 with auxiliary equipment for making up and charging binary mixtures into the viscosimeter.~ The viscosity data on the methane-propane mixtures have been plotted as a function of molecular weight with lines of constant pressure, charts of constant temperature in Figs. I to 3. These charts are extrapolated at temperatures below 77°F. and at pressures above 5000 lb. per sq. inch. Prediction OF Viscosity from Molecular Weight of a NaturaI. Gas At atmospheric pressure the viscosity of light hydrocarbon gases increased with increased temperature, contrary to the change of viscosity of liquids with temperature. The atmospheric viscosities of the normal paraffin hydrocarbons have been determincd by several investiga-tors 3,4,9,10,12,15,16,17,19 and are plotted in Fig. 4 as a function of molecular weight, with extrapolation to 896'F. and to 220 molecular weight. Data for isopentane and normal pentane show less than 2 per cent difference in viscosity, indicating that Fig. 4 can be used for isomeric parafin hydrocarbons with an accuracy of approximately 2 per cent. Trautz and Sorg'7 determined the atmospheric viscosities 01 methane-propane mixtures and showed that they are proportional to the molecular weight. The viscosities of these mixtures

Jan 1, 1944

By Leo B. Bicher, Donald L. Katz

A correlation is presented for predicting the viscosities of light paraffin hydrocarbon mixtures such as natural gases for temperatures from o° to 4o0°F. and for pressures fro1 atmospheric to I0,000 lb. per sq. in. The correlation is based on the viscosity data for the methane-propane system and requires only a knowledge of the molecular weight of the naturaI gas. The viscosities of natural gases reported in the literature up to 2500 lb. were reproduced by the correlation with an average deviation of 5.8 per cent. Introduction The viscosity of a natural gas is required whenever calculations are made of the pressure drop that occurs while the gas flows through pipes or porous media. Methods of predicting the viscosities of gases at the present operating pressures are not available. This paper presents a simple method of predicting the viscosity of a natural gas in the single-phase region from its molecular weight, temperature, and pressure. Viscosity oF Methane-propane Mixtures The viscosity of methane, propane, and four of their binary mixtures, 20,40, 60, and 80 mol per cent, have been determined for pressures from 400 to 5000 lb. per sq. in. and temperatures from 77" to 437 F., with an experimental accuracy of 3.2 per cent.2 The apparatus used in the investigation was a modification of that employed in previous studiesaJ4 on the viscosity of normal paraffin hydrocarbons. It consists of a viscosimeter of the rolling-ball, inclined-tube type,5>k7 with auxiliary equipment for making up and charging binary mixtures into the viscosimeter.~ The viscosity data on the methane-propane mixtures have been plotted as a function of molecular weight with lines of constant pressure, charts of constant temperature in Figs. I to 3. These charts are extrapolated at temperatures below 77°F. and at pressures above 5000 lb. per sq. inch. Prediction OF Viscosity from Molecular Weight of a NaturaI. Gas At atmospheric pressure the viscosity of light hydrocarbon gases increased with increased temperature, contrary to the change of viscosity of liquids with temperature. The atmospheric viscosities of the normal paraffin hydrocarbons have been determincd by several investiga-tors 3,4,9,10,12,15,16,17,19 and are plotted in Fig. 4 as a function of molecular weight, with extrapolation to 896'F. and to 220 molecular weight. Data for isopentane and normal pentane show less than 2 per cent difference in viscosity, indicating that Fig. 4 can be used for isomeric parafin hydrocarbons with an accuracy of approximately 2 per cent. Trautz and Sorg'7 determined the atmospheric viscosities 01 methane-propane mixtures and showed that they are proportional to the molecular weight. The viscosities of these mixtures

