Search Documents

By H. Le Chatelier

Jan 1, 1894

By William R. Webster

This is a subject which our Institute has made peculiarly its own. In the first volume of its Transactions the analysis of steel received attention, and every subsequent volume has borne witness to the acuteness and industry of our members in the investigation of this subject. The keynote mas struck, in this as in so many other lines of progress, by A. L. Holley, in his paper on " Tests of Steel," read at the Easton meeting of October, 1873 (Trans., ii., 116)—an essay which may rank as a classic by reason of .its elegant form, logical force, and clear prevision of all the bearings of its theme, Taken together with the brief report of the discussion which followed it (in which Dr. Drown emphasized the effects of heat-treatment and mechanical handling, and Dr. Sterry Hunt the importance of minute variations in chemical composition, and of possible isomeric and allotropic conditions), it constitutes, after the lapse of twenty-five years, an admirable and adequate introduction to the long list of technical papers which have succeeded it. Three years later came the epoch-making papers of Dr. C. B. Dudley on the relation between the chemical composition and physical properties of steel rails, which, with the voluminous discussion they evoked, constitute a special volume, published by the Institute, and full of useful suggestions. If Dr. Dudley could be induced to resume this investigation, he would doubtless be able to solve many points still uncertain or disputed. But I cannot undertake to review the history of this subject, as represented in our Transactions—still less to restate all the contributions to it which have been made in books or in papers before other technical societies, since the initiative was taken by the Institute. My more modest purpose is to indi-

Jan 1, 1899

By Alden B. Greninger, Victor G. Mooradian

Microscopic examinations of quenched (beta) 60:40 copper-zinc and quenched (beta) 74:26 copper-tin alloys have frequently disclosed long, thin parallel bands or markings within the polyhedral beta grains. Apparently, it has been accepted that these markings are mechanical twin bands, although there is no published account of experimental data that might tend to substantiate this belief for the copper-zinc system, and only meager evidence has been submitted for the copper-tin system. Johnsonl0 commented upon the markings he observed after deforming a quenched brass of 55.6 per cent copper and 44.4 per cent zinc. Clark's papers4 on the heat-treatment of Muntz metal contain many photomicrographs of markings in beta brass; these she referred to as Neumann bands (inasmuch as repolishing and re-etching failed to remove them) and stated that markings present in Muntz metal as quenched were the result of shock imparted during the polishing operation. Van Wert18 first suggested that these parallel markings in quenched beta brass (60:40) might be alpha precipitated along certain crystallographic planes of the matrix lattice. He showed that upon reheating the specimens to temperatures below 800" C., obvious precipitation of alpha within the large beta grains first occurred at the markings. In a discussion of this paper, Phillips stated (pp. 505-507) that in his opinion the markings observed by Van Wert were mechanical twins resulting from contraction strains produced during the quenching operation. In a study of segregate structures in beta copper-tin, Smith17 observed that in the quenched beta phase (containing 74.92 per cent Cu) parallel . bands or markings very similar to those in metastable beta brass could be

Jan 1, 1938

By Alden B. Greninger, Victor G. Mooradian

Microscopic examinations of quenched (beta) 60:40 copper-zinc and quenched (beta) 74:26 copper-tin alloys have frequently disclosed long, thin parallel bands or markings within the polyhedral beta grains. Apparently, it has been accepted that these markings are mechanical twin bands, although there is no published account of experimental data that might tend to substantiate this belief for the copper-zinc system, and only meager evidence has been submitted for the copper-tin system. Johnsonl0 commented upon the markings he observed after deforming a quenched brass of 55.6 per cent copper and 44.4 per cent zinc. Clark's papers4 on the heat-treatment of Muntz metal contain many photomicrographs of markings in beta brass; these she referred to as Neumann bands (inasmuch as repolishing and re-etching failed to remove them) and stated that markings present in Muntz metal as quenched were the result of shock imparted during the polishing operation. Van Wert18 first suggested that these parallel markings in quenched beta brass (60:40) might be alpha precipitated along certain crystallographic planes of the matrix lattice. He showed that upon reheating the specimens to temperatures below 800" C., obvious precipitation of alpha within the large beta grains first occurred at the markings. In a discussion of this paper, Phillips stated (pp. 505-507) that in his opinion the markings observed by Van Wert were mechanical twins resulting from contraction strains produced during the quenching operation. In a study of segregate structures in beta copper-tin, Smith17 observed that in the quenched beta phase (containing 74.92 per cent Cu) parallel . bands or markings very similar to those in metastable beta brass could be

