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By D. D. Smith, D. P. Squier, E. L. Dougherty

A system of differential equations describing the temperature behavior of fluid injected at constant surface temperature in a well is derived and .solved analytically. A formula for the fluid temperature at any time and depth is given, as well us a special formula valid for very large times. These formulas are used to calculate temperatures for several typical cases. The results indicate that, initially, the temperature of the water entering the formation is considerably lower than the injection temperature. This condition lasts for only a short period— less than three days for most cases of practical interest. Following this highly transient period, during which the temperature of the fluid entering the formation builds up to about 50 to 75 per cent of the injection temperature. the system enters a quasi-steady state in which the temperature changes are very slow. After severl years, the bottom-hole temperature will still be 50" to 100°F lower than the injection temperature, hilt the heat losses may he tolerable. INTRODUCTION Predicting the behavior of a hot-water flood requires that the temperature of the water entering the injection interval be estimated. This report describes the development and solution of a system of equations which describes the temperature behavior of the injected water in the wellbore with certain simplifying assumptions. The only previous means known to the authors for describing such a process is that of Moss and White.' Their results appear to be close to those obtained by our method in the practical cases which were compared; this agreement is largely due to the fact that in our method temperature soon approaches a quasi-steady state, as was assumed in their method throughout. However, our model covers all times, is continuous (whereas the Moss-White model depends on breaking the depth into discrete intervals) and. we feel. more closely describes the physical problem. FORMULATION OF THE PROBLEM PHYSICAL SYSTEM AND ASSUMPTIONS The injection procedure consists of pumping water at a fixed surface temperature T., down an infinitely long cylindrical well or tubing of inner radius Any material exterior to the water column such as mud, casing, or cement is regarded as part of the formation. The general behavior of the system may be described qualitatively as follows. When the hot water is first introduced into the system, the temperature difference between the formation and the water is large, resulting in a high rate of heat transfer. As a result, the temperature adjacent to the wellbore rises very quickly. Because the segment of the formation adjacent to the wellbore largely controls the heat transfer rate, the heat transfer rate will become relatively constant when this portion has reached a temperature close to that of the water opposite it. The temperature of the water and formation then increase very slowly with time. The length of the initial highly transient period and the temperature of the water at its conclusion will be functions of depth, injection rate, injection-string radius, surface injection temperature and the physical properties associated with the water-formation system. The following additional assumptions were made. 1. There is no heat transfer by radiation in the system. 2. There is no heat transfer by conduction in the vertical direction in either the injection stream or the formation. 3. The linear volumetric and mass flow rate of the water is constant throughout the injection stream. 4. No horizontal temperature gradient exists in the injection stream. 5. The product of density and heat capacity is constant for both the water and the formation, and the formation thermal conductivity is constant. 6. Initially, both the water in the wellbore and the reservoir are at a temperature given by the (constant) ambient surface temperature plus the product of depth and geothermal gradient (assumed constant). At large distances for the wellbore (r m), the formation will remain at this temperature. 7. The water temperature and the formation temperature at r — r,, are equal for all depths D. DERIVATION OF EQUATIONS The differential equation satisfied by the fluid temperature T,(D, t), which is obtained by writing a heat balance on a cylindrical differential of volume dV of the injection string between the depths D and D i dD, is

By E. W. Cawthorne, R. I. Jaffee, C. M. Craighead

SOLUTION of a solid metal or alloy in a molten metal bath is used daily in melting operations, extractive metallurgical processes, and in brazing. It is generally recognized that temperature, time, agitation, and the composition of the solute metal and the solvent bath all affect solution rate. However, there is little information available in the literature on the kinetics of the process or the relative effect that these variables have on solution rate. In connection with an aluminum brazing study, data on the solution of aluminum in an A1-Si* bath to promote rapid solidification. The chemical analyses were made on drillings taken from the cast plates. The results of this work are listed in Table I. The thermal-analysis data were obtained on 200 gram samples cooled at approximately 1.5" per min. A calibrated chromel-alumel couple was used. The thermal arrests were recorded autographically on a General Electric photoelectric potentiometer recorder. The instrument was calibrated to 22.5 pct. The thermal emf was bucked with a Leeds and Northrup semiprecision potentiometer so that 1 mv represented the full scale of the GE recorder. Referring to Table I, it will be noted that the analytical results tend to be lower than the intended compositions by about 0.3 pct Si in the higher ranges. In view of the known difficulties in obtaining accurate silicon determinations by wet analysis when the silicon content is high and in view of the care that was employed in weighing and preparing the alloys, the intended compositions are believed to be more accurate than the analyses. Furthermore, when the thermal-arrest data are plotted against the intended compositions, a smooth curve is obtained, as shown in Fig. 1. This is not the case when the data are plotted against the analytical results. It will be noted from Table I that the 12.5 pct Si alloy (melt 4) showed a primary arrest at 577.6"C and the eutectic at 576.l°C. The metallographic examination of this chill-cast plate sample showed a small amount of primary silicon. These results, Fig. 1, place the eutectic at slightly less than 12.5 pct Si and are in rather good agreement with the unpublished Hanford data. In all of the subsequent work, the composition of the A1-Si dipping baths was determined by thermal analysis (spread between the primary arrest and the eutectic temperature) employing 12.5 pct Si and 577.2 °C as the composition and temperature of the eutectic. Material Preparation and Selection of the Techniques: At the beginning of this work, it was anticipated that, owing to oxide film present on the surface of the aluminum, difficulty would be encountered in obtaining rapid uniform wetting of aluminum specimens dipped in the A1-Si bath. The following etchants were investigated as possible methods of providing a thin uniform oxide film on the specimen surface: 1—phosphoric acid (H³O4), 2—fluoboric acid (HBFI), 3—sodium hydroxide (NaOH), and 4—hydrofluoric acid (HF). Tests with sheet .specimens (2x½x0.06 in.) of 2s aluminum prepared with these etchants indicated that the fast uniform wetting required for this work could not be obtained if any oxide film existed on the specimen surface. Tests were then conducted by dipping similar specimens etched in 5 pct NaOH and given a thin

