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By George M. Fowler, J. P. LYDEN

T HE relationship of geological structure to orebodies and to the great masses of chert in the Tri-State mining district is of such significance that it prompts a brief recital of the existing information regarding the various periods of structural deformation. We began to note a relationship between structure and orebodies early in our studies of the field, and further work revealed a like relationship of structure to the great masses of chert so commonly associated with the ore-

Jan 1, 1934

By Frances Hurd

WHEN 60:40 brass is heated to 825° C., given a drastic quench to obtain the beta solid solution, and reheated, various changes take place in the structure. Reheating at 200' C. causes a fine, granular, sorbitic structure to appear which has been considered alpha solid solution. These particles coalesce at higher temperatures of reheating, and at 470° C., the alpha forms twins. A further study of these transformations was considered worth investigating.

Jan 1, 1927

By E. G. Dahlgren, Dan O. Howard

THE West Edmond oil field, which covers parts of Oklahoma, Canadian, Kingfisher, and Logan Counties in the State of Oklahoma, is in geographical extent the largest single oil field found in the state. At the present time, its area of 26,800 acres is almost twice as large as the Oklahoma City field, which hitherto was the state's largest field. Many authorities believe that the West Edmond field is the most important oil pool found in the United States since Pearl Harbor. The discovery of the field without the help of geological, geophysical, or other recognized technical information, the fact that the oil and gas accumulated in a stratigraphic or wedge-type trap, and the rapid development of the productive area under wartime conditions are some of the interesting features of the field. The West Edmond field lies west of the Oklahoma City, Britton, and Edmond fields. The field is in an area that has been considered on the west flank of the Granite Ridge line of folding, on which a number of Central Oklahoma's most important oil fields are located. Over a period of years, especially since the discovery of the new pools such as Oklahoma City, Edmond, Britton, and Crescent, the general area of the West Edmond field has been explored intensively by geological and geophysical methods. This led at times to the drilling of a few dry Wilcox sand tests.

Jan 1, 1945

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Jan 1, 1938

By H. H. Dreissen, F. J. Fontein

The operating principle of the classifying cyclone has been described often but some special aspects of the cyclone receive further clarification here. In addition, several uses of the classifiers are summarized and made clear by means of practical examples. In coal and ore washeries, the washing cyclone is widely used for the separation by specific gravity of sizes up to about 12 mm. This application has lately been extended to the separation by specific gravity of particles up to about 50 mm. This use makes special demands on the construction and wear resistance of the cyclone. The sieve bend, a development of the Dutch State Mines which is less well known than the hydrocy-clone, is dealt with at some length. The sieve bend is an apparatus designed for wet screening. Attention is given to the variables influencing the performance of the sieve bend. Hydrocyclones are now so widely applied that it would be difficult to find an industry not, directly or indirectly, using them or knowing how to use them since publications on this subject abound.1-3,5,9-11,13-15 However, because of the large number of variables influencing the operation of classifying cyclones, it is not entirely possible to calculate the results of this type of cyclone. Therefore, a number of lesser known variables will be discussed here along with some special applications of the classifying cyclone. FACTORS INFLUENCING CYCLONE CLASSIFICATION Shape of Particles: The shape of particles may cause a much coarser classification than the one expected, considering the sieve analysis and the cyclone dimensions chosen. This was clearly shown by feeding a mixture of spheres and disks in water into a cyclone. The spheres were 0.36 mm diam and the disks, 3 mm diam and 0.03 mm thick. These dimensions were chosen in order that the disks and spheres might have the same rates of fall under gravity. Both spheres and disks had a specific gravity of 1.05. The results obtained with these particles in a cyclone are summarized in Table I. Test No. 2 shows that the catch of spheres was

Jan 1, 1963

By P. E. Fitzgerald

ACIDIZING, as the terns is used in the petroleum production industry, involves the use of hydrochloric acid in predominantly limestone formations, resulting in the lowering of resistance offered to the flow of oil and gas through the oil-bearing formation, usually with resultant increased production. A number of articles have been written on the chemical treatment of oil and gas wells; a bibliography of these works will appear in Volume 123 of the Institute's TRANSACTIONS (1937), and a few other references are appended to this paper.

