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By Robert J. Linney

IN the latter part of the year 1943, it was decided to experiment with diamond-drill blast holes in the Old Bed magnetite mine at the Mineville mines of the Republic Steel Corporation, in sections of the ore body where vertical dimensions were large and where development for sublevel bench stopes had already been done. Other possibilities of application for this drilling method were in the reclamation of old floors and pillars in the pitching folds of the Lower Old Bed ore body and in the reclamation of large vertical pillars in the " 21 " Bonanza-Joker ore body. The cross sections and views of the two ore bodies will show the conditions to which the diamond-drill method has been applied. The Lower Old Bed magnetite ore body is lenticular and dips approximately 30° toward the southwest and strikes generally southeast and northwest. An intensely folded structure, which pitches generally on an axis approximately at right angles to the strike, is continuous from the uppermost old workings down to the present bottom of the mine, and probably continues with depth. On successively lower levels this folded structure becomes greater in vertical dimensions and the two folds are closer together in a horizontal dimension. As shown in Fig. 1, this folded structure gives to parts of the ore body considerable vertical dimensions, which provide areas that were developed for sublevel bench stoping above a slushing drift, as shown in Fig. 2. It was in one of these previously developed sublevel bench stopes, No. 26 on the 1185-ft. level, that the diamond-drill blast-hole method was applied for mining the upper sublevel. The lower sublevel was underhand-bench-drilled to the finger raises of the scram drift below. The roof of this stoping area began to break and spall on the lower sublevel, causing the roof to become inclined. Along the hanging wall of the stope this reached an elevation about half way between the two sublevels. A smooth schistose seam in the hanging wall causes the ore to break away freely. Therefore, if bench mining had been carried on in the upper sublevel, a dangerous condition of poorly supported benches would have resulted. When the drillers were slashing across the sublevel to footwall and hanging wall to make a bench, spalling roof of the opening below would probably have carried away part of the bench, and would have left a dangerous place in which to continue underhand benching. A 6 by 8-ft. raise had been driven between the lower stope and the upper sublevel about 200 ft. from a manway. It was decided to use this raise for a starting cut and to arrange holes as shown in Fig. 3, so that a slot would be opened across the ore body between the footwall and hanging wall. This slot would then be used for the purpose of breaking into the ore; by blasting vertical rings of holes drilled at right angles to the axis of the pitching folds as nearly as possible. Layouts of this slot drilling and the rings adjacent are

Jan 1, 1945

By Robert J. Linney

In the latter part of the year 1943, it was decided to experiment with diamond-drill blast holes in the Old Bed magnetite mine at the Mineville mines of the Republic Steel Corporation, in sections of the ore body where vertical dimensions were large and where development for sublevel bench stopes had already been done. Other possibilities of application for this drilling method were in the reclamation of old floors and pillars in the pitching folds of the Lower Old Bed ore body and in the reclamation of large vertical pillars in the "21" Bonanza-Joker ore body. The cross sections and views of the two ore bodies will show the conditions to which the diamond-drill method has been applied. The Lower Old Bed magnetite ore body is lenticular and dips approximately 30° toward the southwest and strikes generally southeast and northwest. An intensely folded structure, which pitches generally on an axis approximately at right angles to the strike, is continuous from the uppermost old workings down to the present bottom of the mine, and probably continues with depth. On successively lower levels this folded structure becomes greater in vertical dimensions and the two folds are closer together in a horizontal dimension. As shown in Fig. I, this folded structure gives to parts of the ore body considerable vertical dimensions, which provide areas that were developed for sublevel bench stoping above a slushing drift, as shown in Fig. 2. It was in one of these previously devel-oped sublevel bench stopes, No. 26 on the 1185-ft. level, that the diamond-drill blast-hole method was applied for mining the upper sublevel. The lower sublevel was underhand-bench-drilled to the finger raises of the scram drift below. The roof of this stoping area began to break and spall on the lower sublevel, causing the roof to become inclined. Along the hanging wall of the stope this reached an elevation about half way between the two sublevels. A smooth schistose seam in the hanging wall causes the ore to break away freely. Therefore, if bench mining had been carried on in the upper sublevel, a dangerous condition of poorly supported benches would have resulted. When the drillers were slashing across the sublevel te footwall and hanging wall to make a bench, spdlling roof of the opening below would probably have carried away part of the bench, and would have left a dangerous place in which to continue underhand benching. A 6 by 8-ft. raise had been driven between the lower stope and the upper sublevel about 200 ft. from a manway. It was decided to use this raise for a starting cut and to arrange holes as shown in Fig 3, so that a slot would be opened across the ore body between the footwall and hanging wall. This slot would then be used for the purpose of breaking into the ore, by blasting vertical rings of holes drilled at right angles to the axis of the pitching folds as nearly as possible. Layouts of this slot drilling and the rings adjacent are

