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In Bulletin J 1, recently published by the Traylor Engineering and Manufacturing Co., it is stated that the largest jaw crusher ever built has a jaw opening of 66 in. by 86 in. and weighs 680,000 1b. It is said to be in successful operation and has a capacity of 490 tons per hour crushed to 12-in. size; 415 tons per hour crushed to 10-in. size; 330 tons per hour crushed to 8-in. size. The same company, in its Bulletin G 3, gives a diagram showing the percentage of a crushed product which will pass through screens of different sizes of perforation from a machine adjusted to a certain size screen. This diagram is reprinted below for the information of our members and the following notes apply to it. In order to prevent an excessive amount of fines, crushing machines are usually set so that 15 per cent. of the product will be larger than the maximum size desired, and this oversize is then recrushed by smaller

Jan 10, 1916

HENRY M. Howe, Bedford Hills, N. Y (written discussion*).¬Mr. Foley's explanation of this interesting occurrence is perfectly reasonable. Possibly a word explaining the phenomenon more in detail may not be amiss. In the act of solidification each drop as it starts to solidify splits up into a half drop poorer in carbon and another half drop richer in carbon than the drop itself. The half drop poorer in carbon solidifies and attaches itself to-the already solid walls, whereas the half drop richer in carbon remains molten for the excellent reason that it is richer and hence is more fusible than the original drop, and hence in turn is wholly fusible at the existing temperature. Under usual conditions, as when the steel solidifies in a mold of any form, the successive molten half drops thus enriched in carbon remain present and by their enrichment progressively raise the carbon con-tent of the remaining molten mass, out of which successive half drops are continuously solidifying and attaching themselves to the already solid walls. Because the molten mass thus. becomes progressively richer

Jan 10, 1919

By James Boyd

All mining and milling enterprises must be based on adequate ore reserves. Reserves must be established by physical exploration, and the orebody should be of sufficient size and grade to insure recovery of capital invested in mine purchase, development, and mill construction and to provide a reasonable profit. Determination of these economic factors is so complicated, and present costs of mine development and construction so great, that analysis can be made only by competent persons qualified by experience in this field. What rate for maximum efficiency? Unfortunately, even today mills are built before deposits have been adequately outlined, and there are rusting monuments to such folly in nearly every mining region. Also there is a tendency to be guided by the philosophy that "if a little is good, a lot is better," which leads to the conclusion that mining at a given rate and making so much per ton will yield a profit of so many dollars per day. Consequently, why not build a mill to treat twice as much per day and make twice as much money?

Jun 1, 1956

By L. B. Beneitone

Over the years, the rope changing procedure on the two double-drum San Manuel ore hoists has been streamlined and improved, so that a job that once required eight hours to complete is now finished in four. The ropes, constructed of improved plow steel, 6 x 25 filler wire, pre-formed, right lay, Lang lay with a fiber core and weighing 8 ½ lb per ft, have a 2 ¼ in. diam and are 3200 ft long. They have widely varying lives, but on the average a rope change on one of the two hoists is required every six months. When a rope change becomes necessary, the ropes on both drums of a hoist are replaced. Thorough planning and preparation are essential for efficient rope changes. A briefing session is held on the day prior to the change, during which the entire procedure is reviewed on a blackboard and discussed among the cable rigging crew. These discussions have led to many improvements that have been incorporated into the present rope changing procedure.

Jan 4, 1968

By William B. Plank

Mineral engineering student enrollment in U. S. and Canadian schools for 1955-1956 is 11,408, an increase of 11 pct more than last year. The undergraduate and graduate engineering students in both countries number 251,765, or 13 pct more than last year. These figures have been released by the American Society for Engineering Education. The largest increase in the undergraduate mineral engineering group in the U. S. is in ceramic engineering, with 676 students, or 31 pct more than last year. The next largest increase is in mining which shows a gain of 13.5 pct, compared with a gain of 13.1 pct in the total undergraduate enrollment in all engineering schools approved by the Engineers' Council for Professional Development. This figure is 190,355, which approaches the prewar figure. Metallurgical undergraduates increased 13 pct; geological, 5 pct; and petroleum, 2.5 pct. This year the figures for geophysics are combined with those for geological engineering, making a total of 1610 undergraduates, of which the geophysicists comprise about one seventh.

