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By W. N. Lacey, B. H. Sage

Variations in the composition of the liquid phase of natural reservoirs which are continuous through significant ranges in elevation have been noted by petroleum technologists. In general, there is a greater gas-oil ratio and the gravity of the oil is higher in production from the upper parts of the formation. In the present paper the possible changes in composition with elevation which would result from the attainment of thermodynamic equilibrium in a uniform gravitational field have been evaluated for a naturally occurring hydrocarbon liquid, a binary hydrocarbon liquid phase and a binary hydrocarbon gas. The results indicate a progressive decrease in the mole fraction of the components from methane through the butanes with increasing depth, accompanied by a corresponding increase in the amount of the heavier components making up the system. The magnitude of these variations is perhaps insufficient to explain completely the variations in the properties of the liquid phase that are encountered at various elevations within a particular producing horizon. However, the changes are significant and the treatment presents an example of the application of thermodynamic data to the evaluation of the properties of hydrocarbon fluids under the conditions approaching those encountered in natural reservoirs. Theoretical Considerations Muskat1 has discussed the work of earlier authors relating to the equilibrium relationships of multicomponent systems in a gravitational field. He also presented explicit solutions for several cases and discussed the physical significance of gravitational concentration gradients. In engineering work it is customary to consider the pressure, the temperature and the composition of a phase to be the independent variables sufficient to establish its state. This procedure neglects the effect of gravitational or other types of fields upon the energy associated with the system and assumes, among other things, that the pressure is uniform in

Jan 1, 1939

By Will H. Coghill, P. H. Delano, G. D. Coe

Data concerning the actual net energy required for pulverizing coal are lacking from the literature on coal pulverization. Power data given in the literature concern gross power and frequently include the power expended on the air blast or product-conveyor system, as well as power lost through friction in the pulverizer itself. Consequently, such data supply no information regarding the net energy consumed in pulverizing or the relative grinding resistance of various coals. In the study of coal pulverizing much work has been done on what is known as " grindability-index numbers," but grind-ability tests have seldom considered the energy input (that is, the "cause" part of the system "cause and effect"). There are many records of the effect, but even these have questionable value because the "grindability" tests did not make a pull'erized product by a method comparabLe with- commercial pulverizers. In many of the tests, only a selected part of the coal was ground, and the remainder continued to be an unknown factor. Furthermore, none of the grindability tests provide the balanced circulating load common to all modern commercial pulverizing. In order to obtain better understanding of the fundamental principles of coal pulvcrizing, the Bureau of Mines is investigating the "cause" phase; that is, the net energy input or net power excluding friction between the moving parts of the machine. As a first step in the investigation,it was necessary to design and construct a laboratory machine in which no friction-loss corrections are involved, which could grind and finish a minus-¾-inch feed, which could be emptied rapidly and completely, which could operate with a continuous feed and finish in an air separator; and, most essential of all, which would be equipped with a measuring device for recording only that portion of the total power consumed in actual pulverizing, hereafter referred to as "net energy input" or "net horsepower-hours." The channel-roller pulverizer hereinafter described is believed to meet these requirements. History oF the Machine The, work started when Ralph W. smith, engineer, St. Genevieve Lime Co., St. Cenevieve, Mo., was appointed one of the consultants of the Bureau of Mines, United States Department of the Interior, in cooperation with the University of Alabama, to develop a machine for testing the abrasiveness of coal. Smith had already developed a machine for testing the abrasive-ness of dentifrices,1 and it was thought the same principles might be applied to coal, Smith's machine had a revolving disk with an annular channel in which the sample was placed. Riding in the channel was a small block or runner of selected soft metal held