Jan 1, 1944

By J. G. Richardson, F. M. Perkins

Results and procedures are pre-cented covering a laboratory investigation of the effect of rate of water advance on the displacement of oil from clean water-wet sands. The experiments included water floods at atmospheric pressure with and without gas present over a range of flow rates from reservoir rates to rates ten thousand-fold higher. Water floods were also conducted at various rates at elevated pressure with no gas present. Other tests were made at elevated pressures by forming a free gas saturation by evolution of gas from solution in the oil before water flooding. Recovery of oil was found to be independent of the rate of water advance with or without gas present and independent of the pressure level of the water flood. A dimensionally-scaled model of a reservoir composed of a thick uniform sand was used to study the effect of rate on the tendency of water to underrun the oil because of the greater density of the water. Another model was used to study the effect of rate on the tendency of water to channel down the more permeable sand in a stratified reservoir composed of sands of diffierent per-meability in intimate contact. The effect of the presence of gas on the flooding conformance was studied with both models. The results obtained using these simple models provide a basis for predicting behavior in more complicated systems. INTRODUCTION In spite of the great amount of research on the flow of fluids in porous rocks, there still exists some disagreement as to the influence of the rate of water advance on the displacement of oil by water flooding. Various investigators have found that increasing the rate of water injection would decrease, increase, or have no effect on recovery of oil. One reason for this disagreement has been a lack of understanding of the effects of the capillary forces which influence the results obtained in the laboratory at low rates with short columns. Other causes of the disagreement have undoubtedly been inconstancy and uncertainty of the wetting properties of the porous media studied, inaccurate saturation determinations, and in some instances conclusions based on insufficient data. Capillary forces are involved in the displacement of oil by water in two ways. On the microscopic scale, the capillary forces control the dis- tribution of oil and water in the pore spaces of the sand. The magnitude of these forces is governed by the preference of the sand to be wet by water, the pore sizes and geometrical shapes, and the interfacial tension between the water and oil. On the macroscopic scale, differences in saturation at the flooding "front" when water displaces oil result in capillary pressure gradients. These gradients cause water to flow preferentially ahead of the front. In short laboratory columns at low rates, the front can span the entire column length. Also, at the outflow boundary the preference of sand to be wetted by water results in retention of water and a high water saturation in the region of the outflow face. This effect is commonly called the boundary effect.' The capillary pressure gradients which complicate the interpretation of flooding performance of short laboratory columns at low rates of water advance become negligibly small under certain conditions. The conditions where capillary pressure gradients are negligible are in long, homogeneous reservoir sands,' at high rates of water advance in short laboratory columns,3 and at any rate in laboratory columns as the residual oil saturation is approached. Thus, laboratory water floods, conducted

Jan 1, 1958

By R. G. Carlson, F. E. Westermann

HOT pressing of powder particles has gained importance recently, since it affords a method in which high densities are rapidly attained. In a recent study on hot pressing of alumina powders, Mangsen, Lam-bertson, and Best1 have shown within the limits of their experiment, the validity the rate equation for densification in hot pressing, originally proposed by Murray, Livey, and Williams.2 i.e., where D = fraction of theoretical density, t = time, P = pressure and 77 is the viscosity, all in appropriate units. This equation was derived from earlier work of Shuttleworth and Mackenzie3 which is based on the closing of spherical pores under the action of surface tension. The integrated form of this equation yields a straight-line relation between log (1 - D) and t. Such conditions were found by Felten4 to be true only after extended periods of pressing. In an endeavor to quantitatively evaluate the exactitude of this equation in the initial sintering stage, i.e., prior to sealing of the pores, spherical anti-

Jan 1, 1962

By J. W. Hickman

INTRODUCTION RECENT work by the authors1 on the oxide films formed on alloys of titanium and zirconium with nickel and copper indicated that an investigation of the oxides which form on alloys of copper and nickel might permit the relative rates of formation and diffusion of the ions of. these metals to be determined. This binary system is of further interest since the alloys which form are of the solid solution-type over-the entire range. In addition nickel is much more oxidation resistant than copper. A comparison of the free energies of formation of the simple oxides which may occur on these alloys indicates that nickel oxide should be observed over the entire time and temperature ranges of oxidation for all alloy compositions.1 In. order for nickel oxide to predominate on the surface, it is necessary that nickel ions form and diffuse to the surface. Two factors which may influence the formation of nickel oxide may be the ionic sizes, where Cu+ is 0.96Å and Ni-++ is 0.70Å, and the charges on the ions. On the basis of size, Ni++ should diffuse more readily than Cu+ while on the basis of charge, Cu+ should form more readily than Ni++. According to Uhlig2 passivity to corrosion in an alloy appears at a critical composition which for copper-nickel alloys is related to the tendency of the d band of electronic energy states to fill with electrons. This composition in the copper-nickel alloys corresponds to 40 at. Pct nickel at which composition Uhlig2 (quoting La Que's data) states that the alloy system becomes passive. Magnetic and specific heat data indicate that the d band of copper-nickel alloys is filled at 6o at. pct copper or 4o at. pct nickel. Mott and Jones3 have shown that if, on alloying nickel with copper, one considers a copper atom to be identical with a nickel atom except for an extra electron (nickel -has the-configuration: 3d8 4s2 and copper: 3 d10 4s) then at 60 at. pct copper or 4o at. pct nickel enough electrons are contributed by copper to fill the d band of the alloy. At this composition the magnetic susceptibility approximates zero according to Grew.4 Although the electron diffraction data will not determine the rates of the several reactions which may occur during oxidation, yet a determination of the structures of the surface oxides may yield information concerning the relationships, if any, which may' exist between the oxide structures which form and that composition where the magnetic susceptibility approximates zero. It is quite possible, of course, that the mechanisms of the oxidation and corrosion reactions may be so widely different that no correlations between them may be possible. SURVEY OF LITERATURE The metals, copper and nickel, which are face-centered cubic, form solid solution alloys which are face-centered cubic with no superstructure for all compositions. Three oxides of nickel have been investigated structurally by X ray diffraction. Of

