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By Franklin H. Wilson

COPPER base alloys containing various amounts of aluminum and silicon are of considerable commercial interest. In particular the alloy containing 7 pct aluminum and 2 pct silicon shows an attractive combination of high strength with excellent machinability. Since there is no evidence in the literature that this ternary system has been studied since the recognition by Smith1 and Anderson2 in 1939 of the kappa phase of the binary copper-silicon system, the determination of the equilibrium phase relationships in the copper corner of the ternary diagram has been undertaken to provide a fundamental basis for understanding the behavior of these alloys. Phase boundaries have been determined by the micrographic examination of quenched samples while points on the liquidus surface have been obtained by thermal analysis. The results, of sufficient precision to serve their major purpose of providing a guide for the control of the manufacture of alloys in the region covered, are presented in a series of both isothermal and vertical sections of the diagram. ALLOYS STUDIED For a rough survey of the copper corner of this ternary system the compositions listed in Table I (Series A) were employed. The results of examinations of these alloys indicated that the compositions listed in Table 2 (Series B) would further clarify regions of greater complexity. All alloys were prepared as 1200 g heats, the copper being melted under charcoal, and then first silicon and then aluminum were added. An [ ] excess of 0.05 pct silicon was allowed to cover deoxidation losses. Two small bars 5/8 by 1 ¼ by 1 ¼ in. were cast using Durville type casting equipment. Analyses were made on all alloys using material which was hot-rolled at 800 or 850°C and annealed 17 hr at 650°C. All analyses were found to be within 0.05 pct of the nominal composition. Since the precision of analysis is not much better than this, the points of both isothermal sections and vertical sections at fixed aluminum and silicon contents have been plotted at the compositions indicated by the nominal composition.

Jan 1, 1948

By Alex McCoy

SAMPLING of the fluid from oil wells for percentages of oil, emulsified oil, and water during the last two years has brought out some interesting facts concerning oil-water emulsion. This result led to a laboratory investigation of emulsion, which substantiated the conclusions made from the field observations. The purpose of this paper is to present the information collected, the laboratory experiments, and our interpretation of the same. In order to define emulsified oil exactly, give its synthesis and origin, and to show how and when it is formed in the wells, the work was necessarily divided into two separate lines-laboratory work and field observations. It is hoped that this study may lead to a discussion of such points so that the petroleum engineer, geologist, or technologist may be benefited by its practical bearing on oil-field management. Special credit is due Mr. Everett Carpenter, chief geologist of the Empire Gas & Fuel Co., for his assistance and cooperation in this work. LABORATORY INVESTIGATIONS ON EMULSIFIED OIL Laboratory investigations were conducted in an attempt to learn the composition and some of the properties of emulsified oil, or B. S., as it is more commonly called, also to demonstrate, by laboratory methods, how B. S. may be formed under conditions similar to those existing at the time a well is being pumped, and how it may be broken down. Literature bearing on this subject is widely scattered and very limited in scope. Bacon and Hamor define B. S., or bottom settlings, as "earthy matter, inert organic matter, or, in the case of Pennsylvanian petroleum, an emulsion of paraffin wax and water, which accompanies crude oil." In this discussion we will limit the term B. S. to that heavy,