Jan 1, 1956

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which. the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,000. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation', the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service.

Jan 1, 1952

By David R. Mitchell

THE mineral pyrite (or marcasite) occurs in coal beds as balls, lenses, veinlets and bands. Several million tons are wasted annually on the refuse dumps from coal mining and coal-preparation activities. Sporadic attempts have been made in the United States to recover this pyrite for manufacture of sulphuric acid but only a few plants have succeeded in recovering it on a commercial scale. Several chemical companies in the East became concerned about supplies of pyrite early in 1943, but by late summer of that year the situation had eased. If for no other reason than national security and self-sufficiency during war-time, methods of recovering pyrite from coal-mine refuse should be worked out and made available to coal-mine operators who are potential producers of pyrite. Eastern sulphuric-acid plants are particularly likely to have their sources of raw material blocked by war conditions, so that special studies to determine where supplies of pyrite can be obtained for these plants from inland sources are desirable. Davis's1 summarization of conditions during World War I gives the following facts: During those years, the shortage of pyrite became acute. Shipments of hand-picked pyrite were made from a number of coal mines in Illinois, Indiana, western Kentucky, Ohio and Pennsylvania. A mechanical concentrating plant for separating pyrite from picking-table refuse was built at Danville, Ill., and operated for several years, and a small pyrite-concentrating plant treating washery refuse near Gillespie, Ill., operated for several months in 1918. The Consolidation Coal Co. of Fairmont, W. Va., constructed and operated a sulphuric-acid plant using pyrite recovered from coal-mine refuse. The U. S. Bureau of Mines during 1917-1919 made a comprehensive survey of pyrite-production possibilities from coal mines and estimated that there was a potential yearly production of 435,000 tons from Ohio and Pennsylvania and 928,000 tons from Kansas, Missouri, Iowa, Illinois, and Indiana mines. This estimate included only mines that could produce one per cent or more of their coal production as pyrite containing a minimum of 40 per cent sulphur. PYRITE PRODUCTION According to the Minerals Yearbook,2 approximately 660,000 long tons of pyrite was produced in the United States in 1941, with an average sulphur content of 42 per cent. The average value f.o.b. mines was $3.09 per long ton. Spanish pyrite, 48 per cent sulphur minimum, was quoted at 12 cents a unit c.i.f. U. S. ports, equal to $5.76 a ton for shipments of minimum sulphur content. Most of the pyrite produced in the United States is obtained as a by-product in the dressing of copper and zinc ores. Metal mines in the East making pyrite concentrate for the market or use in company-operated sulphuric-acid plants

Jan 1, 1944

By W. C. Ellis, E. S. Greiner

WHEN metallic materials are deformed plastically, the process may be considered as one in which hardening and recovery occur simultaneously. The net hardening is that produced by deformation in the absence of recovery lessened by recovery during and immediately following deformation. Strain hardening takes place through movements of large groups of atoms acting to a degree as an entity. A complex microstress system is developed. Recovery is a diffusive-type process involving single atoms or, at most, only a few atoms in concerted action. This is accompanied by elastic strain relaxation. Recovery is strongly temperature-dependent. The driving energy for the process resides in thermal fluctuations of the atoms augmented by the energy of the stress field producing the deformation, and by that produced by the deformation. At very low temperatures recovery is essentially absent, or very small. At high temperatures in the hot working range, recovery is so rapid that deformation results in no appreciable net hardening. The interplay of strain-hardening and recovery results in differing end structures depending on the temperature and the strain rate of the process. For example, there is a prominent difference in the spacing of the slip markings and in the detail of X-ray diffraction patterns. High temperatures and slow strain rates favor a wide spacing of slip markings and sharp reflections.',' This suggests that change in rate of the recovery concurrent with deformation modifies to a degree the manner of the deformation. Different slip systems may operate. For very slow rates, the mechanism may, as has been suggested, differ from that of "classical slip." In the experimental work that follows the findings will be interpreted from the point of view developed in this section. Recovery and Electrical Conductivity Electrical conductivity is a sensitive indicator of the state of strain in a material3' * and was used in this investigation. The materials studied in wire form were: OFHC copper, a high purity (99.99 pct) and 2s grade aluminum, and grade A nickel. Wire annealed and initially 0.050 in. in diam was drawn through diamond dies in a simple holder maintained at 25", —75°, or — 195°C. Precautions were taken that for each material all conditions of drawing were the same except the temperature. Electrical resistivity was measured for each condition at 20°C. This was done as soon as practical after drawing to minimize possible room temperature recovery. The data for the four materials are plotted in Fig. 1 in terms of the change in resistivity for drawing at the several temperatures. The effect of temperature of drawing on the increase in resistivity is most pronounced for copper. Drawing at 25°C to 80 pct reduction in area increases the resistivity approximately 2 pct; drawing at —195°C to the same reduction increases the resistivity about 6 pct. The increase in resistivity" & in this metal is due to extra scattering of conduction electrons originating in the lack of orderly arrangement of the atoms induced by the deformation process. It has been suggested

