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By D. W. Fuerstenau

On page 1243, column 1, the first line of the author's reply should read "D. W. Fuerstenau (author's reply)---," rather than D. E., as printed. In the sentence immediately preceding the first equation (page 1243, column 2)' the word "none" was omitted. The sentence should read: "However, if enough ore is put into the mill [so] that none of the energy put into the mill is wasted on metal-to-metal impact, then the product should have size modulus determined by the relation: ..."

Jan 1, 1961

Jan 1, 1915

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Mining Engineer. Graduate of Colorado School of Mines, 1912, experienced in coal, lead manganese and limestone mining, wishes execu¬tive position. A-2146. Graduate Mining Engineer.-Discharged, reserve officer, age 32, single, 7 years' experience holding responsible executive positions, in iron, copper, and talc mining. Well recommended. A-4913. Mine Manager, Superintendent or Engineer. Age 41, graduate of Michigan College of Mines; 20 years' experience in responsible positions in connection with large operations; in iron, copper, pyrites, lead and zinc mines; successful in finding and developing orebodies, increasing production, and reducing costs. Desires a position with a future. A-4081. Mining Engineer.-Graduate from Polytechnicum, Stockholm; 14 years' practical experience in Sweden, United States, Belgium, and Spain, in iron-ore development, mining, and milling; thorough knowledge of English, French and Spanish; desires position as superintendent or assistant manager. Good references; member; now in Sweden. A-4914. Research Engineer. Now in Chile on the erection of a 50-ton mill with modern machinery for the treatment of Chilean nitrate. Desires connection from the first of next year; with firm operating in South or Central America. A-4915. Metallurgical Engineer. Junior member, age 26, single, graduate Columbia School of Mines; recently discharged as lieutenant in the heavy artillery. A-4916. General Superintendent. Technical graduate, age 35, desires position over a group of four or five mines or as assistant general superintendent for a large. company. Has had experience in superintending mines, construction work, opening new and abandoned mines, safety and effi-ciency engineering and handling organized labor. At present employed by a coal company in the middle West. A-4917.

Jan 11, 1919

By John Branner

FIVE of the geologic horizons that yield oil in other parts of the world are represented in Brazil; namely, the Devonian, Carboniferous, Permian, Cretaceous, and Tertiary. Thus far, the first two have shown no, evidences of being oil bearing within Brazilian territory. Not enough exploring has been done to permit trustworthy comparisons of the relative importance of the Permian, Cretaceous, and Tertiary as oil-bearing horizons in this country. The most important, indeed almost the only, information available relates to the locations of the areas and to the structural features of the several horizons. The theories regarding the physical conditions under which these rocks were laid down, however, I regard of the utmost importance. PERMIAN Rocks of Permian age cover an enormous area in Brazil, extending from Rio Grande do Sul to Maranhão on the north, and to Matto Grosso on the west. These Permian rocks in many places are known to include oil-bearing shales and in some locations contain small veins of gilsonite. The geologic map of Brazil shows that the Permian area is widely distributed, but there is considerable doubt about 'the origin of some of the rocks:. Some of the lower Permian beds in southern Brazil contain marine fossils, but in Minas no fossils have as yet been found in them, and in Bahia, at only one locality have a few Permian plants been found. Indications of oil have been found in the states of São-Paulo, Paraná, and elsewhere farther south, but wells drilled in the Permian of São Paulo near the Morro do Bofete did not find oil. One well has been started, by the Brazilian government, in the Permian of Paraná near Marechal Mallet, close to latitude 26° south, but thus far oil has not been found.