Jan 8, 1919

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By C. J. Ramsburg

THE construction and operation of by-product coke-oven plants in America are essential to strong national defense and of the greatest importance to many widely diversified undertakings as well as to safety and health. CARBONIZATION PROCESS Coal used under a boiler or in a locomotive is consumed by combustion. Coal used in a by-product oven is distilled or carbonized, meaning that heat is applied to the coal, out of contact with air, causing a distillation that removes the volatile matter in the coal in the form of gas and vapor, leaving coke as a final product. From the gas and vapor distilled from the coal, many valuable substances can be secured, known as by-products. Hence the name "by-product oven." The simplest example of this principle can be shown by means of an ordinary clay pipe. If powdered coal is placed in the bowl of the pipe, the opening of the bowl is plugged with clay, and the bowl placed in a flame, the bowl will become hot, transferring the heat through the wall of the bowl to the coal within. When this coal attains a temperature of about 950°F., gas will begin to pour out of the pipe stem, and this gas may be lighted. A black liquid also will exude from the stem of the pipe. This is tar mixed with certain other products. What remains in the bowl after distillation is coke. A coke oven corresponds to the bowl of the pipe. A modern oven of the latest type is a refractory brick chamber approximately 42 ft. long and 14 ft. high, averaging 18 in. in width. The oven is filled with coal through closable charging holes in the oven top. Each end of the oven consists entirely of a self-sealing door, the removal of which permits the finished coke to be discharged by means of a power-operated pusher machine. The ovens are built in batteries, and the heating is effected by gas burned in vertical flues in the oven walls, each set of flues heating the walls of two adjacent ovens. Such ovens carbonize a charge of approximately 18 tons of coal in 18 hr., or have a daily throughput of 24 tons per oven, producing about I 7 tons of coke. In times of need, the output may be increased by raising the temperature of flues, thus shortening the coking time. There is one great essential difference in principle between distillation in a clay pipe and in a coke oven. In the 18-in. oven, the distillation proceeds from two parallel walls held at a high temperature (over 2000°F.) and instead of all the coal being heated at once, the distillation is a progressive one creeping inward. The average travel of this heating is 1/2 in. per hour from each vertical wall, and as the volatile products are formed progressively they must push away from the interior toward the wall through the previously formed hot coke, then up the walls and over the top of the coal charge, finally escaping through the outlet pipe. This results in a cracking of the components into many different and valuable substances not formed when the carbonizing temperature is low.

Jan 1, 1942

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By C. C. Furnas, T. L. Joseph

It is well known that particles of different sizes are not distributed evenly throughout the average charge in an iron blast furnace. Just how great the disparity in particle size in different parts of a single plane in a furnace may be is indicated by the results of some recent investiga-tion1,2 conducted by the Bureau of Mines on a furnace operating on Lake ores. The wide variations found in gas velocity, gas composition, and temperature from the periphery to the center of the upper charge column were caused by the great variation in particle size of the raw materials used and were also greatly influenced by the methods of charging. This paper summarizes the results of an investigation of the influence of different methods of charging and of the treatment of raw materials upon the size distribution of the solid particles in the blast furnace. A more complete report will appear later as a Bureau of Mines technical paper. Importance of Gas-solid Contact One of the authors has pointed out in a previous report? that the operation of the blast-furnace process is entirely dependent on contact between the gas stream and the solid particles in the stock. The gas stream carries the necessary heat as well as the carbon monoxide molecules that do the work of rednction. In the parts of the furnace in which there is little or no contact between the gas stream and the solids there can be little work of reduction. Obviously, the part of the apparatus that is not doing the work for which it is intended is inefficient; the ideal condition is one in which all portions of the stock column are

Jan 1, 1929

By G. Sachs, E. J. Ripling, S. I. Liu, J. J. Lynch

It is a generally recognized fact that by repeated straining the fracture stress of any metal is reduced to a fraction of its value for static loading. The value of this fatigue strength depends upon numerous factors, such as the states of strain and stress, the limits of straining, and the number of repeated loadings or cycles The large volume of previous investigations on fatigue is concerned entirely with large numbers of cycles, say exceeding 10,000 and up to 500,000,000. However, the changes in fracture stress and fracture strain occurring after a small number of repeated loadings have attracted little attention. Apparently the only investigations of this type are those byLudwik4.5 who subjected steel, copper, and aluminum wire to repeated torsion. In each test the torque was varied between identical values in the two directions of twisting. Depending upon the magnitude of the moment, fracturing occurred after a number of cycles, up to 10,000. The results of Ludwik's tests will be discussed later Such torsion does not readily yield actual stress and strain values. Therefore a pre- liminary study was made of the effects of repeated direct stresses, that is, tension and compression stresses. Because such tests are considerably more tedious than torsion tests, only high stresses were used in the preliminary work, yielding definite changes in metal properties after a few cycles. It was found in these tests that strains could be controlled more readily than stresses in the investigated range of high stresses. This paper, consequently, deals with the effects of strains of equal magnitude but different signs. The metal was first prestrained in static tension by a certain amount then subjected to compression to yield the same amount of strain after unloading. This loading cycle was repeated up to a maximum of seven times. After various cycles, the stress-strain curves in tension were determined, up to fracturing. As material for these tests, the aluniinum alloy 24ST was selected because it exhibits a comparatively small amount of necking in the tension rest This alloy permitted, therefore rather accurate cont.rol at the high strains necessary to produce fatigue failures at less than seven cycles. The results of this invest~gation appear sufliciently interesting to extend the method of attack in various directions It is intended to study (11 the effects of cycles up to a tew thousands and (2) the effects of strains of different magnitude in tension and compression respectively 'The latter variable also includes a. a special case the effects of compressive strains.