Jan 1, 1953

By A. W. Bitner, A. W. Asman

An analysis is made of three different types of section production units that represent the manner in which most of the nation's bituminous coal is produced. The general delays and production characteristics of these sections are presented along with a method for evaluating section performance based on actual and theoretical production characteristics. THE forerunner of the modern mechanical loading machine first entered the mines in 1890—a Stanley header with a conveyor. Since then progress has been substantial, both in the design and application of mechanized production units. Mechanization is almost a necessity for survival in the economy of today. In this paper an analysis is made of three types of sections, and a method for evaluating section performance based on present production characteristics and theoretical characteristics is presented. In mechanical loading mining sections the loading machine is the unit directly responsible for production. If the face preparation units provide a plentiful supply of properly prepared coal and the transportation system is coordinated and adequate, the loader will be idle a minimum of time. If either of the above do not perform adequately or other delays occur, the effect on production will be reflected in the performance of the loading machine. Therefore, attention is focused on the loading machine and factors that affect the overall performance of the production unit. Three complete mechanized production units are presented for analysis: A track section, a trackless section using battery-powered shuttle cars, and a trackless section using cable-reel shuttle cars. These particular sections were chosen for the following reasons: 1—The daily tonnage and mining conditions are approximately the same. 2— Production in each is 10 to 20 pct above the daily average. 3—The production characteristics and delays are average and typical. 4—They represent the manner in which the most of the nation's bituminous coal is produced. A. W. ASMAN, and A. W. BITNER, Members AIME, are Chief, and Research Assistant, respectively, Div. of Mining, The Pennsylvania State College, State College, Pa. Discussion on this paper, TP 3140F, may be sent to AIME by Oct. 31, 1951. Manuscript, Feb. 22, 1951. St. Louis Meeting, February 1951. Section A Fig. 1 is a layout for the track mining section showing the development to date, the projected plan and the cuts loaded on the shift studied. The seam mined averages 96 in. in thickness with a fireclay bottom and a roof of 10 in. of drawslate topped by sandstone. The mineability is considered good, and roof support is not a difficult problem. Two locomotives are used in the section to minimize the losses occurred in trip changing. The places are driven 20 ft wide, and the crosscuts are angled to permit fast tramming of the equipment. Table I lists the equipment and labor that make up the section. ANALYSIS Production Characteristics: The average loading rate for eight loading machines studied of this type is 1.81 tons per min. This one at 2.78 is considerably above average.

Jan 1, 1952

By H. S. Price, D. A. T. Donohue

The system of equations describing displacement of a hydrocarbon liquid by a hydrocarbon vapor in a porous medium where mass transfer takes place between the phases is solved numerically for a variety of gas injection processes. Even though the method of solution is quite general, only systems with three hydrocarbon components are considered. Computer simulations of displacement processes wherein mass transfer between phases is both considered and neglected are compared, and it is shown that neglecting mass transfer can give pessimistic displacement efficiencies. INTRODUCTION The role of the gas displacement process in the recovery of petroleum has been subjected to a series of detailed analyses; as a result, a number of predictive models have been published in the literature. However, because of major simplifying assumptions, most of these models do not completely represent the physical system. As a result, the effect of making the simplifying assumptions is unknown. Therefore, a complete representation of this process — one without major simplifying assumptions —should lead to a fuller understanding of the process, and perhaps to methods of improving it. The general method of developing a model for two-phase fluid flow in a porous medium is to solve simultaneously the continuity equation, the energy equations and the equation-of-state for each phase under the prescribed initial and boundary conditions. For an isothermal system, the energy equations reduce to the momentum equation. Darcy's law. However, since natural gas is the vapor state of the reservoir liquid, interphase mass transfer may take place with concomitant changes in both the intensive and extensive thermodynamic properties of each phase. It is this phenomenon that has often been omitted in previous mathematical models. An additional relation, then, which accounts for mass transfer between the phases, must be included with the other equations to specify a complete model. Completely formulating the equations to be solved is not a difficult task1 but obtaining their solution has been intractable up to now. Availability of large-memory, high-speed digital computers now makes an attack on this formidable problem possible. This paper presents a preliminary study of the problem. Since this investigation is intended to be exploratory, it is restricted to the linear, horizontal, isothermal, two-phase viscous flow of oil and gas in an oil reservoir. In the early development of predictive models of this process, the reservoir system was considered as a unit and various forms of the material balance equation were proposed.2-4 Pressure and saturation gradients were then added in the Buckley-Leverett model.5 The Buckley-Leverett formulation considered the fluids to be incompressible; thus, the mathematical model reduces to a steady-state system. In the 1950's, studies incorporating numerical techniques were being published.6-9 These mathematical models differed in the efficiency of finite difference techniques, the inclusion or exclusion of capillarity or the number of space dimensions considered. To solve these nonlinear, partial differential equations, each phase was considered to be homogeneous with time; therefore, mass transfer between phases was neglected. The effect of mass transfer on the gas displacement process was first reported by Attra. 10 He simulated the one-dimension flow system by a series of cells in each of which the fluids were equilibrated during a time step. In addition, the pressure throughout the system during each time step was predetermined and constant-phase velocities were calculated according to the Buckley-Leverett incompressible fluid flow model. Welge et al.11 developed a model for the displacement of oil by an enriched gas where composition is considered to be a dependent variable. Fluid