Jan 1, 1938

By H. B. Pulsifer

ABOUT 15 varieties, or modifications, of the best magnesium available were prepared and subjected to etching tests, then examined for microstructure. Of the 30-odd etching reagents that were tried, nearly half, mostly ammonium salts, etched the metal satisfactorily. The surfacing and etching of magnesium is shown to be a very simple and quick operation. The density and hardness of magnesium were determined. The most interesting new observations relate to the finding of the hexagonal etch figures, the crystal laminations, and the fact that the metal is plastic, cold, when restrained or quickly deformed. Under slowly applied pressure cold metal deforms slightly, then shears to fracture without plastic flow: The chief structural features of magnesium are presented in two reduced photographs and 30 photomicrographs.

Jan 1, 1927

By C. S. Sivil

To modern civilization the platinum metals are of inestimable value. Their distinctive properties, both physical and chemical, render them indispensable in an age in which the processes of the laboratory are becoming an essential part of the daily life of the world. Generally, their function, though vital to particular processes, is not spectacular, and so remains unknown to all except the operators. EARLY METHODS OF MANUFACTURE The properties of platinum were recognized as of prime importance for scientific work at. a very early date, probably between 1750 and 1760. The difficulty of making articles from it seemed almost insurmountable, because no means of attaining the temperature necessary to melt it were known at that time. It is true that solid platinum could be obtained by fusing the metal with a more volatile metal such as arsenic, which was subsequently driven off by baking, but such a method, at its best, would give only a very brittle product, which was totally unsuitable for the purposes for which it was intended. Little, if any, progress could be made until it was discovered that platinum sponge, heated to white heat and hammered in an iron or clay mold, would metallize and retain the shape of the mold. This was a process that could not be wholly satisfactory but from it developed the method of pressing the sponge in a mold and forging it at white heat into wire or sheet. At present a somewhat similar process must be used for fabricating articles of tungsten, molybdenum and other metals of high fusing point, as with these metals we face today the same problems that the scientists of the eighteenth century encountered with platinum, but possibly the next significant advance in the metallurgy of these metals will be the devising of means to melt and cast them.

Jan 1, 1931

By J. E. Lamar, J. S. Machin

INSULATING materials include a wide variety of nonmetallic mineral products such as exfoliated vermiculite, expanded gypsum, 85 pct magnesia, diatomite, asbestos, perlite, cellular glass, pumice, silica aerogel, expanded aggregates and mineral wool. Except mineral wool, most of these products, or the materials from which they are manufactured, are described in other chapters of this book. PROPERTIES OF INSULATING MATERIALS The insulating properties of the materials considered in this chapter result in general from entrapping extremely small pockets of air in such a manner that heat is not transferred by convection. The minimum heat conductivities of such insulating materials are slightly greater therefore than the conductivity of still air. In addition, conductivity varies with the overall density of the material, the temperature range in which the measurements are made, and the form into which the material is fabricated. However, the numerical value of heat conductivity should not be the sole criterion of an insulating material; for a particular application it may be advantageous to use a material of somewhat higher conductivity in order to secure other desirable engineering properties. This is especially true with certain materials that are used because of their refractoriness. Comparative insulating values of some commonly used insulating materials are shown in Table 1. In comparing the values presented in this table it should be borne in mind that heat conductivity varies with the mean temperature, with the overall density, and with the amount of moisture present. With fibrous or granular materials it varies with fiber or grain size and with the amount and kind of binder, if any is used. Under some circumstances it may vary with the arrangement of

Jan 1, 1949

For the US coal industry, 1978 was a nightmarish recurrence of 1977 as the United Mine Workers strike cut into production during the first three months of 1978, followed by the strike against the Norfolk and Western Railway during the summer and early autumn. Coking coal production was floored by the one-two punch of environmental constraints on US coke ovens and competition from low-cost, high-quality imports. At the same time, US ex orts of coal fell to their lowest level since 1962. And in the face of all of this, steam coal consumption was sluggish as utilities burned huge amounts of oil to conserve coal stockpiles during the UMW strike. This was followed by decreased electrical demands due to mild summer weather in many parts of the country and dramatically improved availability of hydroelectric power.

