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By William Fink

MANY investigators have attempted to determine the true nature of the internal changes taking place during aging. Merica, Waltenberg and Scott1 were the first to propose a theory of age-hardening. They attributed the age-hardening of duralumin to the precipitation of minute particles of the compound CuA12. Later Zay Jeffries and R. S. Archer2 augmented the above theory by suggesting that the small CuA12 particles acted as "keys" causing "slip interference." Many other investi-gators3 have devoted much time to the mechanism of age-hardening, some corroborating the "precipitation" and "slip interference" theory, others coming to different conclusions because of effects that to them seemed unexplainable by the early theories; e.g., the increase of electrical resistance upon aging, the fact that no change in lattice parameter could be detected during the early stages of aging even at elevated tempera-tures, and the fact that the density did not change as would be predicted. In 1932, Merica revised4 his earlier precipitation theory to take care of these presumably anomalous effects. This revised theory, the "knot" theory, assumes that substantial age-hardening occurs before actual precipitation of solute as discrete particles. The assumed mechanism is one of diffusion of solute atones into groups forming distorted regions which act as "hard" spots and cause slip interference. These "knots" are assumed to have approximately the same lattice arrangement as the solvent.

Jan 1, 1936

By J. W. Koger, R. E. Hurnrnel

QUENCHED, bcc p brass, P1, transforms to a mar-tensitic phase, when it is cooled below room temperature.' This transformation can be followed using resistance measurements since the resistivity of the martensitic phase is considerably larger than that of the parent phase, Fig. 1.' phillips3 first reported that, when Cu-Zn alloys containing between 37.0 and 39.0 wt pct Zn were quenched from the 0 region to room temperature, variable amounts of a phase could be observed depending on the mode of quenching. If the quench occurs very rapidly, the a phase forms by a "massive transformation". The resultant phase has the same composition as the high-temperature P phase from which it was formed. If the quench is less severe, the alloy is retained largely in the p form; however, some a is formed by precipitation. In this case, a contains more copper than the high-temperature 0 phase from which it has formed. The a phase most probably does not undergo a transformation in the temperature range where p transforms to low-temperature martensite. This can be deduced from the Eesistivity-temperature relation which is linear in this temperature range, Fig. 2. The stable a phase which is present along with R. E. HUMMEL is Assistant Professor, Department of Metallurgical and Materials Engineering, University of Florida, Gainesville, Fla. J. W. KOGER, Junior Member AIME, formerly with University of Florida, is now with Oak Ridge National Laboratory, Oak Ridge, Tenn. Manuscript submitted December 13, 1967. IMD.

Jan 1, 1969

By S. M. Wu, R. L. Stone, T. D. Tiemann

The dissolution of silica from quartz in sodium hydroxide solutions was investigated by statistical methods. A second-order predicting equation was developed with 28 experiments expressing the dissolution of silica as a function of the variables quartz size, time, temperature and sodium hydroxide concentration. With this equation a comprehensive picture of the dissolution reaction was gained which included the effect on extraction of each variable and their interactions, fractional extractions, reaction rates and activation energies. A previous investigation of the extraction of silica from low grade siliceous iron ore by digestion in sodium hydroxide solutions presented the extraction as a function of time, temperature and sodium hydroxide concentration.' The present paper is an outgrowth of the previous work and develops by a mathematical analysis the functional relationship between the extraction of silica and time, temperature, sodium hydroxide concentration and particle size. Relatively pure quartz was used in this study in order that the basic quartz-sodium hydroxide reaction could be studied without the influence of other constituents that are commonly found in iron ores. The functional relationship between the dissolution