Jan 1, 1949

By H. Hooykaas

A few years ago Marsal published a method of predicting oil recovery as a function of time for an edge-water-drive reservoir with several rows of wells.' The method is based solely on oil- and water-production data obtained during a short period for the first row of wells and the gross productions (past and future) of all wells. This paper presents a streamlined version of the original publication and experimental evidence showing the reliability of this version. For this purpose scaled experirnents were performed in a large model (750 X 500 X 23 cm, 24.4 ft X 16.2 ft X 8.9 in.) in which edge-water-drive reservoirs with three rows of production wells were simulated. From the results of the experiments it is concluded that the method gives a fairly accurate prediction of the future production behavior of the reservoir and enables us to select the most profitable production plan. Results obtained with the method were always slightly conservative. INTRODUCTION The calculation method developed by Marsal aims at forecasting future reservoir behavior.' It can be applied to floods in which a number of down-dip wells are rapidly going to water. Essentially it is a method for predicting the future behavior of the up-structure wells on the basis of the observed behavior of the down-structure wells. As such, the method is especially useful for predicting behavior of edge-water drives toward several rows of wells. The requirement to be met for justifying the approach is identity of production mechanism in all regions of the reservoir. The attraction of the method then lies in the fact that it applies even when we have no complete description of the prevailing production mechanism. The original publication was in the German language and for this reason, perhaps, did not attract widespread attention. In our opinion it deserves to do so because it does offer in a simple way results which are in fair agreement with observed data. The aim of the present paper is to bring the method to the attention of a wider audience. The method in its most simplified form is reviewed and experimental data in support of it are presented. PRINCIPLES To show Marsal's principle. we will first write the continuity equation for very simple conditions, linear flow (in the positive x-direction) in an incompressible porous body [cross-section A(x), porosity +(x)], saturated with incompressible fluids (oil saturation S). When the oil in this formation is displaced by water, injected at x = 0 (inlet face), we get where q(t) is the total gross displacement rate and f the fractional oil flow. The equation can be solved if we make the assumptions: (1 ) that the fractional oil flow (f) is a univalent function of saturation (S); and (2) that the function is the same throughout the porous medium. Then: f = f(S) Solving this equation with the method of characteristics, we obtain

Jan 1, 1966

By R. W. Fountain, J. Chipman

THE solubility of nitrogen in iron and steel has been of considerable interest due to the role of nitrogen in strain-aging and in quench-aging. It is generally considered that quench-aging is the result of precipitation of carbide and nitride particles from supersaturated solid solution, while strain-aging results from the segregation of carbon and nitrogen atoms to dislocations.1-9 The rate of strain-aging is controlled primarily by the amount of carbon and nitrogen in solution and the temperature. In experiments on strain-aging of pure iron with only carbon or nitrogen as impurities, Fast" has shown that even after 40 hr at 50°C carbon did not give any strain-aging while

