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THIS chapter and Chapter 19 deal with the heat quantities involved in open-hearth steelmaking, including the thermal efficiency of the furnace as a generator of high-temperature heat, the heat storage in the steel and slag produced and in the furnace walls, and the heats of the various chemical reactions involved in combustion, in the formation of slag, and the refining of steel. The fundamental laws to be considered are the first two laws of thermodynamics as applied to problems involving sensible and potential (or latent) heat only: 1. Heat input equals heat outflow plus storage. 2. Heat may be transferred only from a hotter body to a colder one. The first of these laws relates to the various heat quantities or the heat balance of the process. No one has as yet made an open-hearth heat balance that came out almost exactly balanced. The cause probably lies in the difficulties of accurate temperature and flow-rate measurements at the high temperatures involved and the inherent complexities in flow distribution and air leakage present in any real open-hearth furnace system. Some idea of the magnitude of the heat quantities involved can be obtained by a brief, crude outline of the heat balance of a 90-ton heat of steel. We will assume a 60 to 70 per cent hot- metal charge in a fairly fast working and only moderately efficient furnace, burning fuel oil, with a fuel consumption of around 4 million Btu per net ton of ingots produced. The time from start of charge to tap is 9 hr. During this period, the oil burned represents 360 million Btu and the sensible heat in the preheated air at the port ends is 117 million Btu, so that the total heat input at the ports is 477 million Btu. Heat stored in the steel and slag at the end of the heat, plus the various amounts absorbed by certain bath reactions, amounts to a total of 195 million Btu, but 120 million of this is supplied by the heat in the hot metal and by various heat-evolving reactions in the bath,

Jan 1, 1964

By S. Vela, R. M. McKinley, L. A. Carlton

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.' The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measzcrement of the re.rulting pressure changes at an adjacent well with a very sensitive differential pressure gauge. This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusivity, trans-missibility and storage. The primary objective in presenting these data is to demonstrate the potential of the methcid for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (I) pulse-test data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data: (2) pulse-test values for permeability are comparable with core va1ue.s; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should. The pulse-testing technique by Johnson et al.' is an ideal source of data for purposes of reservoir description, for it provides a measurement of formation storage S = +ch, hydraulic diffusivity 91 = k/+cp and transmissibility T — This paper describes an application of this method in a producing oil field. Results were analyzed to give numerical values for the parameters 7, T and S. These values were compared with oil-water production data (for the effect of fluid saturation), with core data and with data from an interference test. The reservoir in which the pulse-test survey was run is the result of a structural trap formed by a fault along the east side of a north-south trending anticline. A down-structure aquifer providcs a natural flank water drive for the pool. The producing formation is a dolomitic lime- stone having mainly vugular permeability; the formation oil has a gravity of 29" API with negligible dissolved gas. The field contains 19 wells, all on pump, arranged on 40-acre spacing along the top of the anticline. Fig. 1 shows the location of all these wells except two at the south end of the field. The dashed line on the right-hand side of the figure represents the approximate location of the fault with respect to well positions. Pulse-Test Survey and Analysis of Data A pulse-test requires a pulsing well and a responding well. In the field, changes were made in the rate of flow at the pulsing well by stopping and starting the pump periodically and measuring the corresponding pressure

Jan 1, 1969

By Carl Swartz

IN the course of a recent investigation1 to develop a more satisfactory white-metal. bearing alloy, a number of alloy systems were studied. The cadmium-nickel system showed characteristics desirable in a bearing alloy, and the system was therefore studied in some detail. EXPERIMENTAL METHOD Alloying cadmium with nickel offered no serious difficulty. After melting the cadmium, clean sheet nickel was added while the temperature was maintained at 500° to 600° C: A few crystals of ammonium chloride2 served to clean the nickel when the latter did not "wet" readily. In preparing the individual alloys for thermal and microscopic investigation, a "hardener" containing about 10 per cent nickel was used.