Jan 1, 1948

By Toshihisa Adachi, Shosei Serata, Shunsuke Sakurai

The present state of knowledge of three-dimensional rock properties does not provide an adequate basis for evaluating the safety of under- ground structures in situ. Most of the triaxial studies reported in the past have dealt with crushing strength, but have failed to consider the intergranular behavior and triaxial strain state of rocks. Without this information, the structural competence of rocks cannot be accurately assessed. The absolute three-dimensional testing method (ATT) was conceived for the purpose of analyzing the three-dimensional states of stresses and strains in aggregate rocks under conditions commonly encountered in underground structures. In-situ stress-strain states are not simple, even in the simplest possible form of opening, excavated in a homogeneous and isotropic rock medium. In general, there are four basic stress-strain states which are present in underground openings, regardless of the complexity of their geological conditions. They are the yielded, brittle-fractured, stress-relieved, stress-concentrated states, as illustrated in the schematic diagram, Fig. 1. The ATT machine was designed to create and study all these states in the laboratory. A theory describing the aggregate behavior of rocks under these diversified states is essential to evaluate the safety of underground structures. The Griffith theory is limited to tensile failure of ductile materials and therefore does not apply to behavior of aggregate rocks under compression. The Griffith theory also fails to consider the grain boundary characteristics of aggregates, which is the determining factor of rock behavior. The Mohr-Coulomb theory of failure ignores the importance of the intergranular behavior of rocks. An application of the continuum theory to

Jan 1, 1972

By H. A. Kendall, W. C. Goins

Several investigations in recent years have shown that drilling rates are increased significantly with increased hydraulic horsepower. But, there has been no over-all method of designing jet-bit programs that efficiently uses the surface power. A study of present practices indicates that frequently as little as 50 per cent of the possible effects at the bit are used. Some observers have indicated that the best utilization of hydraulic horsepower (maximum effect on drilling rate) occurs when the bit hydraulic horsepower is maximum; others have stated that jet impact force is more important, and others have believed that maximum jet velocity is required. Limited efforts to date have shown some optimum conditions for bit hydraulic horsepower and impact, but these conditions cannot exist during drilling of a large part of the hole and do not provide a basis for designing a complete jet-bit program. This paper shows the maximum obtainable bit horsepower, impact force and jet velocity at all depths, taking into account the limitations of the pump, piping, hole and minimum circulating rate for adequate cuttings removal. Ranges of operation are developed; and flow rates, surface pressure and bit pressures are specified for each range to provide a maximum of any one of the desired effects. It also is shown that, by proper selection of nozzle sizes and by following the rules presented, the maximum obtainable quantities can be effectively utilized from surface to total depth. Finally, a simple graphical method of selecting nozzle sizes and flow rates is presented which can be used with familiar bit-company hydraulic tables and calculators to design jet-bit programs for maximum bit hydraulic horsepower, impact or jet velocity, as desired. These programs make most effective use of the pumps. Heretofore, there was no method available for designing field tests which adequately separated the effects of bit horsepower, impact and jet velocity. The programs and procedures developed in the paper are dissimilar and, when used in future field testing, should demonstrate which program is the most important in obtaining the fastest drilling rate. INTRODUCTION During the past decade, rig hydraulics has come into increasing prominence. There has been a definite trend toward providing higher horsepower pumps, jet-type bits have had increased use, numerous investigators"" have reported increased drilling rates as a result of increased hydraulics, and bit manufacturers have provided tablesa-" and calculators that are now commonly used 10 design jet-bit programs. Opinion has varied as to the hydraulic quantity which has the great- est effect on drilling rate. Papers and data have been presented that show pump horsepower,'9 it hydraulic horsepower and jet impact force,' each to be the most significant factor affecting drilling rate. Examinatibn of jet-bit programs of the bit companies indicates emphasis on jet velocity. Only pump horsepower can be eliminated because it can be used to produce any one of the bit effects which, a priori, must be more relevant factors. This contradictory state of opinion and practice regarding the bit effects is unfortunate, but several published references have been concerned with making one or another of the factors maximum; and, because these in each case have given results applicable to only intervals of the hole drilled, there seems to be ample reason to complete the previous efforts. It also is believed that the differences in programs for each effect, where they exist, should be delineated so that future use may determine which hydraulic effect is the more relevant. It is the purpose of this paper to: (1) show the theoretical maximum bit hydraulic horsepower, jet impact force and jet velocity available at all depths, taking into consideration all necessary restrictions on operating conditions; (2) illustrate procedures by which the maximum available horsepower, impact force or veIocity may be obtained; and (3) present a graphical method for rapid selection of jet-nozzle sizes and flow rates to be used with conventional procedures to design jet-bit programs for maximum bit horsepower, impact force or velocity as desired.