Jan 1, 1942

By Richard McCaffery

THIS paper considers certain aspects of the acid Bessemer process, particularly in its relations to the duplex process-that combination in which the pig iron is first desiliconized and decarburized in acid Bessemer converters and then dephosphorized in basic open-hearth furnaces. The acid Bessemer process employs an acid-lined converter and produces an acid slag. The blow is usually thought to eliminate the silicon and manganese as oxides and then to burn off the carbon as carbon monoxide. On account, however, of the relatively large amount of metallic iron present in the converter, compared with the relatively small amount of the impurities it is desired to oxidize, the first reaction in the converter probably is the formation of iron oxide, which dissolves in the bath and acts as an oxygen carrier for the silicon and carbon. As soon as iron oxide is dissolved throughout the bath, the oxidation of silicon commences; but in the early stages of the blow the mass law would indicate that iron oxide must form first, and this oxide probably increases up to some saturation point. The molten metal in the converter from the early stages of the blow right through to its completion remains basic, while the slag produced is siliceous. This fact is shown by the corrosion of the acid bottom and the tuyeres, which is greatest at the tuyere orifice where oxidation is most active and where there is the most iron oxide. Why does this acid bottom corrode? Because it is attacked by a base. The thought, therefore, suggests itself, why not make the bottoms of basic or neutral material?1 As the converter slag is acid, those parts of the converter coming in contact with the slag should be acid; but those parts of the converter that are in contact with the molten metal saturated with metallic oxides should be basic or neutral. Bessemer operators have for some time tacitly admitted this condition, for the blast pressures have steadily increased with the object of keeping the metal in suspension, and so preventing bottom corrosion; if the molten metal were not basic, it would not attack an acid bottom. In addition, the tuyeres are bunched together at the middle of the bottom and a clear space is left around the outside of the bottom; if tuyeres are placed too near the side walls the

Jan 8, 1920

By T. R. Young, S. A. Scott

9.5-1. Introduction. The use of pipelines to transport solids has been successfully accomplished with many different materials. One of the oldest applications is the dredging and placing of hydraulic fill. Many installations have been made and operated for long periods of time with excellent dependability, low operating cost, and low maintenance. It is not the aim of this chapter to give the engineer the answers from which to design a pipeline, but rather to supply helpful information from which to start the project. There are several phases of solids pipelining which as yet have not lent themselves to quick engineering answers. Investigations have been carried on by many, with several theories advanced by the various investigators. In recent years certain notable theoretical advances in hydraulic transportation have been achieved. Vertical transport, using balanced "leg" operation, now appears competitive with other forms of vertical transportation. In addition, horizontal transport utilizing capsules has been proven experimentally to be attractive because of lower pressure drop than the conventional methods of solid transport in fluid media. With the aid of the computer, the laborious calculations associated with pumping calculations have been greatly simplified; and with this tool the pipeline engineers of the future will undoubtedly be able to develop a more comprehensive understanding of solids-fluid transport. 9.5-2. Theory. There have been many excellent studies made and information is available in the literature, but a general comprehensive theory of pipeline transportation of solids has not been advanced. The existing flow theories will give approximations for minimum and optimum flow velocities, friction head losses, energy requirements, and pump and pipe size The principles of dynamic similarity and scaling laws are well understood for the flow of pure liquids. There are no firm methods of scaling slurry pipelines of small diameter to larger diameters except for a few empirical.

Jan 1, 1968

By N. Brown, M. Herman

IT has been pointed out by Cottrell' and Fisher that long-range order would produce superdis-locations, consisting of two partial dislocations separated by an out-of-phase region. The mutual repulsion of the partial dislocations is balanced by the surface tension of the out-of-phase domain boundary joining the dislocations (Fig. 1). The calculation of the equilibrium spacing of the dislocations has yet to be made. The argument uses the Bragg and Williams theory of long-range order." The metal under consideration is the A-B, body-centered type, such as ß brass. The slip system is taken to be [Ill], (110). Since nearest-neighbor interactions are considered, only the atoms position in the two (110) planes adjoining the slip plane have to be labeled. Corner sites are called a and a' in the top and bottom (110) planes, respectively. Similarly ß and ß are the body-centered sites. Thus, a and ß and 0 and a sites are nearest neighbors. Assume that the bottom plane moves and the top plane is fixed during slip; the atoms in a and ß sites exchange sites but atoms in a and ß sites remain fixed. Fraction of A atoms in a sites, for example, is given by fa and fa. for the un-slipped and slipped condition, respectively. Similarly number of A atoms in the a sites is given by n, and n'a for the unslipped and slipped condition, respectively. As the dislocation moves into the ordered region the change in number of A-A bonds is given by