Jan 1, 1933

By G. D. Van Arsdale

This paper describes a series of experiments leading to the development of a method for leaching the mixed ores of the Inspiration Consolidated Copper Co., containing chalcocite and silicates of copper, by the use of solutions acidified with sulfuric acid and carrying ferric sulfate. Iron is added to the solutions and ferric iron is regenerated electrolytically to a percentage high enough to act as an effcient solvent. The decreased yield is partly compensated for by a higher current density. An important problem in modern copper metallurgy, particularly in the Southwest, has been to obtain good recoveries from what are commonly known as mixed ores; that is ores in which the copper occurs partly as oxide and partly as sulfide compounds. The dividing line between mixed ores and ores commonly accepted as concentrating is not definite. In other words, much ore now being concentrated carries considerable copper in non-sulfide form, on which recoveries are not so good as on ores carrying less of these constituents. While treatment by concentration may be commercially profitable on ores carrying oxide copper within certain limits, there are large deposits for which the application of concentration could not be considered, and yet which have not been considered amenable to leaching because they carried too much sulfide. The Inspiration Consolidated Copper Co. has large amounts of such mixed ores, and this paper is an account of the experimental work by which a method was developed for their treatment, and for which a large plant is now being erected by the Inspiration Co. It is not claimed that the method is a general solution of the problem of mixed-ore treatment but it is apparently well adapted for leaching the ores of the Inspiration Co., for which it was designed. The work done has covered preliminary laboratory and test-plant investigation, and a pilot-plant run, extending from March to the middle of December, 1923. Thoroughly consistent and satisfactory results were obtained continuously for more than six months in the pilot plant; and it is believed that the results and probable costs that can be had on a large scale have been definitely proved. The method, however, was designed for local conditions; and while the basic principles are general, there are ores on which it will not work and other ores for which considerable modification may be required.

Jan 1, 1926

By Charles R. Fettke

In the present day manufacture of glass nearly pure quartz sands are used almost exclusively as the source of the silica, which is the major constituent of all common varieties of glass. Ordinary soda-lime, such as bottle, common tableware, plate, and window glasses, contains from 65 to 75 per cent. of silica. Occurrence Glass sands occur in nature either in the form of loose, unconsolidated sediments or in deposits in which the individual grains have been more or less thoroughly bound together by some cementing agent so as to form sandstones. While deposits of sand and sandstones occur both widely and abundantly distributed, deposits that are sufficiently free from other constituents than quartz grains, so that they can be employed in the manufacture of the better grades of glass, are, comparatively speaking, of rare occurrence. The major portion of the glass sand produced in the United States comes from sandstones. In order to be suitable for glass sand, they should be rather friable. The rock should break down readily along the cementing material between the grains and should not break across the grains rather than along the bond. Some of the sandstones used are so friable that only light shots of slow-burning dynamite are necessary to disintegrate them sufficiently for hydraulic mining, while others have to be passed through crushers in order to disintegrate the rock into its individual grains. MINERALOGICAL COMPOSITION An ideal glass sand is made up entirely of grains of the mineral quartz free from inclusions of foreign substances. Sands containing 100 per cent. silica, however, are not found in nature, although some very nearly approach this composition.

Jan 1, 1926

By H. M. Kraner, R. C. Devries, K. H. Gee, E. F. Osborn

On the basis of liquidus measurements in the system COO-Mg0-Al2O3-Sio, and previously published data, diagrams have been constructed at 5 pct Al2O3, intervals from 5 to 35 pct Al2O3,. Liquidus temperatures and primary phase fields are shown. The optimum composition of a blast furnace slag for a given alumina content is indicated. At the optimum point, ordinary slags will be entirely liquid and will have maximum desulphurization potential and minimum viscosity. The relation of optimum composition of slags to the "plateau region" of the liquidus surface, and the application of these data on synthetic quaternary slags to actual slag compositions are discussed. Index of refraction of glasses is given as well as composition, temperature, and phase data for each mixture. THE usual blast furnace slag, as a first approximation, can be considered a mixture of the four oxides, CaO, MgO, Also,, and SiO,. Systematic, extensive data for the quaternary system, CaO-MgO-A1,0,-SiO, is therefore required for the understanding of the properties of such a slag as a function of composition and temperature. With sufficient data, it should be possible to fix unequivocably the relative amounts of lime, magnesia, and silica required for a given alumina content to result in a slag composition having optimum properties. Other constituents, such as FeO, MnO, Ti02, and S, have an effect on the properties of a slag, but as long as they are present in small and approximately constant amounts they produce only a second-order effect superimposed upon the major changes in properties of slags determined by the relative amounts of the four major components. Viscosity and desulphurization data have been reported for mixtures approaching blast furnace slags in composition, but systematic liquidus data have not been obtained. Inasmuch as a slag must be all liquid in order to be most effective as well as practicable, clearly the temperature above which a mixture is all liquid (liquidus temperature) is a type of data needed. Such data have been obtained through the study of 446 compositions and are pre- sented in this paper along with a discussion of their bearing on the optimum composition of blast furnace slags. For an orderly presentation of the data, the quaternary system is viewed as a tetrahedron with one component at each apex. Fig. 1 shows a tetrahedron representing the system Ca0-Mg0-A1,0,-Si0,. The base is the ternary system Ca0-Mg0-SiO,, A1,0, is the top apex, and the front face, the system CaO-

