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

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By M. C. Leverett

The behavior of mixtures of immiscible liquids in porous solids is of rapidly increasing interest to those engaged in the production of petroleum. The operation of artificial water-floods and the control of natural ones immediately raise questions concerning the fundamental nature of such processes. Moreover, it is now recognized that often water occurs dispersed throughout the rock from which the oil issues into the well,' and thus tends to move toward the well simultaneously with the oil. The work reported here is a laboratory investigation of the simultaneous, steady-state flow of oil and water through the same column of uncon-solidated sand. It is thus directly related to the situation in which water occurs in oil-producing sands; it may have less direct implications for the displacement of oil from sands by water. However, it is to be clearly understood that the experiments to be described were performed primarily to obtain information of a more or less fundamental nature, and are not an attempt to reproduce, on laboratory scale, any part of an oil field. The dynamic behavior of a system in which oil and water are flowing simultaneously through sand is best described in terms of its "effective permeability" to either phase. For incompressible fluids flowing through a system of uniform cross section, the effective permeabilities to the two phases, in darcys, may be defined by the equations: Ko = PA6A [la] and Ku = Q [lb] In order to put the results obtained on a comparable basis for different sands, the effective permeabilities will be stated as fractions of the normal permeability of the sand; i.e., fractions of its permeability to a homogeneous fluid. Algebraically, these fractions are: KO' = Ko/K, and KWr = K,/X [2a] and [Zb]

Jan 1, 1939

By M. C. Leverett

The behavior of mixtures of immiscible liquids in porous solids is of rapidly increasing interest to those engaged in the production of petroleum. The operation of artificial water-floods and the control of natural ones immediately raise questions concerning the fundamental nature of such processes. Moreover, it is now recognized that often water occurs dispersed throughout the rock from which the oil issues into the well,' and thus tends to move toward the well simultaneously with the oil. The work reported here is a laboratory investigation of the simultaneous, steady-state flow of oil and water through the same column of uncon-solidated sand. It is thus directly related to the situation in which water occurs in oil-producing sands; it may have less direct implications for the displacement of oil from sands by water. However, it is to be clearly understood that the experiments to be described were performed primarily to obtain information of a more or less fundamental nature, and are not an attempt to reproduce, on laboratory scale, any part of an oil field. The dynamic behavior of a system in which oil and water are flowing simultaneously through sand is best described in terms of its "effective permeability" to either phase. For incompressible fluids flowing through a system of uniform cross section, the effective permeabilities to the two phases, in darcys, may be defined by the equations: Ko = PA6A [la] and Ku = Q [lb] In order to put the results obtained on a comparable basis for different sands, the effective permeabilities will be stated as fractions of the normal permeability of the sand; i.e., fractions of its permeability to a homogeneous fluid. Algebraically, these fractions are: KO' = Ko/K, and KWr = K,/X [2a] and [Zb]

Jan 1, 1939

By Kenneth S. Ritchie

The natural emulsion samples used in this study were shipped directly from twelve California oil fields, through the courtesy of the superintendents of the main producing companies in those fields. Representative parts of each sample were chosen for the slides. Preparation of the slides was generally made in less than two minutes, including time of exposure; in a few cases, about five minutes was required. The short time was intended to minirmize the changes in conditions. Whenever comparison was of value, standard conditions were established. Spreading by gravity was adopted instead of smearing. Cover glasses were not allowed to rest on the films. General Characteristics of Emulsions The main purpose of the general views (Figs. 1-16) is to illustrate the general characteristics of the dispersed droplets together with any other constituent or impurity that may be found in each emulsion. The magnification is given so that dimensions could be measured from the plates. The slides used for these views had spherical recesses; they gave the best light. Where crystals were intended to be shown in the picture a filter (green was the best') was usually used. Emulsions that showed a tendency to move by concentrated light were pictured without a condenser.