Apr 1, 1956

W. H. BLAUVELT (author's reply to discussion *).-The prevention of smoke from byproduct-oven plants is not as simple as would appear from Mr. Moss's statement. All well designed byproduct-oven plants are equipped with ample exhauster capacity, and the suction on the ovens is controlled by highly sensitive pressure governors that control the pressure within a fraction of a millimeter. Of course, this apparatus can get out of order, causing the batteries to smoke, but this does not often happen. As stated by Mr. Thompson, the smoke produced is made almost entirely during the time of charging the ovens, when they are cut off from the hydraulic main. The amount of smoke that escapes at this time is extremely small, compared with -the amount produced by a beehive-oven plant, but the mechanical difficulties in preventing any escape of smoke at charging time are considerable. Several devices are in operation at a number of plants which collect most of the smoke made during charging and several devices are being worked on for its complete

Jan 12, 1918

By Leonard Waldo

(New York Meeting, February, 1911.) THE recent and rapid development of the physics of engineering materials at temperatures as low as that of liquid air and as high is that of the electric are, has drawn renewed attention to the absence of tables, properly printed and spaced, for the convenient and accurate translation of temperature from centigrade to Fahrenheit scales and vice versa. It is to be noted that the Fahrenheit scale is the almost universal usage in foundries and shops in the United States, though the laboratories of the same works employ the centigrade notation. The growing use of the electric furnace in Germany and France calls for much American citation all in centigrade high temperatures, and while the arithmetical calculation is simple, it becomes burdensome when often repeated. I have been surprised at the numerous reprints of Table I. from centigrade to Fahrenheit degrees, first privately printed for personal use, which have been made by works, blue-prints, test-books, and technical journals, and I hope that Table II., from Fahrenheit to centigrade degrees, will be equally useful.

Jan 4, 1913

By H. Hanemann

Discussion of the paper of H. HANEMANN and PAUL D. MERICA, presented at the New York meeting, February, 1916, and printed in Bulletin No. 108, December, 1915, pp. 2371 to 2385. JOHN A. MATHEWS, Syracuse, N. Y.-I should like to ask the authors if there is any evidence of chemical change resulting information of, alpha iron from the gamma crystals found in nickel steel of high nickel content when stressed beyond the elastic limit, similar to the effect produced by drastic cooling. Would the stresses mentioned and the drastic cooling both result in an increase in magnetic induction? I would also like to ask the authors if they have made a test of the hardness. It would be very interesting to see whether the hardness decreased under the conditions of stress, as might be the case if alpha iron were produced. PAUL D. MERICA, Washington, D. C.-While it is impossible to state absolutely, it is my belief that the effect of deformation is approximately the same as, that of -drastic cooling, but we did not make a test, of the hardness.

Jan 5, 1916

Herbert C. Hoover, who became a member of this Institute in 1896 and who is now one of its Vice-Presidents, is the man who in 1914 extended a helping hand to Americans stranded in Europe at the outbreak of the war, and who made it possible for many such travelers to return safely to their homes. When his countrymen no longer needed his services, he turned to the Belgians, whose need of food had been presented to him. Engineers have been among his assistants from the first, and it is because we believe that members of his own profession will still be particularly interested in his work that we thus mention it in the Bulletin. A Minute adopted by the Board of Directors of the Institute, in which the Belgian Kiddies, Ltd., is recommended to the consideration of the members, immediately follows the Proceedings of the Meeting of the Board of Directors. With the thought that members of the Institute may be glad to read Mr. Hoover's own words in regard to his work, we print in full the speech

Jan 3, 1917

By G. Kinder, R. Gilges, W. Stoker, R. Davey

The Bingham Canyon Mine, located 48 km (30 mi) southwest of Salt Lake City, Utah, is operated by Kennecott Copper Corporation's Utah Copper Division. This operation is the world's largest open-pit copper mine and produces 96 000 tons (106,000 st) ore and 327 000 tons (360,000 st) waste each day. This material is loaded by large electric shovels and transported by both truck and rail haulage. To meet the requirements of the Clean Air Act of 1970 (as amended), new facilities for the control of smelter emissions were required and are now nearing the final stages of construction. The facility will be capable of treating all the output from the mine, some 2,530 tons (2,789 st) per day of combined concentrate and precipitate. Costing $280 million and necessitating the replacement of reverberatory furnaces with continuous smelting vessels, the plant, with its massive and complex gas handling and acid-making facility, is required to remain on-stream with the minimum of pollution control equipment outages to conform with Federal Regulation 52.2325.