Jan 6, 1922

By R. M. Howe, J. Spotts McDowell

Preparation and Use.—Magnesite is an important refractory in open-hearth, heating, and electric furnaces for steel-making and in many of those employed in the metallurgy of copper and lead. It is sold in the form of brick, finely ground "furnace magnesite" for bricklaying, and dead-burned grains for making and repairing furnace bottoms. The latter are a mixture of granules varying in size from pieces of about 5/8 in. (1.6 cm.) diameter to very fine but sandy particles. Dead-burned magnesite results from calcining the crude or lightly burned mineral at a temperaturc that will not merely drive off practically all the CO2, but will also cause sintering of the particles. During this process the pieces shrink considerably and become hard, dense, and inert to atmospheric moisture and CO2; under-burned material, on the other hand, will hydrate on exposure to the air. A small percentage of ferric oxide seems to be necessary for the production of a satisfactory sinter; from 4.5 to 8 per cent. in the dead-burned grains is considered the most desirable amount. Dolomite has been little used for brickmaking in the United States, but it is prepared for use in the granular condition calcined or "double-burned" and is the principal ingredient of several materials offered for sale under various trade names for refractory purposes. Dolomitic refractories are almost wholly confined to the open-hearth and electric furnaces, where they are used for fettling and as substitutes for magnesite. Much more magnesite and dolomite are used for basic open-hearth steel-making than for all other refractory purposes. The hearth of the furnace is usually built up of magnesite brick and dead-burned grain magnesite so laid that the brick base is protected by a working bottom of the granular material. The latter is sintered into place in layers 1/2 to 1 in: (1.25 to 2.5 cm.) thick to a total depth of 12 to 18 in. (30 to 45 cm.) at the center of the furnace. After each heat, burned dolomite is thrown against the banks as high as it will stick, and all holes in the bottom are Glled. At most plants such holes, at the end of each week, are also carefully filled with dead-burned grain magnesite. For temporary

Jan 1, 1920

Jan 1, 1966

By W. M. Albrecht, W. D. Klopp, R. I. Jaffee, B. G. Koehl

Kinetic studies were made of the reactions of tantalum with oxygen, nitrogen, and air at 400o to 1500°C. The tantalum-oxygen reaction is linear from 500° to 1250°C. The tantalum-nitrogen reaction follows a cubic rate law at 400° to 700°C and a parabolic rate law at 800" to 1475°C. The reaction behavior in air is initially parabolic followed by a transition to linear behavior. In the search for high-temperature materials, considerable interest is being shown in the refractory metal, tantalum. It is the third highest melting metal with a melting point of 2996°C. Also, tantalum has excellent ductility, making it one of the most workable refractory metals. In considering high-temperature applications of tantalum, the oxidation kinetics of the metal must be known. Such information also serves as a basis for the development of corrosion resistant tantalum-base alloys. Therefore, this study was made to investigate the reaction of tantalum with air, nitrogen, and oxygen. LITERATURE Several oxides of tantalum have been reported. The pentoxide, Taz05, is the only oxide of tantalum whose identity has been established. A high-temperature modification, aTa2Os, has been reported by several investigators.1-4 A low-temperature phase, ßTa2O5, undergoes an allotropic transformation at 1320o to 1350oC. 5-8 Four other oxides of tantalum have been reported. The oxides TaO2, TaO, and Ta4O have been reported by schonberg.9 A suboxide Ta2O, was observed by Wasilewski 6. However, the presence of oxides lower than Ta2O5 is questioned by Lagergren and Magneli.7 In oxidation studies, vermilyeal0 and Peterson, et al.,12 reported one possible phase intermediate between Ta and Ta2O5. Only Ta2O5 was formed in the tantalum air reaction, as reported by Michae1.l3 Several studies have been made on the kinetics of the tantalum-oxygen reaction. vermilyeal4 investigated the range 50° to 300°C and found that the rate of growth of a thin adherent oxide film could be described by the Cabrera-Mott theory. Gulbransen and Andrew15,18 studied the reaction kinetics of tantalum in oxygen pressure of 1/10 atm at 250° to 450°C. At all temperatures the reaction followed the parabolic rate law for periods up to two hours. The oxidation behavior in the range 500" to 1000°C was found to be linear at oxygen pressures of 0.2 to 600 psi according to Peterson. et al.l1 At very low pressures (1 x 10-3 to 2 X lo-' mm of Hg) Gebhardt and seghezzi17 reported linear oxidation at 800° to 1500°C. The reaction of tantalum with air is similar to the reaction with oxygen. Studies have been made by Waber, et a1.,12 and Michae1.l3 Two nitrides of tantalum, TaN and Ta2N are known. Their structures have been determined by Brauer and Zapp 18,19 The tantalum-nitrogen reaction kinetics have been investigated by Gulbransen and Andrews. 15, 16 The reaction follows the parabolic rate law at 500° to 850°C at a nitrogen pressure of 1/10 ,atm. At the same temperature, the tantalum-nitrogen reaction is much slower than the tantalum-oxygen reaction. EXPERIMENTAL TECHNIQUES Material— The material used in this study was high-purity, electron-beam-melted tantalum obtained from the Temescal Metallurgical Corp. The hardness of the as received ingot was 76 Vhn. The analysis of the material is given in Table I. Methods—Cylindrical specimens of tantalum approximately 0.9 cm in diam and 0.5 cm in length

