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By J. H. Henderson, H. J. Ledbetter, N. B. Gove, J. D. Griffith

INTRODUCTION The results of a series of laboratory flood tests using liquid Iso-butane to displace refined oils from test cores are pre- ented and interpreted on an empirical bask. The study Revealed the similarity of the miscible liquid displacement to that of the immiscible-fluid displacement mechanism. The efficiency of the iso-butane flood decreased markedly as the oil Viscosity increased. but the effect of injection rate on the effectiveness of the primary production stage was negligible over the range investigated. The presence of free-gas saturation prior. to iso-butane breakthrough increased the volume of iso- Butane required to recover a given percentage of the oil present. Injection of liquid i.e.-butane prior to water follicle sculpted in a marked improvement in oil recovery by the water flood. INTRODUCTION The production of petroleum is often enhanced by the injec-1i1)n of extraneous fluids into the reservoir. It has been suggeited that the injection or cycling of a wet gas or a liquefied petroleum gas would he instrumental in increasing the effic.ienr!; of oil recover! to a greater degree than the commonly injected fluids. dry pas and water. Although instances of injection of light liquid hydrocarbons are not unknown, a systrmatic recording of the result is unavailable and superfi- cially, the practice gives the impression of being economicaIIy unsound. For specific types of displacement, analytic: solutions have been advanced which aid in understanding the physical mechanisms involved. However, there is no generalized theoretical concept which permits adequate prediction of displacement efficiency from a knowledge of readily measured reservoir rock and fluid properties. The Buckley-Leverett approach to oil displacement by an immiscible phase is an admirable analysiy of that type of mechanism. Dykstra and Parsons have introduced a useful concept in their evaluation of the role of the mobility ratio and its merit in rationalizing displacement phenomena. Everett, Gooch and Calhoun3 in their report on the effect of viscosity ratio and miscibility have pointed out the lack of a comprehensive theoretical approach and the desirability of investigating the mechanism of miscible-miscible displacement. In lieu of a well-developed theory concerning miscible-111isci1)le displacement and in view of the scarcity of engineering information on actual LPG injection trials, the limited program of laboratory experimentation described below was undertaken. OBJECTIVES The original broad objectives of the program, to study the oil recovery process using LPG as the displacing phase, defined the direction and scope of the laboratory tests. The specific objective. of the experimentation were to evaluate

Jan 1, 1953

By Frederick M. Becket

SHORTLY after the Armistice there appeared a few references to numerous attempts that had been made to produce steel without the aid of manganese, or at least with manganese in abnormally low percentage. Some years later, during two consecutive days of train travel, I had excellent opportunity to read Sir Robert Hadfield's book, entitled "Metallurgy-Its Influence on Modern Progress," and also his paper, "The Metal Manganese and Its Properties : Also the Production of Ferro-Manganese and Its History," presented at the spring meeting of the Iron and Steel Institute, 1927. Both the book and the paper are most interesting historically to makers of alloy steels and

Jan 1, 1931

By T. M. Girdler

IN THESE perilous days of world- wide uncertainty, this Institute and the profession represented by it take on new importance in the economic life of the nation. I have long been impressed by the fact that the objects of the A.I.M.E. are purely professional and scientific. The country has benefited from your honorable tradition of adherence to those objectives over a period of 68 years. The Institute's policy of refraining from controversial matters - has made possible the serious, balanced, and uncolored consideration of the particular problems that come before it.

Jan 1, 1939

The opening session was held on Tuesday evening, June 28th. Mr. F. S. Witherbee, of Port Henry, a member of the Local Committee, welcomed the Institute as follows: Mr. President and Gentlemen and (if I my also add) Ladies of the Institute: In the absence of the Chairman of our Local Committee it is my pleasant duty to give you a cordial welcome once more to the shores of Lake Champlain. I think some fourteen years have passed by since we last had the pleasure of receiving you at a meeting in this vicinity ; but the pleasure of that meeting still lingers in our memory; and the profit which we derived from your discussions and from your presence with us has made us heartily desirous to have you here again. If the truth must be known, we were for a time much embarrassed by the difficulty of providing adeqriate and comfortable shelter for the large number of friends whom we hoped (and, as this assembly indicates, had good reason for hoping) to receive. But the liberality and zealous co-operation of the Delaware & Hudson Canal Company and its hotel manager, in offering to open Hotel Champlain, at no little inconvenience, before the usual time, presented a solution of this difficulty, provided the date originally proposed for the meeting could be changed to a week later. This change was duly authorized; .and I think you will all agree with us that it was wise.. At all events, I am sure, I now need offer no apologies for the roof which covers yau. During the fourteen years which have elapsed since your last visit to us, great strides have been made in the industrial development of this country. The meetings of the Institute, held from one end of the land to the other, have permitted you to witness the transformation of small hamlets? like Birmingham, Ala., into populous and thriving industrial centers. You have seen the Minnesota and the