Jan 1, 1931

By D. B. Carson, D. L. Katz

Natural gases under pressure form crystalline hydrates with water. Experimental data are reported on four-phase equilibrium for the methane-propane-water, methanc-pentane-water, and methane-hexane-water systems. Temperatures and pressures for equilibrium between gas, water-rich liquid, hydrocarbon-rich liquid, and hydrate were measured, as well as the percentages of methane and propane in the hydrate. The data indicate that natural gas hydrate behaves as a solid solution and that pentanes and heavier hydrocarbons do not enter into the solid phase. Vapor-solid equilibrium constants are presented that permit the approximation of the conditions for hydrate formation, from the composition of a gas. Introduction Natural gas hydrates have been the object of considerable research in recent years, because of the trouble they have caused in the natural-gas and natural-gasoline industries. Natural gas hydrates are white crystalline compounds of water and gas, which, under pressure, exist at temperatures considerably above the freezing point of water. Because of the relatively high temperatures at which the hydrates exist, they become a nuisance in high-pressure gas operations where water is present, since their formation causes partial or complete plugging of valves and pipes. From a practical standpoint, the trouble incident to hydrate formation has been solved by dehydration of the gas before it enters the plant or pipe line, or by other remedial measures. Extensive work on gas hydrates in the latter part of the nineteenth century, by Villardl and others, gave data on methane hydrate and on ethane hydrate. Schroeder summarized these theoretical studies2 Hammerschmidt3 introduced the information on gas hydrates to the gas industry and Dcaton and Frost4-6 gathered a considerable number of data on the behavior of natural gas hydrates. Recent papers7,8 have extended both the data and the theory of these hydrates. At present, data are available on tem-peraturcs and pressures of hydrate forma. tion for pure methane, ethane, propane, n-butane, methane-ethane mixtures, meth-ane-propane mixtures, methane-butane mixtures, and some Is natural gases, all- in the Presence of excess water. However, up to the Present time no method has been available for predicting the temperature at given pressures or the pressure at given at at which natural gases will form hydrates if hydrates with water. 'This Paper Presents data on the methane-propane-water, methane-pentane-water and methane-hex-""e water systems in four phases, one of which is the hydrate. he application of the phase rule to the methane-~ro~ane-water data Proves that hydrates behave as solid solutions. The data of this paper and those in the literature were used to develop vapor-solid. equilibrium constants,8 which permit prediction of conditions of hydrate formation from the analysis of a natural gas.

Jan 1, 1942

By D. B. Carson, D. L. Katz

Natural gases under pressure form crystalline hydrates with water. Experimental data are reported on four-phase equilibrium for the methane-propane-water, methanc-pentane-water, and methane-hexane-water systems. Temperatures and pressures for equilibrium between gas, water-rich liquid, hydrocarbon-rich liquid, and hydrate were measured, as well as the percentages of methane and propane in the hydrate. The data indicate that natural gas hydrate behaves as a solid solution and that pentanes and heavier hydrocarbons do not enter into the solid phase. Vapor-solid equilibrium constants are presented that permit the approximation of the conditions for hydrate formation, from the composition of a gas. Introduction Natural gas hydrates have been the object of considerable research in recent years, because of the trouble they have caused in the natural-gas and natural-gasoline industries. Natural gas hydrates are white crystalline compounds of water and gas, which, under pressure, exist at temperatures considerably above the freezing point of water. Because of the relatively high temperatures at which the hydrates exist, they become a nuisance in high-pressure gas operations where water is present, since their formation causes partial or complete plugging of valves and pipes. From a practical standpoint, the trouble incident to hydrate formation has been solved by dehydration of the gas before it enters the plant or pipe line, or by other remedial measures. Extensive work on gas hydrates in the latter part of the nineteenth century, by Villardl and others, gave data on methane hydrate and on ethane hydrate. Schroeder summarized these theoretical studies2 Hammerschmidt3 introduced the information on gas hydrates to the gas industry and Dcaton and Frost4-6 gathered a considerable number of data on the behavior of natural gas hydrates. Recent papers7,8 have extended both the data and the theory of these hydrates. At present, data are available on tem-peraturcs and pressures of hydrate forma. tion for pure methane, ethane, propane, n-butane, methane-ethane mixtures, meth-ane-propane mixtures, methane-butane mixtures, and some Is natural gases, all- in the Presence of excess water. However, up to the Present time no method has been available for predicting the temperature at given pressures or the pressure at given at at which natural gases will form hydrates if hydrates with water. 'This Paper Presents data on the methane-propane-water, methane-pentane-water and methane-hex-""e water systems in four phases, one of which is the hydrate. he application of the phase rule to the methane-~ro~ane-water data Proves that hydrates behave as solid solutions. The data of this paper and those in the literature were used to develop vapor-solid. equilibrium constants,8 which permit prediction of conditions of hydrate formation from the analysis of a natural gas.