Jan 1, 1955

By Bruno V. E. Nordberg

Hoisting is one of the earliest endeavors of man with machinery, for hoisting was probably used by the early Egyptians. Treadmills were used for general hoisting until early in the nineteenth century and it was a short step only to attach a Watt steam engine to the rope drum of a hoist. One of the earliest steam hoists was built for a coal mine at Frisne, near Valenciennes, France. It was a remarkable piece of engineering created by James Watt in 1811, using a wooden drum on a vertical shaft. This followed the crude hoist by Holtzhausen in 1803, which used a drum of wood on a horizontal shaft.' In this country there were examples of crude mine hoists, which have been developed into the efficient machines in use today. African and Australian mines show examples of both extremes, and have an array of fine hoisting equipment exemplified in those built by British manufacturers. The influence of both English and American engineering in hoisting is interestingly evident in Canada. The information available to the writer does not reveal this to be true of South Africa, although American-built hoists have been furnished. Mining camps develop their own style of equipment, adapted to local conditions. For instance, the Butte mining district adheres to the straight drum with friction clutches, because of the great number of levels from which hoisting is done or to which men and material are lowered and the necessity for hoisting or lowering unbalanced. The north Michigan copper country uses both straight and cylindroconical drums and hoists continually in balance, so that the drums are not clutched to the main driving shaft. The Joplin mining district, Missouri, has its own peculiar small hoists. Other individual mines or localities in which a number of mines have been developed show individualistic types of hoists, depending upon their particular problems. In each instance, however, the particular problem must be carefully analyzed, as conditions are seldom so near the same that a number of identical hoists can be used to advantage.

Jan 1, 1940

By Bruno V. E. Nordberg

Hoisting is one of the earliest endeavors of man with machinery, for hoisting was probably used by the early Egyptians. Treadmills were used for general hoisting until early in the nineteenth century and it was a short step only to attach a Watt steam engine to the rope drum of a hoist. One of the earliest steam hoists was built for a coal mine at Frisne, near Valenciennes, France. It was a remarkable piece of engineering created by James Watt in 1811, using a wooden drum on a vertical shaft. This followed the crude hoist by Holtzhausen in 1803, which used a drum of wood on a horizontal shaft.' In this country there were examples of crude mine hoists, which have been developed into the efficient machines in use today. African and Australian mines show examples of both extremes, and have an array of fine hoisting equipment exemplified in those built by British manufacturers. The influence of both English and American engineering in hoisting is interestingly evident in Canada. The information available to the writer does not reveal this to be true of South Africa, although American-built hoists have been furnished. Mining camps develop their own style of equipment, adapted to local conditions. For instance, the Butte mining district adheres to the straight drum with friction clutches, because of the great number of levels from which hoisting is done or to which men and material are lowered and the necessity for hoisting or lowering unbalanced. The north Michigan copper country uses both straight and cylindroconical drums and hoists continually in balance, so that the drums are not clutched to the main driving shaft. The Joplin mining district, Missouri, has its own peculiar small hoists. Other individual mines or localities in which a number of mines have been developed show individualistic types of hoists, depending upon their particular problems. In each instance, however, the particular problem must be carefully analyzed, as conditions are seldom so near the same that a number of identical hoists can be used to advantage.

Jan 1, 1940

By G. B. Walker, S. A. Falconer, S. J. Swainson, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By G. B. Walker, S. J. Swainson, S. A. Falconer, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study' that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,' flow in packed columns,' fracture flow capacity' and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

ALABAMA Aldrich.-Lloyd, T W Anniston.-Carrington, F G Gerber, A B Heimrod, A A. White, H E Ashland.-Barton, J C Sturdevant, J C Bessemer.-Abbott, C E Ball, T L Hines, H K Hodgkin, W -0. Salmon, H S Thompson, N E Birmingham.-Adams, J H Adler, J. E Aldrich, T H Aldrich, T H, Jr. Ball, E M

