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By C. R. King

Most of the acid volcanic glasses such as obsidian, perlite, pitchstone, pumice, and pumicite (volcanic ash) are susceptible to some expansion if suddenly subjected to a suitably high temperature in a properly designed furnace, and subsequently suddenly cooled. Expansion results from the action of chemically combined or dissolved water expanding as a vapor within the softened heated rock particles. This expansion forms countless minute bubbles within the pasty mass of the natural glass particles. If the particles are cooled before these bubbles can escape, the resulting products are cellular, more or less spherulitized glass froths or hollow glass spheres of many types. Chemically, they are essentially aluminum silicates containing about 70 to 75 pct silica, 10 to 16 pct alumina, and 2 to 7 pct sodium plus potassium oxides. They are relatively resistant to attack by acids or alkalies, are resistant to heat up to over 1000°F, and are completely inert to insect or fungus attack.

Jan 1, 1949

By Donald Towse

Geothermal energy can substitute for and compete with other fuels, but until now it has been used only in special situations where it costs much less than alternate fuels. Geothermal heat is expected to be developed where it can: (1) compete with alternate fuels, (2) replace scarce fuels, (3) be more environmentally acceptable, or (4) is especially adapted to local needs. Economic problems in development include the often high capital costs of wells and gathering systems and the long lead-times required for electric generating plants. The large investment and long payout times for large industrial uses adversely affect the economics.

Jan 1, 1977

By J. H. Allen

The air lift method of pumping water is discussed. A review of several large diameter hole drilling projects that used reverse- circulation air-lift techniques is presented. Proposals are made for reverse circulation flow rates for slow rates of bit penetration (5 fph) as well as reverse-circulation flow rates for faster rates of bit penetration (10 fph). The Ingersoll-Rand air lift equations are modified for rotary drilling operations. By establishing minimum reverse circulation flow rates and utilizing the modified air lift equations, the establishment of minimum circulation equipment sizes and a more definitive requirement for improved bit body design should result.

Jan 1, 1978

By A. KROENLEIN

THE Cromwell 'Pool has been the outstanding development in Oklahoma during the year 1924. . Tonkawa contributed the deep "Slick Sand" bit apparently its 'peak has been reached and like other pools producing from below the Mississippi lime its decline' mill be rapid. After reaching a daily production of 67,000 bbl., the Cromwell Pool is declining because of a lull in -new completions, but a mile extension has revived activity and an area equal to that of the present producing' area is under development and will cause an increase in the present production of 38,000 bbl. This pool is seven months old, has three dry holes in one hundred twenty completions and is actually defined only on the southern extremity. This area has been one of the chief contributors to the .over-production of high gravity oil in the Mid- continent fields and will be such' for the remainder of ' the year. 1924 and first part of 1925.

Jan 1, 1924

By Scott Tzcrner

WITHIN recent years people have begun to realize the importance and significance of the mining and allied industries. The leading part the engineer plays in civilization is becoming recognized. However accurate quantitative knowledge of the industrial importance of mining is still seldom possessed except by those close to this business. It is true that there are a few who go to the extreme and represent the whole progress of civilization as a reflection of man's gradual mastery of mineral utilization, but on the whole, the magnitude of the-industry is underestimated. In this paper I shall call attention briefly to the importance of mining in the United States, in Canada, and in the world. Ordinarily, the annual primary mineral production of the United States is about $5,500,000,000. The average for the last 5 years has been a little over that, but last year, sadly enough, it was less than 31/4 billion. Just now, we are on the decline, and have been for the last two years. In Canada, the 5-year average was about $268,000,000, and last year it was 227 million. Due in part to gold mines (in 1930, for the first time, Canada's gold production exceeded that of the United States), the Canadian average is holding up better than ours. Average world mineral production over the last -5 years has been estimated at about $12,000,000;000 whereas in 1931 it was less than than 8 billion.