Jan 1, 1937

By F. W. Schaller

TETRAGONALITY is an important aspect of the models of transformation, strengthening, and tempering of ferrous martensite. When the c/a

Jan 1, 1963

By CHARLES W. BENTON

THE following paragraphs comprise such information as the Secretary has been able to obtain concerning the members and associates whose deaths have been reported. Further particulars or corrections of errors, and biographical data concerning deceased members or associates not already noticed in this way, are solicited. Charles IV. Benton was born at Kezar Falls, Maine, Nov. 12, 1843. We have no accurate knowledge concerning the early part of his career. In 1871 he engaged with the N. Y. Honduras Rosario Mining Co., at San Juancinto, Honduras, C. A., and later was employed at the Monserrat mine at Yuscaran, and at Santa Lucia, Honduras, with the Tenero Mining Milling Co. of Pennsylvania. In 1897 he became a member of the Institute. At the time he was stricken with his last sickness he was employed at the Paymaster mine at Tucson, Ariz. He died at Fairmount, Denver, Colo., Sept. 9, 1907. William R. Boggs, Jr.-The notice in the Bulletin for January was incorrect in saying that the murder of Mr. Boggs occurred while he was employed as metallurgical. manager by Mr. W. B. A. Dingwall, at La Maroma, San Luis Potosi, Mex. Mr. Dingwall writes that in March, 1907, Mr. Boggs left him, to return to his home at Winston, N. C., whence he. subsequently went to Durango, Mex., to take, with the Topia Mining Co., a position which he occupied at the tine of his death, Nov. 17, 1907. Mr. Dingwall says that, while in his service, Mr. Boggs never had any trouble with the workmen, but was esteemed and liked by them, as by all who knew him ; and adds, injustice to the State of San Luis Potosi, that the population, even in the mining-camps of that State, is orderly and law-abiding, and that the authorities are vigilant and just. Our

Mar 1, 1908

By Malcolm T. Hepworth

RECENT interest in thermoelectric devices has been directed toward studies of the properties of thermoelectric materials of semiconducting solid compounds with little attention given to ionic and semiconducting liquids such as aqueous solutions, fused salts, and mattes. One type of thermoelectric system is the thermocell: a nonisothermal galvanic cell with two identical electrodes at different temperatures connected by an electrolyte bridge. An electromotive force, v, is generated which is a function of the electrode reactions and the properties of the electrolyte according to the Eastman' equation: where S* is the entropy change of the system arising from the electrode reactions and by heat transferred by ion migration and by thermal conduction. The quantity nF is the product of equivalents passed and Faraday's constant. A value of S* of 23.06 cal per "C is equivalent to 1 mv-Faraday per "C. The symbol, a, is used for dV/dT in analog to the See-beck coefficient of solid-state thermoelements. de Bethune2 has calculated the temperature coefficients of the electromotive force of a large number of nonisothermal aqueous cells from measurements on the nonisothermal temperature coefficients of the standard hydrogen electrode, combined with data on the isothermal temperature coefficients of half-cells tabulated in the literature. Values of these coefficients (a) in de Bethune's compilation ranged up to 3 mv per C. In particular he reported a value of +2.059 mv per "C at 25'C for the cell: Fe (aqueous, unit activity) (aqueous, unit activity) written for the hot-electrode reaction. The positive sign indicates that the hot electrode is positive (an "n-type thermocell"). In analog to a solid-state p-n system, it would be possible to couple two thermocells together to form a system in which the figure of merit could be calculated by adding the temperature coefficients according to the relationship described by offee:' where a is the Seebeck coefficient in volts per "C, p is the specific resistivity in ohm-cm, and K is the thermal conductivity in watts per cm "C. Even though ionic systems have rather high electrical resistivities compared with semiconducting and metallic systems, it was felt that a preliminary study of one ionic system should be made to establish some basis for evaluating the possibility of a p-n thermocell for energy conversion. Accordingly the Fe", Fe"' system was studied as a possible component for a p-n system. A glass system was constructed consisting of two vertical water-jacketed tubes connected by a horizontal tube, Fig. 1. Platinum-black electrodes 1 cm by 1 cm in dimension were inserted in each vertical tube with thermometers to register the electrode-compartment temperatures. The temperature of the electrode compartments was controlled by circulating water from thermostatted baths around the electrode compartments. The electromotive force of the cell was then read by a potentiometer for zero current as a function of the temperature of the hotter electrode. Current output of the cell for varying external loads was also measured. The cell resistance was measured by means of a bridge circuit with 10,000 cps signal and oscilloscope. Resistance measurements were converted to specific resistivity by calibrating the cell with a solution of known conductivity.