Jan 1, 1893

By HARRISON W. CRAVER

LIBRARIES are universally recognized as essential to modern civilization. In a world that gets most of its learning through the printed word, storehouses of print are a vital necessity. In this regard engineering differs in no way from the other learned professions, but until recent times the library needs of engineers have received rather scant attention. When the engineering profession was more of an art and less of a science than it is today, when each problem was solved more through the results of experience than by applying scientific principles, literature was less helpful. The engineer of today, however, is aware that his activities rest upon a scientific foundation and consequently comprehensive books dealing with more limited fields are now being published. Another difficulty for the operating engineer in the past was that the published works on engineering were written chiefly for use as college texts. A third obstacle to the development of engineering libraries has been the lack of librarians with experience in engineering.

Jan 1, 1938

THE National Coal Association held its annual meeting at Cleveland on Nov. 14-16, 1928, having changed the time from the spring to the autumn to avoid conflict with the great number of meetings ordinarily held in the spring. Institute members were \\yell to the fore in its activities, the president, E. C. Mahan (who was reelected for another term!, C. E. Bockus, treasurer, and the secretary, H. L. Gancly, being A. I. M. E. members, as are many of the directors. At the first session, our past president, S. A. Taylor, presented a 1;aper which is reprinted in part herewith. At the Thurs- day session W. D. Brennan presided, Walter Barllum led the discussion on membership, and Otis Mouser led the discussion on taxation. In the afternoon, J. P. Williams, Jr., led the discussion on research. Rembrandt Peale presided at the annual dinner in the evening. At the concluding session on Friday resolutions were adopted, among them one in which the Association "reaffirms its attitude toward proposed Federal legislation affecting the bituminous coal industry by saying that it opposes legislation which would seek to single out this industry for regulatory action. This particularly applies to such bills as S4490."

Jan 1, 1928

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967

By A. R. Gregory

A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy. S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King, 1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. 5- and P-wave velocity measurements on Bandera sandstone and Solenholen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2 and by Gregory 3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fate sand by Gregory, 3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King 1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8 A new shear wave velocity laboratory apparatus has been developed for testing rock samples under elevated pressures. This apparatus employs liquid-solid interfaces as mode converters. The technique for generating pure shear waves at liquid-solid interfaces was developed from studies of critical angle methods.6 Two identical transducers are placed in contact with opposite ends of the rock sample, one transducer acting as an ultrasonic energy emitter or generator and the other acting as an ultrasonic energy receiver or motor. The P-wave energy emitted from the piezoelectric crystal in the generator transducer is converted into pure S-wave energy at the Drakeol-aluminum

By Thomas M. Drown

IN the course of some experiments on the analysis of pig iron, I heated, in a platinum crucible, some borings of a graphitic pig iron with sodium carbonate. When the crucible was at a full red heat and the carbonate was thoroughly fused, I noticed a lively ebullition of the mass, and an escape of gas, which burned on the surface. On investigation this gas proved to be carbonic oxide, and on examining the borings in the bottom of the crucible after an hour or two, they were found to be perfectly malleable, although unchanged in general form and appearance. Analysis showed that the carbon was completely removed. I then repeated the experiment, to ascertain whether the silicon and phosphorus were affected, and found that these elements too were largely removed, and could be found in the fused mass as alkaline silicates and phosphates. In order to ascertain whether the removal of the silicon and phosphorus was merely a surface action or whether the reaction really extended into the mass of the iron, I tried the following experiments : A number of bars of pig iron were cast about one foot long and planed down-accurately to one inch section. These were immersed in a large wrought-iron pot full of molten sodium carbonate made by fusing the commercial bicarbonate of soda. Through the kindness of Mr. Frank Firmstone, Superintendent of the Glendon Iron Works, Easton, I was enabled to keep this pot at a reasonably constant high temperature for a long time in one of the hot-blast ovens. One of the bars was removed from the pot every twenty-four or forty-eight hours, according to the rapidity of the action, and after cooling was broken and the fracture examined. The change from pig iron to malleable iron was progressively inwards and always sharp and easily recognized, the rate of progression being in a decreasing ratio with the time. The temperature of the oven had evidently