Jan 8, 1978

By J. G. Bradley

On February 1, 1971, United States Steel Corporation, Lorain Works began operation of its first BOP facility equipped with a partial combustion gas cleaning system.- This shop consists of two 220 ton vessels. Figure I schematically describes this partial combustion gas cleaning system and highlights the necessary features for it-s safe and efficient operation. Waste gases are drawn into the membrane hood by a 2250 H.P. induced draft fan and are first quenched by the six inch bull nozzle at the top of the hood. Larger solid particles are separated from the gas in the quencher venturi and final scrubbing takes place in the P-A high energy venturi scrubber before the cleaned waste gas is burned in the flare stack. Scrubbing water is routed through a cyclone separator and then cycled into one of two 100' diameter thickeners. Underflow sludge which averages 20% solids is dewatered by 100 H.P. centrifuges. The clear overflow from the thickeners is recycled first to the P-A venturi and then to the quencher before returning to the thickeners.

Jan 1, 1972

By Stuart St. Clair

IN view of the great interest shown in the oil possibilities of Kentucky, one is impressed with the paucity of reliable literature on the oil fields of the state. A few brief reports by the Federal and State Geological Surveys are about the only reliable data available. When the estimated production figures, for 1918, are published by the U. S. Geological Survey, they will show a revival of the oil industry in the Blue Grass State during the past half decade. There will also be an increase in the production for 1919 and 1920, at least. Although as an oil-producing state Kentucky is small, compared with sonic of the other oil states, the present production and the area of undrilled proved territory is large enough to classify it as one of the important oil states of the Union. This paper will be confined to the Irvine District and the immediately adjoining areas which have been prospected with varying success. The Corniferous limestone or Irvine sand is the oil-producing formation in the area discussed.

Jan 7, 1919

By R. H. B. Jones

THIS paper reviews pertinent geology of the Biwabik iron formation, Mesabi Range, Minnesota. This iron formation is divisible into four members. Each member is distinctive and contains marker horizons, which are recognizable throughout all phases of alteration from lean, fresh rock to high-grade iron ore. Some beds have a larger magnetite content than others. During the process of ore genesis, which is essentially an oxidation process, the magnetite content is lowered. Alteration from iron formation to ore includes both oxidation of iron minerals and silica removal by leaching and these distinct processes progress at variable rates for different locations and structures. Magnetic intensities, of each horizon of the iron formation are dependent chiefly upon its preoxidation magnetite content, upon the subsequent degree of oxidation, upon the character of the enclosing rocks, and on the extent of fracturing, folding, or faulting. The results of a number of magnetic surveys are described and are correlated with results of drill-hole and mine exploration and development. The magnetic anomalies obtained are discussed in relation to phases of formation of ore within the iron formation.