Jan 1, 1946

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By R. W. Stahl

Employees and dollars are necessary to all enterprises and any force, such as fire, which destroys either, can bring very serious consequences, including business failure. Since everyone acknowledges the necessity of conserving human life, we will devote most of our paper to the economic factors involved. A coal-mine fire is considerably more difficult to combat than a fire in a surface building because of the combustible surroundings in the mine, the explosive gases emitted from the coal, the suspension of explosive dust when mine timbers burn and the unsupported roof falls, the limited space in which approach to the fire can be made, and the limited avenues of escape. A survey of coal-mine-fire protection indicated that a rather low value was being placed on property and equipment. This prompted comparison with other industries. The comments made in this comparison are not intended as an indictment of the coal industry, since we do have mines that are well protected against fire, but the comments on conditions at the mines visited are factual and may help others to improve similar conditions. SURVEY PROCEDURES Plants of the steel, aluminum, rubber, chemical, and petroleum industries were surveyed, and all facets of the fire-protection scheme were covered. The industrial plant invariably had four times as much water readily available for instant use than the mine. In many mines where water is available, no equipment for applying it is provided, such as hose, nozzles, and adapters, so that time is lost in collecting this equipment. (See Table I.) EXTINGUISHERS Many more and generally larger portable extinpishers are available at the plant as compared to the mine. The extinguishers are generally placed nearer to sources of danger. In addition, respiratory protective equipment is always available at strategic points in plants but only in a few mines. (See Figs. 1 and Table 11) INSPECTING AND TESTING EQUIPMENT Plant water facilities are checked weekly and flushed at 6-month intervals, and hose is pressure-tested at least yearly; some mines check water yearly, but hose is not tested unless used. Fire extinguishers are inspected weekly in plants and completely overhauled yearly; one mine had monthly checks and overhauls only after use. FIRE BRIGADES AND TRAINING Every plant had designated fire-fighters and some complete full-time brigades; at one mine a chief mechanic was designated as being in charge of fires, and other depended entirely upon officials who might not be familiar with the equipment. COST OF FIRES AND PERCENTAGE OF CAPITAL INVESTMENT IN FIRE PROTECTION The direct cost of recent mine fires ranged from $128,000 to $240,000; indirect costs, such as lost tonnage, idled equipment, lost orders, and the like might run the cost to over $500,000. (See Figs. 2 and 3).

Jan 1, 1961

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer's knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer's attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer' for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR'S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR'S have been quite high for the last several years of reported history.

