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By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By R. H. Doremus, E. F. Koch

The first carbide phase that precipitates at 120°C from a iron containing about 0.02 wt pct, C was studied with the electron microscope. In both strained and unstrained material the carbide particles appeared to form on the dislocations in the iron, in agreement with the results of the kinetic study in part II. The structure of the carbide was tentatively identified as an expanded a-iron lattice (body-centered tetragonal) with about 0.7 wt pct C. This phase appeared to be metastable and apparently transformed into cementite or epsilon carbide when the iron was over-aged. WhEN a iron containing less than about 0.025 wt pct C is quenched from 700°C to room temperature the carbon is retained in solid solution and precipitates out slowly with time. The morphology and structure of the precipitating phase are still in doubt, two different carbide phases, epsilon carbide and cementite, have been identified, but there is considerable disagreement about the time and temperature at which they appear.1-4 Epsilon carbide seems to form at lower temperatures than cementite, although one group of investigators4 found only the latter phase over a wide range of aging temperatures. Usually these two phases have been identified after aging times much longer than needed to drain the carbon from supersaturated solution, at least for aging temperatures below 200oC. The precipitated carbides have been observed with the electron microscope,'-5 but again most results have come from samples aged much longer than necessary to reduce the carbon concentration in solution to a low value. In this study the carbide phases were observed in earlier stages of precipitation with the electron microscope, in order to learn more about the shape, size, and distribution of the carbide particles. Samples strained small amounts before aging, as well as unstrained samples, were studied, and the structure of the carbide phase was tentatively identified. EXPERIMENTAL "Ferrovac E" vacuum-melted iron, from which the wires for kinetic studies were also made (Refs. 6 and 7 and the following paper) was used for this work. An analysis of this material is given in Table I; it agrees well with the manufacturer's values. The number of inclusions in the iron was very small, as can be seen in the optical micrograph in the following paper. Pieces of iron about 1 mm thick and 5 to 10 mm in diam were used for all the studies except for those in which the sample was strained before aging; then the specimen was a rod 3 to 6 mm in diam and 20 cm long. The samples were held at about 700°C in wet hydrogen for at least an hour to remove residual carbon and nitrogen, after which they were heated to 950" (in the y region) and cooled to room temperature in the furnace. This treatment gave an average grain diam of more than 1 mm, so that the effect of grain boundaries on the precipitation process was negligible. The samples were carburized at 710°C for about 2 hr in hydrogen that had passed over toluene held at -30°C; then they were rapidly quenched into water. From chemical analysis this treatment gave a carbon concentration of from 0.012 to 0.016 wt pct, which is less than the solubility of carbon at this temperature. After quenching, the samples were aged at 120 "C in an oil bath for vari-

Jan 1, 1961

By John J. Sammarco

This report (Safety File Guidance 6.0) is the eighth in a nine-part series of recommendations and guidance addressing the functional safety of processor-controlled mining equipment. It is part of a risk-based system safety process encompassing hardware, software, humans, and the operating environment for the equipment’s life cycle. Figure 1 shows a safety framework containing these recommendations. The reports in this series address the various life cycle stages of inception, design, approval and certification, commissioning, operation, maintenance, and decommissioning. These recommendations were developed as a joint project between the National Institute for Occupational Safety and Health and the Mine Safety and Health Administration. They are intended for use by mining companies, original equipment manufacturers, and aftermarket suppliers to these mining companies. Users of these reports are expected to consider the set in total during the design cycle. • 1.0 Safety Introduction (Part 1).—This is an introductory report for the general mining industry. It provides basic system/software safety concepts, discusses the need for mining to address the functional safety of programmable electronics (PE), and includes the benefits of implementing a system/software safety program. • 2.1 System Safety (Part 2) and 2.2 Software Safety (Part 3).—These reports draw heavily from International Electrotechnical Commission (IEC) standard IEC 61508 [IEC 1998a,b,c,d,e,f,g]and other standards. The scope is “surface and underground safety-related mining systems employing embedded, networked, and nonnetworked programmable electronics.” System safety seeks to design safety into all phases of the entire system. Software is a subsystem; thus, software safety is a part of the system’s safety. • 3.0 Safety File (Part 4).—This report contains the documentation that demonstrates the level of safety built into the system and identifies limitations for the system’s use and operation. In essence, it is a “proof of safety” that the system and its operation meet the appropriate level of safety for the intended application. It starts from the beginning of the design, is maintained during the full life cycle of the system, and provides administrative support for the safety program of the full system. • 4.0 Safety Assessment (Part 5).—The independent assessment of the safety file is addressed. It establishes consistent methods to determine the completeness and suitability of safety evidence and justifications. This assessment could be conducted by an independent third party. • Safety Framework Guidance.—It is intended to supplement the safety framework reports with guidance providing users with additional information. The purpose is to assist users in applying the concepts presented. In other words, the safety framework is what needs to be done and the guidance is how it can be done. The guidance information reinforces the concepts, describes various methodologies that can be used, and gives examples and references. It also gives information on the benefits and drawbacks of various methodologies. The guidance reports are not intended to promote a single methodology or to be an exhaustive treatment of the subject material. They provide information and references so that the user can more intelligently choose and implement the appropriate methodologies given the user’s application and capabilities. The guidance reports comprise parts 6 through 9 of the series and are listed below: [5.1System Safety Guidance (Part 6).—This guidance supplements 2.1 System Safety. < 5.2 Software Safety Guidance (Part 7).—This guidance supplements 2.2 Software Safety. < 6.0 Safety File Guidance (Part 8).—This guidance supplements 3.0 Safety File. < 7.0 Independent Functional Safety Assessment Guidance (Part 9).—This guidance supplements 4.0 Independent Functional Safety Assessment.] [ ]