Jan 1, 1959

By J. E. Graham, A. H. Glenn

Oil operators engaged in drilling on the Continental Shelf of Louisiana and Texas are in agreement that adverse weather and wave action are two of the greatest hazards to the safety and efficiency of their work. It was ami-pated when the offshore operations commenced that such would be the case, and experience to date has verified this assumption. Because atmospheric conditions and wave action involve tremendous amounts of energy it is highly unlikely that it will be possible to control any but the most localized weather and wave phenomena within the foreseeable future. Thus. as long as the offshore operations involve the movement of small craft and barges over exposed waters, and the transfer of personnel and heavy equipment from these craft to either fixed structures or larger craft at close quarters, the weather and wave problem will remain. Taking into consideration the persistence of the wave and weather problem and the improbability of achieving a direct solution, the Humble Oil & Refining Company, in planning its offshore campaign investigated the possibility of forecasting wave and weather conditions in order to provide warnings of dangerous conditions and increase efficiency in day-to-day planning of work. It was recognized that predictions of wave and weather conditions based on meteorology and oceanography, both geophysical sciences, are not 100 per cent accurate and application of forecasts in the offshore work was dependent on whether they provided information which was sufficiently greater in accuracy than the layman's guess to be worth the expenditure involved. During World War 11. meteorology and oceanography were used with success in reducing danger resulting from environmental conditions and increasing efficiency of operations exposed to the elements. This success was partially the result. of improvement in the scientific techniques involved and the procurement and distribution of observational data, and partially due to the large scope of the military operations which meant that a reduction of losses of a relatively small percentage of the total cost amounted to a large figure expressed in terms of dollars. Since the offshore drilling involves an extremely large financial investment, it was considered that the experience of the Armed Services in successfully employing meteorology and oceanography might be duplicated in the oil industry. In addition. the oil industry's successful experience in utilizing seismology, geology, and terrestrial magnetism; all geophysical sciences, indicated that meteorology and oceanography, also of the family of geophysical sciences and sharing their scientific assets and liabilities, might be profitably put to use. Since the immediate problem involving the sciences of meteorology and oceanography in the offshore campaign is wave action, a program was inaugurated within the Humble Oil & Refining Company during June 1947. the purpose of which was to ascertain the applicability and limitations of wave forecasting in the offshore campaign. A summary of the effective wave forecasting techniques developed during the war was prepared in the form of a forecasting manual for the Continental Shelf off Grand Isle, Louisiana, by Bates and Glenn. After completion of this manual, experimental forecasts were prepared daily over a two-month period by Graham and Thompson to determine the accuracy of the forecasts. It was considered that the accuracy of the experimental forecasts justified a more extensive test under actual operating conditions in the offshore work and the firm of A. H. Glenn and Associates was set up under the sponsorship of the Humble Oil & Refining Company to work with the Humble Grand Isle District in providing forecasts of wave and weather conditions over a one-year period. This paper discusses the service now provided to the Grand Isle District, its applicability and limitations. TYPE OF FORECASTS REQUIRED It was apparent before the commence-mence of the forecasting service that a specialized type of forecast was required. Many of the weather elements of interest to the general public, such as rain and temperature, are of minor concern to offshore operators. On the other hand, such elements as wave height and wind speed and direction are of great concern in the offshore operations since variations in wave height of a few feet in the critical range divide safe from hazardous working conditions. To be of utility. a forecasting service for the offshore work must provide detailed forecasts of the elements which affect the operation. With this in mind, it was decided that forecasts would include the following information: average wave heights to the nearest foot, wind speeds within a range of approximately 5 miles per hour, and wind directions within 221 degrees. Since the procedure for forecasting these elements involves thorough analysis of weather data, it was decided to include a generalized forecast of weather conditions such as rain and cloud cover, although these are of secondary importance.

Jan 1, 1949

By A. H. Glenn, J. E. Graham

Oil operators engaged in drilling on the Continental Shelf of Louisiana and Texas are in agreement that adverse weather and wave action are two of the greatest hazards to the safety and efficiency of their work. It was ami-pated when the offshore operations commenced that such would be the case, and experience to date has verified this assumption. Because atmospheric conditions and wave action involve tremendous amounts of energy it is highly unlikely that it will be possible to control any but the most localized weather and wave phenomena within the foreseeable future. Thus. as long as the offshore operations involve the movement of small craft and barges over exposed waters, and the transfer of personnel and heavy equipment from these craft to either fixed structures or larger craft at close quarters, the weather and wave problem will remain. Taking into consideration the persistence of the wave and weather problem and the improbability of achieving a direct solution, the Humble Oil & Refining Company, in planning its offshore campaign investigated the possibility of forecasting wave and weather conditions in order to provide warnings of dangerous conditions and increase efficiency in day-to-day planning of work. It was recognized that predictions of wave and weather conditions based on meteorology and oceanography, both geophysical sciences, are not 100 per cent accurate and application of forecasts in the offshore work was dependent on whether they provided information which was sufficiently greater in accuracy than the layman's guess to be worth the expenditure involved. During World War 11. meteorology and oceanography were used with success in reducing danger resulting from environmental conditions and increasing efficiency of operations exposed to the elements. This success was partially the result. of improvement in the scientific techniques involved and the procurement and distribution of observational data, and partially due to the large scope of the military operations which meant that a reduction of losses of a relatively small percentage of the total cost amounted to a large figure expressed in terms of dollars. Since the offshore drilling involves an extremely large financial investment, it was considered that the experience of the Armed Services in successfully employing meteorology and oceanography might be duplicated in the oil industry. In addition. the oil industry's successful experience in utilizing seismology, geology, and terrestrial magnetism; all geophysical sciences, indicated that meteorology and oceanography, also of the family of geophysical sciences and sharing their scientific assets and liabilities, might be profitably put to use. Since the immediate problem involving the sciences of meteorology and oceanography in the offshore campaign is wave action, a program was inaugurated within the Humble Oil & Refining Company during June 1947. the purpose of which was to ascertain the applicability and limitations of wave forecasting in the offshore campaign. A summary of the effective wave forecasting techniques developed during the war was prepared in the form of a forecasting manual for the Continental Shelf off Grand Isle, Louisiana, by Bates and Glenn. After completion of this manual, experimental forecasts were prepared daily over a two-month period by Graham and Thompson to determine the accuracy of the forecasts. It was considered that the accuracy of the experimental forecasts justified a more extensive test under actual operating conditions in the offshore work and the firm of A. H. Glenn and Associates was set up under the sponsorship of the Humble Oil & Refining Company to work with the Humble Grand Isle District in providing forecasts of wave and weather conditions over a one-year period. This paper discusses the service now provided to the Grand Isle District, its applicability and limitations. TYPE OF FORECASTS REQUIRED It was apparent before the commence-mence of the forecasting service that a specialized type of forecast was required. Many of the weather elements of interest to the general public, such as rain and temperature, are of minor concern to offshore operators. On the other hand, such elements as wave height and wind speed and direction are of great concern in the offshore operations since variations in wave height of a few feet in the critical range divide safe from hazardous working conditions. To be of utility. a forecasting service for the offshore work must provide detailed forecasts of the elements which affect the operation. With this in mind, it was decided that forecasts would include the following information: average wave heights to the nearest foot, wind speeds within a range of approximately 5 miles per hour, and wind directions within 221 degrees. Since the procedure for forecasting these elements involves thorough analysis of weather data, it was decided to include a generalized forecast of weather conditions such as rain and cloud cover, although these are of secondary importance.