Jan 1, 1962

By Milton T. Pana

Computer techniques now have been applied to the solution of a wide variety of scientific and engineering problems in the mining industry, but generally not in great depth in any one area. In mining, the area covered in greatest depth and with the greatest success has probably been mine planning and to a lesser degree production scheduling. A rather comprehensive review of the literature related to mine planning and production scheduling indicates that contributions in these areas have been geographically, as well as organizationally, widespread. Of twenty-six papers reviewed, eleven were from industry, eight from educational institutions, four from computer vendors, two from the Bureau of Mines, and one from a private consultant. The conclusions that can be derived from the literature are: First, the-state-of-the art has advanced to the point that computing ore reserves and developing mining plans with the aid of the computer is now a routine practice; second, the application of the computer to mine planning problems has markedly improved our ability to estimate ore reserves, more accurately define pit limits, and determine an optimum mining sequence. MINE PLANNING The papers in this section deal essentially with the problem of determining the final pit limits of an orebody and the ore reserves associated with a given pit limit. The problem is probably best described by Soderberg25 and more recently by Reibell. 23. There are two techniques currently being applied to this problem by several mining companies: 1) the multiple-cone technique and 2) the Lerch-Grossman algorithm. The multiple-cone technique is the older of the two techniques and has the advantage of being more flexible, allowing an engineer to easily vary pit slopes in different sectors of the design. The technique can also be used to define intermediate pit contours. The Lerch-Grossman algorithm is appealing in that the final solution is given in the form of a true mathematical optimum. The technique is limited, however, in that the size of the blocks in the orebody model are a function of the desired

Jan 1, 1969

By P. Barnes

THE sums given in the accompanying table are those actually paid for material and labor up to about August, 1875; but, as some parts of the machinery were not wholly completed at the starting of the works in September, 1875, the statement cannot be taken as an absolutely correct note of the total cost. A complete description, with engravings of the building and machinery, was given in Engineering, April 26th, 1878, in a paper by Messrs. A. L. Holley and Lenox Smith, to which convenient reference may be made. A detailed list of the construction accounts has been given in a paper, by the present writer, in vol. vi, Transactions of the Institute. A summary is given in the table of the items in each class which enter into the total cost, and also a note of the proportion which each of these items forms of the whole. A concise view may thus be obtained of the facts embodied in the statement, as a whole, even though it cannot lay claim to completeness in showing the entire or final cost. An urgent suggestion has reached the writer from a distant country that such statements of cost to be really most serviceable should give the details in days of labor, in weight of iron, and in number of brick, and to this an assent is most cordially yielded. It is true, however, that the mere labor of copying and compiling these details to such a degree of minuteness, would be very great, and, in any event, the probable difference between the plans of an existing establishment and one projected, would be so wide as to render even so complete a statement of cost of little more real service than the approximate notes given herewith.

Jan 1, 1879

By G. Howell Clevenger, Bhupendranath Ray

Formerly great divergence of opinion existed in regard to the influence of copper in steel, as affecting its various physical properties. More recently the investigations of Stead,l Breuil,2 Wigham,3 Burgess and Aston: Ball and Wingham,5 Miiller; Dillner,7 and others have shown fairly good agreement in the major points. Copper steel has been shown by these investigators to possess special properties which make it valuable for certain uses. The general range of composition of the useful alloys of copper and iron, and of copper, iron, and carbon, has been quite definitely established, for the former by Burgess and Aston,8 and for the latter by Breuil9 and Stead.10 Stead11 has removed one difficulty in reconciling certain of the earlier data by calling particular attention to the influence 'of carbon in copper steels. Another point which caused confusion in the earlier investigations, particularly in regard to " red-shortness," was the presence of sulphur. Failure to note the presence of sulphur often led to attributing " red-shortness" to the presence of small amounts of copper. Turner12 has called attention to the fact that where copper exists in an iron ore it often occurs as the sulphide, so that the presence of copper in steel made from such ores might also, necessarily, mean the presence of sulphur. It is evident that the effect in this case might be quite different than where pure copper was added.