Jan 1, 1965

By Chas. Y. Clayton, Francis B. Foley, W. E. Remmers

DuRing the summer of 1919, the late Dr. Henry M. Howe, then Chairman of the Division of Engineering of the National Research Council, organized a committee to obtain a better insight into the behavior of carbon steels under the influence of various treatments by a proper control of the time and temperature factors. During part of 1919 and 1920, work in connection with this investigation was carried on at Dr. Howe's laboratory at Bedford Hills, N. Y. During 1921 there was an enforced hiatus in the work, occasioned by the illness which resulted in Dr. Howe's death in 1922. At that time one of the present authors compiled the results of the work which had been done and this was published in 1923.' Following the publication of this work, it seemed desirable to carry on in the same manner an investigation of steel of C 0.75 per cent., which steel had not been as fully treated as had the other steels of C 0.34 and 0.52 per cent., used in the published work. Furthermore, certain unusual results have been obtained in the treatment of C 0.52 per cent. steel by quenching and drawing, and repetition of this part of the work seemed advisable. This has been done during the past year at the School of Mines and Metallurgy of the University of Missouri at Rolla, Mo., by a cooperative undertaking of the School and the Bureau of Mines, working in conjunction with the Committee on Heat Treatment of Carbon Steels of the National Research Council. The present paper is a report of the results obtained in this work.

Jan 1, 1926

By Roger M. Zimmerman

The G-Tunnel heated block experiment is being conducted on the Nevada Test Site (NTS) as part of the Nevada Nuclear Waste Storage Investigations project (NNWSI). The purpose of the ambient temperature testing ph se is to evaluate rock-mass mechanical properties of a block (- 8 m3) under biaxial stress changes up to 7.5 MPa above an initialization in situ value of 3.1 MPa. Results indicate that the modulus of deformation ranges from 9.7 to 17.0 GPa and Poisson's ratio ranges from 0.21 to 0.33. In general, the higher values of the modulus and Poisson' s ratio were influenced by fracture propagations parallel to the compressive stress field. Other measurements indicated that cross-hole compression (p) wave velocities and single fracture permeability values were relatively insensitive to stress changes above the in situ value.

Jan 1, 1984

By R. C. Dalzell, A. E. Wells

In 1866, Thomas Graham1 called attention to the volume of gases, three times the volume of the sample, evolved from a meteoric iron heated in an evacuated porcelain tube. From that time to this the occurrence and significance of gases in metals have been the subject of investigation by many workers, among whom Sieverts,2 Iwasé3 and 0. W. Ellis4 stand preeminent. Sieverts and Iwasé concerned themselves with the solubility of a number of gases in metals in the liquid and solid states. They determined the absorption coefficients of these gases, and in all cases found a sharp change in solubility at the melting point of the metals. Ellis analyzed the gases evolved by solidifying copper and those occluded by the solidified metal. Lobley and Jepson5 endeavored to determine the effects of hydrogen, carbon monoxide and nitrogen on the porosity of copper that was allowed to solidify in the presence of each gas after 30 min. exposure to it in the

Jan 1, 1930

By R. E. Head

UNDER existing economic conditions, the treatment of gold ores occupies an outstanding position in metallurgical activity. The increased price of gold has automatically brought about a reclassification of old dumps and low-grade orebodies, and many that formerly were considered valueless are now being vigorously investigated and worked. This situation has developed problems that have taxed the ingenuity and ability of metallurgists to the utmost. Some gold ores give a high extraction of gold by standardized methods of treatment; other ores of apparently similar character yield but a relatively small percentage of their gold when treated by the same processes.

Jan 1, 1936

By Edward Walsh

In the early history of the production of metallic iron from the native oxides or ores, success attended the labors of the workman according to the care he devoted to his work, and according to the degree of skill he possessed in furnishing the required amounts of fuel and ores to be acted upon by the blast propelled by the bellows, trompe, or wooden tub, and delivered into the hearths of the Persian, bloomery, or Catalan forges. The same skill may also have been of avail in the use of the lower forms of the ".Stück," "Blue,"or" Wolf"