Jan 1, 1957

In 1936 the Institute established the Anthony F. Lucas Gold Medal, which will be awarded from time to time "for distinguished achievement in improving the technique and practice of finding and producing petroleum." These awards will be sponsored by the Petroleum Division. Captain Lucas was a pioneer in the oil industry, one of the early wildcatters and a leading mining and petroleum engineer. He was famous as the discoverer of Spindletop. He became a member of the Institute in 1895 and in 1913 was the first Chairman of the Petroleum and Gas Committee of the Institute, the forerunner of the present Petroleum Division. He also headed the Committee in 1914, 1917 and 1918. The first medal was presented at the annual dinner in 1937, Feb. 17, to J. Edgar Pew. The personnel of the Committee on award as appointed in February, 1937, is as follows: John R. Suman, Chairman Until Feb., 1938 Until Feb., 1939 Hallan N. Marsh R. OgaRRio Russell 6. McFarland H. H. Power John R. Suman CaRl A. Young Until Feb., 1940 Until Feb., 1941 W. B. Heroy Joseph Jensen C. V. Millikan John M. Lovejoy J. Edgar Pew Carroll H. WEgemanN Members ex-officio R. C. Allen John W. Finch Axtell J. Byles H. B. FUQUA

Jan 1, 1937

Jan 1, 1962

By E. L. Vickers

Over the years, the pure theorist in economic analysis has accumulated a formidable array of facts in bringing his subject matter under control. Business managers and mining engineers are aware of the theorist's weapons, but the question of applying them to the mastery of practical problems seems hardly feasible, especially in view of the almost innumerable variables plaguing the everyday scene in the mining enterprise. One such sophisticated tool of long-standing in the theorist's arsenal is marginal analysis. Equally long-standing for the operating company and valuation engineer is the problem of defining the cut-off grade the point below which a mineral re- source ceases to be economically amenable to extraction. In other words, what part of a mineralized body of rock is ore and what is waste?

Jan 6, 1961

Jan 1, 1942

Jan 1, 1887

By P. N. Nikiforuk, M. C. Zoerb

An analog computer model has been developed of a large, walking dragline. This model permits changes in the configuration of the dragline, or changes in its digging cycle, to be readily investigated on a computer. As a result, it is possible to determine ways of improving the dragline performance without having to carry out many expensive experiments on the actual machine. This model can also be used as a simulator for dragline operator training. INTRODUCTION The movement of large volumes of material is always a costly operation and the increasing trend towards the use of large capacity equipment does not necessarily produce the economy desired. This problem is of particular concern to the mining industry in its open-pit operations where large draglines are used to remove the overburden. Since this operation often forms a very large part of the total cost of open-pit mining it is particularly important that it be kept as economical as possible. This requires that the dragline be operated at its maximum possible productivity. In order to optimize the operation of a dragline it is desirable that a suitable model of the dragline be available for study. Once such a model is available the effects of changes in the configuration of the dragline, or changes in its digging cycle, could be readily investigated on a computer and methods of improving its performance could be determined without having to carry out expensive experiments on the actual machine. Such models would be of use not only to dragline users, but also to the manufacturers of draglines for design purposes. Presumably studies of this type could eventually lead to computer-con trolled stripping operations. As far as can be determined very little work1'2 has been done on the derivation of dragline models. Such models must be derived before work of the nature indicated in the previous paragraph can be carried out. As a small contribution to this field this paper describes work that has been carried out by the senior author during the past few years on the derivation of one such model. This model describes the drag, hoist and swing operations of a 35 cu yd, commercially available, walking dragline. This model was derived for use with an analog computer and can be used either for optimization studies, or for the training of dragline operators. DESCRIPTION OF DRAGLINE General: The particular dragline for which an analog computer model was developed is owned by the Great West Coal Company of Estevan, Saskatchewan. It is a walking dragline and its function is to remove 40