Jan 1, 1879

By Thomas M. Drown

In the course of some experiments on the analysis of pig iron, I heated, in a platinum crucible, some borings of a graphitic pig iron with sodium carbonate. When the crucible was at a full red heat and the carbonate was thoroughly fused, I noticed a lively ebullition of the mass, and an escape of gas, which burned on the surface. On investigation this gas proved to be carbonic oxide, and on examining the borings in the bottom of the crucible after an hour or two, they were found to be perfectly malleable, although unchanged in general form and appearance. Analysis showed that the carbon was completely removed. I then repeated the experiment, to ascertain whether the silicon and phosphorus were affected, and found that these elements too were largely removed, and could be .found in the fused mass as alkaline silicates and phosphates. In order to ascertain whether the removal of the silicon and phosphorus was merely a surface action or whether the reaction really extended into the mass of the iron, I tried the following experiments : A number of bars of pig iron were cast about one foot long and planed down 'accurately to one inch section. These were immersed in a large wrought-iron pot full of molteu sodium carbonate made by fusiug the commercial bicarbonate of soda. Through the kindness of Mr. Frank Firmstone, Superintendent of the Glendon Iron Works, Easton, I was enabled to keep this pot at a reasonably constant high temperature for a long time in one of the hot-blast ovens. One of the bars was removed from the pot every twenty-four or forty-eight hours, according to the rapidity of the action, and after cooling mas broken and the fracture examined. The change from pig iron to malleable iron was progressively inwards and always sharp and easily recognized, the rate of progression being in a decreasing ratio with the time. The temperature of the oven had evidently

Jan 1, 1879

By Alfred V. de Forest

WE are now assembled in this hall for the eighteenth lecture in honor of the memory of our greatest American metallurgist, Henry Marion Howe. Many of his most intimate contemporaries, led, as was fitting, by Professor Sauveur, have described his vital accomplishments in three fields: as a leader in technical industrial development; in theoretical research; and finally as a teacher and source of inspiration for nearly two generations of students. In 1914 Professor Howe had retired from active teaching, but maintained his laboratory at Columbia University under the care of Arthur G. Levy, with whom he published many of the papers that later were incorporated into his last book, "The Metallography of Steel and Cast Iron." My position at the time was that of personal assistant to Professor Campbell-no pay, no duties, but the great privilege of preparing specimens, taking pictures and attending to some of the current consulting work. Whenever possible, I visited Howe's laboratory to chat with Levy and gather ideas about the wonderful field of metallography-in which I was a rank amateur, rescued by the quiet enthusiasm of Donald Smith of Princeton from an instructorship in civil engineering. Levy let me act as a fly on the wall during the Professor's occasional visits. Busy as he was, Professor Howe took the time and trouble to encourage my interest, as he had done for hundreds of others. He told me how he went about gathering his own information speculating as to causes, considering experiments, and verifying his conclusions. I ventured to mention some tests I had run on the irregular stretching of wires of different metals. He read the small volume I had prepared of ill-assorted facts and fancies and remarked: "Nobody cares for your theories or the history of your tests. Describe what you found as briefly as possible and perhaps I can help you to publish." Curiously enough, among my discards were some autographically recorded load-versus-electrical-resistance measurements. Taken with inadequate knowledge and equipment, these curves did not reproduce consistently, but if the relationship between strain and resistance had then been explored, the latest type of strain gauge might have been in useful service for the past 25 years. Professor Howe was a gifted teacher, perhaps because he was primarily an ardent and assiduous student. His own eagerness to learn and his willingness to revise and extend his opinions constantly encouraged those of his environment to be diligent and painstaking in the pursuit of knowledge. In honoring his memory, I also wish to bring to mind the kindly, humorous and quiet Levy, and join his name again, as it was for too brief a space in the past, with that of many-sided Henry Marion Howe. FACTORS OF IMPACT STRENGTH The subject chosen for the Howe Memorial Lecture by Dr. Gillett last year

Jan 1, 1941

By Fred C. Bond

JUST four years ago, in March, 1930, Gilbert LaBine discovered the rich deposit of pitchblende and silver ore on the east shore of Great Bear Lake, 30 -miles south of the Arctic Circle, which brought a new mining district into being. His original discovery is now the property of Eldorado Gold Mines, Ltd., but other groups have been active. Vigorous prospecting has outlined a mineralized zone that extends at least 100 miles from north to south. In this area silver discoveries have been relatively common; pitchblende, as might be expected, has been harder to find, though a deposit has been located this spring nearly 100 miles south of Eldorado that may be of great importance.