Jan 1, 1887

By L. A. Willey

IN 1953, a method for filtering a liquid phase from solid phases while in equilibrium at elevated temperatures was devised at the Alcoa Aluminum Research Laboratories. Since then, it has been applied to the investigation of liquid-solid equilibrium in metallic systems. In application, the method simplifies the centrifuge filt.ration procedure as developed by Scheil and described by Gebhardt Fig. 1 shows a sketch of the filtering apparatus located within a thermal analysis furnace. It consists of a stainless steel filter crucible A, into the bottom of which a porous carbon filter disk B, 1 3/4 in. diam by 1/4 in. thick, is sealed to the shoulder and rim with carbonaceous cement. The base of the filter crucible, machined to an angle, fits into a tapered seat at the mouth of a stainless steel vacuum chamber C. A connecting tube from the vacuum chamber to a vacuum line also serves as a means for supporting the apparatus from the base of the furnace. An alundum crucible D of 25 ml capacity is placed with- in the vacuum chamber below the filter for collecting the filtrate. Two thermocouples E, in stainless steel protection tubes, which extend from 1/16 to in. above the center of the filter, are mounted on the rim of the filter crucible. One thermocouple is used in differential connection with the furnace control thermocouple to regulate rates of heating and cooling. The other serves as a means for recording the temperature of the alloy prior to filtering. A suitable mold coating is used on exposed surfaces of stainless steel parts to guard against attack upon these parts as well as to avoid contamination of the alloy samples. A mold wash prepared from precipitated CaCO, is suitable for aluminum alloys. The porous carbon for the filter disks and the carbonaceous cement, grade 200 (graphite base), were obtained from the National Carbon Co. Porous car-bon, grade Nos. 10 to 60, has been employed. Grade No. 40, however, appeared to give the optimum advantages in operation. In operation, an alloy sample is remelted and heated to about 50°C above its liquidus temperature. At the same time, the filter apparatus is preheated to about the same temperature. The alloy then is cast into the filter crucible.

Jan 1, 1957

By N. A. Elmslie

This subject covers much ground, therefore it must be treated in a general way rather than in detail in this paper. Personnel To approach the measure of a mine, it is, of course, essential that the personnel be measured, and this measuring must be done in a circumspect manner and conclusions must be reached slowly. There may be one unit in the personnel of an organization that may be out of step with the remainder of the organization, not always because of lack of ability, but because of misplacement or lack of proper measurement of his capabilities. Too much time can scarcely be spent in the study or measure of the personnel ; in fact, a manager or a superintendent of a mine never completes his work along this line. Mine or Plant Just as no two men are alike, so no two mines or plants are alike; and yet there are many similarities. Find out what the similarities are, and this will help to make clear the dissimilarities. Try to visualize details of the difficulties, not because you will have to deal with them yourself, but to consider them in later studies of general problems. To outline all the steps to be taken in familiarizing oneself with a plant or operation would be impossible, but the following points may be of interest in any investigation. The study of a mine is generally made backwards-—that is to say, one sees the finished product first-—-but this is immaterial, because each step must be considered separately in any event. As a rule, there are certain heads under which the different features of mining can be placed, as follows: Ventilation.—Ventilation is usually the most important item in power cost and safety, especially in gassy mines. Quantity of air, water gage and power consumption, and finally analysis of the return air in full return and separate splits should be considered. Type of fan and type of power unit should enter into this study because it is important to view expenditures which are going on 24 hr. a day and 36.5 days in the

Jan 1, 1931

The discovery of nickel at the Wallace Mine in 1846, recorded in the Report of Progress of the Geological Survey of Canada, 1.848-49, was not the first find in the Sudbury mining district. As long ago as 1770 a company had been formed to work the rich deposits of, copper whose existence was then known. .But it was during the first mentioned year that, incited thereto by fresh finds and a favorable report by Mr. W. E. Logan, then Provincial Geologist, two [ ] groups of Canadians organized "The Montreal Mining Company and "The Upper Canada Mining Company." By the former company the Bruce Mines Location' was purchased and work was immediately commenced upon it. The Wallace Mine acquired by the Upper Canada Mining Company, was abandoned after a shaft had been sunk and a few test pits opened.

Jan 1, 1907

By Russell W. Dayton

The metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concerning the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chalcography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Königsberger,"' i in 1909, was the first to apply polarized light to the microscopic study of opaque substances; Endell and Hanemann(2) were the next, in 1913. In 1919 and 1920, Wright(3,4) prepared two papers on the subject. In the first he developed the detailed mathematical theory from the viewpoint of the electromagnetic theory of light, and in the second described the various methods in use, giving improvements of his own. Schwarz(5)

Jan 1, 1935

By Russell W. Dayton

The metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concerning the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chalcography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Königsberger,"' i in 1909, was the first to apply polarized light to the microscopic study of opaque substances; Endell and Hanemann(2) were the next, in 1913. In 1919 and 1920, Wright(3,4) prepared two papers on the subject. In the first he developed the detailed mathematical theory from the viewpoint of the electromagnetic theory of light, and in the second described the various methods in use, giving improvements of his own. Schwarz(5)