Jan 1, 1914

CHICAGO SECTION CHARLES H. MACDOWELL, Chairman, LUTHER V. RICE, Vice-chairman, HENRY W. NICHOLS, Secretary-Treasurer, Field Museum of Natural History, Chicago, Ill. ALEXANDER K. HAMILTON, G. P. HULST, HENRY P. HOWLAND, FREDERICK T. SNYDER. A meeting of the Chicago Section was held at the Chicago Engineers' Club on the evening of March 30, 1918, on the occasion of the visit of the President, Vice-president. and Secretary of the Institute. The meeting was called to order by Henry W. Nichols, Secretary of the Chicago Section. The first speaker of the evening was Mr. Allen, Deputy Fuel Administrator for the State: of Illinois, who spoke on the problems and difficulties encountered by the Fuel Administration during the past -winter, He paid high tribute to the spirit of cooperation shown by the

Jan 5, 1918

By Earl Bardwell

THE determination of suitable and safe annealing temperatures is one of the most important problems arising in the operation of a copper rolling mill. Certain of the larger mills have worked this problem out for themselves and in these mills the operation has become more or less standardized. In some of the mills pyrometers are used to measure the temperature of the annealing furnaces and careful watch is kept to see that overheating does not take place. In a considerable number of the mills, however, dependence is placed entirely on the judgment of the operator. The almost total lack of literature bearing on this subject seems sufficient warrant for the publication of this paper. The discussion of this subject naturally divides itself into two parts: (1) The effect of annealing temperature on physical properties; and (2) changes in the microstructure of refined copper due to cold rolling and annealing. I. THE EFFECT OF ANNEALING TEMPERATURE ON PHYSICAL PROPERTIES For the purpose of investigating this phase of the subject six test bars were selected, varying in oxygen content between the limits of 0.036 and 0.070 per cent. The chemical composition of each of these test bars was as follows:

Jan 8, 1914

THOSE NOT MARKED ARE MEMBERS; MARKED THUS t ARE ASSOCIATES. HEAVY-FACED TYPE SIGNIFIES HONORARY MEMBERSHIP. JUNIOR MEMBERS ARE MARKED II. THE FIGURES AT THE END OF THE ADDRESS INDICATE THE YEAR OF ELECTION. AARONS, J. BOYD, Genl. Mgr., Chaffers G. M. Co., Boulder City, West. Australia. '05 ABADIE, EMILE R., Min. Engr Box 291, Porterville, Tulare Co., Cal. '76 ABBOTT, CLARENCE E., Genl. Supt., Iron Mines Div., 1405 Minnesota Ave., Bessemer, Ala. '04 ABBOTT, J. W., Min. Engr., "St. Omer," 123 N. Grand Ave., Los Angeles, Cal. '94 ABBOTT, Louis BENJAMIN, Chief Engr., Consolidation Coal Co., Elkhorn Div., Jenkins, Ky. '15 ABBOTT, ROBERT R., Met. Engr., Peerless Motor Car Co., Cleveland, Ohio. '12 ABE, ASAKA Yamagano G. M., Satsuma-Gori, Satsuma, Japan. '14 || ABRAHAMS, A. I., Student 1391 Madison Ave., New York, N. Y. '14 tACKER, E. O'C., Met Bethlehem Steel Co., Bethlehem, Pa. '86 ACKER, Louis K., JR., Min. Engr 565 Highland Place, Bellevue, Pa. '08 ADACHI, JINZOO 11 Shiba Park, Shiba-ku, Tokyo, Japan. '88 ADAMI, C. J., Min. Engr., St. Joseph and Doe Run Lead Companies, Bonne Terre, Mo. '12

