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Apparatus and a method for determining the volumetric behavior of hydrocarbons at pressures up to 10,000 psia and at temperatures between 0° and 460°F are described. The equipment is suitable for measuring the total volume of the system and the volume of a liquid phase as functions of state within these ranges of temperature and pressure. Introduction During the past two decades there has been a marked increase in the ranges of temperature and pressure encountered in underground hydrocarbon reservoirs of commercial interest. In addition, greater interest in the intensive characteristics of the fluids found in these reservoirs has developed. Apparatus Several types of apparatus have been developed in the authors' laboratory for volumetric measurements of hydrocarbon systems. The earliest equipment described1 was characterized by constant volume, and the weight of material present was varied systematically in order to attain the different pressures desired in the study. Later another apparatus2 was built in which the effective volume of the cylindrical cell, which confined a hydrocarbon sample of constant weight was varied by injection or withdrawal of mercury. The effective total volume of the equilibrium cell was measured by ascertaining the position of the mercury surface but no measurement could be made which gave knowledge of the volumes of individual phases existing within the hydrocarbon system. A third apparatus3 was designed for use at higher pressures and temperatures than the earlier equipment would tolerate. This apparatus was of the variable volume type but was built in the general form of a U-tube, the mercury level being measured at the surface which was not exposed to the hydrocarbon system. This arrangement avoided the need of subjecting measuring equipment to the extremes of temperature at which studies were made, but it gave no provision for measurement of the volumes of individual phases. Although this last apparatus was satisfactory as to accuracy and convenience for many purposes, need was felt for measurements of the volume of the liquid phase of the hydrocarbon system. For this reason a fourth equilibrium apparatus was designed and constructed, and it is the purpose of the present paper to describe it. The equilibrium cell has a working range of temperature from 0° to 460°F at pressures up to 10,000 psi. Provision for measurement of both total volume and liquid-phase volume makes it particularly suitable for the equilibrium study of heterogeneous systems consisting either of simple mixtures or of complex field samples of hydrocarbons. The general arrangement of the ap-

Jan 1, 1948

By Morris Muskat

It is pointed out that the application of capillary pressure curves obtained by drainage or desaturation processes to the calculation of the fluid distribution in interphase transition zones involves a number of difficulties; namely: (I) the development of very low nonwetting phase saturations appears to be in contradiction with the lack of mobility of such distributions indicated by permeability-saturation curves, (2) dispersed nonwetting phases are thermodynamically unstable, and (3) discontinuous phases should not be subject to hydrostatic equilibrium requirements. While these difficulties could be obviated by assuming that the capillary pressure drainage curve has an initial horizontal segment, they are automatically circumvented by application of the imbibition capillary pressure curve to the lower part of the water-oil transition zone. These generally show zero displacement pressure at only partial wetting-phase saturations. The countercurrent upward flow of oil into the main oil-saturated pay and downward drainage of water also suggests that wetting phase imbibition processes will control the saturation distribution immediately above the water-saturated section. Similar considerations, with a generalized interpretation of the apparent wetting-phase behavior of the oil and gas phases, provides a basis for constructing the curve for fluid distribution in the oil-gas transition zone. In the transition zones so derived, the oil begins with a nonvanishing saturation at the water-oil contact and terminates with a similar saturation at the top of the gas-oil contact. The gas-oil transition zone begins with an equivalent nonvanishing gas saturation. Introduction It has been a common assumption for some years that the nature of the fluid dis- tribution in virgin reservoirs, and in particular that in the transition zones between the oil and water and between the oil and gas sections, can be computed by a simple application of capillary pressure data. The results of such calculations appear to have been first reported by Leverett.' The latter, however, indicated only the numerical values of the parameters used in the computations, without explicitly describing the procedure. Leverett's illustrative calculated transition zones are reproduced in Fig I. Although no critical study of the apparently obvious method of calculation has been published, one cannot proceed very far in the computation without encountering some rather fundamental questions not yet answered in the literature. This paper is not written under the pretense that the whole transition-zone problem has been fully and satisfactorily solved. Its purpose, rather, is to discuss suggestions for its treatment, much of it admittedly hypothetical, and emphasize the nature of the uncertainties arising therein; for the literature, as now available, gives little indication that there are any problems still outstanding. The Transition-zone Equation The basic equation, which presumably gives directly the fluid distribution without recourse to any further consideration, is: Ap = (r1 - r2)gh [1] where r1, y2 are the densities of the two contiguous fluids, h is the height above the "capillary-free" zone of complete saturation with fluid I, g the acceleration of gravity, and Ap is the capillary pressure across the average interface at the height