Jan 4, 2006

By John J. Sammarco

This report (System Safety Guidance 5.1) is the sixth in a nine-part series of recommendations and guidance addressing the functional safety of processor-controlled mining equipment. It is part of a risk-based system safety process encompassing hardware, software, humans, and the operating environment for the equipment’s life cycle. Figure 1 shows a safety framework containing these recommendations. The reports in this series address the various lifecycle stages of inception, design, approval and certification, commissioning, operation, maintenance, and decommissioning. These recommendations were developed as a joint project between the National Institute for Occupational Safety and Health and the Mine Safety and Health Administration. They are intended for use by mining companies, original equipment manufacturers, and aftermarket suppliers to these mining companies. Users of these reports are expected to consider the set in total during the design cycle. • 1.0 Safety Introduction (Part 1).—This is an introductory report for the general mining industry. It provides basic system/software safety concepts, discusses the need for mining to address the functional safety of programmable electronics (PE), and includes the benefits of implementing system/software safety program. • 2.1 System Safety (Part 2) and 2.2 Software Safety (Part 3).—These reports draw heavily from International Electrotechnical Commission (IEC) standard IEC 61508 [IEC 1998a,b,c,d,e,f,g]and other standards. The scope is “surface and underground safety-related mining systems employing embedded, networked, and nonnetworked programmable electronics.” System safety seeks to design safety into all phases of the entire system. Software is a subsystem; thus, software safety is a part of the system’s safety. • 3.0 Safety File (Part 4).—This report contains the documentation that demonstrates the level of safety built into the system and identifies limitations for the system’s use and operation. In essence, it is a “proof of safety” that the system and its operation meet the appropriate level of safety for the intended application. It starts from the beginning of the design, is maintained during the full life cycle of the system, and provides administrative support for the safety program of the full system. • 4.0 Safety Assessment (Part 5).—The independent assessment of the safety file is addressed. It establishes consistent methods to determine the completeness and suitability of safety evidence and justifications. This assessment could be conducted by an independent third party. • Safety Framework Guidance.—It is intended to supplement the safety framework reports with guidance providing users with additional information. The purpose is to assist users in applying the concepts presented. In other words, the safety framework is what needs to be done and the guidance is how it can be done. The guidance information reinforces the concepts, describes various methodologies that can be used, and gives examples and references. It also gives information on the benefits and drawbacks of various methodologies. The guidance reports are not intended to promote a single methodology or to be an exhaustive treatment of the subject material. They provide information and references so that the user can more intelligently choose and implement the appropriate methodologies given the user’s application and capabilities. The guidance reports comprise parts 6 through 9 of the series and are listed below: [< 5.1 System Safety Guidance (Part 6).—This guidance supplements 2.1 System Safety. < 5.2 Software Safety Guidance (Part 7).—This guidance supplements 2.2 Software Safety. < 6.0 Safety File Guidance (Part 8).—This guidance supplements 3.0 Safety File. < 7.0 Independent Functional Safety Assessment Guidance (Part 9).—This guidance supplements 4.0 Independent Functional Safety Assessment.] [ ]