Jan 1, 1942

By Charles R. Fettke

The permeability of an oil or gas sand is its capacity for transmitting fluids, either liquids or gases, under pressure. The permeability of a sand depends upon the size and shape of the openings in it and the extent to which these communicate with one another, as well as upon the ratio of their volume to the total volume of the sand. The apparatus employed and the method of procedure used by the authors in conducting the permeability tests have been described in a previous pub1ication.l For the tests described here 1/2-in. cubes were used. They were set in the lower end of a 1-in. union, inserted in a square hole cut in a hard rubber stopper which fitted into the lower end of the union. In the tests with air, volumes were measured with a wet American gas meter of 100 cu. ft. capacity. In those with water, distilled water at room temperature was employed, unless otherwise noted. DescRiption of Sands Tested The tests described in this paper were performed upon 18 samples representing typical oil and gas sands from 7 localities in northwestern Pennsylvania. For purposes of identification, the cores from which the samples came have been designated by capital letters, the sequence of the samples in the cores by numerals, and the individual cubes by small letters. All cubes from the same samples came from adjacent portions parallel to the bedding. Core A of the Bradford sand came from the north central part of the Bradford field, from an area where water-flooding operations have proved highly successful. Core B of the same sand was obtained from the southern part of the field. This core contained a so-called "loose streak," 7.5 ft. thick, in the middle portion of which B2 is a representative sample. The "loose streak" has given trouble in water-flooding but responded favorably to an air-drive, using a pressure of 300 lb. The natural production was increased approximately five times over a period of three years in which the air-drive was in operation. Core C, also of the Brad-

Jan 1, 1931

By L. S. Panyity

The inception of this paper may be traced directly to the various discussions of another paper by the writer1 wherein certain indefinite beliefs and opinions were emphasized as to the relative importance of total sand porosity and the actual size of the openings between the grains. Since publication of that paper it has been possible to study various methods of sand analyses and results that have been obtained under different conditions and actual operations in the field. The purpose of this paper is to indicate the value of screen analysis, especially in areas where repressuring by means of water-flood, air or gas is being used in the partly depleted fields. Sand samples have been analyzed for porosity, saturation and grain size. They are mainly from the Bradford water-flood area, where a great reliance has been put upon such analyses, and where many data are available, A few sand studies are included from fields other than the water-flood area, in order to indicate the possibilities of screen analysis in any field. Examples of various conditions are given in Figs. 1 to 7, which show the porosity, saturation and grain-size analyses of submitted cores or drill cuttings. The generally accepted methods of delineating such sand studies on cross-section paper, known as "core charts" has been employed; with the exception that a method of representing grain size has been evolved which is believed to be the best adapted for this purpose. It differs from the block diagrams generally used, in the employment of a linear section. Percentage of grain-size is represented by the subdivision of a given distance, where the total length represents the whole sample of rock chunk, while the subdivisions indicate the percentages of grains of the different sizes that will pass through the various sieves, through which the samples of crushed sand are sorted to determine the size and amount of the components that make up the aggregate. Thus, on Fig. 1, under the heading of Grain Size, the first samples are composed of grains of the following sizes: 16 per cent. through 120-mesh sieve; 33 per cent. through 150-mesh; 25 per cent. through 180-mesh; 26 per cent, through 200 mesh; a total of 100 per cent. A minus sign is placed before