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,' there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By Pol Duwez, Spencer R. Baen

A LTHOUGH the practical importance of Fe-Cr--iV Mo alloys has long been recognized, constitution studies have been limited to a few alloys within rather narrow ranges of composition. The purpose of the present study was to establish the phase boundaries in the ternary diagram at a temperature of 1200°F (650°C).* The identification of phases and the determination of phase boundaries were based primarily on X-ray diffraction measurements and occasionally on microscopic observation. The methods used for locating the phase boundaries were essentially those described in detail by Andersen and Jette,' and by others.', The compositions of 180 alloys, prepared by powder metallurgy techniques, are shown in Fig. 1. The chemical analysis and mesh size of the powders which were used for the preparation of the alloys are given in Table I. The powders were mixed for 48 hr or longer, then compacted under 80,000 psi in a %-in. diam steel die. Each specimen weighed approximately 5 g. The compacts were sintered for 4 hr at 2500°F (1371°C) in an atmosphere of pure dry hydrogen (dew point near the temperature of liquid nitrogen). An open tray of chromium powder was placed upstream of the compacts to act as a "getter" for the last traces of oxygen or water vapor. In many cases this chromium powder was bright after sintering. Occasionally the upstream side of the powder was slightly greenish, but in all cases the downstream side was metallic. Some of the alloys contracted during sintering and some expanded as much as 20 pct. The latter alloys, which in all cases were brittle, were crushed in a tool steel mortar, repressed, and resintered for 4 hr at 2500°F. After sintering, the alloys were aged for ten days at 1200°F (650°C) in evacuated (105 mm Hg or better) fused silica tubes and were cooled rapidly to room temperature following the aging treatment. The use of the powder metallurgy technique in preparing alloys for structural investigation offers a simple method 'of avoiding contamination or non-homogeniety which could result from a melting operation. It is very often possible to dispense with chemical analysis of the alloys which have been prepared by the powder metallurgy method. In lieu of chemical analysis, it is necessary to determine the weight of the compact before and after sintering. The chemical composition of the alloy may be considered as that of the green compact, within the limits of accuracy determined by the loss of weight during sintering. In phase-diagram studies it is important to achieve homogeniety in structure, whether the alloys are prepared by powder metallurgy or by melting. Homogeniety means complete diffusion during the sintering of the alloys which are prepared by powder metallurgy. It has been found from experience that the best criterion for establishing the completeness of diffusion is the sharpness of the X-ray diffraction patterns. This criterion has been used throughout the present study. The X-ray diffraction data were obtained using powder cameras of either 214.86 or 71.62 mm diam. Copper, cobalt, or chromium Ka. radiation was used, the choice being based on the alloy composition. The powder samples were obtained by filing or crushing, depending on whether the alloy was ductile or brittle. In some cases, the powder was annealed for 4 to 6 hr at 1200°F in vacuum. The measurements were corrected for film shrinkage and absorption. The large camera, in which the film is mounted