Jan 8, 2005

By M. P. Tixier, M. Gondouin, G. L. Simard

In the quantitative interpretation of the SP logs, the electrochemical component is generally taken equal to — K log Rm /Rw where K has the theoretical value corresponding to solutions of pure sodium chloride. This method may be misleading when relatively large quantities of salts other than NaCl are present in form-rrtion waters—as is generally the case for low salinities —or in gyp-base muds. In such cases recourse is made in the field to changing the K value or to adding a correction term to the equation on the basis of local experience. An investigation has been made in the laboratory of the influence of HCO3, SO4=, Ca++, and Mg++ on the amplitude of the SP deflection, which included in par-ricular determinations of the activity coefficients of Ca++ and Mg++. The theory, the experimental techniques and a tentative method for applying the results are described. So far, applications to actual field cases where chemical analyses of waters were available have provided an excellent confirmation of the proposed method. The case of the SP in very salty brines is also considered and it is shown that the use of activity data for sodium gives satisfactory results. HISTORICAL In early times of electrical logging, the SP curve was used exclusively as a tool for the location of permeable beds and the definition of their boundaries. Later, with the introduction of methods of quantitative analysis, attention was called to the possibility of deriving from the SP log some information on the formation water resistivity, which constitutes one essential element for the computation of water saturation from log data. The first laboratory experiments&apos; in 1932 had shown that, as a result of electrochemical phenomena arising at the contact of the niud and the formation, the amplitude of the deflection of the SP curve was, at least partly, a function of the salt concentration of interstitial water and accordingly of its resistivity. It was indicated that the amplitude of the electrochemical component of the SP should be equal to K log R1/R2, R1 and R2 being the resistivities of the mud and of the formation water respectively. However, the exact value of the K coefficient was not determined at that time because the surface clay used for a laboratory model was far from an ideal shale membrane. Consequently, the way was not yet open towards quantitative interpretation. In the early forties, Tixier reported2, on the basis of field log observations, the following equation for the case of NaCl solutions, SP = -71 log f1c1/f2c2, c1 and c2 being the concentrations and f1, f2 the mean activity coefficients. The local variations observed in the empirical values of K, chiefly in the Rocky Mountains, led him to advance the opinion that, besides the relative amounts, the nature of the salts present in the solutions had a bearing on the magnitude of the SP. At about the same time Mounce and Rust- ad published laboratory results which emphasized the part played by the shale in the generation of the SP. On the basis of laboratory tests and theoretical considerations, Wyllie in 1948&apos; published the following equation of the electrochemical SP for the case of NaCl solutions, SP= - 71 log (a1)m/(a2)m

Jan 1, 1958

By R. Schuhmann, G. W. Powell

The concept of local equilibrium is examined and, in particular, the applicability of the concept to two-phase binary diffusion couples is discussed. It is concluded that, if binary solid solutions are treated thermodynamically as ternary solutions, vacancies being the third component, then recent experimental observations of nonequilibrium interface compositions (i.e., compositions different from the phase diagram values) are consistent with a state of complete dynamic equilibrium at the interface. CLASSICAL approaches to diffusion and to other irreversible processes often utilize a postulate of "local equilibrium". That is, one assumes even in the presence of gradients, fluxes, and time changes of properties, a) that the Second Law can be formulated locally, and b) that thermodynamic equations of state among intensive properties are identical with those for equilibrium phases. A direct consequence of this assumption, for example, is that one would calculate the total entropy of a nonequilibrium phase simply by integrating the entropy density (eu per unit volume) over the volume of the phase, assuming that entropy density is the same function of energy and particle density as for equilibrium phases. In the study of diffusion and of diffusion-controlled phase transformations, metallurgists take this concept of local equilibrium for granted and utilize it automatically. In fact, experimental evidence of all kinds is overwhelming that "local equilibrium" is a valid limiting law, approached more and more closely as gradients and rates of change approach zero. On the other hand, we have neither experimental nor statistical thermodynamic proof that this principle of "local equilibrium" should remain rigorously valid at high gradients and for rapid processes. Theoretically, in fact, one would expect deviations because interactions between adjacent volume increments of material affect the evaluation of entropy. Also one observes experimentally structural and small energetic differences between equilibrium and nonequilibrium phases. The purpose of this paper is to present a thermodynamic framework for the study and correlation of deviations from strict local equilibrium in isothermal diffusion and related processes. This procedure, in effect, preserves the principle of local equilibrium by thermodynamically assigning the deviations from static equilibrium properties to a defect component. Although this theory is entirely phenomenological, the possibility does exist of correlating the theory with experimental observations of defects under favorable circumstances. The most immediate application appears to be to the equilibria at the interfaces in two-phase binary diffusion couples. A recent pertinent work by Eifert et al.1 has shown that the concentrations of aluminum in the a(fcc) and B(bcc) phases at the 0-8 interface in Cu:Cu-12.5 wt pct A1 diffusion couples are greater than those given by the phase diagram. It is postulated by these authors that the supersaturation of the o phase at the interface provides the driving force for the a-to-B lattice transformation; the excess free energy of the a phase, ?Gaxs, arising from the greater-than-equilibrium aluminum concentration is about 3 cal per g-atom. On the basis of the schematic free energy-composition diagram shown in Fig. 1, Eifert et al. concluded that the thermodynamic situation at the interface is one of the partial equilibrium; that is, = for the more mobile aluminum whereas will be reexamined in the latter part of this paper. THERMODYNAMIC PROPERTIES OF DEFECTS A rigorous analysis of the thermodynamics of defects requires an added degree of freedom in the Phase Rule sense, because the standard formulations of solution thermodynamics (partial molal properties of components, free energy minimization, equality of chemical potentials, and so forth) involve the implicit