Jan 1, 1946

By D. A. Dukelow, K. Li, G. C. Smith

Decarburization in the Fe-C system by oxygen top blowing has been studied in laboratory -scale experiments. It is shown that equilibrium models fail to explain or predict either the course of refining or endpoint conditions, giving results which either are incompatible with the chemistry of the system or do not satisfy material balance requirements. Also the path of decarburization was found to vary even for heats made under apparently identica1 conditions. A promising approach to analyzing the decarburization results is to relate oxygen efficiency fm carbon removal to bath carbon content. This relationship for Fe-C heats shows the same range of oxygen efficiencies as is obtained in pilot-plant and commercial heats using hot metal-scrap charges. This implies that oxygen transfer is primarily controlled by the decarburization reaction itself, independent of other refining reactions. Therefore, it should be possible to study separately decarburization and slag-metal reactions. DECARBURIZATION is probably the most important reaction in steelmaking. Not only is it a main reaction in the refining of iron to steel but it also provides the stirring action in the bath necessary for the diffusion processes to proceed at reasonable rates so as to make a steelmaking process practical. Kinetics of decarburization in the open-hearth process has been a subject of investigation for many years.&apos;-B It is generally accepted that at steelmaking temperatures the rate of homogeneous C-0 reaction is extremely high and cannot constitute a rate-controlling step. Diffusion of oxygen through a boundary film in the metal phase has been suggested by arken&apos; as rate-determining. Recently, Larsen and sordah16 concluded from experiments in a laboratory furnace that, with oxygen supplied from air or combustion gases, the rate of "steady-state" carbon boil is controlled essentially by a diffusion process of O2, Co2, or H2O through a film of nitrogen above the slag surface. Displacing this diffusion film by a stream of nearly pure oxygen produced a ten-fold increase in the rate of carbon boil with the rates of slag-metal oxygen transfer, bubble nucle-ation, and other steps all apparently able to keep pace. In the top-blown basic oxygen process, however, the transport of oxygen takes a more direct route. and the state of bath agitation is much more turbulent than in the open-hearth process. In addition, direct contact of the gas with the metal phase provides opportunity for direct oxidation of carbon. It is likely that the rate-limiting factor for the decarburization reaction will be different. However, only a few descriptive discussions of the subject have been reported in the literature.10-l2 Studies of the decarburization kinetics based on plant or pilot-plant data are necessarily complicated and are influenced by other refining reactions which occur simultaneously. In order to investigate the mechanism of decarburization, experiments have been conducted in which carbon-saturated iron melts were top-blown with pure oxygen over a range of conditions. It is hoped that this study will form a foundation on which a more basic understanding of this important reaction may be built. EXPERIMENTS One group of blowing experiments was made in a standard 200-lb induction furnace and another group in a 500-lb induction furnace. The furnaces were modified to the general shape of a basic oxygen furnace by adding a rammed refractory cone section to the regular crucible body. Crucible and cone were of high MgO (95 pct) material. A water-cooled lance, 1/2 in. in diam and threaded at one end to take a nozzle, was used for blowing oxygen. The lance with its water and oxygen lines was supported on a cantilever arrangement so that it could be moved up, down, or sideways. Oxygen of 99.5 pct purity was supplied from a cylinder and metered through a rotameter equipped with pressure and temperature gages. Another pressure gage was located at the top of the lance. A schematic diagram of the assembly is shown in Fig. 1. Before each experiment, a weighed amount of ingot iron, containing 0.02 pct C, < 0.01 pct Si, 0.10 pct Mn, 0.019 pct P, and 0.015 pct S, was charged in the furnace and melted down by induction heating. Graphite was then added to the molten charge until it became saturated. When the temperature of the charge reached the desired level, the lance was lowered to a predetermined height above the bath

Jan 1, 1964

By M. Kashiwada

The zinc leach residues are introduced into waelz kiln to fume volatile metals and before the end of 1967, the waelz-fume containing zinc, lead, cadmium and indium was directly recycled back to the leaching process for the production of electrolytic slab zinc. However, since 1968, we have been recovering with success those valuable metals contained in the fume separately instead of direct leaching. According to the improved process, the waelz-fume, after being mixed with chloridizing agents, is fed into the rotary kiln to be roasted, wherein most of lead and cadmium content is collected as fume and most of zinc remains in the calcine. Zinc calcine thus obtained, containing 70 to 75 per cent zinc and, less than 1.0 per cent lead is sent to zinc plant for further recovery and the fume containing 40 to 50 per cent lead and 3 to 6 per cent cadmium is further processed to recover lead, cadmium and indium. The advantage of this process can be secured to the utmost when it is combined with the following subsequent treatments. (a) Blast furnace smelting of non-magnetic waelz slag to recover copper, silver and gold as matte. (b) Gallium recovering process from magnetic waelz slag. (c) Soda process of lead bearing cake produced after removing cadmium and indium from the said fume. Thus the extractions of zinc, lead and cadmium from leach residues account for 87 per cent, 72 per cent and 85 per cent respectively.