Jan 1, 1952

By C. W. Hoffman, W. R. Hinken

Probability sizing, a fairly recent development in the field of particle separation, is now under investigation to determine its value to the mining industry. The method employed is probability sizing through a vibrating network of decreasing screen openings. While probability sizing is not new, the possibility of using it for coarse, highly abrasive ores at high tonnage rates has only recently appeared to merit practical consideration. The advantages of probability sizing vs. conventional screening methods are: (1) reduced space requirements for a high capacity unit, (2) fewer moving parts, (3) more versatile product sizing selection, (4) reduced maintenance requirements, and (5) lower power consumption. Screening is a necessary part of virtually every crushing circuit. At some stage in the process, particle separation becomes a controlling factor in the operation. The basic type of screen in use today is the vibrating unit, which usually employs a mechanical vibrator of one type or another to obtain sizing and material transportation across the screen surface. The vibrating screen has its limitations and inherent problems. Operators must live with: (1) high maintenance — worn rods, screen cloth, spacers, cross members, chutes, etc., (2) low capacity in relation to floor space requirements, (3) extreme noise levels, (4) high power consumption, and (5) structural problems in the screens and supporting steelwork. All plant operators have become tolerant of these drawbacks through the years, and little innovation has been developed in screening. The vibrating screens in use today incorporate improved metals, more efficient power sources, better lubricants, and increased manufacturing skill, but the basic machine itself remains unchanged. Screening is a relatively small part of most plants' operating expenditures and gets relatively little attention from research and development. The HiProb sizer is a new approach to the problem of particle separation on a high tonnage basis. Developed by Dr. Fredrik Mogensen (president of Fred-rik Mogensen, A. B. of Djursholn, Sweden), this unit has found its primary acceptance in the sizing of wet or dry materials in the fine ranges. Climax has been working cooperatively with Mine and Smelter Supply Company, the United States licensee, on the adaptation of the sizer to obtain consistent recovery at a high tonnage rate on a — 3/8-in. separation. This was a new application for the sizer and opened up a whole new field of problems. Dr. Mogensen's machine utilizes the control of normal probability of falling particles and is designed to eliminate some of the undesirable features of vibrating screens mentioned earlier. The machine is light, compact, consumes less power than conventional screens and has a low noise level. PRINCIPLES Probability sizing is a process designed to allow solid particles to segregate with a high ratio of the materials reporting into their respective size fractions with a minimum amount of misplaced particles. Sizing is defined in this paper as segregation of dry solid particles into fractions of comparable sizes. Probability is usually estimated as the ratio of the number of ways an event might occur vs. the total number of allowable ways. The probability process described depends upon the fact that particles falling through a network will segregate across the sizing surface even though all openings are larger than the particles. The degree of segregation is dependent upon the particle size and the trajectory applied by the sizing network to each falling particle. Specifically, the process utilizes a maze made up of screen cloth to control the path of a particle in free fall as illustrated in Fig. 1. The usefulness of this probability sizing process is dependent upon the degree of efficiency of an effective maze. Primarily, a maze must be extremely flexible to meet the multi-faceted nature of solid particles and, at the same time, the degree of control must be reproducible so that a desired separation is predictable. Dr. Fredrik Mogensen has formulated a maze that is not only flexible and easily controlled, but, mote importantly, easily adaptable to a working machine.

Jan 1, 1970

By Joseph B. Story, John T. Clarke

A modification, of the Kelvin bridge using an inductor was used to measure the conductivities of molten sodium chloride, calcium chloride, and mixtures thereof. A capillary-type four-lead fused quartz dipping cell was constructed. The effect of a small amount of potassium chloride on the conductivity of the melt was determined. IN the electrowinning of sodium and chlorine from sodium chloride in Downs cells, calcium chloride is added to the sodium chloride in an approximately equimolar amount to permit cell operation at a lower temperature. This lower temperature improves current efficiency and ease of operation, but decreases voltage efficiency by decreasing the electrical conductivity of the melt. A knowledge of the electrical conductivity of the Downs cell melt is necessary to the understanding of Downs cell operation, for the IR voltage drop across the melt is responsible for a significant part of the electrical power consumed by the cell. The work of previous investigators on fused sodium chloride-calcium chloride mixtures was reviewed from the standpoint of consistency with the results of others on the conductivities of the pure constituents. The electrical conductivity of pure fused sodium chloride has been established with accuracy by Van Artsdalen and Yaffe,1 by Edwards, Taylor, Russell, and Maranville,2 and by Lee and Pearson.3 It has also been studied by a number of other investigators.4-13 The best values for calcium chloride are believed to be those of Lee and Pearson,3 since the sodium chloride and potassium chloride conductivity values given by them check the best literature values. A number of other investigators have also reported values for calcium chloride.'-"."' Electrical conductivity data for fused sodium chloride-calcium chloride mixtures have been reported by Sandonnini,12 Vereshchetina and Luz-hnaya,18 Ryschkewitsch,11 Barzakovskii,5 and Alaby-shev and Kulakovskaya.15 Sandonnini reports no data at temperatures lower than 850°C. The conductivity values reported by Vereshchetina and Luz-hnaya, by Ryschkewitsch, and by Barzakovskii for pure sodium chloride and for pure calcium chlor- ide vary somewhat from the literature values believed to be best and the sodium chloride-calcium mixture data of these authors and of Alabyshev and Kulakovskaya (who give no data for the pure compounds) show significant variations. In view of these facts, it seemed that an investigation of the electrical conductivities of fused sodium chloride-calcium mixtures would be worthwhile. Apparatus Bridge System—The bridge used,in this investigation is diagrammed in Fig. 1. In general, the elaborations of this bridge over the simple Wheatstone bridge were for the purposes of a) eliminating lead resistances or making them accurately measurable, and b) eliminating major capacitative and inductive effects or balancing them against each other. Lead resistances in the lower arms of the bridge were kept as low as possible by making the leads short and of low resistance wire. This could not be done in the cell arm of the bridge because of the remoteness of the cell from the other bridge components and because of the high-resistance nickel or chrome1 wires used in the cell. Since maximum sensitivity is attained when the resistances of the four arms of the bridge are equal, 50-O resistors were used in the lower arms of the bridge when fused salt conductivities were being measured, and 1000-O resistors were used when the cell was being calibrated with normal aqueous KCl solution. The cell resistance was of the order of 50 ohms with fused salts and of the order of 1000 ohms with normal aqueous KC1 solution. The resistors used were non-inductive and accurate to 50.05 pct (General Radio Co. Types 500-C and 500-H). The lead resistance between point A in the cell and point E at the measuring resistor was eliminated by using the kelvin bridge principle; that is, the voltape drop across the lead from point A to point E was divided between the cell arm of the bridge and the measuring arm of the bridge in proporation to the resistaxes in the lower arms of the bridge.