Jan 1, 1931

By Ben E. Lindsly

PetRoleum engineers generally are familiar with the investigations of Dow and Reistle,1 Beecher and Parkhurst,2 and Dow and Calkin3 relative to the solubility of natural gas in crude oil. Since the publication of the results of those investigations and the work of Mills and Heithecker,4 little additional knowledge on this interesting and important subject has appeared in the petroleum engineering literature. The reports of Beecher and Parkhurst and Dow and Calkin agree substantially. The data from both investigations showed that, under the conditions of the tests, the solubility of natural gas in crude oil increased in direct proportion to the pressure at which the gas was put into solution, and the solubility decreased to a considerable extent with increased temperature. These facts, and others relating to the changes in viscosity, surface tension and specific gravity of the crude caused by the solution of gas in the oil, have been given due consideration in the petroleum industry, and the recognition of these facts has resulted in a great improvement in the technique of producing oil. However, in these first experiments, various grades and types of weathered crude oil were contacted at various pressures up to 500 lb. per sq. in. gage with gases deficient to a considerable degree in the heavier hydrocarbons, as compared with the gas that was originally in solution in the oil in its natural underground reservoir. The amount of dissolved gas that was liberated upon reducing the pressure to 1 atm. was measured. For these reasons, the complete significance of the effect of dissolved gases in crude oil, as it occurs in nature, cannot be determined directly from the data obtained under the conditions of the tests as described.

Jan 1, 1931

By C. C. Singleterry, D. L. Katz

The critical phenomena have been studied during the past century but our knowledge of the critical temperatures and pressures of complex hydrocarbon mixtures still is very limited. The critical temperatures and pressures of pure substances have been examined in large numbers120 and in great detail.11.17 No experimental determinations of the critical phenomena have been reported on such complex hydrocarbon systems as a reservoir fluid. The critical temperature is defined by Taylor18 as follows: "there is some temperature for each gas above which the gas cannot be liquefied. This temperature is called the critical temperature." The critical pressure of a pure substance is the vapor pressure at the critical temperature. It should be noted that these definitions refer to a given substance in the pure state and do not mean that the pure substance cannot be liquefied in the presence of a second constituent. The normal procedure for obtaining the critical temperature of a substance is to heat it in a glass tube 1,20 under pressure until the meniscus between the liquid and vapor phase disappears, although other methods, especially for mixtures, have been used.13,14 However, when considering oil and gas reservoirs, it is more enlightening to consider a critical phenomenon that occurs when a mixture of oil and gas are compressed at a reservoir temperature until the meniscus disappears because the two phases become equal in composition. This conception, along with erroneous applications of the definition of the critical phenomena of a pure substance to that pure substance when it is part of a complex mixture, has caused confusion even among persons familiar with the classical theories. The purpose of this paper is to discuss the critical phenomena of pure substances and mixtures and to report experimental data on a mixture of

Jan 1, 1939

By C. C. Singleterry, D. L. Katz

The critical phenomena have been studied during the past century but our knowledge of the critical temperatures and pressures of complex hydrocarbon mixtures still is very limited. The critical temperatures and pressures of pure substances have been examined in large numbers120 and in great detail.11.17 No experimental determinations of the critical phenomena have been reported on such complex hydrocarbon systems as a reservoir fluid. The critical temperature is defined by Taylor18 as follows: "there is some temperature for each gas above which the gas cannot be liquefied. This temperature is called the critical temperature." The critical pressure of a pure substance is the vapor pressure at the critical temperature. It should be noted that these definitions refer to a given substance in the pure state and do not mean that the pure substance cannot be liquefied in the presence of a second constituent. The normal procedure for obtaining the critical temperature of a substance is to heat it in a glass tube 1,20 under pressure until the meniscus between the liquid and vapor phase disappears, although other methods, especially for mixtures, have been used.13,14 However, when considering oil and gas reservoirs, it is more enlightening to consider a critical phenomenon that occurs when a mixture of oil and gas are compressed at a reservoir temperature until the meniscus disappears because the two phases become equal in composition. This conception, along with erroneous applications of the definition of the critical phenomena of a pure substance to that pure substance when it is part of a complex mixture, has caused confusion even among persons familiar with the classical theories. The purpose of this paper is to discuss the critical phenomena of pure substances and mixtures and to report experimental data on a mixture of