Jan 1, 1970

By W. Rostoker, A. S. Yamamoto, K. Anderko

ALTHOUGH the corrosion resistance of magnesium and its alloys is closely related to iron content, there has been no direct measurement of the solid solubility of iron in magnesium. Bulian and Fahrenhors;1 and Mitchel]2 agree that pure iron or a limited terminal solid solution crystallizes from the Mg-rich liquid. For this reason a magnetic-moment method was selected to estimate that portion of the total iron content which is not in solid solution. Since iron in solid solution in magnesium cannot contribute to ferromagnetism, the difference between chemical and magnetic-iron analyses should yield the solid solubility. By experimentation it was found that the melting of pure sublimed magnesium (99.995 wt pet purity) in Armco-iron crucibles at about 800°C is a convenient way to introduce small amounts of iron. Melts retained 5, 10 and 20 min at 800°C analyzed 0.003,, 0.005,, and 0.018 & 0.001 weight pet Fe, respectively, after being stirred, heated to 850°C, and cast into graphite molds. The as-cast alloys were pickled in acid (dilute HC1 + HNO3), annealed at 600°C for 3 days, scalped on a lathe to remove the pitted surface, pickled again, extruded at about 100°C to 3-mm wire, reannealed 41/2 days at 500°C, and water-quenched. The specimens were again scalped, pickled, and used both for chemical and for magnetic analysis. Most of the precautions described were intended to prevent iron pickup by contact with tools or superficial iron enrichment by volatilization of magnesium during heat-treatment. It is believed that the specimens ultimately used for test were homogeneous and characteristic of phase equilibria at 500°C. Magnetic Analyses A susceptibility apparatus of the Curie type was used for magnetic analyses. Field strengths of up to 10,400 oersteds could be generated. By this method, an analytical balance measures the force of attraction which a calibrated magnetic field exerts on a suspended specimen. The force equation is as follows f/m = M dh/dy where f/m = force per unit mass of sample M = magnetic moment per unit mass dH/dy = magnetic field gradient The dH/dy characteristic of the instrument is determined by the use of a standard palladium sample, and the calibration is made independently for all values of H. Since a large finite field is required to saturate an assembly of ferromagnets, it is necessary to measure the apparent magnetic moment for increasing steps of H until a saturation value is obtained. The percentage of iron in the sample as free ferromagnetic iron may then be computed simply C= 100 (M1/M1) where C = percent content of undissolved iron in sample M1 = saturation magnetic moment of sample per unit mass M1 = saturation magnetic moment of iron per unit mass taken as 217 emu-cm per gm There is no serious difficulty in applying this method except for the unusual magnetic behavior of very fine particles of ferromagnetic substances. It has been found and is the basis for a widely accepted theory that with sufficient subdivision, the magnetic fields required to saturate and the coercive force after saturation rise to exceedingly high values. Recent work on precipitates of Fe and Co from copper solid solutions8 showed that about 5000 oersteds were necessary to approach saturation. The magnetic moments as a function of field strength measured in the present investigation are listed in Table I. Only the 0.018 wt pet Fe alloy yielded a magnetization curve with a fairly well-defined saturation plateau at 3.76x10 -2 emu-cm/ gm. This corresponds to 0.017 & 0.001 wt pet Fe in the alloy. This indicates that the solid solubility must be of the order of 0.001 wt pet Fe. The magnetic-moment data of the other two alloys are badly scattered, indicating that the amount of ferromagnetic iron in these samples is so low that the magnetic forces acting on them cannot be measured accurately by the analytical balance used. Nevertheless, the fact that even the 0.003, wt pet Fe alloy shows ferromagnetism indicates that the solid solubility must be below that value. Acknowledgment This work was sponsored by the Pitman-Dunn Laboratory of Frankford Arsenal, Philadelphia, Pa. The support and permission to publish are gratefully acknowledged. References W. Bulian and E. Fahrenhorst: Zeic. Metallkunde, 1942, vol. 34, pp. 116-170. 2 D. W. Mitchell: AIME Transactions, 1948, vol. 175, pp. 570-578. 3 G. Bate, D. Schofield, and W. Sucksmith: Philosophical Magnsine, 1955, vol. 46, pp. 621-631.