Jan 1, 1958

Jan 1, 1968

By Ivan B. Cutler, Milton E. Wadsworth

Coprecipitation of anionic and cationic polyelectrolytes has been applied to flocculation of several mineral systems. Results obtained in a study of the flocculation of kaolinite and hematite suspensions of polycationic and polyanionic electrolytes are presented. Greatly increased settling rates were observed following precipitation of positive and negative polyelectrolytes on the surface of finely divided minerals in aqueous suspension. The ratios of polycationic to polyanionic electrolytes required to produce maximum sedimentation have been shown to correspond closely with the equivalence points obtained by light scattering studies of systems containing the positive and negative polyelectrolytes by themselves.

Aug 1, 1956

By W. O. Philbrook, H. E. Burner, F. S. Manning

The equation of continuity for the hydrogen reduction of hematite in a fixed bed of closely-sized particles is solved assuming a flat velocity profile, negligible temperature gradients, md negligible axial diffusion. A kinetic expression from the literature is used which assumes the reduction process is controlled at the oxide-metal interface. The integral fractional conversion is computed, and the importance of particle diameter, flow mte, temperature, bulk axial diffusion, and inter- and intra-particle mass trarnsfer is predicted. Comparison with experimental data suggests one or more additional undefined variable(s) is significant. Equipment modifications are suggested for fidture experimentcll work. WITH the increasing desire to "design" the ore feed of a blast furnace, it has become necessary to define more quantitatively the process variables and to evaluate the extent of their control upon the reduction process. The bulk of the work reported in the literature has centered about the reduction of single particles; however, the blast furnace process more closely resembles reduction of a fixed bed than that of single particles. To simplify this analysis, the isothermal reduction by hydrogen of a natural hematite in a fixed bed of closely-sized particles is examined. With appropriate modifications in the kinetic and flow rate expressions, the approach employed should be extensible to mixtures of carbon monoxide, hydrogen, and inert nitrogen, and to adi-abatic conditions, thus approaching the blast furnace process more closely. The fixed bed variables which are investigated in this study are particle diameter, flow rate, temperature, and bulk axial diffusion, as well as inter-and intra-particle mass transfer. Of particular interest is the effect of particle size upon fractional conversion for a bed operating under constant pressure drop. The constant pressure drop concept bears a close resemblance to the blast furnace process, where regions of larger particles may provide a greater permeability to divert most of the reducing gas flow from the regions of smaller ore particles. Under such conditions one would expect qualitatively that, for sufficiently small particle sizes where the flow rate is small and the total surface area is large, the reduction rate would be limited by the gas flow rate. Initially the gas entering the bed reacts very rapidly and the composition approaches the equilibrium conversion value a short distance from the reactor inlet. This concentration "wave-front" then moves up the bed as the flow of reducing gas is continued, leaving in its wake an ever increasing layer of reduced particles. Providing that the reducing gas leaves the bed at equilibrium concentrations, conversion is expected to increase with an increase in flow rate, and hence with an increase in particle diemater. Conversely, for sufficiently large particles the flow rate will be high but the surface area available for reaction will limit the reduction rate. Since the total surface area decreases with an increase in particle size, conversion, in this case, is expected to decrease as the particle diameter is increased. It is clear then that between these two extremes an optimum particle diameter must exist. THEORETICAL DEVELOPMENT Above the temperature where wiistite is stable (about 560°C) the reduction of hematite proceeds through the series Fe2O3/Fe3O4/FeO/Fe. On the basis of microstructural studies and earlier work, Edström1 has postulated a mechanism for the reduction of an ideal hematite lattice: 1) Iron phase formation at the boundary between wiistite, iron, and gas (for sufficiently porous iron). 2) Diffusion of iron across a wustite layer. 3) Phase boundary reaction of Fe3O4 to FeO. 4) Diffusion across a dense magnetite layer. 5) Phase-boundary reaction of Fe2O3 to Fe3O4. According to the mechanism postulated, gaseous reaction product has to be removed only at the boundaries between wüstite and iron or gas, the only possible exception being enveloped Fe3O4 specks. On this basis McKewan2,3 has proposed that one may consider the hematite reduction process as a simple two-phase system of oxide/metal. If, for FeO and Fe3O4 layers of negligible thickness, the hypothesis is made that the rate of formation of a