Jan 1, 1965

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K' to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K', at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963

By L. E. Young

IT has been said the British Empire was built on British Coal. In all the postwar planning for Great Britain the necessity for producing cheap coal and the prosperity of the coal industry are given first consideration. On Jan. 23, 1945, there was released in London a "Report to the Colliery Owners" which had been awaited with great interest. This was entitled "A Plan for Coal" and was the recommendation of Robert Foot, chairman of The Mining Association (Colliery Owners), prepared at their request. Presentation of the "Plan" at this time is particularly significant as it is an answer to the demand for nationalization of the coal industry by the Labour Party and at the same time is a carefully considered program for postwar reconstruction, prosperity, and stability. In the words of Mr. Foot, If the coal industry for the first ten years after this war is to find itself in a situation similar to the one it occupied for the ten years following the last war, with its record of disputes, strikes, stoppages, short-time working, unemployment, and, with it all, a completely insufficient margin of profit, and all the insecurity and instability in our basic industry that was brought with them, it is goodbye to any real prospect of full employment, social security, and high standard of living. To present an elaborate review of the conditions which have brought to a crisis the unfortunate situation in the British coal industry is here unnecessary, but certain of the salient points

Jan 1, 1945

By J. F. Kemp

The use of nickel-steel has directed increasing interest of late towards the deposits of nickel, and at the same time the parallel advance in our knowledge of the basic igneous rocks has rendered these deposits a subject of important geological inquiry. Investigations have led to some views, more or less new, on the igneous origin of certain ores, which, though not universally accepted, have a growing number of adherents. In Europe, the mines in Norway have been especially suggestive subjects of study, and others somewhat less generally known have also added their testimony; while in this country the great economic importance and scientific interest of the developments in the Sudbury district of Canada, have furnished the principal texts for the discourses that have appeared among us. The purpose of the present paper is to set forth these views through the medium of one interesting ore-body, of which but little has been written ; and, by the description of another, to place in contrast two different geological associations in which nickeliferous pyrrhotite occurs, and to indicate a generalization, based upon these different geological characters, and justified by the experience so far gained. To Prof. J. H. L. Vogt, of Christiania, Norway, is due the chief credit for the revival of interest in the geology of nickel. His important contributions* of recent date have made generally available