Jan 1, 1949

By Burton Atkinson, David Johnston

Evaluation of Ellenburger reservoirs in West Texas has been an uncertain matker at best because of the lack of cores and suitable core-analysis method. Large amounts of oil arc produced from sections from which sample cuttings are obtained that contain litile porosity and no oil saturation. It has long been realized that the formation in some areas contained numerous fractures and solulion cavities that probably contained the major part of the oil present but the magnitude of the porous system conltaining oil has been unknown. Diamond coring cquipmene, used in the mining industry lor many years, has been developed for oil-field use to obtain high core recovery in fractured dolomite that is not possible with conventional coring equipment. A 36ft section of the core recovered from a fractured Ellenburger reseivoir waS analyzed by a unique but simple method to obtain the first defmite evaluation of one section of the producing formation. The cores and the method of analysis used are described and the results arc discussed in some detail. Discussion The first successful known analyses of cores recovered from the Ellenburger formation in the Permian Basin area were made on cores recovered with the use of diamond core heads. Conventionul coring methods previously used have had lour core recovery and standard methods of analysis have proved to be inadequate for evaluation of those cores that were recovered. Core Descriplion The Ellenburger formation to be dis cussed was cored using diamond core heads and oil-base drilling fluid. Of the total 103 ft cored to a depth of 8893 ft in the Ellenburger, 99 ft or 96 pct was recovered. The dolomite cores were described as gray to white, crystalline to coarscIy crystalline, with chert and calcite inclusions. Occasional shale partings ? to ¼ in. in width were noted. A small amount of green clay was found in some of the coarsely crystalline material. So intergranular porosity was found by inspection in any of the cores. The core urns highly fractured over most of its length with not more than two continuous feet that failed to contain fractures. The fractures Were nearly vertical and varied in width from those harely visible to as much as one millimeter. Scattered solution voids, or vugs, as large as 3 cm in diameter occurred in association with same •a

Jan 1, 1949

By Henry J. Welge

Laboortory apparatus has been devised which permits study of the displacement of oil from cores by water and by gas. The cores used contained interstitial brine as well as oil. Experiments were run to determine the comparative effect of varying the properties of the fluids used. No great effect was noted on the maximum displacement achieved. This observation made it unnecessary in initial work to use fluids in their exact reservoir conditions. Consequently, the displacements were run at near-atmospheric pressure in Pyrex glass equipment, using stripped crude oils. Introduction and Theory The chief object of this work has been to determine the efficiency of gas and water as primary agents for displacing oil from reservoir rock under laboratory conditions in which capillary phenomena were predominant. To this end the maximum displacement of oil from cores has been ascertained. This maximum displacement may not be equal to the maximum displacement from a reservoir; but it will be a close approxirnation to it sometimes, and other times the laboratory information will be useful in reservoir engineering predictions. It is] believed that the laboratory experimental maximum represents the upper limit for the reservoir recovery. The experiments were carried out by obtaining cores of interest from the reservoir, and filling the pores with interstitial brine and oil with the restored state tech- nique.1 Then the oil was displaced from the core as described later, either by brine from below, or by gas from above. The former type of displacement suggests analogy to production by water drive, but not to water flooding, for reasons discussed below. The latter type of displacement is believed to simulate production by gas cap displacement. The displacements were performed by what may be termed the capillary-pressure method. The cores are placed in capillary contact with an oil-wetted membrane which has very small pores (about I micron in diameter). Pores of this size will transmit oil but Prevent the Passage of gas or water, unless the Pressures used are higher than the capillary Pressures employed in this work. Accordingly, use of the membrane makes it possible to apply a capillary pressure differential between the displacing phase and the oil in the core. AS in the displacement of brine toward that condition of oil and water distribution existing originally in the reservoir,' it may not always be desirable to reduce the oil saturation in this experiment to an absolute minimum. With reservoirs having small productive closure, it is preferable to evaluate and use a displacing pressure no higher than the capillary pressure, Ap, which will ultimately become available for displacement in the reservoir. This pressure may be calculated from a knowledge of the density of the oil-in-place, do, the density of the displacing phase, dl, and Ah, the vertical distance between the section of the