Jan 1, 1963

By H. E. Cline, E. F. Koch, J. L. Walter

It has been postulated and, in a few instances shown, that some kind of dislocation structure will be present at semicoherent interfaces to accommodate small lattice mismatches. In the present study of the NiAl-Cr eutectic, regular arrays of interface dislocations are observed at the boundary between the chromium-rich rods and the NiAl-rich matrix. The networks were examined by transmission electron microscopy and selected area diffraction. The rods and the matrix have a crystallographic relationship in which all directions and planes of the two phases are parallel. The dislocation networks are cmposed of a<100> dislocations lying on the intersections of the cylinders with (100) planes. Dislocations forming hexagonal rather than square arrays are also observed at certain areas of the network. The morphology of the network is consistent with the interpretation of mismatch being accommodated by interface dislocations in the cylindrical geometry. The measured spacing between dislocations was used to calculate an apparent lattice mismatch between the phases (˜0.35 PCt)interface network energy (-140 ergs per sq cm), and network strengthening (-10,000 psi). It has been proposed by Frank and Van der Merwe1 that dislocations should be present at the boundary between two semicoherent crystallographically related phases. The role of the interface dislocations would be to reduce the internal stresses, caused by the mismatch in atomic spacing across the interface. Such dislocations have been observed at the interface between expitaxially grown films and Substrates.2-4 Interfacial dislocations have also been observed at precipitate-matrix interfaces.&apos;-&apos; Directionally solidified eutectics have been shown to have semicoherent phases1&apos; and would, therefore, be expected to have interfacial dislocations as found by Weatherly at a lamellar fault in A1-A12Cu.11 The NiAl-Cr eutectic appeared to be a promising system to examine because both phases are cubic, the lattice mismatch is small, and the phases are crys-tallographically related. Furthermore, the eutectic is easily thinned for transmission microscopy. Indeed, interfacial dislocations were observed and this report describes the nature of the dislocation networks in the boundary between the NiAl-rich ma-trix-phase and the fine chromium-rich rods.21 I) EXPERIMENTAL PROCEDURE Ingots, 3/4 in. in diam and 6 in. long were made by melting in vacuum and casting under argon using 99.9 pct pure material. The composition, in at. pct, was 33 pct Ni, 33 pct Al, and 34 pct Cr. The ingots were then placed in A1203 crucibles on a water-cooled base, melted by means of induction, and withdrawn from the hot zone at the rate of 1 in per hr under argon.* * T his material was first directionally solidified in this laboratory by E. R. Stover Slices were taken perpendicular to the growth direction of the directionally solidified ingot for metallography and for transmission electron microscopy. The electron transmission samples were thinned mechanically, then thinned electrolytically in A-2 electrolyte* *A-2 electrolyte: 62 ml perchloric acid, 700 ml ethanol, 100 ml butylcellosolve, 137 ml distilled H20. until a hole appeared in the foil. 11) EXPERIMENTAL RESULTS A) Optical Microscopy. The microstructure, viewed on a plane perpendicular to the growth direction, is shown in Fig. 1. The structure consists of cells or colonies of parallel chromium-rich rods in the NiAl matrix. The cells occur when there are impurities present12 or, in a ternary eutectic, if the composition is slightly off the eutectic composition. The axis of the chromium-rich rods is parallel to the growth direction except near the cell boundaries. Here the rods may assume angles to the growth direction; however, examination shows that the crystallographic relationship between the rod and the matrix remains the same. Fig. 1 includes cell boundaries where the rods formed at a large angle to the growth direction. The variation of rod position across the cells made it possible to Fig. 1-Structure on plane perpendicular to growth direction. Rods near cell walls are at large angle to growth direction. Magnification 315 times.