Jan 1, 1949

By E. Hein, R. A. Dodd

The fatigue softening of prior strain-hardened poly crystalline copper has been determined by measuring changes inflow stress resulting from fatigue treatments. Tensile fatigue does not soften the metal, while the softening due to reversed stress fatigue depends on the extent to which fully reversed stressing is approached. True tensile fatigue is shown to be possible only in the case of long wire specimens. Annealing following fatiguing of strain-hardened metal shows that tensile fatigue is very effective in modifying normal recovery and recrys-tallization. OBSERVATIONS by Ludwik and Scheu,' Kenyon,' Polakowski and Palchoudhuri, Kemsley, and Broom and Ham,596 have shown beyond doubt that strain-hardened metals are softened by reversed-stress fatigue. To some extent the softening might be associated with a rearrangement of dislocations, but the results of Broom and Ham5 on the temperature dependency of the fatigue hardening of annealed copper, and those of McCammon and Rosenberg7 on the partial recovery at 100'C of fatigue-hardened copper suggest that point defects may be involved. Since lattice vacancies are the only species of point defect present in appreciable quantities in thermody-namic equilibrium, most attention has been accorded them in the various theories advanced to explain hardening and softening effects resulting from fatigue. Precise mechanisms remain uncertain, and while some effects may be due to single vacancies, defects arising from vacancy clusters may also contribute to the changes in properties. All types of plastic deformation result in point-defect formation, one frequently invoked formation mechanism involving the nonconservative motion of jogs formed by the intersection of, for example, mixed dislocations. But since fatigue deformation is thought to be a particularly effective way of forming point defects, additional mechanisms peculiar to fatigue must be sought. One possibility is that jogged loops contract during the unloading cycle to give rows of vacancies. A local high-vacancy concentration could conceivably promote polygonization and recovery by climb, and, therefore, could explain the fatigue softening of strain-hardened metals under appropriate conditions of temperature. Conversely, the experiments by Broom and Ham6 on the fatigue hardening of copper single crystals involving subsequent tensile testing of previously fatigued specimens, resulted in the observation of distinctly lowered yield points. This could be due to vacancy atmospheres associated with dislocations, possibly augmented by jogs on dislocations. In addition to the yield-point phenomenon, a post-yield hardening was observed, with a temperature-dependence resembling the friction-hardening of irradiated metals,9 this again suggesting a point-defect mechanism. An important development in this field has been the observation,10 by transmission electron microscopy, of high concentrations of prismatic loops in fatigued aluminum. By analogy with quenched aluminum filmso11 it seems certain that these loops originate in the collapse of vacancy clusters formed during deformation. Metals, such as copper, having a relatively low-stacking fault energy would tend to produce Frank sessile loops (in practice tetrahedral defects with stacking faults on all (111) planes) rather than the glissile prismatic loops observed in aluminum. The manner in which these various defects affect the different aspects of fatigue behavior has not yet been fully investigated. The present work was designed principally to indicate whether tensile fatigue gives rise to hardening and softening effects similar to those associated with reversed stress fatigue, and with the hope of providing additional information on the contribution of point defects to fatigue deformation. Despite the uncertain ty often associated with the interpretation of resistivity data, i.e., the relative contribution of stacking faults and other defects, such measurements are conveniently employed to study point defect pheno-

