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By William Alden

A GREAT landslide occurred on June 23, 1925, in the valley of Gros Ventre River, about 35 miles south of Yellowstone National Park (Fig. 1). The relations of the north-easterly dipping rock formations of the slide scarp and of the dam formed by the slide are shown in the diagrammatic cross-section of the valley (Fig. 2). This generalized section is based on unpublished maps and notes by Eliot Blackwelder, in the files of the U. S. Geological Survey. FIG. 1.-MAP SHOWING SCARP AND DAM (LARGE DOTS) AND LAKE (CROSS-LINED) FORMED BY LANDSLIDE BLOCKING GROS VENTRE RIVER. (Scale 1, in. = 1 mile; contour interval 100 ft. From Grand Teton and Mt. Leidy topographic maps). Heavy rains and melting snow in the Gros Ventre Mountains had saturated clay layers in the Carboniferous strata, which dip toward the valley at angles of 18° to 21°, consequently an enormous mass of rock at the end of the north spur of Sheep Mountain became loosened and, on the afternoon of June 23, slid suddenly down into the valley. Within a few minutes this mass of debris-estimated as 50,000,000 cu. yd.-carrying

Jan 1, 1928

By B. Ehgartner, M. Karmis, C. Haycocks

INTRODUCTION Interaction effects between mining operations developed on different levels of contiguously placed bedded deposits are a major problem in many parts of the United States. Efficient design criteria, derived from careful analysis of field studies as well as theoretical and model analysis, have shown that many problems that may result from seam interaction can be avoided, minimized, or on occasion used with beneficial results. Selection of seam mining sequence is rarely based only on ground control considerations, but rather on factors such as seam ownership, characteristics and accessibility. Therefore all possible mining sequences and methods must be considered in the development of multi-seam design criteria. Increased utilization of the longwall method of mining creates special problems in multi-seam mining due to the inevitability of caving and, therefore, subsidence. Considerable valuable experience has been gained in this direction from British mining operations where interaction problems are extremely common and the longwall method is the primary method used. However, limitations persist in the application of much of this information to U.S. conditions due to variation in layouts between advancing and retreating longwall systems and the inherent difference in the geologic environment. Considerable field data is available for U.S. room and pillar operations, and where successful pillaring operations have been carried out close parallels may be drawn with ground control mechanisms in longwall operations. VARIABLES AFFECTING INTERACTION Analysis of ground control multi-seam problems shows that factors contributing to interaction may be classified into variables that are fixed by the geo- logic environment and those that depend on engineering design. These may be described as follows (Haycocks et al, 1982): Fixed: (i) Depth*, (ii) Innerburden thickness*, (iii) Innerburden physical characteristics*, (iv) Stress field, (v) Seam thickness, (vi) Coal characteristics, (vii) Completed mining operations either above or below the seam to ve mined, and (viii) Age of workings. Mining: (i) Height, (ii) Dimensions and geometry*, (iii) Method*, and (iv) Spatial location of entries* *These variables are regarded as being critical effects. Few attempts have been made to quantify the variables controlling interaction. Dunham's (1978) linear regression analysis, combined with the National Coal Board's MRDE Roadway Monogram, is probably the most noteworthy. This study involved eighteen multi- seam longwall mines in the United Kingdom. The following variables were taken into account: seam depth, pillar width, opening shape, floor and roof conditions, rate of face advance, vertical seam interval, and age and geometry of overlying workings. A multi-linear regression analysis of these variables fitted by appropriate field values developed a prediction equation for lower seam stability. Although the study included many variables, it neglected the nature or geology of the innerburden. The prediction equation was found unreliable, but it did show the significance of geometry as a factor controlling lower seam stability. MINING SEQUENCES Irrespective of the type of mining method selected only four possible mining sequences are possible for two seams. Finlay and Winstanley wrote in 1934. .. "Experience has shown that whether the upper or lower seam was worked first, the subsequent working of the other seam in the same area seriously affected the roads in the seam first worked." Those effects depended upon the four basic mining sequences: 1) The upper seam is mined out prior to mining the underlying seam; i.e., the seams are mined sequentially downward and mining of the underlying seam is not commenced until operations above are completed and have ceased.