By J. T. Norton, J. G. McMullin

An 1820°C isothermal cross section of the Ti-Ta-C ternary diagram was prepared from X-ray diffraction and metallographic data. No phases other than those appearing in the three binary diagrams were observed. At temperatures above the titanium transition temperature titanium and tantalum form a complete series of solid solutions containing up to 2 atomic pct C. The phases Tic and TaC also form a continuous series of solid solutions extending across the diagram. PREVIOUS work on this alloy system was very limited. Of the three binary constitution diagrams involved, only one, the Ta-C system was available in the literature. Preliminary data on the other two systems was received from the investigators during the course of the investigation and both have been published in recent months. It had been shown that Tic and TaC formed a continuous series of solid solutions, but the range of carbon content in this phase was not known. While Ta2C had been described, its solubility for or reactions with other carbides had not been reported. It was not known whether or not any ternary compounds occurred in the system. The present program was undertaken to determine experimentally the general form of the ternary diagram. It is hoped that the results will be of value in furthering the development of sintered carbide cutting materials and high temperature ceramets, many of which contain combinations of Tic and TaC. The Binary Systems Of the three binary diagrams involved only that of Ta-C was available at the time this project was started. The diagram of Ellinger¹ redrawn in Fig. 1, shows a hexagonal phase Ta2C having a very small composition range and a cubic TaC phase having a composition range of from 40 to 50 atomic pct C. The authors made a separate determination of the composition range of TaC using lattice constant values and found the range to extend from 40 to 49.7 atomic pct C in good agreement with Ellinger's diagram. Two determinations of the Ti-Ta system have appeared recently.2,3 These two diagrams are in good agreement and show that ß titanium and tantalum form a complete series of solid solutions. The Ti-C diagram by Cadoff and Nielsen4 shows a very limited solubility of carbon in both a and ß titanium. The single carbide formed persists over a wide range of carbon contents. Several values for the upper limit of carbon content of this phase have been reported."' The highest value obtained in the M.I.T. Laboratory was 47.5 atomic pct C with a lattice constant of 4.328?.5 Fattinger7 describes a gas carburization method which he claims produces stoichiometric Tic although he does not present any data showing that he actually had 50 atomic pct combined carbon. Several complete analyses on

Jan 1, 1954

By Sage B. H., Lacey W. N., G. W. Billman

The composition of the coexisting phases in the methane-ethane-n-pentane system was determined at 100°F. This was accomplished by withdrawing samples of the coexisting phases under isobaric-isothermal conditions. The relative amount of each of the components present in the liquid and gas phases was determined by conventional analytical fractionation methods. The phase behavior of this system approximates that estimated from generalized correlations which take into account the influence of the nature and amount of each of the components present upon the equilibrium. It was found that for particular pressures and temperatures the equilibrium constant of each of the components was influenced significantly by the composition of the system and this effect was more pronounced at the lower pressures for methane than for the components of greater molecular weight. However, at the higher pressures approaching the maximum two-phase pressure for the system at this temperature the composition markedly influences the equilibrium constants of all the components at a particular pressure and temperature. The results of this study are presented in graphical and tabular form. Introduction The phase behavior of many of the binary systems containing parafin hydrocarbon components from methane through n-pentane has been investigated during recent years. In addition the compositions of the coexisting phases in mixtures of crude oil and natural gas have been studied.' However, these results do not establish the influence of the nature and amount of the other substances making up a multi-component system upon the gas-liquid equilibrium constant of any one component. A preliminary correlation on the basis of values for binary systems was made2 utilizing such experimental information as was available. However, there is need for much additional information regarding behavior in systems containing more than two components. Study of the phase behavior of ternary systems offers a feasible attack upon the determination of the influence of composition as well as of pressure and temperature upon the several equilibrium constants concerned. An investigation of the phase behavior of the methane-propane-n-pentane system at 100°, 160°, and 220°F was reported.".' This work served to illustrate the marked influence of concentration of the other components upon the equilibrium constants. Variations of as much as 50 pct in the equilibrium constants for methane for fixed temperature and pressure were observed in regions remote from the critical state. Likewise there was a marked variation in the equilibrium constants of propane and n-pentane as a result of changes in the composition. These results indicated the desirability of investigating additional ternary systems. The present paper deals with a study of the methane-ethane-n- pen-tane system at 100°F, which is similar in many respects to the work upon the meth-ane-propane-n-pentane system cited above.

