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By A. W. Gray

Page CRUSHING STRENGTH...................... 659 The Black Dynamometer....................659 A Standardized Procedure for Crushing Strength Tests...... 660 Influence of Height of Test-piece upon Apparent Strength ..... 662 Influence of Packing Pressure and of Packing Time........ 662 Application of the Logarithmic Law...............665 Influence of Amalgamation Variables.............. 665 Influence of Temperature................... 669 The Transition Region Near 70" C............... 671 Influence of Packing Pressure at Various Temperatures ...... 673 Influence of Age upon Alloy and Amalgam........... 676 DIMENSIONAL CHANGES DURING THE HARDENING OF AN AMALGAM .......................... 678 The Black Amalgam Micrometer............... 678 Thermostated Dilatometer Designed by the Author........ 681 Graphical Representation of Reaction Expansions......... 683 The Typical Reaction Expansion Curve ............. 684 Influence of Packing Pressure................. 686 Influence of Trituration Time................. 687 Influence of Temperature................... 688 Influence of Mercury-alloy Ratio................ 689 Influence of Packing Time................... 689 Influence of Annealing the Alloy................ 691 Influence of Size of Alloy Particles...............691 Extension of the Typical Expansion Curve........... 693 Influence of Thermal Softening and of Reamalgamating a Hardened Amalgam.......................... 634 Curves Obtained with a Variety of Dental Alloys ........ 694 Copper Amalgam ...................... 694 PRACTICAL APPLICATIONS OF THE RESULTS.......... 695 Phenomena which reveal chemical and physical processes that probably go on in many alloys at temperatures not far removed from their melting ranges are observable in dental amalgams. These amalgams should. therefore. be of even more interest to the metallographer, the metallurgistl the chemist. and the physicist than to the dentist who uses them for saving decaying teeth. For this reason I am here de-

Jan 1, 1919

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889 ADAM S HEWITT 1890 JOHN BIRKINBINE 1891-1892 H M HOWE 1893 JOHN FRITZ 1894 J D WEEKS 1895 E G SPILSBURY 1896

Jan 1, 1923

By J. Winlock

To have been chosen by you to give the Howe Memorial Lecture is the greatest honor I have ever had and I should like to have you know that I appreciate it deeply. Many years ago I had the privilege and the pleasure of working with Professor Howe in the private laboratory which he had established in his home at Bedford Hills, New York. Without doubt he was one of the world's greatest metallurgists and so you can imagine what a difficult task it has been for me to live up to his teachings. Every morning Professor Howe would outline the work he wanted done and the recollections of those conferences are clear to me to this day. Sometimes he would ask me to ride in his automobile and the chauffeur had full instructions to go no more than fifteen miles an hour. If he did so, Professor Howe was sure to rap upon the man's shoulder with his cane. I assure you, however, Professor Howe's thinking was not at that rate. His homely advice, his patience and his perfect control of the English language still impress me. Many times I heard him dictate a complicated paper on metallurgy and never find it necessary to change a single word. There are no better words to describe the character of Professor Howe, in my opinion, than those used by Professor Sauveur when he presented the John Fritz Medal to him in 1917: "Lover of justice and humanity Public servant and public benefactor, Master of the English Language, Loyal and devoted friend, Untiring and unselfish worker in an important field of science." I hope you will bear with me with the same patience and understanding which he used to give to me. The peculiar behavior of steel at the yield point has long been known and has been the subject of much research, both in this country and abroad.',' Many theories, including some of mine and my colleagues, have been suggested, but none of them, in our opinion, fully explains to our satisfaction why the phenomena occur. Of particular importance has been the work of Nadai,3 Siebel and Pomp,' Sachs and Fiek,5 Rawdon,0 Kenyon and Burns,' Gensamer," Gensamer and Meh1,0 Davenport and Bain,'" Fell," Deutler,12 Brinkman,13 MacGregor,14 Hollomon,15 Cot-trell,16 and Palm." The question of what is occurring during this singular behavior is not only of interest from an academic point of view, but is of great practical importance for at least two reasons: 1—The highly localized plastic flow which occurs during the deep drawing of light-gage steel gives rise to surface markings which seriously mar its appearance, Fig. 1. If the forces causing the deformation are primarily tensile forces, these surface markings occur as depressions in the surface. Whereas, if the forces causing the deformation are primarily compressive, irregular lines of elevations occur. These surface markings are known as Luder's lines, Hartmann lines, the Piobert affect, and, in the shop, as "stretcher strains." 2—The steel is in the most suitable condition for deep drawing after the yield point phenomena have been removed. When this is done, the steel may be deep drawn more easily and to a greater extent.' It should be mentioned that steel is not the only metal which shows this peculiar behavior at the yield point. Stretcher strains occur, also, during the deformation of some copper-nickel-zinc alloys." The purpose of this paper is not an attempt to describe what causes the steel to behave in this peculiar manner, but an attempt: l—to describe what is taking place at the yield point; and 2—to show the influence of the rate of deformation on the tensile properties of some plain carbon steels. As is well-known, there are two methods of deforming a metal in tension: 1—by actually hanging an increasing amount of dead weight on the metal; or 2—by deforming the metal at some given rate or rates by means of oil pressure cylinders, screws, etc. With the first method, the load is always present and, clearly, no drop in load can ever occur while the steel is deforming. With the second method, the registered load is the resistance of the steel to the deformation being imposed upon it. The second method is the one most widely used, and is the one referred to throughout this paper. In order to describe clearly what is occurring at the yield point in steel, it will help, I believe, if a description is first given of what occurs when alumi-