Jan 1, 1949

By Nelson B. Russell, Donald C. Bond

The effects of various antifreeze agents on the formation of hydrogen sulphide hydrate have been studied. On a molar basis the relative lowering of Tm (the maximum temperature at which solid hydrogen sulphide hydrate can exist in equilibrium with the given solution) for the various agents is: sodium chloride 1.00, calcium chloride 1.71, methyl alcohol 0.57, ethyl alcohol 0.68, ethylene glycol 0.73, diethylene glycol 0.73, sucrose 0.87, dextrose 0.71. On a weight basis the relative lowering of TM is: sodium chloride 1.00, calcium chloride 0.91, methyl alcohol 1.08, ethyl alcohol 0.89, ethylene glycol 0.69, diethylene glycol 0.41, dextrose 0.23, and sucrose 0.15. Introduction The solid hydrate of hydrogen sulphide, H2S.6H20,1 is in equilibrium with water and liquid hydrogen sulphide at 85°F at a partial pressure of hydrogen sulphide approximately equal to the vapor pressure Of hydrogen sulphide at that temperature. At temperatures below 85°F, in the presence Of excess hydrogen sulphide (greater than the amount required to react with the water present) the hydrate is in equilibrium with liquid hydrogen sulphide at approximately the vapor pressure Of hydrogen sulphide. In the presence of excess water, the solid hydrate is in equilibrium with liquid water, containing dissolved hydrogen sulphide, at a pressure lower than the vapor pressure of liquid hydrogen sulphide at the same temperat~re.2 The lower the temperature, the greater the difference between the decomposition pressure of the hydrate and the vapor pressure of liquid hydrogen sulphide at that temperature. Conditions conducive to the formation of solid hydrogen sulphide hydrate may exist in wells producing a gas containing a high percentage of hydrogen sulphide under high pressure, or in the lead lines from such wells. This paper gives the results of tests made with various antifreeze agents which might be useful in decomposing the hydrate or in preventing the formation of the hydrate of hydrogen sulphide Apparatus Fig , shows a diagram of the apparatus used. The sample under observation was contained in a glass tube 34 cm long, having a 6 mm id and a wall thickness of 2.5 mm. The lower end of this tube was closed- with a plug of butyl rubber. The upper end of the tube was connected to a diaphragm gauge, with a stainless steel diaphragm, a manometer, a vacuum pump, and a cylinder of hydrogen sulphide, The tube was held nearly horizontal, with the liquid resting along the lower side of the tube. It was found that when the tube was held in a vertical position, it broke with ex. plosive violence as soon as it became filled with solid hydrate. Presumably this was caused by the expansion which occurred on solidification of the hydrate. The difficulty disappeared when the tube was held in an inclined position during the tests.

Jan 1, 1949

By W. T. Cardwell

This paper presents a theory for estimating the rate of gravity drainage of a liquid out of a sand column. Account is taken of the variation in permeability to the liquid as the saturation in the upper part of the sand becomes less than 100 pct. The theory is confirmed by previously published experimental data. Introduction Petroleum engineers have expressed the need for 4 theory of gravity drainage. Brunner,' in particular, has pointed out that some type of mathematical theory is necessary to begin the application of laboratory data to field problems. Muskat and his associates2'3-4 have recently made contributions to the theory of gas-drive behavior and have indicated an intention to apply their methods to water-drive systems. No theory of gravity drainage rates has been developed, however, and it seems desirable to formulate one at this time. Differential Equations of Capillary Flow The flow of liquids in partially saturated porous media has been studied by many investigators.6-10 Richards6 presented derivations of fundamental differential equa- tions governing two-phase capillary flow; and used simplified forms of those equations in solving a steady-state problem. Muskat and Meres6 presented and used equations different from those of Richards. Their equations did not explicitly involve capillary pressure gradients; but included, on the other hand, terms expressing the effects of the evolution of gas from the liquid phase during flow. Leverett8 stated in 1940 that "previous work on the flow of fluid mixtures in porous solids [had] failed adequately to account for all of the three influences that cause motion of the fluids: capillarity, gravity, and impressed external pressure differentials." Leverett's basic equations, however, were specialized forms of the general equations of Richards,5 which had actually taken account of the three influences mentioned by Leverett, but had not been used in a problem involving all three. The fact is that our knowledge of capillary flow and our ability to express this knowledge in differential equations exceed our ability to solve the equations except in a few cases. General differential equations have usually been of little more than formal value. In solving practical problems, it has been necessary to develop specific equations, preserving terms that involved the factors important in those problems, and purposefully neglecting other terms that were not of predominating influence. This is the method followed here. It is believed that the solution of the particular problem and the scheme of the solution itself are new.

Jan 1, 1949

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

The composition of the coexisting phases in the methane-ethane-n-pentane system was determined at 100°F. This was accomplished by withdrawing samples of the coexisting phases under isobaric-isothermal conditions. The relative amount of each of the components present in the liquid and gas phases was determined by conventional analytical fractionation methods. The phase behavior of this system approximates that estimated from generalized correlations which take into account the influence of the nature and amount of each of the components present upon the equilibrium. It was found that for particular pressures and temperatures the equilibrium constant of each of the components was influenced significantly by the composition of the system and this effect was more pronounced at the lower pressures for methane than for the components of greater molecular weight. However, at the higher pressures approaching the maximum two-phase pressure for the system at this temperature the composition markedly influences the equilibrium constants of all the components at a particular pressure and temperature. The results of this study are presented in graphical and tabular form. Introduction The phase behavior of many of the binary systems containing parafin hydrocarbon components from methane through n-pentane has been investigated during recent years. In addition the compositions of the coexisting phases in mixtures of crude oil and natural gas have been studied.' However, these results do not establish the influence of the nature and amount of the other substances making up a multi-component system upon the gas-liquid equilibrium constant of any one component. A preliminary correlation on the basis of values for binary systems was made2 utilizing such experimental information as was available. However, there is need for much additional information regarding behavior in systems containing more than two components. Study of the phase behavior of ternary systems offers a feasible attack upon the determination of the influence of composition as well as of pressure and temperature upon the several equilibrium constants concerned. An investigation of the phase behavior of the methane-propane-n-pentane system at 100°, 160°, and 220°F was reported.".' This work served to illustrate the marked influence of concentration of the other components upon the equilibrium constants. Variations of as much as 50 pct in the equilibrium constants for methane for fixed temperature and pressure were observed in regions remote from the critical state. Likewise there was a marked variation in the equilibrium constants of propane and n-pentane as a result of changes in the composition. These results indicated the desirability of investigating additional ternary systems. The present paper deals with a study of the methane-ethane-n- pen-tane system at 100°F, which is similar in many respects to the work upon the meth-ane-propane-n-pentane system cited above.