Jan 1, 1948

By Sage B. H., G. W. Billman, Lacey W. N.

The composition of the coexisting phases in the methane-ethane-n-pentane system was determined at 100°F. This was accomplished by withdrawing samples of the coexisting phases under isobaric-isothermal conditions. The relative amount of each of the components present in the liquid and gas phases was determined by conventional analytical fractionation methods. The phase behavior of this system approximates that estimated from generalized correlations which take into account the influence of the nature and amount of each of the components present upon the equilibrium. It was found that for particular pressures and temperatures the equilibrium constant of each of the components was influenced significantly by the composition of the system and this effect was more pronounced at the lower pressures for methane than for the components of greater molecular weight. However, at the higher pressures approaching the maximum two-phase pressure for the system at this temperature the composition markedly influences the equilibrium constants of all the components at a particular pressure and temperature. The results of this study are presented in graphical and tabular form. Introduction The phase behavior of many of the binary systems containing parafin hydrocarbon components from methane through n-pentane has been investigated during recent years. In addition the compositions of the coexisting phases in mixtures of crude oil and natural gas have been studied.' However, these results do not establish the influence of the nature and amount of the other substances making up a multi-component system upon the gas-liquid equilibrium constant of any one component. A preliminary correlation on the basis of values for binary systems was made2 utilizing such experimental information as was available. However, there is need for much additional information regarding behavior in systems containing more than two components. Study of the phase behavior of ternary systems offers a feasible attack upon the determination of the influence of composition as well as of pressure and temperature upon the several equilibrium constants concerned. An investigation of the phase behavior of the methane-propane-n-pentane system at 100°, 160°, and 220°F was reported.".' This work served to illustrate the marked influence of concentration of the other components upon the equilibrium constants. Variations of as much as 50 pct in the equilibrium constants for methane for fixed temperature and pressure were observed in regions remote from the critical state. Likewise there was a marked variation in the equilibrium constants of propane and n-pentane as a result of changes in the composition. These results indicated the desirability of investigating additional ternary systems. The present paper deals with a study of the methane-ethane-n- pen-tane system at 100°F, which is similar in many respects to the work upon the meth-ane-propane-n-pentane system cited above.

Jan 1, 1948

By J. H. Henderson, J. Naar

The displacement of a wetting fluid from a porous medium by a non-wetting fluid (drainage) is now reasonably well understood. A complete explanation has yet to be found for the analogous case of a wetting fluid being spontaneously imbibed and the non-wetting phase displaced (imbibition). During the displacement of oil or gas by water in a water-wet sand, the porous medium ordinarily imbibes water. The amount of oil recovered, the cost of recovery and the production history seem then to be controlled mainly by pore geometry. The influence of pore geometry is reflected in drainage and imbibition capillary-pressure curves and relative permeability curves. Relative permeability curves for a particular consolidated sand show that at any given saturation the permeability to oil during imbibition is smaller than during drainage. ' Low imbibition permeabilities suggest that the non-wetting phase, oil or gas, is gradually trapped by the advancing water. This paper describes a mathematical image (model) of consolidated porous rock based on the concept of the trapping of the non-wetting phase during the imbibition process. The following items have been derived from the model. 1. A direct relation between the relative permeability characteristics during imbibition and those observed during drainage. 2. A theoretical limit for the fractional amount of oil or gas recoverable by imbibition. 3. An expression for the resistivity index which can be used in connection with the formula for wetting-phase relative permeability to check the consistency of the model. 4. The Iimits of flow performance for a given rock dictated by complete wetting by either oil or water. 5. The factors controlling oil recovery by imbibition in the presence of free gas. The complexity of a porous medium is such that drastic simplifications must be introduced to obtain a model amenable to mathematical treatment. Many parameters have been introduced by others in Iprogressing" from the parallel-capillary model to the randomly interconnected capillary models independently proposed by Wyllie and Gardner3 and Marshall4. To these a further complication must be added since an imbibition model must trap part of the non-wetting phase during imbibition of the wetting phase. Like so many of the previously introduced complications, this fluid-block was introduced to make the model performance fit the observed imbibition flow behavior. THE IMBIBITION MODEL ASSUMPTIONS The following assumptions are common to many two-phase models previously described. 1. The wetting characteristics of the medium are clearly defined. 2. When two fluids co-exist in the medium, the wetting phase will fill the smaller pores and the non-wetting fluid the bigger ones. 3. The pores have a circular cross section. 4. Apparent pore radii are related to the capillary pressure (drainage) by

By W. T. Lankford, Edward Saibel

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By Edward Saibel, W. T. Lankford