Jan 1, 1923

By John V. W. Reynders

Our entry into the World War suddenly brought home to us in a startling way the vital importance of manganese. Since the war, much has been written and said upon the subject of manganese and a great deal of time and money have been spent in attempts to find an adequate substitute for this metal in the manufacture of steel; none has been found. It is true that ways are known by which it is possible to make small amounts of good steel without manganese, but taking into consideration the diminishing quality of iron ores and fuels as well as the increasing exaction of specifications for finished products, it may safely be assumed that, high-grade manganese ore will be more and more a necessity in the production of steel as time goes on. Taking world resources as a whole it may be well to point out that the problem of obtaining needed supplies of manganese from a strictly commercial viewpoint is now less serious than it was before the war. Formerly it was feared that world resources of high-grade manganese ore might be exhausted in a relatively short time, but, largely as a result of the stress laid upon the importance of manganese during the war, the world's available supply of high-grade manganese ore has been greatly augmented by new discoveries and fuller development of previously known deposits. Sources of Production Russia alone, of countries producing the major part of the world's stee1, has within its geographical boundaries sufficient manganese to supply its needs. The domestic production of England is inadequate and English requirements for high-grade manganese are supplied principally from India. France also draws largely upon India, as it depends upon foreign sources of supply except with respect to a small tonnage of silico-manga-nese and silico-spiegel produced in the Hautes-Pyrénées. Germany and the United States likewise depend upon foreign sources of high-grade ore, though each possesses comparatively large reserves of ferruginous manganese ore and manganiferous iron ore. At present the world demand for high-grade manganese ore is met with ease by the production of Russia, India, Gold Coast and Brazil.

Jan 1, 1927

By B. Zondek, W. T. Cardwell, J. W. Sheldon

The fundamental equations that are used to describe two-phase fluid flow in porous media are Darcy's law for each phase and an equation of continuity for each component. The special case of one-dimensional, incompressible, two-phase flow has received much attention in the petroleum engineering literature.1-10 The basic paper on the subject is that of Buckley and Leverett.2 Buckley and Leverett showed that one could eliminate the pressure and obtain a single partial differential equation for the saturation. They solved this equation for the case when gravity and capillary forces are negligible. A frequently encountered property of the solution of the basic partial differential equation is that, as time progresses, the saturation becomes a multiple-valued function of the distance coordinate, x. Buckley and Leverett interpreted the formation of multiple values as an indication that the saturation-distance curve had be-come discontinuous. They developed a method of determining the position of the discontinuity from a material balance. We solve the Buckley-Leverett partial differential equation using the method of characteristics and the concept of shocks. Our treatment is analogous to treatments used in the theory of supersonic compressible flow." Although the numerical results obtained are the same as those obtained by previous methods, we believe that this approach is more logical and has broader applicability. It can, for example, be generalized to treat the case when the fluids are compressible. It is not clear how one would go about doing this using the method of Buckley and Leverett. To illustrate the power of the method of characteristics with shocks, we solve a problem in gravity segregation which has not been treated previously in the literature. A special case of the general method developed here was used by Welge, to solve a particular fluid displacement problem. We consider two-phase incompressible flow along the vertical direction x in a porous medium. We assume that there is no flow transverse to .x. We measure positive in the upward direction. The fundamental equations are obtained from Darcy's law and the mass conservation law. Since the two phases are incompressible, mass conservation is equivalent to volume conservation.