Jan 1, 1970

By J. O. Edstrom, G. Bitsianes

Parabolic rate constants were determined for the formation of wiistite by the solid state reaction between magnetite and iron. The reaction was diffusion controlled and inert marker studies indicated that the mass transport through the wiistite layer was accomplished by means of iron migration. Relationships between rate constants and self-diffusivities are discussed. The transport capacity for iron through dense wustite layers was found to be sufficient to carry on reduction, even in gaseous reduction processes. REDUCTION of iron oxides has been the subject of many investigations. Most of the work, however, has been done on rather crude material and there have been difficulties in correlating the data on a quantitative basis. The reverse process of the oxidation of iron has been studied more thoroughly and usually by starting from the pure metal. As a result, the mechanisms of oxidation are now fairly well known.It has generally been found that the oxidation of metals follows the so-called parabolic 1aw;Q hat is, when the oxides are formed as dense layers, their thicknesses are proportional to the square root of the reaction time. This parabolic law follows directly from Fick&apos;s first law of diffusion The flux, J, is defined as the quantity of diffusing substance passing per unit time through unit area of a plane at right angles to the direction of diffusion. This flux is proportional to the concentration gradient of the diffusing substance, and the factor D, known as the diffusion coefficient, is introduced as the proportionality factor with dimensions of (length)&apos;/time. If the flux is measured as the increase of thickness of the oxide layer (Ax) per unit time (t) and the assumption is made that the concentrations of the reactants at the phase boundaries of the layer are independent of time, Eq. 1 reduces to Integration of this expression yields the parabolic function ax = k . t. [31 The product of the diffusion coefficient and the concentration difference across the oxide layer is included in the constant k. When iron is exposed to a highly oxidizing atmosphere, the oxide phases are formed normally in a topochemical fashion, i.e., the interfaces between the phases maintain parallel positions to the original surface of the specimen. Above 570°C, the phases are orientated usually in the order of iron, wiistite, magnetite, and hematite, a condition in conformance with the requirements of the Fe-0 system. Below 570°C, the wiistite phase is unstable and has not been found as a normal constituent in the oxidation products of iron. There is a strong probability that continuous layers of the solid oxides are formed as the specific volumes of the phases increase in direct order from iron to hematite.&apos; , &apos; Regarding mass transport through dense solid oxide layers, Wagner&apos; has postulated that diffusion in oxides generally may be interpreted as migration processes of ions and electrons. There must be normally a concentration gradient across the growing oxide layer for diffusion to occur. This condition requires that there be deviations from the ideal stoi-chiometric composition of the oxide and accordingly deviations from the strict order of an ideal lattice. Such "lattice defects" include interstitial ions, cation and anion vacancies, quasi-free electrons, and electron holes and are decisive for all migration processes.&apos; Cations, anions, and electrons all may have some mobility in the oxides but the movement of one of the particles generally far exceeds that of the others. Previous work&apos;, 1,2,7 has shown that during the oxidation of iron the migration through the wiistite layer, and probably also the magnetite layer, is confined to the movement of iron ions. Migration through hematite, however, has been found to take place by oxide ion movement. These behaviors are in direct agreement with the type of vacancies present in the respective oxides. Reduction of Iron Oxides The gaseous reduction of iron oxides, like the oxidation of iron, takes place in a topochemical fashion at distinct interfaces between the appearing phases."-&apos;" Porosities might be expected in these reaction products, since their specific volumes are less than that of the starting material. Frank and van Der Merwe" have shown, however, that it is theoretically possible for nonporous layers to form if the degree of misfit in specific volume is less than about 15 pct. These aspects on porosity formation