Jan 1, 1935

By William H. Spice

Exploratory drilling in South Central Texas for the year 1944 showed a marked increase over that of 1943 and resulted in a similar increase in new fields discovered. In this area, which comprises the 30 counties included in district No. I, Oil and Gas Division, Railroad Commission of Texas,? 61 exploratory wells were drilled during 1944 as compared with 29 exploratory wells drilled during 1943, or an increase of over 100 per cent. Three new oil fields, two new gas fields and one gas-distillate field were discovered during the year, as compared with one new oil field and one new gas field discovered during 1943. These new fields were the result of exploratory drilling throughout the district along the Wilcox trend and the deeper Edwards lime trend, which was started during the previous year. The Wilcox trend yielded the new Loma iilta-Wilcox oil field and the San Caja gas-* tlistillate field, both in McMullen County. The Charlotte field, in Atascosa County, was discovered along the deeper Edwards lime trend. These three discoveries were of considerable importance and subsequent development should indicate the desirability of continued exploration along these trends. The other three discoveries, United oil field in Guadalupe County, Pederson gas field in Milam County and Van Cleve gas field in Zavalla County, were of minor importance. Charlotte Field, Atascosa County, was discovered by the Humble Oil and Refining Company's No. 3 Pruitt, completcd on Aug. 9, 1944, flowing 176 bbl. per day, 3/16-in. choke, 710 lb. tubing, 475 lb. casing pressures, 37.7º A.P.I. gravity, from the top of the Edwards lime from 6917 to 6923 ft. Two oil wells were completed during the year in this field. This discovery is 14 miles southwest of the same company's Imogene field, also producing from the Edwards lime but with considerable difference in reservoir characteristics. The discovery of this field is the result of surface geology and subsequent seismograph survey of the area. Loma Alta-Wilcox Field, McMullen County, was discovered by the Atlantic Refining Company's No. I Atkinson, completed on June I, 1944, flowing 102 bbl. per day, 9/64-in. choke, 1900 lb. tubing pressure, 37º A.P.I. gravity, from Wilcox sand from 6866 to 6869 ft. after being drilled to a total depth of 7185 ft. This discovery is the result of subsurface geology and an extensive seismograph survey of the entire area. Sun Caja Field, McMullen County, was discovered by Edwin M. Jones No. 2-C Ezzell, completed on June 2, 1944 as a dual completion in the Wilcox sands, flowing 1,740,000 cu. ft. gas with 53 bbl. distillate, 1/4-in. choke, 2035 lb. tubing pressure, 53.2º A.P.I. gravity, from sand 6416 to 6453 ft. and flowing 2,000,000 cu. ft. of gas with 127 bbl. distillate, 1/4-in. choke, 2500 lb. tubing pressure, 50º A.P.I. gravity, from sand 6889 to 6916 ft., after being drilled to a total depth of 7264 ft. Three gas-distillate wells were completed during

Jan 1, 1945

INTERNAL The year 1976 was another outstanding year in the operation of the Institute and in the success of its varied activities. Total AIME membership reached 59,773 for a gain of. 6.4 percent. Total revenue increased to $5,111,2 10, up 22.4 percent, and balance sheet assets increased to $8,479,612, up 12.2 percent from the previous year. AIME and its constituent units conducted 30 technical meetings during the year, and attendance was up at most of them. Publications issued by the Constituent Societies continued a healthy growth. During the year 9 new local Sections were established, and at the end of the year the Institute had 150 Sections, with 19 of them overseas. Details on all of these operations are on pages 2 and 3 of this report.