Jan 1, 1934

By Frank T. Sisco

DURING the past year the iron and steel industry of the world as a whole operated on a satisfactory basis. No discoveries nor new processes of outstanding importance were announced either here or abroad, although rumors of such were persistent. In general, the efforts of operating and research men in the iron and steel industry seemed to be confined to improving quality and reducing cost, not a new aim, for the same efforts have been noted in nearly all of the annual reviews of the industry for at least fifty years. Most published papers on blast furnace or steel-making practice were of minor importance, at least when judged by the criterion of radical change in process or product. If the number of reports in the technical journals, or articles in the trade press, is used as a basis for comparison, continuous-mill sheet is still the most important single product of the industry; papers were published detailing the results of the investigation of various phases of the

Jan 1, 1938

W. M. Courtis, Detroit, Mich. (communication to the Secretary) : Having made a rapid examination of the deposits described in this paper, I am not inclined to generalize confidently concerning its geological relations. But, since an analysis furnished by me has been included in the paper, it may be of further use to give the results of other samples and analyses. I give, therefore, a table of analyses by different parties, showing the average from surface-specimens:

Jan 1, 1901

By F. Keller, A. H. Geisler

Some of the important changes that take place in the structure of aluminum alloys are largely submicroscopic in character. This is especially true of the changes that accompany age-hardening and recrystallization. Although improved metallographic practices have been helpful in indicating some of these changes indirectly, results are limited by the resolving power of optical microscope lenses. The electron microscope, however, provides a new and important means for investigating the fine structure of metals in a range not possible heretofore. It is anticipated that this microscope will yield new and useful information to metallurgists when suitable techniques are developed to utilize its very high resolving power. Several unique methods have been devised to permit the examination of the structure of opaque samples by the electron microscope. These are all based on the principle of producing a very thin film that represents the prepared surface of the opaque metal sample, which can be examined in the transmission microscope; however, the available methods fall into three categories, depending on the manner in which the film is obtained. With the oxide-film method developed by Mahl3-17 a very thin surface layer of the metallographic sample is converted into oxide by a thermal, chemical or anodic treatment. After removal from the metal sample by one of the special techniques described by Evans,19 this oxide film is examined in the electron microscope, and is found to portray the structure of the original metal surface. Films formed on aluminum,8,17 nickel,7 iron 3,8,9 and a nickel-beryllium alloy" by heating; films formed on iron 8.9 by chemical action; and films formed on aluminum3-16 by anodic oxidation, have been examined. The other two are more recent methods developed principally in this country; they consist in making the thin film in the form of a mold or replica of the surface contour of an etched sample. With the negative replica method the thin film is made directly on the sample; with the positive replica method it is made on a negative reproduction of the sample. With both methods, variations in the contour of the metal sample, caused mainly by etching, produce variations in the thickness of the surface replica. Because of the direct dependence of the amount of scattering of the illuminating electrons upon the thickness of the film penetrated, only the variations in thickness of the replica are responsible for tones in the electron image. Negative replicas are made by forming a thin film of some suitable material directly on the polished and etched metal sample, and derive their name from the fact that after removal from the sample they have the high and low points in the sample reversed, as shown in Fig. I. Nega-