Jan 1, 1954

By L. Dudley Stamp

In my last report on Petroleum in Burma and India1, details were given of production and development up to 1932. It was pointed nut, that the only statements available for Burma were those published officially by' the Government of India in the Annual Review of the Mineral Production of India (Records of the Geological Survey of India), which are issued about 10 or 11 months after the close of the year. Operations in Burma are almost entirely in the hands of three companies—the Burmah Oil Co., the British Burmah Petroleum Co. (with its subsidiary, the Rangoon Oil Co.) and the Indo-Burma Petroleum Co.—and these companies preserve a policy of secrecy, so that details are not available of new wells, depth, wells abandoned, or of other figures, except in so far as the Government considers it advisable to publish the information in its possession. GeneRal Developments in 1933-1934 As predicted in 1933, there have been no spectacular developments and no new fields have been discovered. Nor are there any new indications of a likelihood of fresh discoveries. The policy of extremely careful exploitation. has been continued and intensified; production is being maintained at an almost steady level and can be so maintained for many years to come—indeed, it is the policy of the leading company to permit refinery and local market requirements to dictate the production required. Contrary to experience in practically every other part of the world, India has shown a slightly decreased demand for petroleum products—especially kerosene, but also for gasoline. The increased use of electricity would explain the lower demand for kerosene, but the falling off in the demand for gasolinc can only be attributed, according to the Chairman of the Burmah Oil Co., to the depression and to the incidence of heavy taxation. In India (including Burma) as a whole, production was 305,018,751 Imperial gallons in 1931 (8,714,822 U. S. barrels); 308,606,031 Imp. gal. in 1932; 306,009,022 in 1933 and is estimated at 308,000,000 in 1934.

Jan 1, 1935

By C. R. King

Most of the acid volcanic glasses such as obsidian, perlite, pitchstone, pumice, and pumicite (volcanic ash) are susceptible to some expansion if suddenly subjected to a suitably high temperature in a properly designed furnace, and subsequently suddenly cooled. Expansion results from the action of chemically combined or dissolved water expanding as a vapor within the softened heated rock particles. This expansion forms countless minute bubbles within the pasty mass of the natural glass particles. If the particles are cooled before these bubbles can escape, the resulting products are cellular, more or less spherulitized glass froths or hollow glass spheres of many types. Chemically, they are essentially aluminum silicates containing about 70 to 75 pct silica, 10 to 16 pct alumina, and 2 to 7 pct sodium plus potassium oxides. They are relatively resistant to attack by acids or alkalies, are resistant to heat up to over 1000°F, and are completely inert to insect or fungus attack.