Jan 1, 1962

By W. H. Somerton

The effects of drilling variable on rotary drilling rates and efficiencies have been studied by a series of laboratory drilling tests. TWO-cone 1.25-in. diameter hits were used to drill vertically upwards into rock samples at corltrolled weights and rates of rotation. Shale, sandstone and specially prepared concrete samples were used in this study. Power input to the ririllirig systeln was measured and drilling chips collected for energy — .size reduction studies. Reasouably good correlations between drilling variables and rates of penetrotion were found. Qrrantities that are difficult to evaluate include rock strength parameters and the effects of bit wear. Effects of bit size and geormetry require further investigation. Analysis of the drilling chips confirmed the premise that, for rocks containing two or more mineral constituents of diflerent strengths, a greater amourrt of rock breakage occurs in the weaker constituent. Drilling conditions which required greater amounts of energy produced finer drilling chips. As bit tooth wear progressed, drilling chips became finer. Efficiency of rotary drilling as a rock breakage mechanism was extremely low. Comparison was made with theoretical energy requirements and with energy requirements for size reduction by comminution methods. INTRODUCTION Many technological developments and innovations have made possible the successful drilling of oil wells by the rotary method to depths exceeding 20,000 ft. Bigger, more powerful rigs, better steels, improved bit design and more careful control of the circulating system have all contributed to this success. Despite these advances comparatively little is known regarding the basic mechanism of rock breakage by the rotary drilling process. Future improvements and, in particular, reduction of drilling costs will undoubtedly require a clearer understanding of the variables controlling effectiveness and efficiency of rotary drilling. Rotary drilling is inherently an inefficient means of producing rock breakage. Loss of energy in transmission from the surface to the cutting mechanism may be large, thus limiting the total amount of energy which may be applied to rock breakage. Increased efficiency may be realized by improved energy transmission methods such as the turbodrill. Conversion of transmitted energy to rock breakage by use of rotating cutter teeth is likewise inefficient. Improvement of cutter efficiency has been obtained essentially by empirical means —changes in bit tooth size, shape and spacing, and tooth deletion to give clean bottom-hole patterns. The present work was undertaken to investigate the factors controlling rates of bit penetration under laboratory drilling conditions. Laboratory drilling apparatus is shown in Fig. 1. The effects of rock strength and bit wear on drilling rates were investigated. Drill cuttings were analyzed to determine the character of breakage and to compare this with other methods of producing rock breakage. VARIABLES INVOLVED IN ROTARY DRILLING Some of the variables controlling bit penetration rates can be studied conveniently by dimensional grouping. R/DN f(F/D2S) or