Jan 5, 1979

By H. W. Graham

[ ] Even though we have a small audience, I am sure there are some here who are interested in sponge iron. It is a large subject, with a lot of economic interest, and one that will continue to grow in importance as the years go by and as the conditions that urge action in that direction increase. The authors have chosen to deal in this paper with one particular narrow phase of a long program of work by the Bureau of Mines. Before asking for any general discussion, I would myself like to ask Mr. Buehl if he would tell us just a little bit about the mechanism of discharge and the form in which the material was discharged; that is, when dolomite is added, what happens to the dolomite? R. C. Buehl (author's reply)-You are interested in the equipment that was used? H. W. GRAHAM-No, just the product. R. C. Buehl-The product was in granular form, of a shape very similar to that of the ore used. Using minus 10-mesh ore, the product is essentially minus 10-mesh, mixed with the coal and dolomite. It is then passed through a belt type of magnetic separator, which picks up the magnetic iron and allows the dolomite and coal to fall off. If the coal is sufficiently valuable, it can be separated from the dolomite and, provided the coal has a sufficiently low ash content, it can be reused. For instance, if a low-ash reducing agent like petroleum coke is used, it can be reused until all the carbon is consumed. H. W. Graham-That clears the point for me. I was not quite sure whether the experi-

Jan 1, 1947

Jan 1, 1956

By W. J. Carlson, S. M. Parmerter, I. Iwasaki

This article discusses the effect of physical and chemical modifications of starches on the anionic and cationic flotation of silica from oxidized iron ores and magnetite-taconite concentrates. It also deals with the results of the interaction of starch, pH, and calcium ions on the flocculation, clarification, and filtration of iron ore slimes and magnetite-taconite tailings. Starches, particularly when an-ionically modified, were found to be effective depressants in anionic silica flotation. British gums and dextrins were beneficial for oxidized iron ores, but none of the starches or starch derivatives appeared to have any effect on magnetite-taconite concentrates. The flocculation and filtration of iron ore slimes were affected most strongly by the level of starch, to a lesser degree by the pH, and virtually not at all by the level of calcium chloride. The clarification of iron ore slimes was complexly dependent on these three factors. The flocculation of magnetite-taconite tailings depended mainly on the level of starch, whereas their clarification depended on the level of lime. As previously reported in the literature, selective flocculation and partial upgrading of a semitaconite could be readily attained with starch and calcium chloride. A previous article discussed some of the parameters that are important when various corn starches are applied to the soap flotation of activated silica from iron ores and to the flocculation of iron ore slimes.' Methods of solubilizing the starches and the molecular size after mechanical and thermal treatments, as inferred from the viscosity measurements, were shown to influence the adsorption characteristics on iron ores, and the residual concentrations of both calcium ion and starch in the pulp liquor were in direct correlation with the flotation and flocculation behavior.2-4 The present article summarizes the results of more recent tests conducted to ascertain the role of starches and starch derivatives in various phases of iron ore beneficiation. The scope of this investigation has been extended to include not only anionic and cationic flotation, but also the flocculation and filtration of iron oxide slimes, the selective flocculation and partial upgrading of semitaconites, and the flocculation and clarification of magnetite-taconite tailings —all problems that are of vital importance to the iron ore industry of Minnesota. By combining a practical approach with adsorption studies and by using single-mineral systems5 in these research efforts, it is believed that the ultimate goal of developing a suitable modification of starch structure may be realized. The topics covered in this article are limited to the empirical aspects of the research program on the depressant activity of starches and products in the cationic and anionic flotation of silica and of their role in flocculation, water clarification and filtration. ANIONIC SILICA FLOTATION In the soap flotation of activated silica from iron