Jan 1, 1952

By Francis R. Conley, John A. Sievert, John N. Dew

A brief review is presented of the past performance of a number of large, thin, highly permeable reservoirs with low dips in the Bolivar Coastal fields of Venezuela. The performance of these reservoirs indicates that the fluids are segregated vertically within the sand section by gravity. With this assumption, equations are developed which describe the performance under pressure maintenance operations. Methods of solving these equations and results of simple example calculations are presented. Example calculations indicate that under pressure maintenance conditions injected gas tends to {tow preferentially along the top of the sands and that encroaching water has a tendency to flow preferentially along the bottom. The expected performance of segregated fluids is discussed and compared with that of fluids which are uniformly distributed in any sand section. INTRODUCTION The field performance of a number of reservoirs described herein indicates that the fluids are segregated vertically within the sand section by the force of gravity. Thus, it was felt that any method used to predict the future performance of these reservoirs should consider the effects of segregation in the sand sections. A study of the available information on some of the reservoirs suggests that increased recoveries may be expected if the reservoir pressure is maintained by either crestal gas injection or flank water injection. To predict future performance of reservoirs under pressure maintenance operations, a method of analysis was needed which would account for segregation of fluids in the sand sections. Several methods of analysis have been developed to take into account the segregation of fluids in the reservoir as a whole1,3 To our knowledge no method considers segregation of the fluids within sand sections in the manner indicated by the past performance of several reservoirs in the Mara-caibo Basin. This paper outlines part of the work done in studying some of these reservoirs and contains a description of their performance characteristics. The analysis presented is restricted to pressure maintenance conditions, since space limitations prevent a full discus- sion of the development of the mathematical relations and the various methods of solving them. Only a sketch of the development of the mathematical relations is given. The various methods of solving these relations are pointed out, but the actual determination of solutions to various problems are omitted except for one example. It is felt that these results may aid in the study of reservoirs outside the Maracaibo Basin. Some concepts on which the present analysis is based are outlined by D. N. Dietz. However, the analysis presented herein includes several factors not considered by Dietz: (1) variations in permeability and in the cross section, (2) various shapes of the cross section, and (3) the production of fluids. Also, the mathematical development presented by Dietz differs considerably from our corresponding analysis. RESERVOIR CHARACTERISTICS The reservoirs under consideration, large and thin, with low dip and high permeability, are large to the extent that they contain from 0.5 to over four billion bbl of oil initially in place. The section thicknesses vary from 100 to 400 ft and the lengths from 10,000 to 40,000 ft. Thus, a length-wise cross section of the producing formation appears to be long and thin. The dip angles vary from 0 to 6 degrees and the average permeabilities vary from 0.5 to over three darcies. The reservoirs contain from 20 to 50 per cent shale inter-laminated with the productive sands. Most shale breaks within the major sands do not correlate from one well to the next, and correlation is often difficult, even between wells drilled from the same location. However, it is often possible to correlate the shale breaks between major sands for some distance. Herein we are concerned with the performance of reservoirs containing oil of gravities over 20" API. Past reservoir performance indicates good pressure communication and, in cases where pressure sinks have developed, large amounts of fluid migration have occurred. Few of the reservoirs have had initial gas caps, but also, few have been found to be highly under-saturated. Due to gravity segregation, secondary gas caps usually form before the pressure has been reduced more than 25 per cent of its initial value. The effect of gravity has not only been apparent on a reservoir-wide basis, but has also caused segregation of the reservoir fluids in productive sections. Proof of this is found from the results of selective well tests, workovers, and electric and various other types of logs. Evidence that