Jan 1, 1959

By D. L. Feucht, R. L. Longini

The semiconductor heterojunction is considered in terms of simple models which may lead to an understanding of move complex heterojunctions. Metallurgical and electrical properties of hetero-junctions aye discussed including the interface structure, energy -band diagram, and carrier transbovt across the interface. It is found that in a heterojunction all mechanisms such as injection, tunneling, and junction recombination found in simple junctions play modified voles. INTERFACES between materials (grain boundaries, the electrical junction between two differently doped materials in a single crystal, the oxide-metal interface, or metal-metal junctions) are of considerable importance in many situations. These various interfaces all have one very fundamental thing in common. Quantum mechanically speaking, the wave functions of the electrons in one material may penetrate the other material but, in general, only to the extent of angstroms. From an electrical point of view the conduction mechanism changes as a current passes through such junctions. In some cases the change is tremendous, in others almost negligible. The interface, then, is the locus of a change of conduction mechanisms. Some of these, particularly in semiconductors, are well-understood. The ordinary p-n junction in a single crystal can be the locus of an injection mechanism or a tunneling process, depending on conditions. The mechanisms are probably best understood in semiconductors because of the possible simplified view of particlelike conduction. The bands are either nearly filled or nearly empty and band overlap is seldom involved. The same fundamentals are probably important in other situations too but they are very difficult to look at naively. Although the simple look at the semiconductor case only gives us a relatively rough picture which must then be refined, the other systems, which involve a more complex situation, immediately are in many ways too difficult. There are too many initial choices of complex systems and therefore it is not possible to be even reasonably certain of any one model. Because of the relative simplicity of semiconductors, their good and controllable structure, and because of the ability to make many measurements on them not normally available to either metals or insulators! they are probably the best understood materials. It is therefore desirable to use them as a tool to further the understanding of interfaces in general. Semiconductor-heterojunction concepts were first proposed by kroemer1 in 1957. This was followed several years later by reports on the fabrication and experimental characteristics of heterojunction structures by Anderson2 and Diedrich and jotten.3 I) THE HETEROJUNCTION STRUCTURE To get down to hardware, when we refer to a semiconductor heterojunction we imply that there exists an intimate contact between different semiconductor materials. We could put two pieces of material together, complete with oxide layers, we could remove the oxides, or we could even melt the interface and hopefully get wetting and a good "bond" on solidifying. In fact we could by some means grow a crystal of one material using the other as a seed. Essentially we are interested only in the last two because they are the simplest to look at analytically. The degree of perfection of fit varies greatly and is reflected somewhat in the arc welder&apos;s joint strength. The lattice match of the two materials, their orientation, and so forth. is obviously necessary for a good bond but so is the continuity of any polar bonds which are involved such as in the III-V semiconductors. The mechanical misfit between two similar lattices can be described in terms of edge dislocations. The edge-type dislocations must be very close together for the usual misfit and there must be dislocations for each of several different Burger&apos;s vectors in order to produce a lattice match. The .&apos;dangling bonds&apos;&apos; resulting will be involved in producing interface charge. Order of magnitude estimates of the charge density extrapolated from low densities of dislocations in homogeneous materials give 5 x 1013 cm-2 Ge-Si and 1 X 1012 cm-2 Ge-GaAs electronic charges. Edge dislocations also act as very active recombination centers between holes and electrons. One lattice "matching" difficulty usually exists even if two structures have essentially the same lattice constants as they will have different coefficients of therma1 expansion. Thus, on cooling from the usually high temperature of fabrication to room temperature, dislocations are produced, a good fit not existing at both temperatures. In brittle materials this shrinkage may even result in cracking. For the Ge-Si interface the mismatch is about 2 x 10 -6 per degree whereas it is less than 10"7 per degree between germanium and GaAs. The exact effect of the misfit is dependent on the thickness of the materials involved. For a very