Jan 1, 1948

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

The composition of the coexisting phases in the methane-ethane-n-pentane system was determined at 100°F. This was accomplished by withdrawing samples of the coexisting phases under isobaric-isothermal conditions. The relative amount of each of the components present in the liquid and gas phases was determined by conventional analytical fractionation methods. The phase behavior of this system approximates that estimated from generalized correlations which take into account the influence of the nature and amount of each of the components present upon the equilibrium. It was found that for particular pressures and temperatures the equilibrium constant of each of the components was influenced significantly by the composition of the system and this effect was more pronounced at the lower pressures for methane than for the components of greater molecular weight. However, at the higher pressures approaching the maximum two-phase pressure for the system at this temperature the composition markedly influences the equilibrium constants of all the components at a particular pressure and temperature. The results of this study are presented in graphical and tabular form. Introduction The phase behavior of many of the binary systems containing parafin hydrocarbon components from methane through n-pentane has been investigated during recent years. In addition the compositions of the coexisting phases in mixtures of crude oil and natural gas have been studied.' However, these results do not establish the influence of the nature and amount of the other substances making up a multi-component system upon the gas-liquid equilibrium constant of any one component. A preliminary correlation on the basis of values for binary systems was made2 utilizing such experimental information as was available. However, there is need for much additional information regarding behavior in systems containing more than two components. Study of the phase behavior of ternary systems offers a feasible attack upon the determination of the influence of composition as well as of pressure and temperature upon the several equilibrium constants concerned. An investigation of the phase behavior of the methane-propane-n-pentane system at 100°, 160°, and 220°F was reported.".' This work served to illustrate the marked influence of concentration of the other components upon the equilibrium constants. Variations of as much as 50 pct in the equilibrium constants for methane for fixed temperature and pressure were observed in regions remote from the critical state. Likewise there was a marked variation in the equilibrium constants of propane and n-pentane as a result of changes in the composition. These results indicated the desirability of investigating additional ternary systems. The present paper deals with a study of the methane-ethane-n- pen-tane system at 100°F, which is similar in many respects to the work upon the meth-ane-propane-n-pentane system cited above.

Jan 1, 1948

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By C. E. Lesher

Coal has been fighting a rear-guard action since the last World War. The battle against competitive fuels has been largely guerilla warfare with more sniping within the ranks than of organized opposition. Oil and natural gas are the fuels that over these twenty odd years have driven coal backward and out of many profitable markets. Now, somewhat timidly, the coal industry is trying a new weapon; namely, Research, or let us more properly say, Organized Research. Engineers have been designing this weapon for many years, supported by those interested in coal, including some coal producers. A part of this pioneer work has been Fundamental Research, the Ph.D. kind that is over the heads of most of us. Another part has been aimed at immediate objectives and realizable profits, the practical, man-in-the-street sort. That is Industrial Research. Enough has been accomplished to make a fair exhibit, but whether this new weapon will have sufficient fire power to rout the opposition, whether the industry will really go into production and use it, the next few years will tell. Need foR Coal Research To utter "Research" is to use the modern magic word; to conjure up the miraculous—rubber from weeds; radar; magnesium from sea water; yes, even gasoline from coal. Research is a very general term. It means something different to every man. What is the coal industry seeking with its research; or what should it seek? And, specifically, how is it going about the job; and is it taking the best way? There are many who say that Coal has been asleep at the switch, while Oil and Gas have been taking the energy business. In an organized way this is true. Large-scale, privatelyfinanced research is just started in the Pennsylvania anthracite industry, and it is still a dream for bituminous coal. What has been done so far collectively is purely defensive; as, for instance, to improve mechanical devices for burning coal so as to be able to recover markets for house-heating fuel long since abandoned to oil and gas. To appreciate just how seriously bituminous coal has slipped back in the national economy in the past 2 5 years, one has only to recall that, in the last war the Navy required for its operations all the high-grade, low-volatile coal that could be produced, and that anthracite was withdrawn from the middle and northwest markets to keep the eastern seaboard warm. All coal was "rationed" by zones, if not to individuals. Now the Navy, the Armed forces and the Merchant Marine are propelled by oil and gasoline. Gasoline and heating oil are rationed to individuals. Production of all coal in this country in 1918 reached the historic figure of 678,200,-000 tons, and in 1943, after 25 years, it is expected to reach a special wartime total of 660,000,000 tons. Meanwhile, production of crude oil this year may exceed 1 ,500,000,000 bbl., and like that of natural gas, reach four times the amount produced in 1918.