Jan 1, 1939

By J. Versluys

A well can flow exclusively through the casing or exclusively through a tubing but can also flow partly through a casing and at the top part through a tubing. The main principles of the flowing of wells under these conditions were explained in the author's former paper.' Practically all factors that influence the regular flow are dealt with therein. The question of irregular flow, however, will be discussed briefly here. As a rule, an irregular flow must be avoided, as it may be assumed that the efficiency is thereby very small, while on many fields it is injurious to the sand of the oil-bearing layer. Periodical flowing often occurs with rising mixtures of gas and liquid. The phenomenon can be explained if it is accepted that two conditions are possible in the mixture; namely, the foam condition and the mist condition. If there is no stabilizer in the liquid, the foam condition can exist only when the liquid forms a greater portion of the volume than the gas. The mist condition, on the other hand, can exist only when the liquid occupies a smaller part of the volume than the gas. The foam condition occurs when there are gas bubbles in the liquid mass, while in the mist condition drops of liquid are disseminated in a gas-filled space. For sake of simplicity, it has been assumed that the mist condition prevails when 50 per cent. or more of the volume is occupied by gas, while with less than 50 per cent. gas the foam condition will arise. For distilled water and for oils which do not tend to form stable foams this is probably approximately true. If this does not hold good, however, two cases are possible: (1) The fields of the two conditions overlap or (2) they do not meet. If the fields of the conditions overlap there is an intermediate field where either of the two conditions can exist, depending on the history of the mixture. Suppose the foam condition prevails first and the gas

Jan 1, 1931

By Allen D. Garrison

The chemistry of clays and shales has been assuming increasing importance in the petroleum industry, and two factors have greatly influenced this trend. The first has been the growing evidence that the marine shales are source beds, and that the petroleum compounds have migrated to the sand reservoirs overlying or underlying these shales: the second has been the demand for drilling fluids better adapted to penetrate these marine shales without difficulty and expense. Origin and General Composition of Clays and Shales Clays, shales and surface soils are all closely related materials. They are mixtures of finely divided compounds formed during the weathering of the solid crust of the earth. Their nature is essentially colloidal; that is, their behavior is determined by the state of division of the materials and the surface reactions of the smallest grains. Many of their chemical changes affect only the exposed areas and do not involve the interior of the grains of matter. The extent of these reactions is more nearly proportional to the area of the substances than to their mass, therefore it is possible for a small amount of a material in an extremely fine state of division to completely dominate the character of the mixture. More than 83 per cent of the crust of the earth is composed of three elements—oxygen, silicon and aluminum. Consequently, the corrosion products of the crust are predominantly aluminosilicates, or compounds of aluminum, silicon and oxygen. If we add the compounds of six elements—iron, calcium, sodium, potassium, magnesium and hydrogen—more than 98 per cent of the crust has been accounted for. These six elements, together with the first three, also appear in soils, clays and shales. But direct chemical analysis is of little value in describing the nature of such materials. Many chemical individuals may be present in variable amounts, and the extreme subdivision of any one of the individuals may contribute qualities that dominate the mixture.

Jan 1, 1939

By Allen D. Garrison

The chemistry of clays and shales has been assuming increasing importance in the petroleum industry, and two factors have greatly influenced this trend. The first has been the growing evidence that the marine shales are source beds, and that the petroleum compounds have migrated to the sand reservoirs overlying or underlying these shales: the second has been the demand for drilling fluids better adapted to penetrate these marine shales without difficulty and expense. Origin and General Composition of Clays and Shales Clays, shales and surface soils are all closely related materials. They are mixtures of finely divided compounds formed during the weathering of the solid crust of the earth. Their nature is essentially colloidal; that is, their behavior is determined by the state of division of the materials and the surface reactions of the smallest grains. Many of their chemical changes affect only the exposed areas and do not involve the interior of the grains of matter. The extent of these reactions is more nearly proportional to the area of the substances than to their mass, therefore it is possible for a small amount of a material in an extremely fine state of division to completely dominate the character of the mixture. More than 83 per cent of the crust of the earth is composed of three elements—oxygen, silicon and aluminum. Consequently, the corrosion products of the crust are predominantly aluminosilicates, or compounds of aluminum, silicon and oxygen. If we add the compounds of six elements—iron, calcium, sodium, potassium, magnesium and hydrogen—more than 98 per cent of the crust has been accounted for. These six elements, together with the first three, also appear in soils, clays and shales. But direct chemical analysis is of little value in describing the nature of such materials. Many chemical individuals may be present in variable amounts, and the extreme subdivision of any one of the individuals may contribute qualities that dominate the mixture.