Jan 1, 1970

By G. H. Matheson, J. M. W. Mackenzie

The flotation rate of coal has been studied using a continuous laboratory flotation cell and a multiple exposure photographic technique. The effects of particle size, reagent additions and cell turbulence on the flotation rate of coal have been investigated. The results have been analyzed in terms of current theories of particle bubble encounter and adhesion. The rupture forces which occur during particle bubble encounter have been shown to have an important effect on the flotation rate of coarse coal particles. The flotation of coal is a time dependent process, and in order to obtain a complete understanding of the operation it is necessary to determine the kinetics of the process. In coal flotation, the flotation rate and the associated values of cell productivity in terms of tons per kilowatt-hour and tons per cubic foot of cell volume are of greater importance than in most other mineral flotation operations. The reasons for this are associated with the low unit value of coal and the relatively high cost of coal flotation compared with other coal cleaning processes. An important aspect of coal flotation kinetics is the design of coal flotation cells. The cells used in many coal cleaning operations are often replicas of those used for the treatment of sulfide ores and are not necessarily suitable for the treatment of coal washing pulps, which usually contain a higher percentage of coarse and floatable material than the sulfide pulps for which the cells were designed. This disadvantage of many coal flotation cells has been recognized by Russian engineers who, by the addition of baffles to their subaeration coal flotation cells have increased the cell capacity by 100%. Investigation of the variables which influence flotation kinetics and cell productivity are, therefore, important to the coal industry where flotation is the only accepted method of cleaning the fine (-1/2mm) coal. The kinetics of the flotation process have been investigated in detail by Schumann10 who developed a continuous flotation cell which permitted the study of flotation under steady state conditions. This technique has been used by Gaudin et a1.,6 Brown and Smith and recently by Jowett and Savfi.7 The latter authors have developed a refined mathematical treatment for interpreting the results of continuous laboratory tests. Attempts have also been made to study flotation kinetics using conventional batch testing techniques. The experimental difficulties, however, and the problems of determining the order of the flotation rate process have made this technique of dubious value. A summary of the proposed rate equations for batch testing and the difficulties associated with this technique is given by Brown and Smith. 2 The experimental techniques described above are concerned with the rate of production of froth product. However, several authors, notably Sutherland, 11 Bogdanov1 and Philippoff, 9 have analyzed flotation

Jan 1, 1963

Jan 1, 1904

By E. M. Wise, T. E. Kihlgren, N. B. Pilling

SYSTEMATIC data are presented on the relation of composition of nickel silvers to color, tarnish resistance, hardness and liquidus temperatures, for alloys containing up to 30 per cent nickel and 50 per cent zinc, further modified at certain nickel and zinc contents by 0 to 8 per cent of tin and 0 to 10 per cent of lead. Attention has also been directed, using a still more limited range of alloys, toward a study of tensile properties and such casting properties and characteristics as fluidity, shrinkage and pressure tightness. In some of these, rather broad ranges of composition are dealt with; in others, it has been expedient to focus attention on the Federal Specification 20 per cent nickel silver casting alloy, WWP-541.