Jan 4, 1977

GENTLEMEN Herewith are transmitted reports from the Treasurer and of the principal standing committees of the Institute. To these special reports members are referred for details as to the year's work. Despite the unfavorable business conditions obtaining throughout the year, the Institute was able to carry on its various activities without curtailment and without drawing on the surplus accumulated through previous years. In fact, small additions were made to the Life, Member¬ship and various other funds. It is highly desirable that such additions should continue to be made, especially to the Life Membership fund, for reasons reported last year. At present, money must be used from current receipts in order to enable the Institute to fulfill its obligations to those who on joining the organization commuted their dues by a single payment. In addition, with the passage of years the number increases of those who have paid dues forty years or more and who, by reason of age or dis¬ability, are unable longer to practise their profession. These men have supported the Institute through their active professional life and it would be a pity to lose them as members through resignation or for failure to keep up their dues. In accordance with the By-laws the Board has authority to advance such members, on application, to the Honor Roll of Senior Members and to relieve them from further payment of dues. It has been the policy of the Board to do this liberally, but to keep up this, as well as to meet other obligations, it is necessary for money to be provided. It has been estimated by the Treasurer that nearly $50,000 additional should be placed in the Life Membership fund as soon as possi¬ble to meet these obligations without using current income and to that end it is necessary, not only to avoid running behind currently but to earn, if possible, some surplus each year. The small amount transferred to the Life Membership fund from surplus this year was, as a matter of fact, made possible by certain members paying personally bills that were properly chargeable to the Treasury. Such generosity is common among those active in Institute work and probably no year would have closed with a surplus except for it.

Jan 1, 1923

By George Sachs, S. M. Clark, George Espey

he tendency of a commercially drawn cartridge case to crack in the mercury test and the relation of cracking tendency to residual stress retained after drawing were studied. The fourth drawpiece (next to the final) of caliber 0.30 cartridge cases produced by Frankford Arsenal were selected as test pieces. These exhibited an exceptionally high cracking tendency, making a detailed study possible. To obtain fast cracking in the mercury test, about 0.0015 to 0.003 in. must be removed from the wall thickness of the drawpiece by pickling, and it must be subjected to the mercury test immediately after washing. Removal of the adhering mercury by annealing and subsequent squeezing of the case in a vise was used to reveal definitely the presence or absence of cracks. Various lots of apparently identically fabricated cases were shown to possess a different cracking tendency. Machining off or boring a hole in the base gradually reduced and eventually eliminated the cracking tendency. On the contrary, shortening of the wall (body) reduced the cracking tendency only if the wall became so short that the cracking zone was directly affected. By boring out the base and pickling from the outside and then splitting the resulting rings, it was possible to determine the approximate stress distribution in the base and in the adjacent part of the wall. Small compression stresses were present in the core and the major part of the base, while the surface of the base and the adjacent wall contained high circumferential tensile stresses. On the contrary, the wall when parted from the base contained only insignificant residual stress. The conception is advanced, that the stress distribution in a drawn cartridge case corresponds fundamentally to that of a tube (wall) shrunk on a disk (base). Such a stress distribution results from the tendency of the base to recover elastically by an increase in diameter from the biaxial compression during drawing while the wall exhibits little tendency to change its diameter after progressing through the die. This is confirmed by measurements which show the base diameter to be slightly larger than the wall diameter.

Jan 1, 1945

TWO American students entered the École des Mines in 1856, Joseph Lesley of Philadelphia and Thomas Egleston of New York. Lesley remained there only one year, but Egleston completed the whole curriculum and received, in 1860, the certificate given to foreign students in lieu of the official appointment and degree awarded French students. Returning home he received, in 1861, an appointment by Secretary Henry of the Smithsonian Institution to sort, label, and arrange the collections of mineralogical and geological specimens which had been brought to Washington by the various government exploring expeditions in the West. Thomas Egleston, born in New York City on Dec. 9, 1832, was the son of Thomas Jefferson Egleston, who came to New York from Massachusetts some time before 1829. The first American ancestor of the family had settled near Dorchester in 1630. T. J. Egleston and Joseph Battell established an iron-merchandizing business* at 166 South St., New York, which prospered exceedingly; so much so that when Thomas J. Egleston died, July. 12, 1861, his estate had a book value of over $500,000. Since an older brother was expected eventually to take over this business, Thomas, who had a liking for science, went to Yale, where he completed the regular four-year course in 1854, and then remained another year for advanced work in chemistry under Silliman. One biographer says he went to Europe, early in 1856, on account of his health. It was the custom at that time for wealthy young men to make a tour of Europe after completing their academic education. Whatever the precise reason, he began scientific work at the Jardin des Plantes in Paris but soon trans-

Jan 1, 1941

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949