Jan 1, 1970

By Clark L. Corey, Bogdan Lisowsky

Electrical resistivity, X-ray line positions, degree of order, and microstructures have been investigated for Ni-A1 alloys near the Ni3Al composition. The results indicate that Ni3Al undergoes disordering between 1250oC and the mp; also supersaturated y, produced in y + y&apos; alloys by gas quenching, is extensively ordered prior to y&apos; (Ni3Al) phase separation. The latter reaction, if not both, must follow the cooperative phenomena model. Shifts in line position as a function of quench-indulced super satulration are shown. Lattice pavarneters of equilibriunz and nonequilibrium phases are given. THE objective of this investigation was to determine the mechanism and kinetics of the reactions which occur in Ni3A1 and hypostoichiometric Ni3A1 alloys. The results are of particular significance relative to pre-precipitation phenomena. Early work on Ni-A1 binary compositions near the Ni3A1 composition (13.6 wt pct Al) has been adequately reviewed by Hanssen,1 whose phase diagram is presented in Fig. 1. williams2 verified the suggestion made by Taylor and Floyd3 and others4 that y&apos;, Ni3A1, may precipitate coherently on (100) planes of the y phase (see Fig. 1 for phase nomenclature); he further suggested a two-step precipitation mechanism consisting initially of probably short-range ordering followed by actual precipitation of y&apos;. The precipitation stage in low-aluminum hypo-eutectic compositions has been studied by a number of investigators;*"7 short-range order or "zone" formation have been suggested as explanations for various diffuse X-ray scattering effects. The ordering reaction in Ni3A1 alloys is characterized by a) a very rapid rate of ordering in nonstoi-chiometric compositions, b) absence of a disordered phase region for the stoichiometric compound, y&apos;, or Ni3A1, c) precipitation phenomena as a dominant aspect in hypoeutectic alloys, and d) an increase in elec-trical resistivity on ordering.&apos; The latter two factors were found by Newkirk to characterize ordering in Co-Pt, for which an extensive and detailed analysis was made.&apos; An electrical-resistivity increase on ordering has also been reported for cuAu3.10 PROCEDURE Ni-A1 alloys in the form of 1300-g chill-cast ingots were prepared by vacuum melting electrolytic nickel and high-purity (99.99 pct) aluminum. Very small heats prepared from high-purity carbonyl nickel, supplied through the courtesy of Dr. Goff of the Naval Research Laboratory, were used for comparison with the larger ingots and no differences were noted. The cast material was homogenized in purified argon for a minimum of 72 hr at 1200°C and water-quenched from 1350°C. Compositions studied are given in Table I. The 10 pct A1 alloy was both hot- and cold-rolled. X-ray superlattice line intensities and peak positions were obtained from -270 mesh filings, using CuK, radiation with a LiF crystal monochromat adjusted to receive both 01 and a2. One-degree slits and a 1/8 deg per min scan rate were used to record line traces. A standard tungsten powder, obtained through the courtesy of G.E. Research Laboratory, was used to calibrate line positions.

Jan 1, 1968

By B. M. Larsen

A discussion based on three commercial furnace tests and electrical analogue calculations is presented. It shows that while regenerator efficiency is mainly dependent on loading or relative amount of heat exchange surface plus the heat transfer coefficients as effected by flow velocity, the actual air preheat temperature can be high or low, largely independent of regenerator efficiency, mainly due to the diluting or unbalancing effects of cold air leakage into various parts of the furnace system. THERE are many signs of a renewal of interest in the heat regeneration aspect of the open hearth process, among them being the recent paper by Marsh,&apos; the introduction of auxiliary checkers in the stacks of the Isley furnace design, and a number of recent installations of two-pass checkers in new and old furnaces. However, there are also signs of yielding to the usual temptation of oversimplifying a problem. Faced with the job of obtaining better draft on a furnace, for example, a good designer always recognizes that focusing attention on some one factor, such as height of the stack or capacity of the exhaust fan, does not make his problem any easier; rather he must look at the whole system, including such items as valve resistances, bends in the flues, and flow resistance in the waste heat boiler; then he must make his design in relation to the available draft so as to avoid any serious bottleneck in the system. Yet this example is really much simpler than the problem of air preheating, and again, the latter problem is not really made easier by concentrating on air temperature in uptakes and on the more obvious methods for making this air as hot as possible. Also to be considered are such things as the total amount of air needed theoretically for complete combustion at any selected fuel rate, together with that needed for oxygen absorbed into the bath and for burning the combustible gases given out from the bath, plus some excess air. Furthermore, how does this total air requirement relate to the regenerator efficiency at various loadings? How much of the total air equivalent in stack gases will come from preheated air passed through the whole length of the incoming regenerator and how much from air leakage into various zones of the whole furnace system? Does the effect of leakage air differ depending on whether it leaks into the ingoing regenerator, the furnace above floor level, the outgoing regenerator, or the stack zone? Over a number of years we have in this Laboratory experimented with methods for measuring hot gas temperatures; we have measured, approximately, the efficiency of a few regenerators on commercial furnaces and we have developed an electrical analogue&apos; for calculations of regenerator efficiency. The whole problem is too complex to cover in one paper even with a more complete background of data than we possess, but we can attempt here to clarify certain aspects in a general way, hoping to assist specific plant studies on individual furnaces. Some of our earlier experience has been incorporated into chaps. 4, 19, 20, and 21 in the book "Basic Open Hearth Steelmaking,"" and on the assumption that this text is available to most readers, this discussion has been shortened by references to that book. The most recent design of a flowing-gas thermocouple which we are now using for measurement