Jan 1, 1956

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick&apos;s First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood&apos;s analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner&apos;s diffusion-controlled kinetics is based upon the same form of mass balance using Fick&apos;s First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By Robert Baschwitz, John Chipman

The distribution of silicon between liquid silver and Fe-Si-C alloys has been studied at 1420oand 1530°C. The data are consistent with earlier studies. New data of Hager on the liquidus lines of the system Ag-Si and the distribution data are used to obtain the activity coefficient of silicon in both liquid phases. Data on the heat of mixing in iron permit accurate extension to 1600°C. Equilibrium data involving SiO2 and silicon in liquid iron together with revised data on the free energy of SiO2 are used to fix the activity of silicon in the infinitely dilute solution. The binary system exhibits strong negative deviation from ideality. At infinite dilution ? Si at 1600" is 1.25 x 10&apos;3, and at concentrations up to NSi = 0.4 the slope d InySi/dNSi has a constant value of r; = 13. It is found that logysi in the ternary solutzon is approximately but not exactly the same function of Nsi + NC as of NSi in the binary. The results are consistent with currently available data on the free energy of Sic and its solubility in molten iron. LIQUID solutions of the system Fe-Si-C have acquired considerable importance as the laboratory prototypes of blast furnace hot metal. Equilibrium studies involving such solutions and slags approximating those of the blast furnace have yielded useful information concerning the thermodynamic properties of blast furnace slags. In studies of this kind great importance attaches to a knowledge of the thermodynamic activity of silicon in the solution as a function of temperature and composition. An attempt was made by Chipman, Fulton, Gokcen, and askey&apos; to evaluate all of the pertinent data on this system and to deduce the desired relation between activity, composition, and temperature. These authors published data on the solubility of graphite and Sic in molten Fe-C-Si solutions and on the distribution of silicon between liquid iron and liquid silver. They showed further how the activity of silicon in very dilute solutions in liquid iron could be calculated from equilibrium data involving the molten alloy and solid SiO,. These calculations rested on the published thermodynamic properties of SiO, in- cluding its heat of formation which at that time was recorded as -209.8 kcal. This value has been under suspicion for some time and has recently been replaced by the concordant results from two independent laboratories2,3 which place the heat of formation of a-quartz at -217.6 kcal. This revision necessitates a re-evaluation not only of the activity of SiO2 in slag but also of silicon in molten iron. It is the purpose of this paper, therefore, to recalculate the activity of silicon, and in furtherance of this objective to present new data on its distribution between liquid Fe-Si-C alloys and liquid silver. HEAT OF SOLUTION OF SILICON IN IRON In order to determine the effect of temperature upon the activity coefficient it is necessary to know the heat of solution of silicon in iron as a function of composition. This is found in the data of Korber and Oelsen4 shown in Fig. 1. The curve corresponds to the following equation, which is of a form suggested by Wagner:5 Here AH is the heat absorbed in kilocalories in forming one gram atom of molten alloy from its molten elements and the N&apos;s are atom fractions. The relative partial molal enthalpies of the components, each referred to its pureliquid state and defined as zFe = aFe - PFe and zsi = HSi — -psi, are shown graphically. At low concentrations zSi = -28.5 kcal, in agreement with Kijrber and Oelsen&apos;s computation. This is in good agreement with the value of -29.3 kcal obtained by Chipman and Grant6 using an entirely different method. ACTIVITY AT INFINITE DILUTION From the known free energy of SiO, it is possible to obtain the activity of silicon in dilute solution in liquid iron from equilibrium studies. The heat of formation of a-quartz is —217.6 kcal and the heat capacity and entropy data are given by Kelley and ~ing.&apos; The free energy of formation of ß-cristo-balite at temperatures above the melting point of silicon is expressed by the following equation: Si(Z) + O2(g) = SiO2 (crist); AF" =-226,500 + 47.50T [I] The value of the deoxidation product for silicon [%Si] x [%O]2 at 1600°C according to Gokcen and chipmans is 2.8 x 10"5, in agreement with results of Hilty and Crafts.9 More recent works of Matoba,