Jan 1, 1932

By L. A. Creglow

IN common with many other companies engaged in the mining and processing of ores, research has always been an important activity of the United States Smelting Refining and Mining Company. Much of this research has been carried on at the various plants of the Company by the operating staffs, and over the years has been an essential factor in developing new methods and improving existing methods of operation. In 1917 arrangements were made with the Massachusetts Institute of Technology under which the Company had the exclusive use of one or two small laboratories in the then newly constructed MIT buildings and the use of the metallurgical laboratories, subject of course to the Institute's needs. After about two years this work was temporarily discontinued but was resumed in 1920 under the direction of G. H. Clevenger, consulting metallurgist for the Company, who recently retired. Becoming cramped for space, the laboratory was moved to a location near MIT on Amherst Street, Cambridge, in 1924. Establishment of a general research laboratory in metropolitan Boston naturally followed from the fact that the head office of the Company was located there and that the library facilities available for all types of research were, and are, unsurpassed. The disadvantages in carrying on research at great distances from the operating units of the Company were always apparent, but with widely scattered plants this disadvantage could not he overcome. With

Jan 1, 1948

By A. W. D. Hills, M. R. Moore

An apparatus has been developed in which metals can bc solidified under closely controlled unidirectional heat flow conditions. The metals are cooled by a multiple-air jet system, designed so that the heat transfer coefficient is uniformly distributed over the cooled surface. They are contained in a special furnace system of low thermal mass which enables unidirectional heat flow conditions to be rigorously maintained for certain specific cooling rates. This apparatus has been used to study the solidijication of pure lead and pure tin at zero superheat, solid metal thicknesses being determined by thermal analysis, and by dipstick readings. Detailed thermal balances have been drawn up on the experiments in order to determzne the cooling conditions that most rigorously correspond to unidirectional heat flow. Solid metal thicknesses, measured experimentally for these conditions, have beetz shown to agree closely with the theoretical wedictzons of different integml-profile methods. lt is concluded that any errors inherent in the integval-profile method are no greater than the errors inherent in experimental investigations of solidification. A knowledge of the influence of heat transfer rates on the solidification of metals is essential to the understanding and control of industrial casting processes. Since very few formal methods are available for solving the heat conduction equation under solidification conditions several authors have developed approximate techniques for doing so. One of the most promising is the integral-profile technique that has been used by Goodman,1 Hills,2,3 Tien4 and Hills and ~oore' to predict solidification rates under certain specific heat transfer coniditions. In the first of this present series of papers6 Hills has further generalized the method and developed a universal integral-profile technique that can be used to predict solidification rates under a wide variety of unidirectional heat flow conditions. Since the method is approximate it is necessary to investigate the accuracy with which it predicts actual solidification rates. A review of the literature7 shows that solidification rates have seldom been measured under accurately known heat transfer conditions and it was therefore decided to develop experimental techniques that would enable this to be done. Results obtained would then be available as a check on the approximate solutions already developed, and in the development of further solutions that would be applicable under more complicated conditions. The initial work in this experimental program which is described here, is concerned with the solidification of pure metals at zero superheat under unidirectional heat flow conditions. Subsequent experiments have been concerned with the solidification of pure metals at appreciable superheats, under varying unidirectional heat flow conditions and under two dimensional heat flow conditions. In a series of experiments recently initiated, the solidification of binary alloys is also being investigated. The results of these subsequent experiments, together with relevant theory, will be described in later papers. The solidifying metal has been cooled in all the experiments, by a multiple air jet system designed so that the heat transfer coefficient to the cooled surface is constant and is uniformly distributed over the surface. This type of system has been chosen since only one parameter is needed to specify the heat transfer conditions and since these conditions are analogous to those met in certain continuous casting processes.' Air cooling was chosen in preference to water cooling, however, since it offers a wider range of heat transfer conditions, and since it can be investigated by analogous mass transfer techniques. The first part of this paper discusses the existing integral-profile solutions that correspond to the heat transfer conditions used in the experiments, and describes the development and use of the experimental apparatus. In subsequent sections the heat transfer and solidification results are presented, and the various theoretical predictions are compared with them, and with one another.