Jan 1, 1944

By C. E. Lesher

Coal has been fighting a rear-guard action since the last World War. The battle against competitive fuels has been largely guerilla warfare with more sniping within the ranks than of organized opposition. Oil and natural gas are the fuels that over these twenty odd years have driven coal backward and out of many profitable markets. Now, somewhat timidly, the coal industry is trying a new weapon; namely, Research, or let us more properly say, Organized Research. Engineers have been designing this weapon for many years, supported by those interested in coal, including some coal producers. A part of this pioneer work has been Fundamental Research, the Ph.D. kind that is over the heads of most of us. Another part has been aimed at immediate objectives and realizable profits, the practical, man-in-the-street sort. That is Industrial Research. Enough has been accomplished to make a fair exhibit, but whether this new weapon will have sufficient fire power to rout the opposition, whether the industry will really go into production and use it, the next few years will tell. Need foR Coal Research To utter "Research" is to use the modern magic word; to conjure up the miraculous—rubber from weeds; radar; magnesium from sea water; yes, even gasoline from coal. Research is a very general term. It means something different to every man. What is the coal industry seeking with its research; or what should it seek? And, specifically, how is it going about the job; and is it taking the best way? There are many who say that Coal has been asleep at the switch, while Oil and Gas have been taking the energy business. In an organized way this is true. Large-scale, privatelyfinanced research is just started in the Pennsylvania anthracite industry, and it is still a dream for bituminous coal. What has been done so far collectively is purely defensive; as, for instance, to improve mechanical devices for burning coal so as to be able to recover markets for house-heating fuel long since abandoned to oil and gas. To appreciate just how seriously bituminous coal has slipped back in the national economy in the past 2 5 years, one has only to recall that, in the last war the Navy required for its operations all the high-grade, low-volatile coal that could be produced, and that anthracite was withdrawn from the middle and northwest markets to keep the eastern seaboard warm. All coal was "rationed" by zones, if not to individuals. Now the Navy, the Armed forces and the Merchant Marine are propelled by oil and gasoline. Gasoline and heating oil are rationed to individuals. Production of all coal in this country in 1918 reached the historic figure of 678,200,-000 tons, and in 1943, after 25 years, it is expected to reach a special wartime total of 660,000,000 tons. Meanwhile, production of crude oil this year may exceed 1 ,500,000,000 bbl., and like that of natural gas, reach four times the amount produced in 1918.

Jan 1, 1944

By C. R. Holmgren

A large consolidated sand core was used in this investigation. Four groups of experiments including gas drives, water drives, and water drives combined with gas injection, were made. The results of the gas-drive experiments indicate that greater ultimate recovery may be obtained by higher pressure gradients. However, other considerations challenge the absolute veracity of this conclusion. Results indicate that with connate water present and a low pressure gradient during a gas drive, less gas is required to produce a given amount of oil. The saturation gradient determined during a gas drive is presented. Results of the water-drive experiments indicate that the recovery of oil is not a function of either gradient Or input rate. The presence of initial gas saturation resulted in a slightly lower final oil saturation. Injection of sufficient gas to maintain the initial gas saturation during a water drive resulted in lower final oil saturation. Introduction With the demand for petroleum products reaching an all-time record high and the location and exploitation of new reserves becoming more difficult and expensive, the oil industry must look to more thorough and efficient methods of producing the petroleum already located. Much of the previous work along these lines is exploratory and suggests a more complete investigation. For example, a great amount of laboratory work has been done on flooding sands initially saturated roo pct with oil. Since sands saturated roo pct with oil rarely, if ever, exist in nature, and because the water content is a vital factor in the ultimate recovery from the sand, laboratory investigations on cores without water must be supplemented by comparable work on cores with water present.1'2 Other investigators have done a considerable amount of laboratory work using gas and water drives.3 Krutter and Day4 have reported results of investigations using cores saturated IOO pct with oil and have concluded that " the ultimate recovery obtained, using air drive, from a completely oil-saturated core depends on the pressure gradients used. The higher the pressure gradient, the greater will be the recovery until a certain Pressure range is reached above which the reward of increased recovery is much smaller for similar increments in pressure." Yuster and Day6 conclude that less gas and less time are required to produce a given quantity of oil at high pressure gradients than at low pressure gradients; they also conclude that an increase in the viscosity of the oil requires a proportionate increase in the gas needed for recovery. Their results indicate that the gas required to produce a given quantity of oil is greatly reduced by the presence of connate water. R. C. Earlougher2 concluded, based on results of water-flooding a large number of