Jan 1, 1935

By Ernest F. Burchard

Fluorspar is found in most of the states from the Rocky Mountains westward, and commercial production of the mineral has been reported from Arizona, Colorado, Nevada, New Mexico, Utah and Washington. The map in Fig. 1 indicates the general distribution of many of these deposits but it is by no means complete. In the summer of 1926 the writer examined certain deposits of fluorspar in Arizona, California, Colorado, New Mexico and Washington; in November, 1927, revisited the Jamestown, Colo., district, and in earlier years examined deposits in Colorado and New Mexico. Based on notes of his own and on descriptions and other data by H. A. Aurand, H. W. Davis, R. B. Ladoo, V. C. Heikes, W. D. Johnston, Jr., and by producers of fluorspar, he prepared the following brief descriptions of deposits and estimates of reserves of fluorspar, originally for the use of the subcommittee on fluorspar of the Joint Committee on Foreign and Domestic Mining Policy and on Industrial Preparedness respectively of the Mining and Metallurgical Society of America and the American Institute of Mining and Metallurgical Engineers. Descriptions of many fluorspar deposits in various western states and districts have been published. It is not feasible to summarize this literature here, but the appended bibliography will indicate to the interested reader what papers are available. Arizona Fluorspar has been reported as occurring in Arizona in the following localities: near Duncan, Greenlee County; near Naco, Tombstone, and Paradise, Cochise County; Black Mountain, Mojave County; 25 miles southwest of Tucson, and at Helvetia and Silver Bell, Pima County; near Mammoth mine, Pinal County; in Yavapai County, 7 miles from Aguila, and in the Bradshaw Mountains; and near Dome, Yuma County. Production has come principally from the Castle Dome district, Yuma County, with minor quantities from Greenlee, Pima and Yavapai counties. The writer examined deposits in the Castle Dome district, Yuma

Jan 1, 1934

By L. G. Huntley

The occurrence of oil or "tar" in Mexico was mentioned as early as the seventeenth century by Friar Sagahun, who gives the Indian name "chapopote," by which these asphalt seepages are still called. This asphalt was apparently used, as it has been used by primitive people in many parts of the world, in religious ceremonies and for medicinal purposes. Travellers also report that the ruins in Yucatan and the pyramids in southern Mexico show traces of the use of "chapopotel' as a building cement.l DeGolyer says that the first attempt to exploit oil or gas in Mexico in a commercial way is shown by the records of the Memoria de Fomento of 1865, when permission was granted to a Senor Ildefonso Lopez to exploit the deposits of petroliferous substances in the San Jose de las Rusias area in the State of Tamaulipas. Other concessions follow, and probably refer to surface seepages which occur in that district. This was several years after the discovery of oil in Pennsylvania. In 1868, a well 125 it. deep was :drilled by a company organized in Mexico City, in what is now known as the,, Furbero district, and a little oil was refined there. In 1873, residents of Tampico denounced seepages along the Tamesi River, and asphalt was mined near Tempoal in the Canton of Tantoyuca. No drilling was attempted. But between 1880 and 1883 several shallow wells were drilled for oil in Mexico, two of them being near the present Potrero de Llano field west of Tuxpam. The wells were drilled by a Boston company with Canadian rigs, and are said to have reached a depth of about 400 ft., while one is reported to have flowed. Several other abortive attempts were made to drill for oil between 1885 and the beginning of the present century, about which time the Mexican Petroleum & Liquid Fuel Co., Ltd., in which Cecil Rhodes was interested drilled 24 wells unsuccessfully, several of them as deep as 1,500 ft., in the State of Vera Cruz. Also Messrs. Doheny and Canfield of California pur-

Jan 1, 1916

By F. Lynwood Garrison

It is not intended to make in the present paper any deduction or to formulate any theories from the results obtained by experiments. The further expenditure of considerable time and labor would be required to obtain a sufficient basis for positive assertions as to the microscopic structure of the different varieties of iron and steel, and the structural changes which take place in them. It is therefore my purpose at this time to offer simply a synopsis of the general results arrived at in a few months' work, a brief description of apparatus used, and a few hints as to the preparation and preservation of the material which it is intended to investigate. The study of the microscopic structure of iron and steel is not altogether new. Some attention has been given it in both England and Germany. But the foreign publications on the subject have thus far been confined, so far as I am aware, to two papers, one by Herr Martens, of Berlin, contributed to the Verein zur Befoerderuny des Gewerbfleisses and the other a lecture by Dr. H. C. Sorby of Sheffield. Dr. Sorby, it seems, was induced to investigate the subject as bearing on the structure of meteoric iron ; and the results he obtained are certainly very interesting. At the Boston meeting of this Institute, in February, 1883, Mr. J. C, Bayles called attention to the subject in a neat and exceedingly interesting paper, in which the work of Messrs. Martens and Sorby was summarized,* and original suggestions were added. It is at present difficult to say what will he eventually the practical value of the microscope, thus employed, in the sciences of engineering. The role which it seems most likely to play is that of' an adjunct to the testing-machine, and not (as some have supposed) a rival to the chemical laboratory. That it will be a most valuable accessory seems, to say the least, highly probable. I need hardly go at length into the details of preparing the material for examination. Mr. Bayles has described the process in such a plain and comprehensive manner that if his instructions are

