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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 R. A. David, D. J. Vink, D. L. Katz

A phase diagram showing boundary curve and quantity of liquid in the two-phase region was determined for a mixture of natural gas and natural gasoline in the region of its critical conditions. The temperatures and pressures of phase measurements were in the range of 85 to 212 F. and 1300 to 2600 Ib. per sq. in., respectively, with the critical conditions at 169.5 F. and 2615 Ib. per sq. in. abs. Color phenomena were observed in the region of the boundary curve from 102' to 192 F. Approximate densities of the single-phase and two-phase regions and analysis of the system are included. Boundary curves between the single-phase and the two-phase regions have been determined for several binary mixtures containing hydrocarbons. 2,3,4.6,7,10,11,12,14 These investigators did not report the relative amounts of liquid and vapor within the two-phase region. The equilibrium values obtained from the dew-point and bubble-point data can be used to compute the lines showing percentage of liquid on the pressure-temperature phase diagram8 but the positions of the lines near the critical temperature and pressure are uncertain. Relative amounts of vapor and liquid were obtained for a gasoline and a naphtha1 within the two-phase area but not in the region of the critical temperature and pressure. The bubble-point and dew-point lines, as well as the percentage liquid lines within the two-phase region, were determined by visual observations in glass apparatus. Apparatus An arrangement of the apparatus is given in Fig. 1, showing the Jerguson gauge A with glass windows B. Pressure was supplied by the

Jan 1, 1940

By R. A. David, D. L. Katz, D. J. Vink

A phase diagram showing boundary curve and quantity of liquid in the two-phase region was determined for a mixture of natural gas and natural gasoline in the region of its critical conditions. The temperatures and pressures of phase measurements were in the range of 85 to 212 F. and 1300 to 2600 Ib. per sq. in., respectively, with the critical conditions at 169.5 F. and 2615 Ib. per sq. in. abs. Color phenomena were observed in the region of the boundary curve from 102' to 192 F. Approximate densities of the single-phase and two-phase regions and analysis of the system are included. Boundary curves between the single-phase and the two-phase regions have been determined for several binary mixtures containing hydrocarbons. 2,3,4.6,7,10,11,12,14 These investigators did not report the relative amounts of liquid and vapor within the two-phase region. The equilibrium values obtained from the dew-point and bubble-point data can be used to compute the lines showing percentage of liquid on the pressure-temperature phase diagram8 but the positions of the lines near the critical temperature and pressure are uncertain. Relative amounts of vapor and liquid were obtained for a gasoline and a naphtha1 within the two-phase area but not in the region of the critical temperature and pressure. The bubble-point and dew-point lines, as well as the percentage liquid lines within the two-phase region, were determined by visual observations in glass apparatus. Apparatus An arrangement of the apparatus is given in Fig. 1, showing the Jerguson gauge A with glass windows B. Pressure was supplied by the

Jan 1, 1940

By R. V. Lukes, H. W. Scheeline

Knowledge of a large number of the physical properties of the hydrocarbons is needed in the calculations and studies of the production engineer. Since experimental data on these properties of the individual hydrocarbons and their mixtures are available in only a relatively few cases, the use of generalized correlations has developed rapidly in the last decade. The generalized correlations of pressure, volume and temperature,' enthalpy2 and vapor-liquid equilibria13 on the basis of reduced temperatures and pressures, are outstanding examples of this development. These correlations are of particular value to the production engineer interested in the flow of oil and gas, since they can be used to estimate the conditions under which segregation of phase occurs as well as the composition, density, and relative amounts of the phases. The technique of using the correlations for such estimations has been published by several authors4 and will not be considered in this paper. A considerable number of data have been obtained to check the generalized pressure-volume-temperature correlations, and these data indicate that such relations hold for the hydrocarbons from methane to heptane. The accuracy is in general sufficient for most engineering pressure-volume-temperature calculations. However, the generalized correlations of enthalpy and vapor-liquid equilibria have in general been developed from the pressure-volume-temperature correlations by thermodynamic calculations and only a relatively few experimental data are available to check these calculated values. The calculations from pressure, volume and temperature are likely to lead to large errors in the calculated enthalpy and vapor-liquid equilibria. Thus, in the calculations of enthalpies, slopes of the pressure-volume-temperature data are employed, and determining these slopes can greatly amplify small errors in the original data. In the vapor-liquid equilibria calculations it is necessary to have the pressure-volume-temperature relations of the mixture, and the latter propertics are much more questionable than those of pure components, particularly in the critical region. A considerable number of experimental data are