Jan 1, 1944

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

The Enquirer of October 13, 1835 carried a letter signed "G," calling attention to the great number of Virginians who were leaving the state and to the lack of enterprise shown in not developing the ample natural resources available. He mentioned coal in particular and in closing said: "Besides the coal mines owned by individuals, the Black Heath company of colliers are carrying on extensive operations. Owing to the derangement of the currency, and the immense expenses incurred in boring and sinking new shafts, I understand that their dividends have not yet been so large, as they may be confidently expected in future.-Another company, under the title of the Midlothian Coal Mining Company, is now about being organized by the Messrs. Wooldridges of Chesterfield, for the purpose of establishing an extensive coal business. Having examined the lands embraced in the charter and the principles upon which the company is designed to be organized, I am persuaded that more productive stock can no where be found. The charter embraces a space nearly equal to a mile square, adjoining the mines of the Black Heath company, those of Mr. N. Mills, and those of Stone Henge, which space must contain coal of great thickness of excellent quality, as the strata of coal of those other mines pass through it; exhibiting a field so extensive, that centuries may elapse before it is exhausted. A shaft has been sunk on these lands, from which a very large quantity of the best coal is being raised. The terms of the charter require the Proprietors to sell one-half of these lands and mines, from the sale of which they will appropriate $100,000 as permanent capital, to purchase hands and engines, and to sink other shafts to work the property and thus going into operation with such decided advantages, as to produce a profit as great as a reasonable man should desire. Here is an opportunity for investing capital, which I think should satisfy the wishes of many Virginians who speak of emigrating. Will they not embrace it?-I have confined my remarks to the coal mines, because they are in the heart of our State, and their operations are familiar to many who can verify the statements. I might extend them to the other mineral treasures of our State; but if I do so, they must be reserved for another number, this being longer than I intended, and perhaps longer than you can conveniently find room for in your crowded columns. G." In January 1828 the Tuckahoe Canal Company was authorized to construct a canal along Tuckahoe Creek, from the James River up the stream about five miles; later this was amended to allow the use of the stream with a depth of water of two feet, no tow path was required, or provided: A toll of one cent per bushel was collected and the canal company made large profits. The service was so poor that in December 18, 1835, John G.,

Jan 1, 1942

By PAUL P. ZElGLER

Rapid growth of the aluminum industry continued through 1948 with an acute shortage of the metal in all forms marking the year. Estimates based on shipments made during the first nine months indicate that, in 1948, the industry shipped more than two billion pounds of aluminum products or roughly four times the amount shipped in the greatest peacetime year prior to the war. The rapid expansion of the aluminum industry is particularly reflected in the production of sheet. Last year, the industry as a whole shipped an estimated 40 per cent more sheet than was produced in the peak war year of 1944.

Jan 1, 1949

By A. William Johnson

It was pointed out in an earlier paper1 that our understanding of the atomic mechanism by which diffusion occurs in metallic alloys is scarcely in an advanced state. This unsatisfactory condition is the result not of any lack of interest, but of the difficulty of designing experiments that .will yield suitable data. The diffusion coefficient of an alloy, measured in the usual way, is simply a number specifying the rate of homogenization of a nonhomo-geneous metal; this number, of itself, can furnish neither the rate at which the individual atoms move nor information as to the mechanism by which they move. It does not necessarily follow, however, that such information cannot be obtained, even if the path to be followed is still not clear. Much success has been attained in the study of diffusion in ionic crystals. A number of experiments, for which there are few counterparts in connection with metals, yield information often indicating a detailed mechanism by which diffusion probably occurs. From such work, quite acceptable theories of lattice imperfections have been developed by Wagner, Schottky, Frenkel, Jost and others.2 It is postulated that real crystals of stoichiometric composition contain, in equilibrium, certain imperfections of which the most importarlt types are: (I) vacant cation sites, with an equal number of interstitial ions; (2) vacant anion sites, with an equal number of interstitial ions; (3) equal numbers of anions and cations in interstitial positions; (4) equal numbers of vacant anion and cation sites. The classification of a particular crystal according to this scheme then follows from studies of the variation of electrical conductivity with pressure of the electronegative component surrounding the crystal, with ion size, and with temperature; other physical phenomena, such as the Hall effect, have aided in establishing the classification. The relative mobility of the anion and cation may be determined by chemical analysis of the salt at the electrodes following electrolysis. With such information, and knowing that one ion never occupies the lattice site normally belonging to an ion of opposite sign, it is usually possible to ascertain the diffusion mechanism. It is clear that the same experiments are not applicable to metal crystals, and substitute experiments that yield as much information have not yet been devised. Much can be learned, however, about the mobilities of the two* kinds of atoms in alloys by the use of radioactive metals as indicators. Only one such experiment has been performed in the past. In 1933, Seith and Keil,3 in an effort to explain the great difference between the rate of diffusion of gold in lead and of lead in lead, measured the rate of diffusion of radioactive lead in 3 gold-lead

Jan 1, 1942