By W. C. Hagel, J. H. Westbrook

THERE has been a recent revival of interest in the intermetallic compound AgMg as an experimental material for study of the physical and chemical properties of simple ordered structures. Studies of mechanical behaviors,1-4 diffusion,5,6 and thermo-dynamic properties7'8 have been reported. In several of these studies, heat treatments have been carried out in argon-filled silica capsules at temperatures as high as 750°C with no apparent adverse effects. The present authors were, therefore, startled to discover in the course of some yet unpublished work, that gross melting of near-stoichio-metric AgMg compositions occurred in such samples more than 100 deg below their melting point of about 800°C. This note is to report a brief series of experiments carried out to establish the reason for this behavior. Gross errors in sample composition and failure of furnace temperature controls were quickly eliminated as causes of melting. The first tangible lead came from chemical analysis of an AgMg sample which had melted during treatment at 750°C. A silicon content of 3.3 wt pct was found. Since satisfactory analyses had been obtained on the original as-cast ingot, contamination by diffusion and/or reaction with the fused silica capsule seemed a distinct possibility. A perplexing fact, however, was the apparently capricious incidence of the effect. Not only was it previously unknown, even in the experience of the present authors; but, in the early part of the present study, melting sometimes occurred and sometimes not with specimens treated under constant conditions. Indeed, one sample successfully survived a 750°C heat treatment and yet melted completely during the course of a subsequent anneal in an identical capsule at a lower temperature. To obtain evidence that silicon contamination could lower the melting point to the extent observed, the following experiment was performed. A series of ternary alloys was made up with a stoichiometric AgMg base and containing 0.1, 0.2, 0.4, 1, 2, and 4 wt pct Si. Melting was done in MgO crucibles under a cover of argon gas. After holding 10 to 20 min in the temperature range 850° to 900°C, the alloys were allowed to solidify in the crucible and the temperature during cooling automatically recorded with a Pt/Pt-10 Rh thermocouple. Results from the cooling curves are shown in Fig. 1. Checks within 2 to 5C° were obtained upon repeated melting, cooling, and freezing. The whole series of cooling curves as well as metallographic examination of the melted alloys established that the AgMg rich portion of the AgMg-Si quasibinary is an eutectic-type system. The melting point of AgMg is lowered from approximately 820°C in the pure stoichiometric binary9 to about 710°C in the saturated intermetallic phase. Since second phase was observed in all samples on cooling to room temperature, the solid solubility of AgMg for silicon evidently falls rapidly with decreasing temperature as indicated schematically by the dashed solvus in Fig. 1. It is thus established that a silicon content

Jan 1, 1963

By H. E. Nold

THIS paper is an effort to explain in a simple manner the fundamental principles involved in examining a clay deposit for both quantity and quality and in operating a clay mine, either open-pit or underground, so that the best quality of finished material can be made from the raw material available. The writer is aware that what is recommended in this paper is everyday practice in many refractories plants and in some other heavy-clay products plants, but observations made while visiting practically every clay mine in Ohio have convinced him that the practices herein discussed are not as widely used as their importance warrants. It is true that the problem of mining for quality is more acute in refractories plants than in most heavy-clay products plants, yet some of the latter are finding it profitable to pay more than ordinary attention to the selection and blending of their raw materials. It is hoped that this short paper may prove helpful to some who are now finding it difficult to produce a uniform product of as high quality as their clay deposit seems to warrant. The coordination of the work of the clay mine or pit with the manufacturing plant, to the end that the best product possible be made from the raw material available, presupposes a rather intimate knowledge of the clay deposit. The knowledge must include not only information of the amount of clay-available but also rather detailed information about both vertical and horizontal variations in quality of the clay. This information should cover three things: quality, quantity, and location.

Jan 1, 1929

By D. H. Gieskieng

Published tables of jaw crusher capacities are compiled for the most part from field performance data, interspersed with interpolations, extrapolations, various safety factors, and other modifications. Such a table attempts to balance and equalize field data from widely Werent materials, with differences of crushability, efficiency of feeding, sizing of the feed, and so on. The tests described in this paper were undertaken with the objectives of checking previously reported capacities; of studying the effects of various factors upon the capacity, including jaw plate curvature; and, if possible, of deriving a general capacity equation. Such an equation has been derived from the data obtained in these tests. It is given together with factors for its use. While more accuracy than is usually required may be obtained by careful application of the equation, it is of simple form and provides a convenient reference plane upon which the potential capacity of various crushers may be compared, and with which operating adjustments may be made on existing installations. The principal deviation in these tests from the usual approach consists of a laboratory technique which has been developed for the production of selected capacity data. Recording instruments are connected to crushers in such a manner that a continuous record is produced which discloses the inherent maximum capacity of the crusher and shows capacity decreases caused by hangups. The capacity effects of various crushing conditions are made more evident by this arrangement. The recording instruments were first applied to a standard sized 10 by 7 in. Blake-type jaw crusher in the laboratory. Suficient tests were run on this with various combinations of setting, throw, speed, feed sizing, shapes of jaw plates, and other operating features, to establish the individual effect of each on the capacity. The instruments later were applied to much larger crushers in the field, through the excellent cooperation of the managements in the Mesabi Iron Range, and data were obtained which closely corroborated the established trends. The capacity equation resulting from the test work is made up of a series of factors, each representing the contributing effects of setting, speed, width of chamber, nip angle, feed density, type of jaw plates, stroke, and the overall operating technique. Fortunately, most of these factors were revealed to be in direct proportion to the capacity for straight plate chambers. This equation is also applicable to chambers using curved plates, with slight modifications resulting from the capacity limitation of the upper portion of the crushing chamber. The equation has been derived from tests covering a very wide range of feed density and hardness. It has been found valid, providing that the feed material is either nonpacking in character, as is usual, or allowance in designing the crushing chamber shape has been made to accommodate this characteristic. Preliminary investigation has shown that the equation is also applicable to single-toggle jaw crushers. Conditions of this are that the top of the flywheel rotate towards the top of the crusher opening, and that the horizontal motion of the swing jaw relative to the stationary jaw at the discharge opening be considered as the stroke. The relatively large upper chamber jaw motion would probably result in realiza-