Jan 1, 1917

By R. F. Mehl, C. S. Barrett, A. G. Guy

INTRODUCTION IN the last few years this laboratory has published a series of papers on the mecha¬nism of age -hardening.14,1,6,11,20 Briefly stated it has been proposed that hardening is caused by lattice strains created by lat¬tice coherency between matrix and precipi¬tate; much experimental evidence has been advanced to support this thesis. The system Cu-Be is an attractive one to study. It is a system that exhibits marked age hardening; it ought to be subject to the type of analysis of structural changes hitherto explored and it is a prominent example of "discontinuous precipitation," which, though studied in other cases, 6,20 remains largely unexplained. This research shows that hardening in the Cu-Be system proceeds essentially as proposed earlier.14 Guinier-Preston zones have been observed to form on the {100) planes of the matrix; no transition lattice was found. Aging and overaging were ob¬served to occur most rapidly in the region of discontinuous precipitation-the grain boundary-apparently accelerated there by strain. The Constitution of the Cu-Be System The Cu-Be constitution diagram is shown in Fig I. The structure of the ? phase was determined by Misch16 as of the caesium-chloride type with a lattice con¬stant of 2.598 Å High temperature X ray photograms of 7.2 pct Be alloy made by Kossolapow and Trapesnikow13 led them to conclude that the structure of the P phase is simply disordered body-centered cubic with [ao] = 2.79 Å at 750°C. Previous Work The initial work on the age-hardening of Cu-Be alloys was that of Masing, Dahl, Holm, and Haase. Their numerous papers were published in book form in 1929, sub¬sequently translated.18 The effects of Be content, solution temperature, aging tem¬perature, and cold work on the hardness developed in these alloys were studied. An initial decrease in the electrical conduc¬tivity was observed when strips of a 2.5 pct Be alloy were aged at temperatures from 200 to 350°C; a wire of the same analysis failed to exhibit this decrease when aged at 350°C. A volume decrease of 0.6 pct oc¬curred during aging at 250°C. Microscopic investigations of quenched and aged alloys disclosed a regularly ori¬ented "striping" (ripples) on the a and on the ß grains. In the case of the ß the cause of the striping was held to be decomposition

Jan 1, 1948

By J. A. Fellows, Earnshaw Cook, H. S. Avery

THE increased use of heat-resistant alloys (26 per cent Cr, 12 per cent Ni; 16 per cent Cr, 35 per cent Ni; 12 per cent Cr, 60 per cent Ni; etc.) in recent years has been accompanied by continued demands by the consumer for improvement in properties. The manufacturers of these materials, of necessity, have resorted to more critical studies of the basic causes of variations in fundamental properties. To keep pace with the need for augmented information, previous techniques of investigation have been refined and new test methods and instruments created. It is the purpose of this paper to describe the apparatus, experimental technique and precision of measurement that were employed in the exploration of properties of heat-resistant alloy presented in a companion paper.? The detailed precautions in experimental procedure essential for attainment of accurate and comparable data at elevated temperatures cannot be too highly emphasized. THE CREEP TEST Since the fundamental concepts of creep testing have been recognized for the past 20 years, present interest is restricted to refinements in equipment and experimental procedure. The creep-test laboratory constructed for the American Brake Shoe and Foundry Co. is designed to permit 1000-hr. tests in the temperature range of 1200° to 2200°F. with a choice of applied stress extending from 50 to 50,000 lb. per sq. in. in increments of 50 lb. per sq. in. To simplify the calculation of weight combinations, the loading beams (Fig. I) are provided with counterweights to eliminate the tare. The precision of the knife-edges (10.1 ratio) is such that a 10-gram weight placed on the upper specimen grip will be exactly balanced by a 1-gram weight attached to the loading shackle. Check of the loading weights proved the maximum error to be 0.06 per cent. Axial alignment is provided by crossed knife-edges in the grip seats. The furnaces are similar in design to those of Crane and Company, Battelle Memorial Institute, and the U.S. Steel Corporation. An 80 per cent Pt, 20 per cent Rh No. 19 B. and S. gauge wire is used as the heating element. The details of construction are shown in the radiograph reproduced in Fig. 2. The windings are held in place on an alundum tube with alundum cement; the distribution of turns is adjusted to give a maximum temperature gradient of ± 1°F. over a 4-in. gauge length (Fig. 3). To avoid sharp temperature differentials at the ends of the test section, the length of the furnace is four times the gauge length. Sixteen-inch coupons are used to reduce the temperature of the threaded