Jan 1, 1949

By Vaughn Moyer

A method for incorporating well drawdown effect into reservoir calculations is presented in detail, together with examples of its use for widely divergent conditions that could be normally encountered in oil reservoir sands. Tentative conclusions as to the effect such factors as permeability, producing interval, well spacing, or well damage caused by completion or repair practice could have upon economic ultimate recovery are reached. It is carefully pointed out that the conclusions reached are subject to limitations indicated in the text, and placed upon all calculations made in the paper. Introduction Papers have been presentedl-3 in which theoretical depletion histories for reservoirs under equilibrium conditions and no appreciable well-bore drawdown pressure are determined. However, except for a limited number of cases, appreciable drawdown Pressures in a well bore exist, and Pressure and saturation gradients consequently vary throughout a reservoir. This Paper is an attempt to incorporate well-pressure drawdown into reservoir history, and to analyze certain factors, such as those involving recovery, well spacing, and productivity index, from the standpoint of permeability and drainage radius. BY incorporation of drawdown into reservoir history, it is believed that theoretical considerations will more closely approxi- mate actual reservoir behavior experienced in an oil field. For purposes of simplification, a solution gas-drive type field1 without primary gas cap, has been selected. Basic Data and Assumptions Details of equilibrium saturation conditions for no drawdown production for various pressures in a reservoir are deter-minable by methods described by several are permitting the construction of a curve of oil saturation vs Pressure for any selected combination of initial interstitial water and hydrocarbon saturation (Fig I). This curve is then a description of equilibrium saturation conditions at any given pressure in a reservoir. Developing the above, details of saturation and flow permeability may thus be determined for any increment or portion of a well drainage area or reservoir. In this manner the effect of pressure differential (drawdown) may be incorporated into reservoir and well drainage considerations. It is pointed out that this method thus makes use of no-drawdown equilibrium production data, superimposing a draw-hwn effect upon them. It also assumes that net flow conditions in any considered increment of reservoir are not materially altered by the entrance of fluids from other increments into them, but approach equilibrium for the existing pressure and saturation (i.e., each increment behaves in more or less independent fashion, dependent largely upon the equilibrium considerations mentioned above)

Jan 1, 1948

By Vaughn Moyer

A method for incorporating well drawdown effect into reservoir calculations is presented in detail, together with examples of its use for widely divergent conditions that could be normally encountered in oil reservoir sands. Tentative conclusions as to the effect such factors as permeability, producing interval, well spacing, or well damage caused by completion or repair practice could have upon economic ultimate recovery are reached. It is carefully pointed out that the conclusions reached are subject to limitations indicated in the text, and placed upon all calculations made in the paper. Introduction Papers have been presentedl-3 in which theoretical depletion histories for reservoirs under equilibrium conditions and no appreciable well-bore drawdown pressure are determined. However, except for a limited number of cases, appreciable drawdown Pressures in a well bore exist, and Pressure and saturation gradients consequently vary throughout a reservoir. This Paper is an attempt to incorporate well-pressure drawdown into reservoir history, and to analyze certain factors, such as those involving recovery, well spacing, and productivity index, from the standpoint of permeability and drainage radius. BY incorporation of drawdown into reservoir history, it is believed that theoretical considerations will more closely approxi- mate actual reservoir behavior experienced in an oil field. For purposes of simplification, a solution gas-drive type field1 without primary gas cap, has been selected. Basic Data and Assumptions Details of equilibrium saturation conditions for no drawdown production for various pressures in a reservoir are deter-minable by methods described by several are permitting the construction of a curve of oil saturation vs Pressure for any selected combination of initial interstitial water and hydrocarbon saturation (Fig I). This curve is then a description of equilibrium saturation conditions at any given pressure in a reservoir. Developing the above, details of saturation and flow permeability may thus be determined for any increment or portion of a well drainage area or reservoir. In this manner the effect of pressure differential (drawdown) may be incorporated into reservoir and well drainage considerations. It is pointed out that this method thus makes use of no-drawdown equilibrium production data, superimposing a draw-hwn effect upon them. It also assumes that net flow conditions in any considered increment of reservoir are not materially altered by the entrance of fluids from other increments into them, but approach equilibrium for the existing pressure and saturation (i.e., each increment behaves in more or less independent fashion, dependent largely upon the equilibrium considerations mentioned above)