Jan 1, 1955

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By N. J. Grant, B. C. Giessen, R. Koch

The system Nh-Ir was investigated over the complete concentration range by metallography and X-my techniques, using forty one alloys. The solubility limits of terminal and intermediate phases and the solidus temperatures were determined. Five intermediate phases were found: a Nb3Ir, cubic, Cr3O type; tetragonal, ofecr thorhomhic, isostruc-turn1 with (ta-Rh); and a Nhlr3. cubic, AuCu, type. a Nb3lr and a Nbfr3 melt congruently; three eutectic and three pentectic reactions occur. The phase diagram of the Nb-Ir system had not been fully treated in the literature; only surveys of intermediate phases were found.1"5 In this study, the details of the phase boundaries were investigated as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS The experimental procedures such as arc melting of powder compacts, heat treatments, solidus measurements, X-ray, and metallographic observation were identical with those used in the work on the Nb-Rh phase diagram.&apos; They will therefore not be repeated here except where the conditions differed. The purity of the niobium powder was as stated in Ref. 6; the iridium powder of 99.9+ pct purity from J. Bishop and Co., Malvern, Penn., did not contain impurities exceeding 100 ppm, except rhodium (200 ppm). The melting points and vapor pressures of both elements are very similar. This fact contributed to a very small weight loss on melting and facilitated preparation of homogeneous alloys. As shown in Ref. 6 for Nb-Rh, no oxygen pick-up exceeding 200 ppm had to be considered; this was regarded as valid also for Nb-Ir. A total of forty one alloys were used in the determination of the phase diagram; their concentrations are shown in Fig. l, which presents the phase diagram. The concentration limits as determined by the weight-loss method averaged <0.2 at. pct, and never exceeded 0.5 at. pct. Heat treatments were carried out as described in Ref. 6. Depending on the concentration, only tantalum, tungsten, or iridium containers were employed, avoiding oxide crucibles altogether. Alloys from 0 to 25 and from 65 to 100 at. pct Ir were homogenized at 2095°C for 15 hr, intermediate compositions from 25 to 65 at. pct Ir for 65 hr at 1780°C. A typical annealing-time schedule is presented in Table I. Solidus points were measured as described in Ref. 6 with the modification that samples rich in niobium were held between pieces of tantalum foil and samples of high iridium concentrations were held between rhenium platelets or in iridium wire. After each run it was ascertained metallographically that no reaction with the holder had occurred. Rhenium was selected as holder material after it had been shown in separate tests that the melting points of Re-Ir alloys rise continuously from 2440°C. Metallographic examination was carried out as described in Ref. 6, and the same procedure and etchants were used successfully. While metallographic discrimination between a Nb3lr and o was easily possible, X-ray diffraction was necessary to separate al and ct2. X-ray powder patterns were taken and evaluated as for Nb-Rh6 yielding the error limits indicated in Table 111, to be introduced later. For the determination of the invariant reactions and phase boundaries, the same techniques as for Nb-Rh6 applied. The general accuracy of invariant concentrations is regarded as somewhat higher than for Nb-Rh due to the small slope of most solvus lines.