Jan 1, 1967

Jan 1, 1915

By Cyril Smith

ISOLATED alloys of copper and silicon were prepared and examined by chemical methods more than one hundred years ago, but it was not until the work of Rudolfi1 that the equilibrium relations. were studied. The early history of the alloys was well described by Baraduc-Muller2 PERCENT SILICON-BY WEIGHT FIG. 1.-COPPER-SILICON EQUILIBRIUM DIAGRAM ACCORDING TO RUDOLFI (1907). and need not be further discussed here. The diagram of Rudolfi, based entirely on thermal observations, showed silicon to be soluble in copper up to 4.5 per cent. at 849° C., at which temperature there was a peritectic horizontal resulting from the formation of a 0 phase with about 7.4 per cent. silicon from a and liquid with 7.85 per cent. silicon. The ß phase was believed to form a eutectic with Cu3Si at 820° C. and 9.8 per

Jan 1, 1928

By Henry Louis

Henry Louis, Newcastle-upon-Tyne, England (communication to the Secretary*).—In this paper Mr. Simons derives the various forms of revolving slime tables, of which the Harz and the Linkenbach tables are typical examples, from the old rectangular or box buddle. This I believe to be an error, at any rate if Mr. Simons attaches the same meaning as I do to the ((evolution" of a dressing appliance. By the '(evolution" of such an appliance I understand the progressive development and improvement of an appliance acting on a definite principle, such improvements having usually for their object the economy of labor in working the same, or the increase of its capacity; when an entirely new principle is introduced, I no longer look upon this as evolution from the old type, but as the origination of an independent type of appliance. The box buddle was no doubt the predecessor of the old Cornish round buddle, which was evolved from it with the object of saving the labor required to work the box buddle; both machines are horizontal-current separators, in which the separation of sands of different densities is effected by their differential rates of fall in a horizontal current of water of considerable depth. These appliances, though well suited to sands, are for obvious reasons not adapted to the treatment of slimes. The revolving tables of the Harz and similar types, on the other hand, act on the principle which I have called separation in thin films of water, and which Mr. Simons calls the film sizing principle, in which the resistance of the surface over which the pulp flows plays an essential part in determining the separation of the particles, and which is well suited to the treatment of slimes. Unlike the last principle, it will not work in deep bodies of water and cannot be used where considerable depth of material accumulates in the appliance, as in the box buddle and round buddle. As I have shown in my book, The Dressing of Minerals, p. 326, these revolving tables are a development of the appliance known variously as the flat buddle, flat table, or frame, the last name, which is the old Cornish one, being the one that I personally prefer. These primitive appliances, as well as the continuous-acting round tables described by Mr. Simons (his Figs. 10 et seq.) all work on the principle of separation in thin films, and are all adapted for the treatment of slimes; his buddles and round tables (Figs. 1 to 9) do not work upon this principle, and should therefore be sharply differentiated from the former. The evolution in each case of the continuous acting, more or less automatic, circular appliance from the primitive, intermittent, hand-worked, rectangular appliance has proceeded upon strictly parallel lines. The question of the evolution of the respective types involves a point of some importance as regards the principles of ore dressing.

Jan 1, 1915

Oct. 8-13, 1917 The St. Louis Meeting of the Institute will be held Oct. 8-13, 1.917. Various committees are being organized to perfect the arrangements for the meeting. A number of excellent technical papers have already been secured end an attractive series of excursions has been outlined. The following is the outline plan for the meeting. More detailed announcements will be made as the plans mature. MONDAY, OCT. 8 Morning: Registration and Technical Session. Afternoon: Boat ride to Herculaneum, Mo., to visit smelter. and Evening: Dinner on boat and social evening.