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By R. G. Hawthorne

This report is concerned with fluid displacement in porous media, in those cases where viscous and gravitational forces control the displacement. Such a system would usually be found in a sand body of large physical dimensions such as an oil reservoir, although it is possible to create such a system in the laboratory. It is shown that the position of the fluid interface can be predicted by numerical calculations using a basic idea presented by Dietz. Fluid flow is considered in a vertical plane in a homogeneous, porous medium of sufficient thickness that the capillary transition zone is small in comparison with the total reservoir. A theory developed by Dietz' is used to make numerical calculations of the position of the fluid interface. The results for several conditions are compared with scaled model experiments. The results show that, for gas drive in a reservoir of steep dip, a relatively low flow rate can displace large volumes of oil before gas breakthrough. On the other hand, water injection at favorable mobility ratio and low dip may show best performance at high rates. Water tends to underride the oil and, given sufficient rime, will break through without much oil displacement. For certain conditions, which include relatively low flow rate, the interface is a straight line and its behavior is simple to calculate. At higher flow rates, the interface is unstable, and a numerical solution was programed for an automatic computer. In general, good agreement is shown between the fluid model and the computed results so long as gravitational forces have control. For a water drive at very unfavorable mobility ratio, many small water fingers appear. These viscous fingers are not controlled by the relatively small gravitational forces. When viscous fingering becomes the controlling factor, the mathematical model is oversimplified, and results do not check the fluid flow model. INTRODUCTION Present methods of reservoir analysis depend upon certain simplifying assumptions to obtain mathematical descriptions of practical use. Material-balance methods (Muskat2 or Tarner2) assume uniform fluid saturations in the entire reservoir, or in a few subdivisions of the reservoir. An unsteady-state flow calculation by West, er at considered pressure and saturation changes in flow to a well during solution gas drive, and neglected gravity effects. Results showed only a 4 per cent difference for ultimate oil recovery by the Muskat method, even though the case chosen for study was one in which unsteady-state effects should be high. The Buckley-Leverett5 method commonly assumes a one-dimensional flow system. It is applicable at high flow rates where viscous forces predominate over gravity forces. Simultaneous, parallel flow of the two fluids is assumed, and the concept of a fluid interface is not introduced. Permeabilities to each fluid for a given saturation must be known. The method is not applicable for a two-dimensional system where cross flow becomes possible. Less well known is the displacement equation derived by Dietz. This method is designed for two-dimensional flow systems and assumes a definable fluid interface within the porous medium. Dietz showed that, for a range of low flow rates, the interface would be stable. straight and at an angle of inclination which could be simply calculated. At a certain critical flow rate, the calculated interface tilt would equal the formation dip. For higher flow rates, a finger of displacing fluid would invade the displaced fluid. Dietz indicated that his method applied only to macroscopic reservoir behavior, while the Buckley-Leverett method applied to the small transition zone at the fluid interface. The examples worked out in this report are based on the fluid-displacement theory of Dietz. It is shown that the Dietz theory may be used to derive equations analogous to the Buckley-Leverett equations. In contrast to the Buckley-Leverett method, flow is considered in a plane rather than being limited to a line. Rather than a frontal advance, the movement of a fluid interface is followed. For flow rates substantially exceeding the critical rate and for high viscosity ratio, many fingers of invading fluid occur-—rather than the single finger assumed by Dietz. On the other hand, so long as some gravitational influence remains, the flow is not entirely parallel to the bedding planes as assumed by Buckley and Leverett; therefore, both methods fail to give an adequate descrip-

By E. C. W. Perryman

The recovery and recrystallization characteristics of superpurity aluminum have been investigated using electrical resistivity, X-ray line breadth, and hardness measurements for the former and the micrographic method for the latter. The three different properties recover at different rates and have different activation energies. The recrystallization results agree well with Avrami&apos;s theory and furthermore indicate that the perfect subgrains formed during recovery are not the nuclei for re-crystallization. WHEN a metal is plastically deformed, its physical and mechanical properties generally undergo considerable changes and by subsequent annealing these changes are partly or wholly annihilated. Thus, a recovery process can be discussed, taking this term in its general sense. In practice, however, there is reason to discriminate between two apparently different processes, one most easily followed at low temperatures, in which the properties return to an almost constant value between that of the cold worked and fully annealed material, and a second process in which the properties return to their original values before cold working and which is accompanied by the formation and growth of new grains having an orientation different from that of the matrix. In this paper the word recovery will be taken to mean the changes in some property as a function of annealing time which occur either without the appearance of new grains or under conditions such that the new re-crystallized grains are very small (= 2 microns), are very few in number, and substantially do not affect the property being measured. This definition is rather abitrary, for it will depend upon the sensitivity of the technique used for the observation of new recrystallized grains, which in the present work was about 1 to 2 microns. However, it is helpful to use the term recovery in this sense and to reserve the term recrystallization for the processes of nucle-ation and growth of new grains in the cold worked matrix. Although considerable work has been done on recovery and recrystallization, most workers have based their study on the measurement of one or perhaps two parameters. Since very small amounts of impurities have such a profound effect on the recrystallization characteristics of a pure metal, it becomes extremely difficult to correlate one piece of work with another. With this in mind, the present work on recovery and recrystallization was done on the same material. Experimental Procedure Material Used and Fabrication: The composition of the superpurity aluminum used throughout this investigation was 0.002 pct Cu, 0.003 pct Fe, 0.003 pct Si, and <0.001 pct Mg. The ingot was hot rolled to 0.250 in., annealed, and cold rolled to 0.034 in. A large number of reductions and intermediate anneals were carried out so as to produce material with a minimum of preferred orientation and maximum homogeneity. For the recovery part of the investigation, the final cold reduction was 20 and 80 pct and for the recrystallization part, 20 pct. After each pass in the cold rolling process, the material was quenched in cold water in order to keep the rolling temperature as near room temperature as possible. Annealing Procedure: For the recrystallization work, specimens 1x1 in. were cut from the 0.034 in. cold rolled sheet and a hole was drilled in each through which a wire was threaded to support it in the salt bath. The temperature of the salt bath was controlled to +2°C and the time taken for a specimen to reach temperature was approximately 5 sec. These 1 in. squares were then divided into three groups, one of which was given 5 min at 318°C and another 2 hr at 244°C. These treatments were such that recovery was almost complete and a well defined subgrain structure produced. Separate specimens of each group were annealed for different times at 301°, 318°, 355°, and 373°C, i.e., three specimens for each annealing time. The delay between finish of cold working and start of annealing was about 1 hr. For the recovery work, strips 0.062 in. thick were cut from the cold worked sheet, annealed, and then given the last cold rolling operation. This was done for each annealing temperature. By this means it was possible to minimize the delay between cold working and annealing. In general, all measurements were carried out within 1 hr of the last cold rolling operation. Annealing at low temperatures was done in an oil bath the temperature of which was maintained constant to +1°C. Electrical Resistivity Measurements: Strips 20x0.5x0.05 in. were machined and the electrical resistance measured using a Kelvin double bridge. Measurements were made in an oil bath maintained at 20rt0.1°C. The same specimen was used for the complete isothermal annealing curve.