Jan 1, 1964

By Prescott Greene

AVAILABLE MACHINES Machines discussed in this section include only rubber tire mounted kerf cutting machines of a self¬propelled electrically powered design. Such machines handle bars up to 4.6 m (15 ft) in length, cutting kerfs of from 115 to 191 mm (4.5 to 7.5 in.). The basic design concept of all machines currently in production is very similar. The chassis features dual driving wheels on the cutter-bar end, fixed directly to the main frame. The steering wheels on the outby end of the frame are articulated in some manner to keep all four wheels on the floor over uneven bottom. Machine power for tramming, and all other functions except powering the cutting chain, is furnished from a pump motor that drives the specific pump or pumps required by a given machine. The cutter chain is driven through a mechanical drive train from a separate electric motor having no duty other than driving the chain. The general arrangement of a cutting machine is shown in Fig. 1; two types of machines, with their specifications are shown in Figs. 2 through 5. A hydraulically powered cable normally is included to eliminate the need for manual cable handling and make this a one-man machine. A bug duster, though optional, is needed for most applications. The bug duster is an hydraulically driven scroll conveyor located directly behind the cutter chain drive sprocket. Its function is to move the cuttings away from the sprocket to prevent them from packing up in this area and consuming a lot of machine power to further pulverize them. Available machines vary from models 610 mm (24 in.) high that can cut horizontally only from 203 mm (8 in.) below ground line to 229 mm (9 in.) above, to machines 1143 mm (45 in.) high that can cut in any plane from 178 mm (7 in.) below the ground line to 3.7 m (12 ft) above it. Most currently manufactured machines fall in the 17 200 to 20 400 kg (38,000 to 45,000 lb) weight range, but can be dis¬assembled for underground installation where weight and size are a problem. Maximum teardown results in all pieces having a weight of 5400 kg (12,000 lb) or less and a size allowing passage through a 1.2 x 2.1-m (4x7-ft) opening. Further reduction in either size or weight of the parts becomes a serious problem. Machines currently being manufactured are avail¬able for use with power supplies of 250 v dc; 500 v dc; 440, 550, or 950 v ac (60 Hz). Also available are machines for use on 415, 500, and 950 v 50 Hz. De¬signs to allow operation on other voltages of either 50 or 60 Hz can be made available without any serious problems. As of September 1977, a typical medium-seam ma¬chine without the extra options needed for unusual conditions, but fully equipped to operate, was selling for about $185,000. CAPABILITIES Materials That Can Be Cut The problem of deciding before a machine is put on the job whether it can work effectively is an old one that has never been completely solved and probably

Jan 1, 1982

By Harry M. Mikami

Chromite is the only ore mineral of metallic chromium and chromium compounds and chemicals. Because of this fact, chromite and chrome ore are used synonymously in trade literature. In commercial market quotations, chrome ore is the term commonly used. Chromite per se, because of properties imparted by its chromium content, is used in refractories and in special purpose molding sands for metal casting. There are many other minerals containing some, generally minor, amounts of chromium, but none are commercial sources of the element (Thayer, 1956). Chromium and chromite have many diverse uses that, directly and indirectly, critically affect vast segments of our modern industrial system. Most important are probably the metallurgical applications wherein chromium is a component of heat-, abrasion-, corrosion-and oxidation-resistant and high-strength alloys of many types. Stainless steels are the largest volume category of chrome-bearing alloys. Chromium chemicals are used in leather tanning, in pigments, dyes and mordants, printing, chemical process industries, photography, pharmaceuticals, metal plating, pure chromium metal production, and for many other purposes. Chromite is a necessary constituent in basic refractories indispensable for the production of steel, copper, cement, and glass. Under present conditions, the US and North America, with the possible exception of Cuba, have no commercial ore reserves. There are chromite deposits, as will be described, but they would be used only under highly abnormal conditions if all outside sources were cut off for an extended period. All chromite used in the US is imported from the eastern hemisphere in which are contained the principal world reserves. The main suppliers in 1980 were the Republic of South Africa (43%), the USSR (21% ), the Philippines (12%), Albania (11 %), Turkey (8%), and others (5%). The strategic nature of chromite is obvious. End Uses-Grades and Specifications As noted before, the three principal uses for chromite are metallurgical, refractories, and chemical with a fourth minor use as foundry molding sand. For metallurgical applications chrome ore is first reduced in electric carbon arc furnaces to various types of ferrochromium alloys. There are high, medium, and low carbon ferrochromiums with carbon ranging from 0.01 up to 10%. Chromium itself ranges from 50 to 73 %. Ferrosilicon chromium and ferrochromium-silicon grades have chromium from 33 to 67% and silicon from 3 to about 48%. Since iron is reduced with chromium, the Cr:Fe ratio of the ore will determine the ultimate grade of the ferrochromium whereas carbon and silicon can be controlled during processing. MgO, A12O3, CaO, and excess SiO2, are removed in slag. A small amount of pure chromium metal is prepared by alumino-thermic and electrolytic processes from essentially iron-free chrome components that have been made via the chemical route. The higher grades of ferrochromium with chromium in the 66 to 73% range can only be made from ores with not only high chromium content, but low iron, i.e., high Cr:Fe ratio. These ores, conventionally termed metallurgical grade, have Cr2O3 contents of 45 to 56% with Cr: Fe ratios of 2.5 to 4.3. A standard composition is generally 48% Cr2O3 and 3:1 Cr:Fe ratio. Very high grade ores are often blended with lower grades even with the high iron chemical grade. For some ferrochromiums, additions of high alumina refractory grade are used as slag conditioners to facilitate smelting while still contributing chromium values. A lower grade ferrochromium, the high carbon charge chrome, has become the predominant grade in use today for making chromium-bearing steel alloys. This