Jan 1, 1949

By A. T. Churchman

The deformation modes of rhenium have been identified as those typical of the hexagonal metals, titanium, zirconium, and beryllium whose c/a ratios, in common with rhenium, are less than ideal for close packing. Slip is observed on (1010), (1011), and (0001) planes and twinning on (1121), (1122), and (1012) planes. The very high rate of work hardening is believed to be associated with intersecting partial dislocations on two (1010) systems which can combine to form sessile barriers. If the stacking fault energy is low, as postulated by Seeger, these barriers should be strong and not easily bypassed by cross slipping. Such an explanation could also account for the very small temperature dependence of the yield stress which was observed. RHENIUM is interesting scientifically as a member of the group of high melting point hexagonal metals: titanium, beryllium, and zirconium with a c/a ratio less than that for ideal close packing. Unlike them, however, it work hardens at a very high rate. This rate is greater and continues to a much higher degree of deformation than for nickel, normally considered to have a high rate of work hardening. This paper presents experimental observations on the modes of deformation of rhenium and, by comparison with other hexagonal metals, some speculation on the cause of the high work hardening. MATERIALS Johnson, Matthey rhenium powder of both 99.9 pct and 99.5 pct purity, see Table I, was compacted at 10 tons per sq in., part sintered at 1350°C in vacuo, and finally arc melted in a "gettered" argon atmosphere arc furnace to produce small buttons. Little difference was observed in the as-cast hardness or working down behavior of the two purities suggesting that either silicon and potassium do not have a significant effect on the working properties of rhenium or they were lost during arc melting. SPECIMEN PREPARATION The cast structure was broken up by cold-rolling with inter-stage annealing at 1600o or 1800°C in a vacuum high-frequency furnace using a tungsten susceptor. Strip for tensile testing was taken from two thicknesses of material 0.011 and 0.064 in. The former with intermediate anneals at 1800°C had a grain size of 900 grains per sq mm, while the latter with inter-stage annealing at 1600°C had a grain size of 3600 grains per sq mm. A coarse grain size was obtained by secondary recrystallization in a half button cold-worked by 30 pct reduction. Annealing times of from half an hour to several hours at 2200° to 2600°C in a "gettered" argon atmosphere arc furnace1 resulted in grains of up to 2 mm diam.

Jan 1, 1961

Univ of Alabama-University, Alabama-Mining and Metallurgical Society William L Mason, Faculty Sponsor, E C Wright, Dept Head Univ of Alaska-College, Alaska-Mining Society of the Univ of Alaska Douglas W Huber, Faculty Sponsor, E H Beistline, Mining & Metallurgy Dept Head, Troy L Pewe, Geology Dept Head, James Crawford, Chapter Counselor Univ of Arizona-Tucson, Arizona-Miners Society Willard C. Lacy, Faculty Sponsor, J D Forrester, Mining & Metallurgy Dept Head, F. W Galbraith, Geology Dept Head Univ of California-Berkeley, California-Mineral Technology Association H E Hawkes, Faculty Sponsor, Joseph A Pask, Dept Head Carnegie Inst. of Technology-Pittsburgh, Pa -The Metals Club William R Bitler, Faculty Sponsor, Robert F Mehl, Dept Head