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By L. G. Graper, E. L. Ramsey

THE present program of increased production of armament and lend-lease material for mechanized war has created a problem for the shops that must do the machining. They have naturally turned to the steel producers to provide them with a steel that can be accurately machined with the greatest possible speed. The adding of sulphur to steel as an aid to machinability has long been practiced; however, it may cause red shortness in rolling and may result in billets with seams and cracks, which must be removed before rolling can be continued. This conditioning of billets slows down production and adds to the cost of making steel. Experience with various grades of sulphur steel made to different specifications has shown that Bessemer sulphur steels roll better than similar grades made in the open hearth, and also that low-carbon steels that are open or semi-killed as tapped roll better than completely deoxidized or killed steels. This has led to the belief that oxygen plays an important part in the rolling qualities of sulphur-bearing steels. It is generally held that the red shortness of sulphur steels is due to the low melting point of the sulphide compounds that separate out at the grain boundaries when the steel solidifies. At the rolling temperature of steel these sulphide compounds melt and cause cracking. ADDING SULPHUR AS A SULPHITE These difficulties can be avoided if sulphur is introduced into the steel by means of an anhydrous sulphite, such as sodium sulphite or sodium bisulphite, which-upon decomposition-forms sulphur dioxide. It is assumed that, in this case, the oxygen of the sulphur dioxide forms part of the sulphide inclusions in the steel, and raises their solidification temperature enough so that the formation in the steel of a low-melting eutectic is prevented. The result is the prevention of hot shortness and a more uniform distribution of inclusions. Fig, I shows photomicrographs of steels made with sulphur, while Fig, 2 illustrates the structure of steels made with sodium bisulphite. These samples were cut from the steels as cast-that is, before rolling and were polished and lightly etched to bring out the grain boundaries. Fig. I shows that sulphide inclusions segregate more or less at the grain boundaries, and it can be seen how the continuity of these low-melting inclusions would cause red shortness. Fig. 2 shows that the sulphide inclusions are more or less uniformly distributed throughout the matrix. This arrangement of inclusions has no apparent effect on the rolling qualities of a steel. This statement has been substantiated by the observation of the rolling of over 6000 tons of steel made with a sulphite addition. RESULTS As stated before, the sulphur dioxide is added to steel by means of the decompcsi-

Jan 1, 1942

By E. L. Swarts

In the course of a program on high-temperature processing and electrowinning of uranium at the Knolls Atomic Power Laboratory,'' it became necessary to give attention to the interaction of molten uranium with graphite. Although it is known3 that a protective interface layer may form, details of this reaction have not been reported. Unfortunately it was impossible to complete the planned experimental program. However, the general problem is considered of sufficient interest to warrant reporting those preliminary results actually obtained. EXPERIMENTAL PROCEDURE Interface carbide layers were formed by melting samples of cleaned uranium metal in small closed graphite crucibles. Equilibrations were conducted in vacuo or in an atmosphere of dry helium at temperatures ranging from 1150" to 1400°C and for periods of from 24 to 240 hr.

Jan 1, 1960

By R. C. Hall

The magnetic anisotropy and magnetostriction of single crystals of alloys between 25 and 59 wt pct Co in Fe have been determined in the disordered and ordered states. The magrzetostriction is large and positive for all alloys in both states of order (up to 150 x 10-6 for A,, and 40 x 10-6 for 111). The magnetic anisotropy becomes zero rzear 41 pct Co for the disordered state. Ordering shifts the zero-anisotropy composition to about 50 pct Co. COBALT-iron alloys have for many years been of interest as magnetic materials because they have unusually high magnetic saturation values.' This interest was increased recently by the development of Supermendur.' Supermendur is an alloy of 49 pct Co-49 pct Fe-2 pct V* which was found by suitable purification and heat treatments, including a magnetic anneal, to possess excellent magnetic properties. These included a square hysteresis loop with a low coercive force and a high magnetization, and a low total loss. Two factors which are important in determining the magnetic hysteresis properties are the basic magnetic properties of magnetostriction and anisotropy. Alloys having zero anisotropy and zero magnetostriction show improved hysteresis properties.3 Since very meager data4-' are available in the literature on the single-crystal anisotropy and magnetostriction of the cobalt-iron alloys, the present program was undertaken to determine these two properties in the disordered and ordered states. EXPERIMENTAL TECHNIQUES Ingots of the cobalt-iron alloys containing from 25 pct to 59 pct Co in iron were vacuum melted from electrolytic iron and cobalt of 99.9 pct purity. The ingots were cooled at a rate of about 1°C per hr through the transformation temperature (950" to 980°C dependent on the alloy content) for the growth of large grains. From these grains, single-crystal disks were fabricated with either the (110) or (100) plane parallel to the faces of the disk. The crystals were given two heat treatments to produce either the ordered state (cooling rate of 20°C per hr from 850 "C) or the disordered state (water quench from 850 °C). Since the iron-cobalt alloys order very rapidly, the water quench may not have produced complete disorder in all cases. Due to the method of growth, the crystals were not perfect. Most of the samples had low-angle boundaries and a few had some small included grains. These imperfections could and probably did affect the accuracy of both the magnetic anisotropy and magnetostriction measurements. Much of the scatter in the data may be attributed to the crystal imperfections. The methods of determining the spontaneous saturation magnetostriction and the anisotropy have been previously described.419110 MAGNETOSTRICTION The magnetostriction in the [loo] and [Ill] directions (hO0 and ?111 respectively) is illustrated in Fig. 1 for the disordered state. Both ?100 and ?111i became large positive values as cobalt was added to iron. The state of order did not have a large effect on the magnetostriction. The effect of order did not appear too consistent in these data. Tentative curves are shown in Fig. 1 for the ordered magnetostriction near the FeCo composition; here ?100 appeared to be lowered and ?111 raised as the degree of order was increased. These results agree qualitatively with the