Jan 1, 1939

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By A. C. Wingrove

The paper outlines the selection of a dewatered tailings backfill system for the Johannesburg Consolidated Investment Gold Division, and covers the following aspects: (i) 16 Shaft pilot testwork; (ii) engineering design problems relating to the Cooke 3 Shaft backfill operation; (iii) in-line mixing - applications with respect to the Randfontein Estates Gold Mine and Western Areas Gold Mine backfill operations; and (iv) pipeline friction losses.

Jan 1, 1988

By A. Bobet

Design of a new underground laboratory is underway through the auspices of the United States National Science Foundation. The Deep Underground Science and Engineering Laboratory (DUSEL) is scoped to provide a diverse group of researchers with a dedicated underground facility capable of supporting a broad spectrum of fundamental and applied research at depth in the Earth?s crust. Key research partners in the endeavor are physicists, biologists, geoscientists and engineers. Engineers are not only designing the underground facilities, but are also actively involved in developing research initiatives. This paper will introduce the DUSEL engineering research program to the mining community, provide an overview of the site, geology, and laboratory facilities, and describe some key program initiatives. The particular technical challenges and opportunities afforded by the construction of DUSEL and the performance of the integrated science-engineering program will be discussed by reference to a subset of research initiatives that are currently under development: Cavern Design, CO2 Sequestration and Transparent Earth. These research initiatives target the development of new techniques that can support improved subsurface investigation, design and construction procedures. An increased use of the subsurface can actively contribute to the development of new, more sustainable solutions for use in mining and civil engineering practice.

Jan 1, 2011

By Everett G. Trostel

AMERICAN industry in 1943 emerged from the construction phase into the production phase, and American military operations passed from preparation into full action in the many theaters of the global war. The increased pace of industrial and military operations has resulted in a tremendous demand for petroleum and its products.

Jan 1, 1944

By Chairman Hill H. H.

The Round Table Discussion on Petroleum Engineering Research was planned for two purposes. First, to review the work that has been done by petroleum engineers during the past few years on problems that have confronted the industry and, second, to suggest new studies that should be made either on the problems that have been the subject of research during the past or on problems that have arisen only recently. It was believed that by holding an informal discussion of the problems in which the petroleum engineer is vitally interested it would be possible to bring out new ideas as to the relative importance of the different problems that should be studied and to suggest new methods for attacking some of the problems that have resisted the energies of research workers throughout the industry. It was also believed that by arranging for an exchange of experiences between the different engineers it would be possible to prevent a large amount of duplication of effort in conducting research work. Those engaged in petroleum engineering research realize that there is a broad field for study and by coordinating the work it will be possible to obtain the maximum amount of information in the shortest possible time. In planning the program on Petroleum Engineering Research, nine subjects were selected for discussion and each was assigned to a man who is doing work on that subject. These men were asked to lead the discussion on the problem assigned to each one. An effort was made to choose problems of a practical nature and upon which considerable work is being conducted at the present time. Some of the men who were asked to lead the discussion were unable to attend the meeting but most of them submitted a written discussion- of the subject assigned, with the result that there was a discussion of eight of the nine problems. Professor Uren, who was asked to lead the discussion on the subject of Recent Developments in Methods for Reducing Gas-oil Ratios, was unable to attend the meeting and advised that he did not have any new ideas to contribute.

Jan 1, 1928