Jan 1, 1963

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-&apos; because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:&apos; J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.&apos; As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA&apos; and CC&apos; define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970

By Jeff Steinhoff

INTRODUCTION The Henderson mine utilizes a highly mechanized, continuous, panel-caving, mining system to extract ore from a deep, massive, molybdenite deposit. The mine is located 80.5 km (50 miles) west of Denver, Colorado. The mine surface facilities are located 3,170 m (10,400 feet) above sea level in a steep valley on the eastern side of the Continental Divide. Milling facilities are 24 km (15 miles) west on the western side of the divide at an elevation of 2,804 m (9,200 feet) above sea level. The ore- body is located approximately 3,000 feet south of the valley under Red Mountain. Access to the ore for men and materials is through a 915 m (3,000-foot) deep, 8.5 m (28-foot) diameter, vertical, concrete-lined, service shaft. Access from the mill is through a 15.5 km (9.6-mile) rail haulage tunnel. The mine is ventilated through an additional intake shaft and two exhaust shafts. Mine production at this time is 27,255 mtpd (30,000 stpd). The mine ventilation system supplies 1,038 cubic meters per second (2.2 million cfm) through approximately 60 miles of drifting or 2.7 tons of air per ton of ore mined. There are 130 fans in the mine in fixed locations and in vent lines with 6,900 connected horsepower in the mine. MINING METHOD AND LAYOUT The orebody is divided vertically into two major zones. The upper zone is the 8100-level production area. The bottom zone is the 7700- level production area which is in the early development stage. The rail haulage level at 7500 feet is common to both production zones. Each mine production zone consists of five associated sublevels. The cave undercut level is 16.8 m (55 feet) above the production level. Two boundary cutoff levels are located 44.2 m (145 feet) and 62.5 m (205 feet) respectively above the production level. The fresh-air level is positioned 15.2 m (50 feet) below the production level, and the exhaust vent level is 19.8 m (65 feet) below the production level. Horizontally, each production zone is divided into three panels each, 224 m (800 feet) wide. These panels are caved from south to north. As the caving in one panel nears completion, caving in the adjacent panel is initiated. Development for the caving panels is continuous so that the sublevels above the production level and the production level itself have a combination of development drifting and production-related activities. UNDERGROUND VENTILATION NETWORK The ventilation system is zoned in the same manner as the orebody itself. One major split of 600 cubic meters per second (1,270,000 cfm) ventilates the 8100-level production zone; one split of 100 cubic meters per second (210,000 cfm) ventilates the development of the 7700- level production zone; and one split of 165 cubic meters per second (350,000 cfm) ventilates the 7500 rail haulage level. The haulage tunnel requires an additional 188 cubic meters per second (400,000 cfm) of air. Development-drift ventilation is accomplished by hanging 1.0 m (3.5-foot) diameter steel ducting in the drifts with 40-horsepower, 0.96 m (38-inch) diameter fans supplying 9.4 cubic meters per second (20.000 cfm). The normal maximum length for these systems is 300 m (1,000 feet). The 8100-level production-area ventilation system is especially suited to a high level of mucking activity confined in a small area. Approximately 93 per cent of the mine&apos;s total production is transferred from the drawpoints to ore passes in 10 production drifts. The active area in each drift is 300 m (1,000 feet). Twelve 5-cubic-yard LHD units with Cat turbo- charged 170-horsepower engines are assigned to the area. Under these conditions, more than one LHD is assigned to a particular production drift. Adequate ventilation is maintained by making an air change every 97 m (320 feet) along the production drifts. Fresh air is brought into the production drifts from the fresh-air level through 1.37 m (4.5-foot) diameter raises. Air travels south along the production drift to the ore pass where it is exhausted down the ore pass to the exhaust level. The ore pass is followed by another intake which is followed by an ore-pass exhaust. At the south end of the production area, a series of exhaust fans maintain a southerly air- flow through the production level.

Jan 1, 1981