Jan 1, 1956

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By John W. Weeton, Max Quatinetz, Robert J. Schafer

Nickel powders of 1-, 0.4-, and 0.2- average particle size were combined with 0.05- p MgO powder. Oxide was added in quantities of 4, 12, and 20 vol pct. The mixtures were vacuum hot pressed and extruded at 2100°F. In spite of a general tendency to growth of oxide particles during processing, dispersions of fineness comparable to those of Sintered Aluminum Powder, SAP, were achieved. A small amount of oxide considerably improved 1800°F stress-rupture strength, but further oxide addition resulted in a decrease of strength. RECENTLY there has been much speculation concerning the requisites for strong and stable dispersion-strengthened alloys. The nature of the dispersed phase, the stability of the alloys, and variables influencing the mechanical properties of alloys have been given consideration. Such topics have been reviewed by Bunshah and Goetzel. Of the many parameters related to the mechanical properties of dispersion alloys, mean free path between dispersed particles (a measure of the fineness of the dispersion), particle size, and vol pct of the dispersed phase have been shown to be very important. Generally, strength increases with decreasing mean free path, and there is an optimum vol pct of dispersed phase. Just how fine a dispersion ought to be is somewhat open to debate, but Irmann, Lenel, Backensto, and Rose, Gregory and Grant,4 and others have shown in the original SAP-type alloys, aluminum plus aluminum oxide alloys, that better strength is generally obtained with finer dispersions and the best strengths were obtained when the mean free path was less than . Further, Cremens, and rant&apos; showed that in nickel plus aluminum oxide alloys, stress-rupture strength at 1500°F was definitely increasing with decreasing mean free path. In their investigation, however, the finest dispersions that were produced were about 2.0 mean free path. To determine the potential of the nickel plus oxide type of product, it would be neces- sary to obtain dispersions analogous to those of SAP alloys; namely, ones where the mean free path between oxides is less than . Unfortunately, however, it is very difficult to produce extremely fine dispersions of oxides in metals other than those which naturally form refractory oxide skins. There are several approaches to this problem including such procedures as mechanical mixing, internal oxidation, reduction of mixed oxides, and metal deposition from solution. Work at the Lewis Research Center has shown that metal powders 0.1p or finer could be produced by ball milling, when selected grinding aids were utilized.&apos; Because these unusually fine powders were available, it was an initial objective of this study to determine if by mixing of these fine Ni powders with various amounts of MgO (0.05) a fine dispersion of MgO in Ni comparable to those in Al-Al203 might be achieved. A second objective was then to attempt to relate the parameters of structure to 1800°F stress-rupture strength of the alloys. Nickel powders of 1-, 0.4-, and 0.2-p average particle size were combined with 0.05- average particle size MgO powder. This oxide was added in quantities of 4, 12, and 20 vol pct. The mixtures were hot pressed and extruded at 2100°F.

Jan 1, 1962

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study&apos; that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,&apos; flow in packed columns,&apos; fracture flow capacity&apos; and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy&apos;s law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-