Jan 1, 1895

By David B. Dill, Edgar R. Lea

The zinc deposits of the Balmat-Edwards Division of the St. Joseph Lead Company in northern New York State provide some 10 per cent of the domestic zinc produced annually within the United States. These complex ore deposits are contained within marbles of the Precambrian Grenville series, in a repetitive sequence of dolomites and silicated units. The Balmat ore bodies are localized at various intervals throughout some 1800 feet of the stratigraphic column on the northwest side of a band of gneiss that has continuity to the Edwards area, some 10 miles to the northeast. The Edwards ore bodies are located to the southeast of this gneiss. The marble formations are thought to have included repetitive intervals of marine sedimentation that provided mineralized source "beds" and were subsequently folded, flooded, and injected with melts at great depth and were sheared, recrystallized, and reconstituted. Detailed structural and stratigraphic studies throughout the northwestern Adirondacks, in the Balmat-Edwards district, and at each mine in particular indicate the close dependence of the ore deposits on the enveloping structure whether it be local, district-wide, or regional in scope. Primary folding has developed a northeast regional trend with northwest dips. Secondary folding has been developed by an almost horizontal northeast-southwest-oriented shear couple in the plane of the regional trend. The secondary folding has produced crossfolds that intersect the regional northeast trend and plunge north to northwest at various angles. The ore bodies are found within certain stratigraphic horizons where repeated alternation of competent and incompetent beds encouraged unusually complex folding. Analysis of individual mine structures indicates that the location of each deposit is controlled by structural crossing of primary and secondary folding. The ore bodies, which are tabular, lenticular, or pod-like in form, have features that suggest parallelism to true bedding or modified flow banding, developed by northeast-southwest shearing stresses related to the development of the crossfolds. The ore deposits in general follow both structural and recrystallization trends within the wall rocks. Mobilization of the pre-metamorphic ore minerals is believed to have involved a combination of plastic flow under stress and solution of the sphalerite, minor galena, and pyrite. The ore fluids are thought to have been guided by secondary shearing and microbrecciation into structurally prepared areas where reprecipitation took place. The presumed premetamorphic mineralization now exhibits epigenetic high-temperature features related to late-stage metamorphism.

Jan 1, 1968

By G. G. Oberfell

THOUGH the largest volume use of natural gas has been, is. and in all probability will continue to be as a fuel for domestic and industrial heating, it has various market outlets, both as a fuel and as a raw material for the chemical industry. Natural gas is a preferred type of fuel where ease of control, fuel uniformity, and freedom from ash are of primary importance. Other industrially important uses are as a source of carbon black and as a fuel in various low-cost heating operations. Many other uses are of varying importance and new potential uses are continually being uncovered, some being of economic importance to the gas indus¬try as a whole, but most of them involve such small volumes of gas that they are only of passing interest. Since various products extracted from natural gas and recovered as by-products from petroleum refining, such as liquefied petroleum gas and fuel oil, are being utilized in many industrial and domestic heating applications, some consideration will have to be given such materials in order to present a reasonably complete story of the importance of natural gas. Some of these materials may prove to be transient competitors and will not be available when more profitable uses are found for them. Meanwhile, however, the potential volumes of such materials available, the current volumes being marketed, and the nature of the utilization are considered as constituting an essential part of the over-all fuel picture.

Jan 1, 1946

By J. Pohlig

It is with more than ordinary pleasure that I have complied with the request of the President of the Verein Deutscher Eisenh?tten leute, to read before this meeting and in this country a paper on a system of transport by wire ropeways which, during the past twenty years, has advanced with rapid strides in Europe, and more partic ularly in Germany. America, with its immense network of railways and water communications, should offer peculiarly favorable oppor tunities for the introduction of these ropeways as feeders, more par ticularly in the mining districts, where, as in Europe, a hilly or mountainous region frequently opposes serious obstacles to the em ployment of surface railroads. The importance of the aerial ropeway as a factor in the develop ment of mineral resources deserves the consideration of every mining engineer. As a case in point, the rich iron-ore of the sierra de Bedar in southern Spain, would probably remain untouched to this day but for an aerial ropeway, 15.6 km. (9 3/4 miles) long, which con nects the mines with the shore of the Mediterranean near the town of Garrucha, affording cheap carriage to the nearest shipping point. A railway would have cost about $480,000 (£100,000), but such a heavy outlay would have more than absorbed all prospective profits on the sale of ore. As the aërial ropeway could be built for a little more than one-fourth of that amount, or $124,800 (£26,000), its erection furnished the successful solution of a profitable mining enterprise. This line has been in satisfactory operation for over two yearn; its details will be referred to later. But beside their importance as feeders, ropeways are valuable as a means of conveyance between works and distant warehouses, and between separate buildings in the same works. Their rapidly spreading introduction for such purposes indicates how keenly the necessity of effecting economies is felt under the stress of an everaccentuating competitiop.

Jan 1, 1891

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By Austin E. Dwight

IT has been shown by Oelsen and Wever' that the effect of a solute element on the allotropic transformation in iron is dependent upon the quantity

Jan 1, 1957