Jan 1, 1983

By F. O. Shuck, F. E. Butler

A diaphragm diffusion cell suitable for use with liquid metals was designed and tested by measuring the diffusion coefficients for a Hg-10 pct In alloy at 25°C. The binary diffusion coefficient and the coefficients for In and Hg tracers were measured at this composition. The measured coefficients for both tracers were less than the binary diffusion coefficient. When these coefficients were combined with the activity correction term of Darken, the predicted binary coefficient was somewhat higher than the experimental value. In recent years a number of investigators have been studying diffusion of liquid metals in order to gain a better understanding of the liquid state and to examine possible applications to liquid metal processing. The bulk of this work has involved either self-diffusion or diffusion of low concentrations of solute metals in an essentially pure solvent metal. The most common experimental technique employed has been the capillary-reservoir method of Anderson and saddington1 since it is well-suited to measurements involving low concentrations of solutes. As an expansion of previous studies, an investigation of the variation of diffusion coefficient over large composition ranges has been undertaken in this laboratory. Although it is possible to modify the capillary-reservoir method for such measurements, the technique loses its principal advantage of requiring only small quantities of solutes. Therefore, it was felt desirable to investigate other possible experimental techniques applicable to measurements over large composition ranges. A technique which has been used widely in measurements of other liquid systems and seemed potentially applicable to studies of liquid metals was the diaphragm cell. This method has been found to combine relative simplicity of operation with accurate and reproducible results. In use with normal liquids, the tyiical diaphragm cell utilizes a porous glass disk. However, because of the high surface tension, it is not possible to use a diaphragm of such fine pore structure with liquid metals. Furthermore. projected use at high temperatures makes the use of glass undesirable. Consequently, the first problem was the search for an appropriate cell design. EXPERLMENTAL Diaphragm Cell. A number of possible cell designs were examined. Prototypes of several were constructed and tested. The final design is shown in an exploded view in Fig. 1. The cell consists of two identical chambers, one on either side of a 0.20-in.-thick partition. The chambers are 0.15 in. deep and have a volume of 3.45 cu cm. Each chamber is provided with two small threaded holes for filling and emptying. The filling holes may be sealed with stainless-steel screws. Drilled lengthwise through the center partition is a 0.250-in.-diam hole. Inserted into this hole is a rod having seven 0.059-in.-diam holes drilled radially through it. The total "hole" volume is 0.078 cu cm. When the rod is properly aligned, the holes in it constitute the "diaphragm" through which diffusion occurs. The center section was of Teflon and the rod and face plates were of Plexiglas. Four such cells were constructed and used in this study. Subsequent to this investigation, a similar cell constructed entirely of iron was fabricated and tested at higher temperatures. Several considerations led to this final design. It is desirable to minimize the volume of the cell chambers to decrease the time required for a measurement. However, the total volume of metal in the diaphragm must be small in comparison with that in the chambers. To facilitate filling and emptying it is desirable to have a diaphragm which may be closed.