Jan 1, 1939

By R. V. Lukes, H. W. Scheeline

Knowledge of a large number of the physical properties of the hydrocarbons is needed in the calculations and studies of the production engineer. Since experimental data on these properties of the individual hydrocarbons and their mixtures are available in only a relatively few cases, the use of generalized correlations has developed rapidly in the last decade. The generalized correlations of pressure, volume and temperature,' enthalpy2 and vapor-liquid equilibria13 on the basis of reduced temperatures and pressures, are outstanding examples of this development. These correlations are of particular value to the production engineer interested in the flow of oil and gas, since they can be used to estimate the conditions under which segregation of phase occurs as well as the composition, density, and relative amounts of the phases. The technique of using the correlations for such estimations has been published by several authors4 and will not be considered in this paper. A considerable number of data have been obtained to check the generalized pressure-volume-temperature correlations, and these data indicate that such relations hold for the hydrocarbons from methane to heptane. The accuracy is in general sufficient for most engineering pressure-volume-temperature calculations. However, the generalized correlations of enthalpy and vapor-liquid equilibria have in general been developed from the pressure-volume-temperature correlations by thermodynamic calculations and only a relatively few experimental data are available to check these calculated values. The calculations from pressure, volume and temperature are likely to lead to large errors in the calculated enthalpy and vapor-liquid equilibria. Thus, in the calculations of enthalpies, slopes of the pressure-volume-temperature data are employed, and determining these slopes can greatly amplify small errors in the original data. In the vapor-liquid equilibria calculations it is necessary to have the pressure-volume-temperature relations of the mixture, and the latter propertics are much more questionable than those of pure components, particularly in the critical region. A considerable number of experimental data are

Jan 1, 1939

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 Sylvan Cromer

The need for a clear understanding of the physical nature of the flow of gas-liquid mixtures in vertical pipes is ever becoming more apparent. This type of flow is encountered when gas and oil are produced from a well; when water is removed from gas wells with siphon lines and when liquids are elevated by means of air or gas lift. Although a number of investigator1-7 have published data on the flow of gas-liquid mixtures, in only a few cases has the experimental setup been devised to permit visual study. In the fields of heat transmission, such as the boiling of liquids and the study of the critical phenomena of the hydrocarbons, researchers have been able to throw additional light on heretofore unexplainable happenings through actual observation in glass apparatus. This investigation was therefore undertaken in order to obtain qualitative as well as quantitative results for air-water flow. Experimental Apparatus and Procedure The flow column used in these tests was made of standard 2-in. pipe and was approximately 98 ft. in height. Pyrex observation sections 2 ft. long having the same internal diameter as the wrought-iron pipe were placed at 14-ft. intervals in the column. The bottom of the tube was cut off square and terminated in the mixing chamber. No perforated nipple or footpiece of any kind was used. To the top of the column was fastened a semicircular return bend having a 4-ft. radius. The flow column was supported by a standard cable-tool drilling derrick (Fig. 1) into which were built observation platforms at each Pyrex section.