Jan 1, 1970

H. W. Turner, Portland, Ore. (communication to the Secretary*) :—Mr. Brown's paper on the complicated groups of veins exposed in the workings of the Bodie mine forme a valuable contribution to the literature of the structural features of ore-depoeits. It is much to be desired that managers should put into print the results of their observations of the mines under their charge. These observations, as well as data of production, kind of ores, etc., usually accumulate for years, and unless the mining geologists of the Geological Survey happen along before the mine is worked out, such data seldom get into print. About the year 1899 I went through the mines at Bodie with R. C. Turner, then superintendent, and made some notes on the veins and gangue-minerals, and collected some specimens. Mr. Brown refers to crystals of feldspar (albite) found on fragments of quartz on the surface. I collected a number of specimens of these crystals, mostly from Queen Bee hill, and

Jan 1, 1909

By Charles H. Behre

UNDER the caption "fault," geologists intend to include all mass movements of solid rocks over adjacent rock masses. When these are studied long after their origin, however, circumstances make it possible to recognize as "fault" only formations showing clear evidence of actual movement of one side with respect to the other. Necessarily the chief evidence consists of the offset of a vein, bed, or other key structure. Planes of movement parallel to the bedding, or nearly so, are recognized with difficulty or are overlooked and hence many important faults are wholly unrecorded. Indeed, among standard American references on structural geology, one alone emphasizes the importance of bedding-plane movements and that one only briefly1. For some time the writer, cognizant of this difficulty, has paid special attention to such movements, both as observed in the field and as recorded in the literature. It is believed that enough data are now at hand to justify a short discussion. Its purposes are fivefold. It is desired first to briefly classify and describe at least the more common kinds of bedding-plane faults, and second, to examine the causes and manner of their formation, at least in instances where the subject has not yet been well covered by other investigators. Third, certain by-products of bedding- lane movements are of such conspicuous importance to the economic geologist and mining engineer as to merit mention. Fourth, concrete illustrations should be placed before the reader in order to lend reality and to furnish a basis of comparison with his experience; such illustrations will necessarily be scattered through the text of this paper. They are only in part from the writer's own field observations. The fifth and prime objective of this paper is to direct attention to the great importance of movements on the bedding planes, in the hope that the recognition of such movements and their significance may simplify mining problems.

Jan 1, 1937

By AIME AIME

THE quarters provided for the session on Milling Methods, Monday afternoon, Feb. 17, were filled to capacity. Galen H. Clevenger presided and notables, such as A. W. Fahrenwald, A. O. Gates, F. A. Thomson, W. L. Zeigler and others who had not graced a milling meeting in New York in recent years, or per- haps even never before, were actually present and spoke "in person." The first paper, by A. W. Fahrellwald (T. P. 275), entitled "Classifier Efficiency ; An experimental Study," was summarized by the author, who clearly showed the inconsistency of determining the efficiency of a classifier by means of sizing tests, especially where the material classified consists of a mixture of minerals of different specific gravities. In place of sieve analysis the procedure recommended involves the use of a glass settling-tube which is considered to give ideal classification and thus serve as a standard against which mill classification will be compared and relative efficiency calculated. This procedure sounds logical. Perhaps the greatest difficulty may lie in securing an ideal classifier acceptable to every one.

Jan 1, 1930

By Howard Eavenson

PRIOR to 1907 nearly all coke was made in beehive ovens, and most of the gas produced was made in the old-style gas retorts, and while there were a few coke plants in southern West Virginia, southwest Virginia and Kentucky operating on high-volatile coals the proportion of the total product made by them was small and was usually used locally. The greater part of the coke made, and the coal gas produced, came from the Pittsburgh seam of western Pennsylvania and northern West Virginia-which was then regarded as the standard coking and gas coal of the coun, try, and the best coal available anywhere for these purposes. With the advent of the by-product oven and the building of coke plants at the furnaces, the restriction of the use of one grade of coal for making coke was removed and the use of mixtures of low-volatile and high-volatile coals began. The change in the locations of the coke plants removed the necessity of using Connellsville coal and also made sources of gas available to the public utilities other than of their own manufacture. Most of the first oven plants were built at points distant from the Connellsville region and this afforded an opportunity for the use of coals from the southern Appalachian fields, which were at approximately equal distances from the ovens. Since that time development has been made on a number of seams of coal of great purity in southern West Virginia, southwestern Virginia and eastern Kentucky, which have been largely used for cokemaking, gas and other metallurgical purposes where low amounts of ash, sulfur and phosphorus are determining factors. These coals are much lower in the objectionable elements than the best of the coal from the Pittsburgh seam, or than any northern coal, and in by-product ovens produce coke that is not excelled for any purpose by any coal mined in this country, and is equaled very seldom. Coal from several of these seams is shipped in great quantities without beneficiation and is lower in ash and sulfur than the best washed product from any seam mined in the north.