Jan 1, 1961

By John W. Vanderwilt

The unpredictable behavior of ground movement and subsidence has complicated the problems that attend the extraction of large quantities of ore. Special studies, particularly relating to coal mining, have yielded such a voluminous literature and so many involved controversial theories that a partial review would be difficult. Limited space makes any kind of a review impractical. The features to be considered cover only a relatively small part of the broad problems of ground movement and subsidence, but it is believed that this small part is critical. The practical aspects are important, since they bear directly on safety of mine workings, on recovery of ore and on dilution of ore in block caving and related systems for extracting large quantities of rock. The ground movement to be described occurs outside the vertical boundaries of a caved block in the area that is commonly referred to as being in the "zone of draw." "Draw" is a term that originated in the subsidence problems related to coal mining, and it is defined by a line drawn from the margin of the area caved underground to the most distant fracture at surface on the same side of the caved area as shown in Fig. I.' A line thus drawn is called the cave line, and its angle with respect to the horizontal is the cave angle or angle of draw. It is understood that the line is taken normal to the limit of mining, and in a vertical plane. The prevailing theories as to draw and angle of draw assume that appreciable movement occurred along the cave line, which has been described as a fracture resulting from the shearing action brought about by the weight of the overlying load. Fig. 3 shows diagrammatically the mechanics of ground movement adjacent to an area of subsidence according to the prevailing theory of draw (A, from Royce2) and, for comparison, ground movement observed in the Climax mine (B). The text in Peele's Handbook2 referring to Fig. 2 does not state the meaning of the "original position of top of workable ore" in the rectangular space above "ore in place," and the arrows are not explained. However, this presentation is most concerned with the zones outside the rectangle. According to the prevailing theory, as shown at the extreme left under A, Fig. 2, the vertical tension cracks at surface change at a shallow depth to shear fractures forming the cave line, and it is assumed that appreciable movement takes place along the cave line toward and into the subsiding caved block. The mechanics of ground movement observed in the Climax mine, as shown under B, Fig. 2, does not accord with the prevailing theory, particularly as regards the cave angle and draw. The vertical tension cracks seen at surface die out at depths of 150 to 225 ft. and shear fractures do not develop. Movement is confined at surface to a mantle of rock 50 to roo ft.

Jan 1, 1949

By Colin Baker, G. C. Smith

Investigation of the initiation and propagation of ductile failure in OFHC copper was undertaken to determine the role of nonmetallic inclusions. The effect of inclusion initiated voids on the formation of the internal cavity and the final shear separation was studied by metallographic eranzination of strained test pieces. A strain anneal technique was used to enlarge the voids under uniaxial stress conditions to elinzinate triaxial stress effects. Measurements of void size us stress and strain were made to show the point at which void im'tiation begins and becomes an important factor in the deformation process. The work of separation of copper-cuprous oxide was determined to attempt to correlate the breakdown of the matrix inclusion interface with void initiation and propagation. The zloid shape and position relative to the tensile axis suggested an interface breakdown mechanisnz of initiation. Evidence is presented that shows a basic similarity between the central cavity propagation and the 45-deg shear portions of the failure. DUCTILE fracture has been studied by a number of workers1-lo and attention drawn to the importance of hard second phase particles in the initiation of the failure. Holes formed at the matrix-particle interface can elongate by plastic deformation and then subsequently expand sideways to link up and produce a major crack. This is usually observed first in the center of the macroscopically necked region of a test-piece where the hydrostatic stresses are at a maximum. As the crack spreads sideways towards the free surface of the specimen, well defined shear zones develop from the crack tip and the final separation is along a direction at approximately 45 deg to the stress axis. This shear failure may also be associated with voids formed adjacent to second phase particles. In this way a cup and cone type fracture is produced. The stage at which separation takes place between particles and the surrounding matrix has not been clearly identified. In addition, although researchers have dealt with anisotropy of tensile behavior" as a result of material fabrication variables, not much is known about the microstructural features of aniso-tropic behavior. In the present work evidence on these points is presented in relation to the behavior of copper containing second phase particles of cuprous oxide. I. MATERIALS AND PROCEDURES EMPLOYED The material used was +-in. diam or 2-in. sq cold-drawn OFHC copper bar which contained 0.6 pct by volume of cuprous oxide inclusions. These ranged in COLIN BAKER, Junior Member AIME, formerly at -mnF of Metallurgy, University of Cambridge, Cambridge, England, is presently Research Scientist Reynolds Metals Co., Richrnand, Va. G. C. SMITH, Member AIME, is Senior Lecturer, Department of Metallurgy, University of Cambridge. Manuscript submitted June 20, 1967. IMD size from approximately 1 to 6 p in length and 1 to 4 p in width. The shape was generally slightly ovoid. Tensile tests were made on specimens having a gage length of 2.5 cm and diameter of 0.643 cm. Metallographic examination was carried out by sectioning deformed and fractured specimens; in addition fracture surfaces were examined optically and with a scanning electron microscope. Some measurements of the work of separation between copper and cuprous oxide were made, using a sessile drop technique which was a modification of that used by Kingery and umenick." The best metallographic results were obtained by using a vibratory polisher, which minimized smearing of the surface. 11. RESULTS A) Initial Experiments. Specimens from the +-in. diam rod were annealed for 2 hr at 650°C in uacuo, at which temperature complete recrystallization occurred without any change in the form of the inclusion. They were then fractured at temperatures from -190" to 600°C. Cup and cone fractures were obtained at all temperatures from -196" to 400°C. With increase in temperature there was, however, a continuous increase in the extent of the central transverse area and a corresponding decrease in the shear portion of the fracture. Above 400°C, the fractures became intergranular. Sections of specimens tested below 400°C revealed extensive small voids which were always associated with inclusions. However, the voids only reached dimensions greater than the inclusion size in the region of the macroscopic neck, where they were many times longer. Lateral expansion was found only near the fracture surface of the test pieces. As observed by Puttick, the voids were either (a) triangular holes initiated in the direction of the tensile axis and elon-