Jan 1, 1970

By R. L. Rickett, S. H. Kalin, J. T. Mackenzie

Aluminum killed low carbon steel, § which is now used extensively for severe deep drawing or other difficult forming operations, is unusual in that its grain structure, after cold reduction and box annealing in accordance with conventional continuous sheet or strip mill practice, often is elongated, although at times it is equiaxed. Since this unusual structure has been found superior for many, but not all, severe forming operations, recrystallization of the steel, both at constant temperature and on continuous heating, was investigated and compared with that of rimmed steel in the hope that something might be learned about the mechanism of, and the factors controlling, the formation of such elongated grains. In this structure, the grains are elongated both in the lengthwise direction of the strip and transverse to this direction, even though nearly all of the extension in both hot and cold rolling is in the lengthwise direction. The grains are thus roughly pancake-shaped, being longer and wider than they are thick, as observed also by Burns and McCabe,1 and as illustrated by the typical structures shown in Fig 1. Fig la, representing a conventional longitudinal section, shows the length and thickness of the grains, whereas Fig Ib shows their length and width as seen by examining a section parallel to the sheet surface. Both illustrate the very irregular grain boundaries usually associated with the elongated grain shape. A finer equiaxed grain structure in this same grade is shown in Fig Ic. Either the elongated or the equiaxed structure may be present in the annealed product, and in rare instances the two types may coexist in a single specimen, as shown in Fig 1 d. Isothermal Recrystalliza-tion of Rimmed and Alamimum Killed Steel An aluminum killed steel known to have an elongated grain structure after conventional processing (Steel B, Table l), was selected for the initial recrystallization studies; for comparison, a rimmed steel, A in Table 1, was used. Samples of each in the form of hot rolled strip 0.075 and 0.095 in. thick, respectively, were cold rolled on a small laboratory mill in steps of about 0.010 in. per pass to obtain total reductions of 40 and 60 pct. Small pieces of the cold reduced strip were heated in lead at selected constant temperatures for one of several periods of time, then cooled in air. Rate of heating in the lead was, of course, very fast. Hardness of the cooled specimen was measured and a longitudinal section examined metallographically. Isothermal recrystallization curves for these two steels at 1050°F, based on hardness of the air cooled specimens, are shown in Fig 2 in which the amount of recrystallization corresponding to each plotted point is indicated. The marked difference in the behavior of these two types of steel is evident. After a corresponding amount of cold reduction, the rimmed steel recrys-tallizes in a much shorter time than the killed steel and the shape of its recrystallization curve, (plotted on a logarithmic time scale), is very different. The curve for rimmed steel indicates that recrystallization is analogous to isothermal transformation of aus-i.enite in that it proceeds at a progressively faster rate up to some 50 pct recrystallization, then at an increasingly slower rate. For the aluminum killed steel, however, the start of

Jan 1, 1950

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS&apos; calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c&apos;, in certain bee metals and alloys are the result of large negative contributions to c&apos; = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.&apos; On this basis, and following Zener,2 the association between high c/c&apos; ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

By D. L. Soreck

The hazards to the public posed by abandoned mine shafts are well documented. As private development encroaches on previously mined areas, the potential for fatalities and serious injuries from abandoned mine shafts increases. The U.S. Bureau of Mines has conducted research into cellular concrete as a material for sealing these openings. The current work involves testing the characteristics of cellular concrete before and after it had been pumped or dropped from different heights into a simulated mine shaft. Cellular concrete was pumped vertically up to and subsequently dropped from heights of 18 and 37 m into concrete forms. Wet density measurements were made at multiple sampling points in the test circuit. Air content determinations and uniaxial compressive strength testing were conducted. Research results showed significant loss in air content and changes in the characteristics of cellular concrete during pumping or dropping from various heights. Recommendations on effective use of cellular concrete for sealing abandoned mine shafts are made.

Jan 1, 2010

By C. Bazin

The fundamental error associated to the sampling of heterogeneous ore particles is unavoidable and can only be minimized by an adequate selection of the sample mass and/or size reduction of the sample before division into sub samples for testing or assaying. The preparation of ore batches to carry out the mineral processing evaluation of an ore is a sampling process. The fundamental error associated with the division of the ore into batches is responsible for the differences in the composition of the batches. This paper attempts by various means to assess the reproducibility of the gold content of test batches prepared from a gold ore sample. The results of the investigation shows that for fine gold grain sizes the variability in the composition of the batches is less than that predicted by Gy?s formula and that the gold grain size is a strategic information in the assessment of the gold content variability of test batches.

Feb 23, 2014

Production scheduling of open pit mining is a key area as it deals with the management of operating cash flows of mining companies. The efficiency of long-term schedules is usually assessed with economic criteria such as net present value (NPV), discounted cash flow rate of return (DCFROR) and payback period, which are not sufficient on their own for revealing the complex picture of the decision-making process.This paper offers a thorough analysis of the most important contemporary criteria of long-term production scheduling, as way to provide the mining practice with a new approach to the decision-making process. The list of criteria includes technological, economic and probabilistic ones. A&#160;detailed case study is provided aiming to illustrate the applicability of the criteria for comparing the scheduling approaches regarding the economic interests of a mineÆs owner and contractor. The results obtained can be used for revealing new trends in the current methodology of open-pit production scheduling optimisations.

Sep 26, 2011

As a bubble travels through the pulp region of a flotation cell, it will collect the most hydrophobic particles of an intermediate particle size range, this being the primary source of true flotation selectivity. Despite its role on bubble-particle attachment, however, particle hydrophobicity is still missing a mathematical definition that can be used for plant simulation. In this paper, particle hydrophobicity is defined in terms of the induction time necessary for attachment and then linked to the mass of collector adsorbed per particle. This allows particle hydrophobicity to be written as a function of density of collector adsorption as well as particle size and mineralogy. The model is calibrated from the experimental measurement of the flotation rate constant. Liberation data from an industrial flotation rougher is used for model validation. It is demonstrated that the model can describe a broad experimental dataset by means of a minimal number of parameters. Main industrial application is in simulating the effect of the chemical environment upon plant metallurgical performance.

Jan 1, 2006