Jan 1, 1942

By Charles Will Wright

The application of the camera as an adjunct to topographic mapping began practically with its invention, and it has been employed with varying success since that time. With the exception of the camera to be described, the plate-camera has been universally used in this work, thus giving a projection of the area photographed on a flat surface. From such projections or photographs, by the rules of geometry and of perspective, points defining topographic features and seen from at least two camera-stations may be projected upon a ground-plane—the map.' In 1904 I employed the plate-camera for this purpose in Alaska, but found that the labor necessary to plot the maps, even in a general way, was long and tedious. In 1905 a small Eastman panoramic camera was fitted with spirit-levels, a sight-alidade and a transparent scale, introduced inside the camera to register the degree-points in the sky-line of the film-negative ; also, arrows to indicate the horizon-line. This was, on the whole, successful; but the details in the topography were not brought out in the views with sufficient clearness, aid the photographs were too small. These difficulties were overcome by obtaining a larger and more carefully constructed instrument, which was satisfactorily employed in the field during the year 1906. A panoramic view is made up of an integral number of perspective views upon flat surfaces, and logically is the most accurate and direct means to obtain an impression of a field of * Published by permission of the Director of the U. S. Geological Survey. Stanley, H. M. Photographic and Co-ordinate Surveying, Bans., xx., 740 to 766 (1891). Also, Flemer, J. ,4. Phototopographic Methods and Instruments, Report U. 8. Coast and Geodetic Survey, pt. 2, app. 10, pp. 619 to 735 (1897).

Jan 1, 1908

By Claus G. Goetzel

SOME of the reactions and procedures upon which modern techniques in the production of metal powders are based were used for 2000 years by the ancients to reduce iron and other metals from their ores. Despite this, however, the art of powder metallurgy is relatively new and probably stems from the introduction of incandescent electric lamp filaments. Attempts to improve upon Edison's carbon filaments led to the production, in order. of metallic filaments of osmium. tantalum.. and finally of tungsten, which ha, replaced the others and is the commercial product of today. These metallic filaments were originally manufactured by the extrusion and sintering of a mixture of the metal or its oxide with a reducing agent which also served as a binder. Further progress in this direction was in the pressing of a small percentage of nickel with the tungsten. The sintering operation was carried out in an atmosphere of hydrogen, at a tem-

Jan 1, 1944

By AIME AIME

Adjustable Pyrometer-Stand. By L. W. BAHNEY, xxxvii, 33. Agency of Manganese in the Superficial Alteration and Secondary Enrichment of Gold-Deposits in the United States. By WILLIAM H. EMMONS, xlvi, 767. Application of Descriptive Geometry to Mining-Problems. By JOSEPH W. ROE, xxxix, 173. ARNOLD, C. EVERARD. The Giroux Shaft at Kimberly, Nev., xlii, 461. BAHNEY, L. W. An Adjustable Pyrometer-Stand, xxxvii, 33. BALL, SYDNEY H., and SHALER, MILLARD K. Mining-Conditions in the Belgian Congo, xxxix, 253. BEALS, ROGER L., and TWEEDY, GEORGE A. Cyanide-Plant and Practice at the Minas del Tajo, Rosario, Sinaloa, Mexico, xxxviii, 123.

Dec 1, 1910

By R. Ehrlich, F. E. Crane

A consolidated porous medium is mathematically modeled by networks of irregularly shaped, interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached. 1. Relative permeability at a given saturation is everywhere independent of flow rate. 2. Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting-phase relative permeability. 3. Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity. 4. lrreducible wetting-phase saturation following unsteady-state drainage is lower than fir steady-state drainage. 5. Irreducible nonwetting-phase saturation 101lowing imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualithtiveIy verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. INTRODUCTION Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting liquid by a gas. 1-5 It has long been recognized that relative permeability depends not only on saturation but also on saturation history as we11.6,7 Naar and Henderson8 described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt9 proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and slobod,10 Rose and Witherspoon,11 and Rose and Cleary12 each considered flow in a pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. They limited

Jan 1, 1970