Jan 1, 1948

By L. K. Oliver, Marshall

The use of model studies for the development of invasion patterns for cycling is .illustrated by model studies obtained with a recently developed apparatus in the solution of actual cycling problems. Introduction Depletion of a gas reservoir by cycling under pressure maintenance may be divided into three general phases. In the first phase, injection of dry gas is used to move all possible wet gas to producing wells prior to breakthrough of appreciable quantities of dry gas into producing wells. In the second phase, injection moves additional wet gas to producing wells while moderate quantities of dry gas are being produced. The third phase consists of production without injection to deplete the commercial gas reserve which remains after the cycling operation. Thus, in the first phase, a portion of the reservoir is invaded by dry gas, and the dry gas usually displaces something less than 100 pct of the wet gas from the invaded portions of the reservoir. The second phase enlarges the invaded portion of the reservoir and, at the same time, increases recovery from that zone invaded by dry gas in the first phase of the cycling operation. The result is an early yield of a substantial quantity of the liquefiable hydrocarbons in the reservoir with a minimum of the retrograde losses which occur in some reservoirs. The overall recovery from such an operation is usually high. The summation of the paths taken by dry gas in a cycling operation can be termed an invasion pattern. The use of electrical models to predict invasion patterns has been the subject of several contributions to the literature.1-3 The results of such model studies as applied to actual cases has been discussed by Kelton4 and Miller and Lents.= Recently, an improved apparatus for conducting potentiometric model studies has been developed, as described by Lee.V he purpose of this paper is to present model studies or invasion patterns obtained with this instrument in the solution of actual cycling problems. The percentage of displacement of wet gas within the invaded portion of the reservoir in cycling, increase in recoveries of wet gas by continuing cycling after dry gas breakthrough, recoveries of wet and dry gas by production after cycling, or economic factors in cycling are beyond the scope of this paper. Discussions which follow will be limited entirely to the development of suitable invasion patterns for cycling under pressure maintenance and the use of model studies therein. Discussion OF Results In using model studies to predict invasion patterns in cycling, some factors which influence the results are the following:

Jan 1, 1948

By Marshall, L. K. Oliver

The use of model studies for the development of invasion patterns for cycling is .illustrated by model studies obtained with a recently developed apparatus in the solution of actual cycling problems. Introduction Depletion of a gas reservoir by cycling under pressure maintenance may be divided into three general phases. In the first phase, injection of dry gas is used to move all possible wet gas to producing wells prior to breakthrough of appreciable quantities of dry gas into producing wells. In the second phase, injection moves additional wet gas to producing wells while moderate quantities of dry gas are being produced. The third phase consists of production without injection to deplete the commercial gas reserve which remains after the cycling operation. Thus, in the first phase, a portion of the reservoir is invaded by dry gas, and the dry gas usually displaces something less than 100 pct of the wet gas from the invaded portions of the reservoir. The second phase enlarges the invaded portion of the reservoir and, at the same time, increases recovery from that zone invaded by dry gas in the first phase of the cycling operation. The result is an early yield of a substantial quantity of the liquefiable hydrocarbons in the reservoir with a minimum of the retrograde losses which occur in some reservoirs. The overall recovery from such an operation is usually high. The summation of the paths taken by dry gas in a cycling operation can be termed an invasion pattern. The use of electrical models to predict invasion patterns has been the subject of several contributions to the literature.1-3 The results of such model studies as applied to actual cases has been discussed by Kelton4 and Miller and Lents.= Recently, an improved apparatus for conducting potentiometric model studies has been developed, as described by Lee.V he purpose of this paper is to present model studies or invasion patterns obtained with this instrument in the solution of actual cycling problems. The percentage of displacement of wet gas within the invaded portion of the reservoir in cycling, increase in recoveries of wet gas by continuing cycling after dry gas breakthrough, recoveries of wet and dry gas by production after cycling, or economic factors in cycling are beyond the scope of this paper. Discussions which follow will be limited entirely to the development of suitable invasion patterns for cycling under pressure maintenance and the use of model studies therein. Discussion OF Results In using model studies to predict invasion patterns in cycling, some factors which influence the results are the following:

Jan 1, 1948

By A. J. Miles, A. D. Topping

in this paper, the theory of elasticity has been applied to the rock about a deep well, It is assumed that the rock has a modulus of . elasticity and a Poisson's ratio and that the theory of elasticity applies. It is necessary to know or assume the state of stress existing in the rock before it is penetrated by the well drill. The application of this theory indicates that stress concentration of shear, tensions, and compressions about the bore hole are of a high order. This is particularly true when a horizontal compressive stress exists in one direction only in the formation before drilling. If such an initial state of stress exists before drilling, then the rock will have stress concentrations of both tension and compression at the same elevation and of such magnitude that failure of the rock is likely. Accompanying these is a shearing stress of large proportion which is likely to produce spalling of the well walls. Internal pressure applied to the well bore will relieve the extreme compression but not the tension and has little effect upon the shear. Plastic deformation of the rock through a geological time tends to mitigate the stress concentrations. IntroductioN It has long been known that the stresses about holes and re-entrant corners of elastic solids under the influence of loads are different and generally more intense than those imposed upon the body else- where. Stress concentration at a re-entrant corner can be reduced by increasing the radius of the fillet at the corner. Stress concentration at the end of a crack in a plate undergoing either tension or compression Can be relieved appreciably by drilling a hole at the very end of the crack. Also, stresses can be increased in an elastic body in tension or compression by making a hole in it. The stress concentration is greatest at the edge of the hole. Considerable knowledge of the stresses which exist about the bore hole of a deep well may be had by applying our knowledge of engineering mechanics; or more particularly the theory of elasticity. It is, of course, necessary to make the assumption that the rock is elastic and behaves as an elastic solid, that is, that it obeys Hooke's law, has a modulus of elasticity, and a Poisson's ratio. It is also necessary to know, Or assume, the state of stress which exists in the rock prior to the penetration of the drill. With this knowledge it is possible to compute the stresses about the bore hole. The problem can be simplified by considering several simple cases separately and then by applying the principle of superposition to solve the more complex cases which are made up of the simpler ones. Case i—Rock Strata in Compression Penetrated by a Hole This case was first worked out by G. Kirsch* for structural material, but applies equally well to a horizontal rock strata in a state of in in one direction