Jan 1, 1960

Discussion of the paper of E: D. Gardner, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin No. 91, July, 1914, pp. 1467 to 1471. H. V. WINCHELL, Minneapolis, Minn.-There are two questions I should like to ask: First, does the Department still adhere to the decision made in the East Tintic case? Second, does the Department require placer ground to he of such value that, in the opinion of the Forest Service employees, it will pay to work, before admitting the location to be valid? T. C. HOYT,* Ogden, Utah.-With reference to the first question: the Department does not hold to that decision, as it was reconsidered by the Secretary Of the Interior, and the Department is governed by the decision of the Secretary Of the Interior, on those points always. The Department of Agriculture makes no decision as to what constitutes a sufficient discovery. The mineral examiners simply report their findings and Opinions. These are transmitted to the chief of the field division of the General Land Office, who in turn transmits the reports to the Commissioner Of the General Land Office, who decides whether the report raises an issue requiring a hearing. If a hearing is ordered, expert testimony is given on the question of the discovery, as well as the evidence of practical people who operate in the vicinity of the claim in question. As to the extent of placer values considered sufficient to justify a location, my answer will need a little amplification. I couldn't answer it directly for the reason that sometimes people resort to placer claim location as a means of acquiring land for Other purposes than placer mining, which makes it absolutely necessary that the government give close attention to the question of whether good faith has been shown, as it is the evidences of good faith that largely determine whether a report adverse to a claim shall be made. That is a difficult point to cover sometimes. For instance, in the region I have recently visited there are some 17 miles of a valley, from ¼ to ¾ mile in width, all covered by placer locations. It is valuable stock-grazing land, and is stocked at the present time. It also contains a stand of timber, and is on the watershed of an important stream-important from the fact that it furnishes the water supply to government storage reservoirs, and to pending reclamation and Carey Act projects. In this case the placer claims will not be disturbed as mere locations. They will simply remain there, and there will be no action with reference to them until the claimant asks for patent or, before patent, begins to denude that watershed and remove that timber. Then the government would direct that the mineral experts go on to the ground, examine it, prospect it, and submit their report, with a view to seeing if

Jan 11, 1914

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Opening for man as head of laboratory of large brass manufacturing plant in Ohio; must also be competent to manage foundry making brass castings, following practice of malleable iron castings and insulating materials. Good opportunity for right man. No. 36. Professorship in Mining at a Western university; requires man competent to give instruction in ore dressing, in metal and coal mining, and in zinc smelting, and capable of gaining confidence of mining interests. Salary $2,200 to $3,000. No. 37. ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of - the Institute by members or other persons introduced by members.) Member, graduate engineer, aged 44, with over 20 years' experience in connection with large coal and coke operations in different parts of the country, desires position as general superintendent of large coal company, or will take an interest with the management in a smaller company. No. 206.

Jan 6, 1915

By A. N. Rogers

Jan 1, 1883

By WILFRED SYKES

THE story of the rolling of strip steel is not limited to any one plant or individual or group of individuals. It is a story with many ramifications. First of all, it should be understood that the strip mills we are considering are continuous mills, in that the steel passes directly from one mill to the other in a more or less straight line. Continuous mills are not new; in fact, they have been used for many years in the rolling of a few simple shapes. They were, however, driven by one motor through jackshafts, and as a result the speed of each roll stand had a fixed relation to that of every other stand in the series. This in turn fixed the reduction that could be made in each stand. The mill could produce simple things, but was not satisfactory for the production of the variety of strip now required. It was, therefore, necessary to get away from the restrictions of that kind of drive. To accomplish this, the designer could either separate

Jan 1, 1936

J. L. CHRISTIE, Chairman T. S. FULLER, Past-chairman W. M. PEIRCE, Vice-chairman W. A. SCHEUCH, Vice-chairman E. M. WISE, Secretary International Nickel Co., Bayonne, N. J. W. M. CORSE, Treasurer Executive Committee H. A. BEDWORTH G. O. HIERS D. K. CRAMPTON R. H. LEACH E. H. DIX, JR. R. F. MEHL J. A. GANN J. WALTER SCOTT' JEROME STRAUSS Finance Committee T. S. FULLER, Chairman W. M. CORSE H. S. RAWDON C. H. MATHEWSON SAM TOUR

Jan 1, 1934

By George H. Deike

DURING the past year a survey was conducted by the Committee on the Promotion of Student Interest in Coal Mining to determine whether the program as laid down in past years was operating effectively. It is a source of satisfaction and pleasure to be able to report considerable headway among operating companies in putting cooperative scholarship plans into operation. In previous committee reports the pioneer work along this line by Eugene McAuliffe, president of the Union Pacific Coal Co., has been cited. That Company now has in its employ, in responsible positions, three men who received their education under such scholarship plans. One student under a similar plan is now studying at the Colorado School of Mines.