Jan 1, 1932

By G. Stuart Jenkins

CONDITIONS at the properties of the Consolidated Coal Co. had reached a point where improvements were almost impractical. The mines, sunk years ago, had shafts and entries so small as to preclude the use of large mine cars. A radical change was necessary in the type of mining and also in the type of mine to accommodate such haulage units. After due consideration, the company decided to enter the field of trackless mining, utilizing belt conveyors and chain-flight conveyors, the belt conveyors to take the long haul, and the chain-flight conveyors to be used for gathering. It was decided not to sink a shaft, but to drive a slope on an inclination of 17 1/2°, which the company believes to be about the limit on which coal can be carried on a belt without rolling back unduly.

Jan 1, 1939

By James G. Blaine, David A. Summers, L. John Tyler

There has been a considerable amount of research developed which shows that the close contour cutting of an excavation prior to removal of the central core will increase ground stability while concommitantly, reducing the number and size of blastholes required to create the excavation. To date, the industrial development of this technique has however, centered on the development of equipment based on simple cutter movement and mechanical rock cutting. The advent of reliable field operable high pressure waterjet cutting equipment with the very low reactive force required to hold the head in position has opened the way for a much smaller and more manueverable system. The advent of small, micro-computers allows the programming of accurate profiles for cutting tools on excavation equipment. The combination of these two technologies will allow the generation of complex as well as simple, excavation profiles and lead to the potential pre-support of the opening before major excavation is completed. A brief description of the necessary components and their functions is encorporated in the initial prototype design as given.

Jan 1, 1984

By T. Sterry Hunt

Jan 1, 1891

By John M. Dale

As much as half of the world's known reserves of elemental sulfur occur at or near the earth's surface in natural or native sulfur deposits of volcanic or sedimentary origin. Yet these reserves constitute only a small percentage of the world's supply. Looked on as marginal materials, they remain relatively untouched despite the current demand and improved prices for sulfur. There are two main reasons for this. The first is the nature and occurrence of the deposits. They are generally small and widely scattered in remote and often arid locations, and the gangue constituents of the ore are apt to vary considerably-not only between deposits but also within deposits. The second reason is the lack of workable and economically feasible processes for recovering sulfur from the ores in such deposits. Historically, the older thermal processes in which the sulfur is vaporized away from the gangue were probably the most successful, but they were inefficient and created pollution problems. A few of the historical processes remain in operation today. Recently, however, an improved thermal process to handle all sulfur-containing surface ores has been designed under sponsorship of the Pan American Sulfur Co. A schematic diagram of this process is shown in Fig. 1. The process equipment consists of a paddle trough conveyor retort which is operated as a closed unit to prevent any air or oxygen from entering the system. Ground surface sulfur ore and heated pebbles are fed to this unit simultaneously. The ore and heated pebbles are slowly conveyed and continuously mixed down the conveyor retort. Heat from the pebbles and heat supplied to the outside walls of the trough conveyor retort raise the ore temperature above the boiling point of sulfur. Sulfur vapors and steam originating from moisture in the ore are ducted to a condenser, and the sulfur is recovered as a liquid. The gangue and the pebbles are discharged from the trough conveyor and separated-the gangue being discarded, and the pebbles being conveyed to a direct-fired rotary pebble heater where they are reheated before they are again charged into the rotary trough conveyor retort. The hot gases which pass countercurrent to the pebbles are ducted to the outside of the rotary trough conveyor where they pass countercurrent to the flow of the ore in order to maximize heat recovery and utilization.