Jan 1, 1950

By A. H. Geisler, J. H. Keeler

Preferred orientations in rolled and annealed titanium sheets were determined by the Geiger counter spectrometer X-ray diffraction technique. Five annealing textures dependent upon the temperature range of annealing were found, and in order of increasing annealing temperature pendent upon the temperature range are: 1—a deformation like texture, 2—a rotated inorder a-recrystallization temperature texture, 3-a retained u-recrysraIlization texture, on annealing at lower temperatures of the ß-region, 4—a transformation texture based on recrystallized a and predicted by the Burgers' relationship, and 5—a ,ß-cube texture. These results are examined in terms of current theories of recrystallization textures. UMEROUS investigators have described the tex- ture obtained by cold rolling the hexagonal metals, titanium, zirconium, and beryllium, which have c/a ratios less than that of ideal packing, 1.633. The basal planes are rotated out of the rolling plane, about the rolling direction, so that the basal poles are tilted toward the transverse direction as shown schematically in Fig. la. In all instances but one,' it was also reported that the [1010] direction was parallel to the rolling direction (see Fig. lb). Hot rolling has been reported as causing a similar tilt of the basal poles in the transverse direction (see Fig. la) and causing the [1010] direction also to be parallel to the rolling direction as shown schematically in Fig. lb. Annealing after deformation does not appreciably change the tilt of the basal poles in the transverse direction." Beryllium2-7 continues to have the [1010] direction in the rolling direction after annealing, and similar observations for titanium and zirconium' . have been reported for annealing at fairly low temperatures, again as in Fig. lb. At higher annealing temperatures, however, the recrystallized grains of titanium" and zirconium have an orientation such that the [1120] direction is approximately in the rolling direction, although the basal poles are still inclined in the transverse direction. Figs. la and lc show the resulting orientations schematically. This change in orientation has been described as a nominally ±30° rotation of the hexagonal crystallites about the basal poles of the cold rolled texture and is apparent from the results which are summarized in Table I for investigations with the X-ray diffraction technique employing film. The angles y, , and ß are indicated in Fig. 2 which represents the stereographic projection of (1070) poles for the mean orientation of a pole figure. Texture determinations for titanium using the Geiger counter spectrometer have provided similar results except that in some instances additional components of the texture were proposed, as shown by the summary of data in the upper half of Table 11. On the other hand, the spectrometer technique, when applied to zirconium,* has revealed a splitting Recently completed studies of the textures of annealed zirconium", show zirconium to possess textures very similar to those reported here for titanium. Therefore, much of this discussion will include zirconium by virtue of its close similarity to titanium in pref erred orientations. of the intense areas of the pole figure for samples annealed at 600°C. This splitting could be described by a 7" rotation of the tilt axis about the normal to the rolling plane. Such a splitting for the annealed texture relative to the cold rolled texture was not observed in other determinations for either zirconium or titanium using the less sensitive film X-ray methoe and makes the relationship between the two types of texture more complex than the simple rotation about the (0001) pole based on film work. The more precise investigations on zirconium permit the descriptions in the lower part of Table 11, which show that the texture depends quantitatively on the temperature of annealing. When zirconium is annealed at temperatures up to 400°C, the texture is similar to the cold rolled texture, while annealing in the range 500" to 900°C produces a texture which is only approximately described as [11%] in the rolling direction. More precisely described results for zirconium show that the two types of splitting ( 1—about an axis in the rolling plane through an angle given in the second column in Table II and 2—about the normal to the rolling plane through an angle given in the third column of Table 11) depend on annealing temperature. The [1120 is the rolling direction only when the annealing temperature is in the vicinity of 900°C

Jan 1, 1957