Jan 1, 1942

By C. W. Wark, Fred Wise

The Getchell mine, a comparatively recent gold discovery, is in the old Potosi mining district, Humboldt County, Nevada. All ore is mined from open pits using Diesel shovels and gasoline trucks. Two types of ore are mined, oxide and sulphide. Oxide ores are siliceous or shaly; sulphide ores either gougy, siliceous or shaly. In mining, the sulphide ore is segregated into hard and gougy ore, because the gouge must be dried before it can be crushed. The oxide ore is not segregated. General Metallurgy The oxide ore is the leached outcrop that overlies the sulphide ore body. All of the iron and arsenic sulphides found in the sulphide ores have been thoroughly oxidized. The sulphur and arsenic have been leached out while the iron is present as hematite and limonite. The oxide ore is amenable to direct cyanidation, and although no visible free gold is present it is released at a comparatively coarse grind. The sulphide ore is more refractory, since the gold is all of micron size and some of it is locked in fine sulphides. It has been established microscopically that the free gold is coated with an impervious shell, which is probably some form of iron compound. The sulphide ores contain from 1.5 to 2 per cent of arsenic, which is present as orpiment and realgar with minor amounts of arsenopyrite. The orpiment and realgar are of a later mineralization than the gold and are barren. Roasting and washing of the sulphide ore prior to cyanidation is necessary to eliminate , the arsenic, to alter the gold coating from an insoluble form to a soluble form, and to release the gold associated with the fine sulphides. Washing the ground calcine in weak sulphuric acid, trona, or hot water are beneficial in the order named, but to date the water is the best from an economic standpoint. Metallurgical tests as well as plant practice indicate that a certain amount of gold cannot be recovered even by going beyond economic practices. On this basis metallurgical results are viewed in the light of an optimum tailing rather than a percentage of extraction. Milling Practice Crushing (Fig. I).—There are three primary ore bins, one each for oxide ore, gougy sulphide ore, and hard sulphide ore. In front of each bin a substantial yard is maintained, which makes it possible to Stockpile 2500 tons of oxidized ore, 1000 tons of hard sulphide ore, and 1000 tons of gougy sulphide ore. The bins are fed by a 60-hp. caterpillar bulldozer from the stockpiles. Fig. I shows the method and

Jan 1, 1943

By Fred Wise, C. W. Wark

The Getchell mine, a comparatively recent gold discovery, is in the old Potosi mining district, Humboldt County, Nevada. All ore is mined from open pits using Diesel shovels and gasoline trucks. Two types of ore are mined, oxide and sulphide. Oxide ores are siliceous or shaly; sulphide ores either gougy, siliceous or shaly. In mining, the sulphide ore is segregated into hard and gougy ore, because the gouge must be dried before it can be crushed. The oxide ore is not segregated. General Metallurgy The oxide ore is the leached outcrop that overlies the sulphide ore body. All of the iron and arsenic sulphides found in the sulphide ores have been thoroughly oxidized. The sulphur and arsenic have been leached out while the iron is present as hematite and limonite. The oxide ore is amenable to direct cyanidation, and although no visible free gold is present it is released at a comparatively coarse grind. The sulphide ore is more refractory, since the gold is all of micron size and some of it is locked in fine sulphides. It has been established microscopically that the free gold is coated with an impervious shell, which is probably some form of iron compound. The sulphide ores contain from 1.5 to 2 per cent of arsenic, which is present as orpiment and realgar with minor amounts of arsenopyrite. The orpiment and realgar are of a later mineralization than the gold and are barren. Roasting and washing of the sulphide ore prior to cyanidation is necessary to eliminate , the arsenic, to alter the gold coating from an insoluble form to a soluble form, and to release the gold associated with the fine sulphides. Washing the ground calcine in weak sulphuric acid, trona, or hot water are beneficial in the order named, but to date the water is the best from an economic standpoint. Metallurgical tests as well as plant practice indicate that a certain amount of gold cannot be recovered even by going beyond economic practices. On this basis metallurgical results are viewed in the light of an optimum tailing rather than a percentage of extraction. Milling Practice Crushing (Fig. I).—There are three primary ore bins, one each for oxide ore, gougy sulphide ore, and hard sulphide ore. In front of each bin a substantial yard is maintained, which makes it possible to Stockpile 2500 tons of oxidized ore, 1000 tons of hard sulphide ore, and 1000 tons of gougy sulphide ore. The bins are fed by a 60-hp. caterpillar bulldozer from the stockpiles. Fig. I shows the method and