Jan 1, 1949

By H. G. Doll

The S.P. log is shown to be a measurement of the potential drop along the drill hole, caused by ohmic effect in the mud. The notion of static S.P. is brought forward, and its relation to the S.P. log is discussed. Other factors influencing the shape and amplitude of the log are considered; attention is given to conditions encountered in practice. Numerous figures are given illustrating graphically the results; these figures are of particular interest for comparison with field examples. The S.P. log, although indicating permeability, is not an absolute measurement of permeability, nor of porosity, of the formations traversed by a drill hole. It is affected by several parameters, such as resistivity of formations and mud, thickness of formations, and others, which should be appraised carefully. Simple rules have been established for a better distinction of the boundaries of permeabl: sections, particularly in difficult cases, such as those encountered in highly resistive formations. A systematic application of the established principles will assist in obtaining more information from the S.P. log than was possible thus far; for instance, under favorable conditions, presence of oil may be detected, or amount of shale in sands may be estimated. Introduction The S.P. log, or spontaneous potential log, has been known and widely used during the last 15 years for the location of permeable beds traversed by drill holes.1,2 In electrical logging practice, the S.P. log is shown on the left hand side track of the record (as may be seen in later examples) where it can be easily correlated and interpreted with the resistivity curves located to the right. Usually, the S.P. log consists of a base line, more or less straight, having excursions or "peaks" to the left. The base line frequently has been found to correspond to impervious beds, while the peaks are usually found opposite permeable strata. Measurements which will indicate positively the presence of permeability in the formations, and which will give accurately the boundaries of the permeable zones, are of great importance in oil-field practice. Thus far, the S.P. log is the best approach to such determinations; unfortunately, its interpretation is not always evident. With respect to the base line of the S.P. log, it may be noticed that this line is not always at a definite location on the chart. Sometimes it may shift abruptly, while other times a gradual drift is apparent. As far as the peaks are concerned, their shape is not uniform; some are rounded while others are sharp. Also, from other data, it may be found that occasionally the peaks extend appreciably beyond the boundaries of permeable zones into zones which are not everywhere permeable. A comparison with permeability measurements made on cores has often confirmed that there was no definite correspondence between the magnitudes of the peaks and the permeability values. In the same geological horizon, it generally will be found that most of the thick and permeable for-

Jan 1, 1949

By Morris Muskat

The detailed analogy between flow systems in porous media and the corresponding poten-tiometric model systems is developed under conditions where it may be desirable to take into account variable pay thickness, variable porosity, and permeability, and also the dependence of the fluid density on pressure. It is shown that in such models it is only necessary that the electrolyte thickness be made everywhere proportional to the millidarcy-feet of the formation. In contrast to the iso-vol type model, previously suggested as a basis for the analogy, the porosity does not enter directly in the construction of the model. It is introduced only in translating the electrical voltage gradient measurements into the equivalent fluid travel times. A discussion of this procedure is given. I NTRODUCTION It is now some 50 years since it was pointed out' that on the basis of Darcy's law Laplace's equation must govern the steady state flow of homogeneous fluids through porous media. It is 16 years since the obvious implication of this fact, namely, that such steady state homogeneous flow systems in porous media could be simulated by electrical analogies, was first applied2 to problems of practical interest with respect to oil production. In these initial studies major emphasis was placed on the use of electrolytic models, made of blotting paper, to give a direct and graphic history of the fluid particle motion in regular and infinite well networks. However, it was also noted there that the basic requirement of the model was that it give a potential distribution similar to the pressure distribution in the flow system, and that from the electrical measurement of the potential distribution the fluid particle motion could be graphically or numerically determined. This was demonstrated by application to the five-spot infinite network, for which a conducting metallic sheet was used to establish the equipotential contours. As anticipated, the fluid particle motion computed from these contours agreed well with that given directly by the blotting paper model. For irregular well distributions it was found more convenient to use electrolytic bath analogs rather than metallic sheets. Several investigations,3'4 as applied specifically to cycling well patterns, have been reported with these models, which have become known as "potentiometric models." However, the extremely laborious nature of both the electrical measurements by direct probing and the associated interprctive computations retarded the widespread use of these procedures. The electrical measurements can be accelerated by using a four-probe electrodc,5,6 which provides a means for simultaneously determining the streamline paths along which the fluid particles must move and the voltage gradients along these paths which are proportional to the fluid velocitics. With the increasing frequency of discovery of condensate pools, as drilling depths are becoming greater, the applicability of the potentiometric model to production problems, and especially to the study of well patterns for cycling, has been given a fresh impetus. Although the formal theory for determining the motion of fluid particles in porous

Jan 1, 1949