Jan 4, 1917

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By A. Steiner, K. L. Komarek

Activities of aluminum in solid Ni-A1 alloys have been determined between 20 and 60 at. pet Al and 1200" and 1400°K by an isopiestic method in which nickel specimens, heated in a temperature gradient, are equilibrated with aluminum vabor in a closed all-alumina system. The activity of aluminum shows a strong negative deviation from Raoult's law at low concentrations but increases by three orders of magnitude within the ß(NiAl) phase. The partial molar enthalpy and entropy of mixing are negative. Using Wagner and Schottky's theory of ordered compounds, a degree of disorder of 4 x 10 -4 for NiAl and 1.25 X 10-2 for FeAl has been calculated THE Ni-A1 system has been studied by a great number of investigators, and the results, as far as the phase diagram is concerned, have been compiled by Hansen.1 The phase boundaries from 0 to 50 at. pet Ni are well-established. At higher nickel contents the boundaries are still in dispute and an additional phase, A12Ni3, has been reported.' The phase diagram is dominated by a very stable high-melting compound, NiA1, with a relatively wide range of homogeneity. Heats of formation of solid alloys have been determined calorimetrically by Oelsen and Middel3 from 20 to 95 at. pet Ni and by Kubaschewski4 from 25 to 80 at. pet Ni. According to the most recent compilation5 no other thermodynamic investigations have been reported for the Ni-A1 system. Due to the corrosive nature and the low vapor pressure of aluminum, a method has been employed for determining activities of aluminum which was previously developed for the Fe-A1 system.= Nickel specimens, heated in a closed evacuated alumina system in a temperature gradient, were equilibrated with aluminum vapor from a source within the system kept at constant temperature. After complete equilibration the specimens were analyzed and activities calculated from the known vapor pressure of aluminum. APPARATUS AND EXPERIMENTAL PROCEDURE Materials. The nickel specimens were made from wafers of electrolytic nickel (International Nickel Corp.) of 99.99 pet purity which were rolled to a 0.001-in.-thick foil by Driver-Harris Co. and to a 0.005-in.-thick sheet in our laboratory. The aluminum (Aluminum Corp. of America) had a purity of 99.99+ pct. The alumina tubes and crucibles were made of impervious recrystallized alumina with an alumina content of 99.7 pet (Triangle RR, Mor-ganite Inc.). Experimental Procedure. Annular specimens were punched from the sheet, the punching burrs removed, and the specimens degreased in carbon tetrachloride and acetone and weighed on a micro-balance to within an accuracy of ±0.01 mg. The specimens were positioned with alumina spacers along an alumina tube, and the positions measured. Aluminum metal was machined into cylindrical shape, and placed into an alumina crucible. The tube with the specimens was then inserted into a hole drilled into the aluminum metal. An alumina tube with its closed end at the top was slipped over the specimens so that its lower end fitted snugly into the alumina crucible. The assembled reaction tube was inserted into a mullite tube with a water-cooled brass head which had an opening for a quartz thermocouple protection tube and a metal-to-glass connection to a conventional vacuum system. A Pt-Pt 10 pet Rh thermocouple could be raised and lowered in the quartz tube which was placed along the outside of the alumina reaction tube. The mullite tube was heated by two separately controlled resistance-tube furnaces so that in the experimental temperature range an over-all temperature gradient of approximately 150o to 250°C could be imposed on the reaction tube. The position of the mullite tube was adjusted so that the surface of the aluminum metal was always at the temperature minimum. The reaction tube was thoroughly evacuated before and during slowly heating the assembly up to the melting point of aluminum. A pressure of less than 2 µ (Hg) was maintained during an experiment. Once the aluminum had melted, it isolated the contents of the alumina tube from the surroundings. Several times during an experiment the temperature gradient was carefully measured. An experiment lasted from 3 to 6 weeks and it was terminated by air cooling the evacuated mullite tube. For further details of the experimental procedure the paper on the Fe-A1 system6 should be consulted.