Jan 1, 1943

By Charles H. Fulton

IT is assumed that the word "college" for the present purpose signifies technical school or technical department of a college or university. About ten or fifteen years ago, and more recently in some instances the contact between the technical school and the industry, as represented by the operating companies, was very limited. The school made no effort to place its graduates in the industry and the graduate's first position was obtained by his own or his friends' efforts; the friend often was a professor. The industries, or the operating companies, seemingly had little interest in the training of the technical graduates they employed or in seeking to discover their personal characteristics and fitness for the work. In the public mind there was little relation between technical training and industry. Such training was in the field of education; industry was in the field of business; and the interrelationship was not a matter of common knowledge or concern.

Jan 1, 1929

By AIME AIME

AT FOUR O'CLOCK members gathered in the auditorium for the annual business meeting of the Institute which, according to its charter, must be held on the third Tuesday of February each year. President Turner presided and after the usual formal action on minutes announced that he would create a precedent by transferring the President's annual address (which by tradition has always been delivered at the banquet on Wednesday evening) to the business meeting, and, furthermore, would only present a brief abstract of it. Since it appears in full on pages 127-131 of this issue it can be followed with the careful attention its thoughtful analysis of current conditions deserves.

Jan 1, 1933

By V. A. Zanadvoroff

THE mine and concentrator of the Howe Sound Co., Chelan Division, are at Holden, in a remote section of the Cascade Mountains of northwestern Washington. Holden is at an elevation of 3200 ft., in the narrow valley of Railroad Creek. This creek drains into Lake Chelan, at a point some 40 miles up the lake from the town of Chelan. The concentrator treats 2000 to 2500 tons of low-grade copper-gold-zinc ore per day. Concentration is achieved by the differential flotation process, with recovery of 94 per cent copper and 82 per cent gold in the copper concentrate, followed by the recovery of 65 to 70 per cent zinc in the zinc flotation circuit. The final flotation tailing is deslimed, and coarse sands, representing 60 to 70 per cent of the total, are cyanided. The tonnage of tailing material amounts to 1900 to 2370 tons per day. GENERAL CONSIDERATIONS The property is within the Chelan National Forest. Railroad Creek is a fishing stream, being stocked regularly with trout from State hatcheries. Consequently, in planning a milling operation, the Howe Sound Co. was obliged to avoid any pollution of the stream by tailing material, and also destruction of valuable stands of timber. Moreover, the selected tailing disposal sites should not mar the natural beauty of the valley. In addition to these requirements, the problem of tailing disposal at Holden was complicated by topography and climatic conditions. The valley is long and narrow, averaging 1200 to 1500 ft. in width. Its walls are flaring at a steep angle. There are no extensive flat areas suitable for deposition of tailing. All valleys tributary to Railroad Creek, also the well-marked paths of snowslides, must be avoided. Finally, the direction of prevailing winds and possible dust hazard arising therefrom dictated the necessity of selecting the tailing-disposal sites downstream from the mill building and two campsites. Heavy snowfall during the winter months of November to March, inclusive, impedes building of the retaining dike, making it necessary to prepare the needed storage space during the summer months. It is inadvisable, also, to do any dike building during the freezing weather, because the dike becomes unstable with the spring thaws, producing inevitable "sloughing" of the built-up borders. TAILING-DISPOSAL SITES The existing tailing-disposal areas are near the south wall of the valley. They were developed, and put to use in the following sequence: No. I. Area.-Covers approximately 10 acres. Built up to the height of 60 ft.

Jan 1, 1946

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