Jan 1, 1965

By L. A. Rapoport, W. J. Leas

The original Burkley-Leverett theory has been extended and a more detailed formulation of the waterflood behavior in linear horizontal systems is presented. Particular consideration has been given to the evaluation of capillary pressure effects and differential equations permitting an explicit evaluation of these effects have been derived. On the basis of the developed theory it is recognized that the flooding behavior is dependent upon the length of the system and the rate of injection. At the same time it has been determined that systems of different lengths yield the same flooding behavior if the injection rates and or the fluid viscosities are properly adjrrsted or "scaled." It has also been found that the sensitivity of the flooding behavior with respect to rate and length decreases as any one of these {actors increases in value and that for sufficiently long systems and high rate.; of water injection the flooding behavior becomes independent of rate and length. or "stabilized." To such stabilized conditions the theory formulated by Buckley and Leverett is applicable. A number of laboratory flooding tests have been made and good agreement Iraq been found between theory and experimental observations. The experimental results are discussed and it is shown that under field conditions the flooding behavior is usually stabilized. As a result of these finding; a procedure is indicated for evaluating field performances either on the basis of tests performed with commonly available core samples or by means of calculations using relative permeability data INTRODUCTION In recent years the development of methods for evaluating oil recovery by waterflooding has been the object of considerable research. A theoretical analysis of the mechanisms involved in the displacement of immiscible fluids was originally established by Buckle!- and Leverettl and experimental investipatio~~s have been made by numerons workers." Many of the experimental results are in mutual agreement and bear out several significant features of the flooding mechanism as predicted by theory. Thus it lias been generally recognized that a flood corresponds to the movement of a steep saturation hank or "front" (primary phase), followed by additional gradual oil displacement (subordinate phase). It has also been found that for any porous medium the flooding behavior is largely dependent upon the oil-water viscosity ratio and that for increasing values of this ratio the relative importance of the primary displacement phase decreases while that of the subordinate phase becomes more pronounced. Although the studies to date have clarified certain aspects of the flooding process. they have given rise to observations of a somewhat contradictory nature that cannot he explained in terms of the original theory. These observations pertain mainly to the effect of injection rate or pressure gradient upon recovery. Some investigators report laboratory tests that indicate incresing oil recoverieq with increasing rates of water injectill, others find the flooding behavior to be independent of and other. mention lower oil recoveries with increased injection rates.3 The conflicting evidence indicated above creates considerable uncertainty with respect to laboratory testing procedures and the utilization of the resulting data for field evaluations. The principal purpose of this paper, then, is to resolve these Uncertainties by means of a comprehensive theoretical and experimental investigation of the flooding meanism. THEORETICAL DEVELOPMENT Derivation of Flooding Equations The mathematical description of transient flow phenomena is based upon the consideration of the various processes occurring during an infinitesimal time interval in an infinitesimal volume element and upon the correlation of these processes with those occurring in the adjacent elements. The volume elements are defined as being infinitesimal in comparison to the overall dimensions of the porous system, yet each sufficiently large so aS to encompass the full range of pore openings encountered throughout the system. If a porous system can arbitrarily be subdivided into an infinite number of volume elements all possessing the same distribution of pore openings and if this distribution is unformly continuous. the system may be said to be homogeneous. Such a homogeneous porous medium is considered in the present studivs. It is furthermore postulatecl that only oil and water are present in the pornu wediu. that they act a- totally incompressible and immiscible fluids. and that gravity effects are negligible. In n linear flow system of unit cross sertional area. as treated here. the infinitesimal volume element.; to he considered are cylindrical ".slices" of thickness dx. oriented perpendicularly to the direction of flow. The equations applicable to any such volume element. at my time. describe the movement. of oil and water across the element:

Jan 1, 1953

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats&apos; technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats&apos; technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given&apos; by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By D. J. Wynnemer, G. W. Preckshot

Precise electromotive force measurements have been made on the zinc-cadmium system over the temperature range 700° to 900°C. Activity coefficients, partial free energies, enthalpies, and entropies have been determined .for the entire composition range. The integral heat of mixing is positive and compares favorably with calorimetrically determined values. Vapor-liquid equilibrium compositions were determined .for a total pressure of 1 atm and these agree well with previous values determined in other ways. The use of electromotive force measurements to obtain thermodynamic data for liquid metal systems is a simple and well-known method. Several reviews of the various experimental methods and results have been published.2,3,11 However, most of the past work using this technique was carried out at temperatures slightly above the melting point of the alloy system where alloy composition changes due to vapor transport and increased metal solubility in the electrolyte are not important factors. One advantage of extending the electromotive force measurements up to and including the normal boiling point of the alloy is that it is then possible to evaluate the vapor-liquid equilibrium of the alloy at various pressure levels up to 1 atm. A detailed discussion of the thermodynamics of reversible electromotive force cells can be found in most advanced physical chemistry or chemical thermodynamic textbooks. The expression stating the inter-relation of the electromotive force and the thermodynamic functions is the Gibbs-Helmholtz equation.

Jan 1, 1962