Jan 1, 1940

By Sylvan Cromer

The need for a clear understanding of the physical nature of the flow of gas-liquid mixtures in vertical pipes is ever becoming more apparent. This type of flow is encountered when gas and oil are produced from a well; when water is removed from gas wells with siphon lines and when liquids are elevated by means of air or gas lift. Although a number of investigator1-7 have published data on the flow of gas-liquid mixtures, in only a few cases has the experimental setup been devised to permit visual study. In the fields of heat transmission, such as the boiling of liquids and the study of the critical phenomena of the hydrocarbons, researchers have been able to throw additional light on heretofore unexplainable happenings through actual observation in glass apparatus. This investigation was therefore undertaken in order to obtain qualitative as well as quantitative results for air-water flow. Experimental Apparatus and Procedure The flow column used in these tests was made of standard 2-in. pipe and was approximately 98 ft. in height. Pyrex observation sections 2 ft. long having the same internal diameter as the wrought-iron pipe were placed at 14-ft. intervals in the column. The bottom of the tube was cut off square and terminated in the mixing chamber. No perforated nipple or footpiece of any kind was used. To the top of the column was fastened a semicircular return bend having a 4-ft. radius. The flow column was supported by a standard cable-tool drilling derrick (Fig. 1) into which were built observation platforms at each Pyrex section.

Jan 1, 1940

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

The volumetric behavior of isobutane at temperatures below its critical temperature has been studied by several investigators. Seibert and Burrelll measured the vapor pressure of isobutane from the ice point to the critical temperature. Dana and co-workers2 determined among other thermodynamic quantities the density of the saturated liquid and the saturated gas and the vapor pressure from approximately 0 to 130 F. Sage and Lacey3 studied a number of the thermodynamic properties of this hydrocarbon from 70" to 250" F. The specific volume in the gas and liquid region was determined at pressures up to 3000 Ib. per sq. in.? throughout this temperature interval. In addition, the vapor pressures were measured at 30" intervals. These data taken together serve to establish the thermodynamic behavior of isobutane at temperatures between 0" and 250" F. with reasonable accuracy. However, apparently there are no data available at the higher temperatures. For this reason an investigation of the volumetric behavior of isobutane at temperatures between 100" and 460" F. was carried out with apparatus that has been described in another paper (p. 136, this volume). Materials The isobutane used in this investigation was obtained from the Philgas Division of the Phillips Petroleum Co. That company's special analysis upon this sample indicated it to contain less than 0.03 mol per cent of impurities. In order to avoid traces of noncondensable gases, this hydrocarbon material was subjected to two successive fractionations at a high reflux ratio in a column approximately 4 ft. long and % in. in diameter, which was packed with small glass rings. The middle portion of distillate from the first fractionation was used in the second fraction-ation and a portion of the overhead from this second distillation process was repeatedly condensed at liquid-air temperatures at a pressure only slightly above the sublimation pressure of isobutane at this temperature.

Jan 1, 1940

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

The volumetric behavior of isobutane at temperatures below its critical temperature has been studied by several investigators. Seibert and Burrelll measured the vapor pressure of isobutane from the ice point to the critical temperature. Dana and co-workers2 determined among other thermodynamic quantities the density of the saturated liquid and the saturated gas and the vapor pressure from approximately 0 to 130 F. Sage and Lacey3 studied a number of the thermodynamic properties of this hydrocarbon from 70" to 250" F. The specific volume in the gas and liquid region was determined at pressures up to 3000 Ib. per sq. in.? throughout this temperature interval. In addition, the vapor pressures were measured at 30" intervals. These data taken together serve to establish the thermodynamic behavior of isobutane at temperatures between 0" and 250" F. with reasonable accuracy. However, apparently there are no data available at the higher temperatures. For this reason an investigation of the volumetric behavior of isobutane at temperatures between 100" and 460" F. was carried out with apparatus that has been described in another paper (p. 136, this volume). Materials The isobutane used in this investigation was obtained from the Philgas Division of the Phillips Petroleum Co. That company's special analysis upon this sample indicated it to contain less than 0.03 mol per cent of impurities. In order to avoid traces of noncondensable gases, this hydrocarbon material was subjected to two successive fractionations at a high reflux ratio in a column approximately 4 ft. long and % in. in diameter, which was packed with small glass rings. The middle portion of distillate from the first fractionation was used in the second fraction-ation and a portion of the overhead from this second distillation process was repeatedly condensed at liquid-air temperatures at a pressure only slightly above the sublimation pressure of isobutane at this temperature.

Jan 1, 1940