Jan 1, 1969

INTRODUCTION Engineering studies of many near surface coal deposits that are amenable to strip mining can be enhanced and expedited by the application of computer techniques for defining coal reserves and overburden and intraburden yardage and their stripping ratios. The case study discussed herein could be from the western coalfields of Colorado, Wyoming, or Montana; the lignite deposits of the Dakotas or Texas, or from the strippable coal seams of the midwest. Because the techniques can be applied so universally, the actual map locations are not identified. The same computing principles apply to one seam or multiseam deposits, and the capability of the computing programs and plotting routines to display the coal seams in plan and sections provide excellent base maps for further engineering planning and mine layout studies. MANAGEMENT OF DRILL HOLE DATA Drilling for coalfield information is usually done at much wider centers than for other mineral deposits. The geologic logs of the holes are generally quite simple, and frequently record only major lithologies and depths to the top and bottom of the coal seams, together with hole collar survey information. A header card is prepared for each drill hole showing: Hole ID Northing Fasting Elevation Azimuth Dip The header card can be followed by any number of downhole lithologic intercept records: [Hole Depth Lithology Hole ID From-To Coal] Less data errors occur if the computer cards are punched directly from drill hole logs, thus eliminating opportunities for mistakes in transcribing data. All arithmetic manipulations should be left to the computer to avoid as much human error as possible. The SURVEY program is run over the raw data file and all lithologic intercepts are computed and defined in XYZ space. BOUNDARY SURFACES-COAL SEAMS AND LITHOLOGIC UNITS The most useful computer program for defining coal seams in 3D space is a linear inter-

Jan 1, 1980

By H. R., Collins

THE purpose of pulverizing coal before burning it is to make available every heat unit it contains. Machinery has been developed which will pulverize coal in one operation, delivering it to bins in front of the furnaces at an expenditure of about 17 hp.-hr. per ton, in a medium-sized plant. The cost of the operation depends upon the amount of moisture that must be expelled before pulverizing, the cost of labor, and the cost of coal delivered at the plant. At a small plant, requiring a pulverizer with a capacity of only ½ ton per hour, the cost per ton pulverized will naturally be greater than at a plant requiring the largest pulverizer, with a capacity of 7 tons per hour. The first step is to reduce large lumps to a size suitable for drying uniformly, before passing to the pulverizing mills; this is done in rolls, at a single pass. The second -step is the elimination of moisture, in order to facilitate pulverizing to great fineness, while also increasing the heating effect and the temperature attainable when the coal is burned. There are other mechanical advantages in the handling of, dried coal. Driers are now manufactured which are able to eliminate moisture without distilling any of the volatile combustible matter in the coal; they are fired by hand or with pulverized fuel. The heat first surrounds the shell of the drier, being confined within a chamber where complete combustion takes place; the heated gases are then led through a duct to the discharge end of the drier and enter the inside of the shell at a temperature not exceeding 300° F. This temperature is maintained by the operator and is indicated by a pyrometer. Volatile combustible matter is not likely to be distilled until the temperature rises above 400° F. On discharging from the drier, the coal is usually passed over a magnetic separator in order to prevent pieces of iron from going to the pulverizer. Two types are used: a magnetic pulley which automatically discharges its collection of iron, and a lifting type, from which the iron is removed by hand when convenient.

Jan 4, 1918