Jan 4, 1969

By Roy J. Helfinstine, Gilbert H. Cady

One of the most urgent needs in the field of coal combustion is the ability to predict the performance of a coal from knowledge gained from small-scale tests. Numerous types of analyses and tests are conducted on coal, including the proximate and ultimate analyses, heating value, varieties of sulphur, ash analysis, ash fusion temperatures, free swelling index, petrographic analysis, and Gieseler. plasticity. The Illinois Geological Survey has made an intensive study of the value of these tests for judging the performance characteristics of the coal as actually utilized. To date, three reports1,2,3 have been issued, and another is being prepared. The present paper briefly summarizes some of the results found in the studies. Equipment The equipment used for the tests is described in some detail in the above mentioned publications. Briefly, it consisted of a domestic stoker, cast-iron boiler, and water-cooled heat exchanger, which were operated as a forced circulation hot-water system. The entire unit was mounted on scales. Instruments for recording the per- formance of the coal included a hot-water meter to indicate the quantity of water flowing through the boiler; a two-pen, mercury-actuated thermometer to record the temperatures of the water entering and leaving the boiler; a chemical-type meter to record the percentage of CO2 in the stack gases; a pressure gauge to record the static pressure in the stoker-air duct; and a multipoint potentiometer to record the temperatures in the stack and room, and the opacity of the stack gases. A 16 mm motion picture camera was available for taking pictures of either the fuel bed or the scale dial. Procedure The tests described in this report can be conveniently divided into three phases. For the first phase, a load of 5 or 6 tons of unwashed coal (usually screenings) was obtained from each of fourteen Illinois mines. These coals were all crushed and screened to a size of 35 in. (square hole) by 8 mesh. Combustion tests were made on a part of this raw, screened coal. Another portion was passed over a concentrating table to reduce the ash to what was considered to be commercially reasonable, and combustion tests were made on this upgraded coal. The ash content of the remaining coal was reduced to a still lower figure by passing it over the washing table with greater reject, or by standard float-sink procedure. This cleaned fraction was then tested in the stoker-boiler unit. Thus three coals with varying ash content were tested from each mine. For the second phase reported here, coals were obtained from four Arkansas mines and tested as received and after passing over the concentrating table with a normal reject. One Illinois coal was tested in the "washed" condition only. The third phase included tests on commercially prepared stoker coals

Jan 1, 1950

By E. A. Swedenborg, J. S. Ross

Oil-field waters enter into many underground problems with which the petroleum engineer has to deal. Whether the problem is one of infiltration or natural encroachment, it is always desirable to determine the source of the water before commencing repair or remedial work. The usual mechanical tests for determining the source of extraneous water in wells are slow and expensive. An excellent means for the identification of oil-field waters may be afforded by their chemical characteristics when the chemical character of waters from the various sands has been established by careful sampling and analysis cautiously interpreted. In the Salt Creck field, Wyoming, a fairly high degree of efficiency has been attained in the control of field operations by utilizing the information afforded by the analysis. All of the operating companies appreciate this means of identifying waters, with the result that water-sampling has become general practice. Most of the chemical work dealing with Salt Creek waters has been done since the laboratories of the Midwest Refining Co. and the U. S. Geological Survey, were established in the field; the former in 1922, the latter in 1924. A spirit of cooperation has existed between the company and the government personnel by which many of the data for this paper were made available. Sands of the Salt Creek Field The principal sand horizons in the Salt Creek field are the Shannon, First, Second, and Third Wall Creeks, Dakota, Lakota, Sundance and Tensleep. Of these the important oil producers are the First Wall Creek, Second Wall Creek, Lakota and the Sundance. The Third Wall Creek is lenticular and is productive in only a few wells in the southern end of the field. There are also a number of shale wells, but they do not produce water in any appreciable amount. The stratigraphic position of these sands and their relative thicknesses are shown on the condensed composite section of Salt Creek