Jan 1, 1886

By S. F. Emmons

The first paper which appears in the published Transactions of our Institute is that read by our respected Secretary at its first meeting in Wilkes-Barre in May, 1871. It is entitled " The Geographical Distribution of Mining Districts in the United States," and presents a brief but masterly review of what was known of the distribution of our deposits of useful minerals, particularly the metals, not only from a geographical but from a geological stand-point. At the request of Dr. Raymond I agreed, somewhat hastily, perhaps, to write for this occasion a brief sketch of the geological distribution of the deposits of the useful metals in this country, in the light of the increased knowledge of the present day. In the time given no personal investigation was possible, and as it was therefore out of the question to attempt to make anything that could be considered an original contribution to the history of our ore-deposits, I have been obliged to limit myself to an examination of such pub-

Jan 1, 1894

By Bruce W. Gonser

TIN is not yet classed as a rare metal, but it has taken a long stride in that direction in the last ten months. It is now in Group 1 of the War Production Board's critical list, along with such company as magnesium aluminum, and nickel. This is in sharp contrast with the position a year ago when the supply well exceeded demand, and tin was used when feasible in place of really scarce metals. The geographical sources of tin production in recent years are shown in Table 1. Preponderance of former production in southeastern Asia, particularly Malaya and the Netherlands Indies (but all now controlled by the Japanese). is entirely too marked to be funny. Of the 1940 known world production of 237,000 long tons nearly all was controlled by the United States, Great Britain, and their friends. Now their supply is from countries that produced only 28 per cent of that amount. This excludes China and Australia, which because of shipping difficulties and local consumption, cannot be expected to export much tin. In spite of some expected increase in production, therefore, the supply is, and will continue to stay for at least several years, way below that desired for even normal uses. Although deliveries to consumers in the United States alone

Jan 1, 1942

By William Hurst

Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This nietkod of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined tern? for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and sec-ondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. INTRODUCTION The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent move- ment of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation. The type of depletion performance equation chosen for predicting the future performance of a reservoir depends on the amount of past history available. When the reservoir is somewhere past the halfway mark in depletion, some form of decline curve is often used. With less past history, material balance equations which incorporate empirical factors based on the past performance are often used. When, however, the amount of past history is small, the Muskat depletion performance equation will usually be used. The distinguishing feature of this type of equation is that empirical factors based on the over-all or macroscopic reservoir behavior are almost or entirely absent. Each parameter affecting the reservoir performance is ascribed an independent set of values based on measurements made on laboratory samples; that is, incorporating microscopic empirical factors. In establishing Muskat-type depletion performance equations, it is necessary to consider the reservoir as consisting of a number of associated blocks, in each of which the saturations and pressures may be considered uniform, and in each of which all substances have uniform pressure-volume characteristics. Thus, a primary gas cap can usually be considered as one block and an aquifer as another. Gravity segregation may be negligible for practical purposes when the rock and oil properties are adverse and/or the dip or thickness of the reservoir is too small. In this case the whole oil leg may be considered as one block, except in very large reservoirs. In very large reservoirs the fluid and rock properties may vary enough, particularly in the dip direction, for it to be necessary to divide the oil leg into a number of blocks, in each of which the relevant quantities may be considered uniform. When gravity segregation of the oil and free gas is not negligible, it is necessary to consider the space occupied by the initial oil leg as divided into two blocks, a secondary gas cap and an effective oil leg, in each of which saturations may be considered to be uniform. The total volume of these two blocks is thus constant, but the secondary gas cap grows continuously at the expense of the oil leg. Muskat1 derived depletion performance equations for the basic case of an oil reservoir with closed boundaries and without segregation, and for the case of an oil