Jan 1, 1964

Jan 1, 1937

By C. W. Parmalee

The ideal fuel for burning ceramic wares is the one that, among other characteristics, has little or no sulfur. For that reason wood was long considered the most desirable fuel but its high cost has practically eliminated its use except in regions where it is very abundant or other circumstances warrant its choice. The fuels commonly employed are natural and producer gas, oil, and coal. The last named is undoubtedly the most important, not only in this country but abroad. Occasionally anthracite is used but the larger part is bituminous. The quality of the coal used depends on the kind and the value of the products being manufactured. For some materials, such as common brick, hollow block, etc., the quality of the coal is of less importance than in the manufacture of polychrome terra cotta, pottery, porcelain, etc. It is obvious that in burning clays that contain notable amounts of pyrite, marcasite or gypsum, as is the case with many common clays, the sulfur content of the fuel is of much less importance. The permissible amount of sulfur in the coal used will depend on the kind of product being manufactured. "A good sample1 of coal commonly used in pottery ovens has something like this quantity of sulfur: total sulfur, 1.20 per cent.; sulfur in ash, 0.11 per cent.; volatile sulfur, 1.09 per cent." This is based on English pottery practice. Correspondence with a. number of leading manufacturers in this country has produced the following figures: Sanitary Ware.—(a) 1.0 per cent, maximum, (b) 0.5 per cent. Sewer Pipe.—(a) 1.2 per cent., (b) 1.1 per cent, present run, 3.0 per cent, has been used. Terra Cotta.—(a) 0.5 per cent, basis of contract, 1.0 per cent, approximate. Pottery.—1.0 per cent, contract, 1.5 per cent, probable content. Enameled Brick.—1.3 per cent, maximum, (a) and (6) designate different firms giving figures. Since a pottery kiln for sanitary ware will require about 14 tons of coal for a bum, the quantity of SO2 that will be generated from a 1-per

Jan 1, 1920

By A. G. Weber, K. H. Coats, M. H. Terhune, R. L. Nielsen

Two computer-oriented techniques for simulating the three-dimensional flow behavior of two fluid phases in petroleum reservoirs were developed. Under the first technique the flow equations are solved to model three-dimensional flow in a reservoir. The second technique was developed for modeling flow in three-dimensional media that have sufficiently high permeability in the vertical direction so that vertical flow is not seriously restricted. Since this latter technique is a modified two-dimensional meal analysis, suitably structured three-dimensional reservoirs can be simulated at considerably lower computational expenses than is required using the three-dimensional analysis. A quantitative criterion is provided for determining when vertical communication is good enough to permit use of the modified two-dimensional areal analysis. The equations solved by both techniques treat both fluids as compressible, and, for gas-oil applications, provide for the evolution of dissolved gas. Accounted for are the effects of relative permeability, capillary pressure and gravity in addition to reservoir geomety and rock heterogeneity. Calculations are compared with laboratory waterflood data to indicate the validity of the analyses. Other results were calculated with both techniques which show the equivalence of the two solutions for reservoirs satisfying the vertical communication criterion. INTRODUCTION Obtaining the maximum profits from oil and gas reservoirs during all stages of depletion is the fundamental charge to the reservoir engineering profession. In recent years much quantitative assistance in evaluating field development programs has been provided by computerized techniques for predicting reservoir flow behavior. Because of the spatially distributed and dynamic nature of producing operations, automatic optimization procedures, such as those now in use for planning refining operations, are not now available for planning reservoir development. However, present mathematical simulation techniques do furnish powerful means for making case studies to help in planning primary recovery operations and in selecting and timing supplemental recovery operations. A number of methods have been reported which simulate the flow of one, two or three fluid phases within porous media of one or two effective spatial dimensions>-4 However, applying computer analyses to actual reservoirs have been limited mostly to two-dimensional areal or cross-sectional flow studies for two immiscible reservoir fluids. To obtain a three-dimensional picture of reservoir performance using such two-dimensional techniques, it has been necessary to interpret the calculations by combining somehow the results from essentially independent areal and cross-sectional studies. To the authors' knowledge, the only other three-dimensional computational procedure, in addition to those presented here, was developed by Peaceman and Rachford8 to simulate the behavior of a laboratory waterflood. Two computational techniques which may be used to simulate three-dimensional flow of two fluid phases are described in this paper. The first method, called the "three-dimensional analysis", employs a fully three-dimensional mathematical model that treats simultaneously both the areal and cross-sectional aspects of reservoir flow. The second method, called the vertical equilibrium (VE) analysis", is applicable