Jan 1, 1929

By H. C. Boynton, Albert Sauveur

In the course of some experiments conducted in the Metallographical Laboratory of Harvard University, some interesting facts were brought to light which appear to be worth recording in advance of a more elaborate and exhaustive paper which the authors hope to present to the Institute in the near future. Fig. 1 shows, under a magnification of 100 diameters, the microstructure of the cross-section of a steel bar 1/2-inch square, containing 0.52 per cent. carbon, heated to 1100 degrees C. and cooled slowly with the furnace. Fig. 2 illustrates the structure of the same steel, heated to the same temperature but cooled more rapidly in the air. Both samples were cut from the same bar and heated side by side in the furnace. When a temperature of 1100 degrees C. had been reached, one sample was taken out of the furnace and allowed to cool in the air, while the other was cooled with the furnace. The only difference, therefore, in the treatment of both samples will be found in their respective rate of cooling. This variation in the rate of cooling resulted, as shown

Jan 1, 1904

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By P. B. Baxendell

The performance of a water-drive reservoir having a gas cap depends primarily on the movement of the gar-oil and oil-water contacts. The movement of the contacts during production depends in turn on fluid withdrawals and how the reservoir pressure changes as fluids are produced from the reservoir; that is, on how effectively the aquifer maintains pressure by replacing withdrawals. inasmuch as pressure changes, fluid withdrawals, contact positions, and produced gas-oil and oil-water ratios are interdependent, the analysis and prediction of the performance of a reservoir produced in a given way must take into account this interdependence throughout depletion. This paper presents an analysis which, within the limitations of the assumptions made, yields an engineering approach to predicting future performance based on reservoir pressure and production history. The most significant assumption is the method of extrapolation of future gas-oil and water-oil ratios. The extrapolation procedure smoothly increases both ratios to preselected values as the remaining oil column undergoes a specified decrease in thickness. This preselection is made on the busis of previous field experience in depletion of similar reservoirs under similar conditions. For computing future performance a vdumebic balance L combined with the differential equation defining pressure distribution in the aquifer to obtain positions of water-oil and gas-oil contacts. From these positions are extrapolated produced water-oil and gas-oil ratios. Reservoir performance can be investigated when oil production rates are dependent upon various factors including the performance of the reservoir itself. Examples of practical application of the procedure are included. INTRODUCTION To predict performance of water-drive reservoirs with gas caps and thin oil columns, it is necessary to describe the motions of the fluids within the reservoir during the entire production period to depletion. These motions depend on the pressure changes and on the withdrawal of oil, gas and water. Production of oil from the oil zone primarily causes water to move in to take its place; production of gas from the cap tends to cause oil to migrate into its place. In addition, the volumes of oil and gas remaining in the reservoir depend on changes in the pressure, since a decrease in pressure causes fluid expansion, gas liberation and oil shrinkage. A method of relating the future pressure to total withdrawals is used to describe the motions of fluids within the reservoir under conditions arising in possible modes of production. The analysis is based on two relationships and will reduce the problem to one amenable to digital computation. The first of these concerns the dependence of the pressure distribution in the entire aquifer furnishing the water drive upon the total reservoir withdrawals. This dependence is dictated by the permeability distribution and the extent of the aquifer; at present, such information is most readily obtained from the performance history by means of the resistancecapacitance reservoir analyzer. The second relation involves withdrawals, pressure in the reservoir, and movement of oil, gas, and water within the reservoir. The analysis is subject to certain simplifying assumptions that are necessary to permit solution of the problem. A comparison of the methods of this paper with those presently practiced is pertinent. One method of analysis is to use the reservoir analyzer to predict reservoir behavior based on aquifer characteristics determined from production history. Inasmuch as the total withdrawal rate depends upon the gas-oil and water-oil ratios, which depend in turn upon, among other things, the positions of the gas-oil and water-oil contacts, these ratios must be assumed in advance. In this paper these ratios are, instead, related to the computed positions of gas-oil and water-oil contacts. Thus, our method can be applied to problems in which the oil production rate is limited by produced gas-oil ratio, or to problems in which it is desired to determine the variable gas injection rate that will maintain the gas-oil or water-oil contact stationary. These problems cannot be worked satisfactorily on the analyzer. Another method presently used is based on a paper by Hurst.' Since his procedure is dependent upon using the solution of the heat flow equation, which requires constant permeability within the aquifer, and our procedure recognizes variations of permeability in