By B. K. Larkin, H. R. Bailey

One of the most complicated and potentially one of the most promising secondary recovery methods is that of underground combustion. A number of field tests1,2,3 have been performed recently, apparently indicating that the underground combustion process is technically feasible. Relatively little has been published concerning laboratory or theoretical investigations of the underground combustion process. A few results of laboratory tube runs have been published4,5 and these data are valuable in understanding the process. The tube run data also emphasize the complexity of the thermal recovery process. Under various conditions, problems in heat transfer, multiphase fluid flow and combustion rates arise. For example, at low temperatures the combustion process proceeds so slowly that the front cannot be propagated. It is a problem in heat transfer to predict what injection rate of air is necessary to sustain combustion in a particular reservoir. Certain fluid flow aspects of underground combustion have been studied by Wilson, et a13. In the development of some of the flow equations, assumptions of adiabatic combustion were made. Vogel and Krueger1 have devised an analog model of the heat conduction process for a constant temperature cylindrical source moving radially outward in a homogeneous conducting medium. Jenkins and Ramey7, in a discussion of the Vogel and Krueger paper, present an analytical solution of a heat conduction problem related to problems considered by Vogel and Krueger. In the present paper an idealized model of the heat conduction problem is considered, which is more general than the model of Vogel and Krueger or Jenkins and Ramey. In particular, initial well heating, vertical heat losses and arbitrary frontal velocities are included. Equations for the temperature are obtained in terms of integrals. These integrals have been evaluated numerically for the case of frontal movement corresponding to a constant air injection rate and the case of constant frontal velocity. These results are presented graphically. From these graphs one may estimate conditions under which nearly adiabatic temperatures are obtained. The application of these results requires some knowledge of reservoir thermal properties, combustion rates and residual fuel content. Assuming no vertical losses it is possible to obtain explicit evaluations of these integrals in the linear con- stant velocity case and in the radial case corresponding to a constant air injection rate. PRESENTATION OF RESULTS The geometry of the radial system is illustrated in Fig. 1 where the reservoir is represented as a slab of thickness h. By making an energy balance for an infinitesimal volume, one obtains the following equation. T= x T+F(z.r).........(1) where F (z,r) =HWv1/pc (r-r1), if z h/2 = 0, if z >h/2 . In Eq. 1, V- represents the Laplacian operator and 8 is the Dirac delta function. Eq. 1 is the well-known diff-sion equation with a source term and may be applied to a linear system. For example, if the source is moving in the direction of the x axis, then the argument of the delta function is x - 1,. In deriving Eq. 1 the following approximations were made concerning the actual combustion process: (1) all heat transfer is by conduction in a homogeneous medium, (2) the formations bounding the reservoir have the same thermal properties as the reservoir, (3) the combustion fuel is consumed instantaneously as the front arrives, (4) there is a constant fuel concentration

Jan 2, 1951

By C. P. Proctor, J. T. Crawford

TROUGH washers were among the earliest methods used for concentrating ores; they are referred to by Agricola about the middle of the sixteenth century as already being used while the hand- operated jigging sieve had only recently come into use. For cleaning coal the trough washer apparently was first used in France and Belgium about 1841. The early trough washers were intermittent and the refuse at least was shoveled out by hand. The invention of a continuous jig washer, by a Frenchman, Berard, in 1848, acted as a stimulus to coal washings in jigs and retarded progress in trough washing in the nineteenth century. Chapman and Mott' describe a number of trough washers developed in England and on the Continent from 1850 to 1900, such as the Bell and Ramsay, Ramsay, Bell and Green, Wunderlich, Scaife, McLellan, Lodge, Elliott, Blackett, and Murton. The later of these removed the refuse mechanically, either intermittently or continuously, but in ways that interfered with stratification.

Jan 1, 1943

By Robert W. Bartlett

A computer model for predicting the rate of oxidative leaching of copper from fragmented low grade sulfide ores is presented. The model involves the kinetics of the dissolution of chalcopyrite grains and solution diffusion of oxygen within rock pores. Adjustable curve fitting parameters are not used. The model was tested by comparing computed extraction curves with experimental results for a -11 inch ore obtained by block caving and leached at 90°C and 400 psi oxygen for one year at the Lawrence Livermore Laboratories.

Jan 1, 1973

By David H. Browne

One of the most difficult problems in the chemistry of iron-ore, and one, the solution of which, so far as I am aware, has never been attempted, is the distribution, throughout a given vein, of Bessemer ore, and its relation to the formation of the deposit. In those hematite-mines in which both Bessemer and non-Bessemer ore occur, the sorting of the ore as it lies in the deposit becomes a problem of much economic as well as scientific interest. It would seem, from a superficial examination. or, indeed, from any examination not conducted for this especial purpose, as if high- and low-phosphorus ores were mixed in inexplicable confusion ; and a mining-chemist is very apt to fall into a system of adventitious analyses, taking first-class ore wherever he can find it, and overlooking its relation to the formation and position of the vein. I hope that a few notes which I present on this subject may be found worthy of consideration, as throwing a new light upon this obscure topic. During the last three years, while acting as chemist of the Lumberman's Mining Co., I have made some 3000 analyses of iron-ore from the Ludington mine at Iron Mountain, Michigan. These analyses were necessary in order to separate Bessemer and non-Bessemer ore which occurred intermixed in the deposit. During the last year, I attempted in several ways to find some reason or method in the distribution of phosphorus, and have finally become cognizant of the arrangement herein outlined. I have been obliged to confine my attention to our new mine, and, in that, to that portion wherein

Jan 1, 1889

By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-