Jan 1, 1982

Jan 1, 1913

By J. H. Bain, D. C. Haigh, L. C. Parsons

Jan 1, 1964

By O. M. McRae

The Courtland-Gleeson area is in Cochise County about 15 miles east of Tombstone in southeastern Arizona. Rocks exposed in the area range in age from Pre-cambrian to Quaternary. The Precambrian is repre-sented by the Pinal schist. Paleozoic rocks include the Cambrian Bolsa quartzite and Abrigo limestone, Mississippian Escabrosa limestone, and the Permo-Carboniferous Naco Group limestones. Rocks believed to be of Triassic and/or Jurassic age include the Copper Belle monzonite porphyry, Turquoise granite, and Gleeson quartz monzonite. The Cretaceous is represented by andesitic volcanics and various sedimentary rocks. Tertiary rocks include the intrusive and extrusive Sugarloaf quartz latite porphyry and numerous dikes of various rock types. Quaternary conglomerates cover the northern and eastern part of the area. The geologic structure is extremely complex. All rocks as old as early Tertiary have been involved in either tilting, normal faulting, high angle reverse faulting, imbricate thrusting or folding and overfold-ing. Major deformation was initiated during the first half of the Tertiary. Northeast-southwest compres-sional forces caused thrust plates containing lower Paleozoic rocks to override Cretaceous rocks. Subsequently, two large slide blocks of lower Paleozoic rocks, acting under the influence of gravity, moved eastward. The imbricate structure and the gravity slide blocks were then broken by late Tertiary normal faults. INTRODUCTION The Courtland-Gleeson area, or Turquoise Mining District, has long been recognized as an area of extreme structural complexity. Gilluly 2 referred to the entire district as a "gigantic thrust breccia". In 1962, Bear Creek Mining Company completed a two year program of detailed geologic mapping supported by exploration drilling. The purpose of this paper is to present some of the results of this investigation and to provide a structural interpretation based on these results. The geologic map that accompanies this report is generalized and shows only the major and significant features. The area was initially mapped on aerial photographs on a scale of 1 in. equals approximately 500 ft. These data were transferred to a planimetric base using a vertical sketch master. LOCATION The Courtland-Gleeson area is in central Cochise County, about fifteen miles east of Tombstone, and about twenty-two miles northeast of Bisbee in southeastern Arizona (Fig. 1). The area is readily accessible over graded gravel roads from both Tombstone and Elfrida. GENERAL GEOLOGY Rocks exposed in the area range in age from Pre-cambrian to Quaternary. wilson3 and Gilluly2 have published very detailed descriptions of the principal rock units exposed in the area. Only a summary description is provided in Table I. A great number of previously unmapped narrow Tertiary dikes and small irregular masses of hornblende andesite porphyry, lamprophyre, and aplite intrude the Gleeson quartz monzonite in the western part of the map area. The scale of the map prohibits showing them. The aplite dikes are related to, and bear the same structural relationships as, the Sugarloaf quartz latite dikes found in this area. For that reason, and because both the hornblende andesite porphyry and the lamprophyre are post-mineral and post-thrusting, their omission from the map is not considered significant. Because so many of the contacts in the district are fault contacts, because bedding faults appear to be prevalent but are difficult to recognize and map, and because igneous intrusions are so common throughout the sedimentary section, it is virtually impossible to measure an exact total thickness of any of the sedimentary rock units. Nevertheless, neither the field mapping program nor the diamond drilling provided any basis for suspecting that the thicknesses of the sedimentary units are significantly greater or less than what might be inferred from surrounding districts.

Jan 1, 1967

By Earl R. McMillan

Though much has been written during the past several years about the Russian success in using hydraulic jets for coal mining, little or none of the published information, in so far as this writer has observed, has been of any use or practical application in this country. It is true, according to their published reports, that the Russians were pioneers in the use of high-pressure water jets in the mining of coal. They report the use of water jets for this purpose as early as 1936. However, according to a survey of foreign literature on the subject made by the U.S. Bureau of Mines1 a few years ago, water jets in the USSR, as well as in other nations including New Zealand, Poland and West Germany, were used principally to sluice the loosened coal after it had been previously drilled and blasted, rather than to cut or break it from the solid face. The interest of the Northern Pacific in the potential application of a high-pressure water jet to the actual extraction of coal, particularly in steeply dipping beds, originated in a visit by this author to the operations of the American Gilsonite Co. at Bonanza, Utah, in March 1958. After seeing the extraction, on a commercial basis, of gilsonite from a 22-ft wide vertical vein of this solid material with a 3/8-in. diam stream of water under approximately 2200 psi, it was felt that, with some modifications, water jets were the solution to the problem of economically mining the steeply dipping (i.e., steeper than 20º) coal beds in the State of Washington.

Jan 6, 1962

By S. Grinsfelder

Although wildcatting was hampered by the general overproduction and low price of crude, several developments, worthy of note in the history of the petroleum industry in the Rocky Mountain region, were made in 1927. This district records production from six new fields, two of these having been heretofore productive of gas. Deeper pay horizons were found in two other oil fields. In order to facilitate transportation from fields, six new oil pipe lines were completed or in the course of construction at the end of the year, and one line is proposed for 1928. Four gas lines were completed, one was under construction, and one was proposed for 1928. The total production in 1927 in the Rocky Mountain district was 29,591,379 bbl.,' a decrease of 7,771,991 bbl., or 21 per cent., fro111 the previous year. This was occasioned by natural decline and the general curtailment of production and drilling. A review of the development by states follows. Colorado Production from horizons in the Morrison and Sundance at Craig and at Ilrs Dome, and the bringing in of the deepest producing well in the Rocky Mountain district on North McCalluin anticline (Waltlrn) in Jackson County are the outstanding developments for the year in Colorado. In March the Midwest Refining Co.'s Parkinson 21 SD, SW SE, Sec. 22 T p. 4 N R 92 W, Iles Domr, Moffat County Colorado, found gas in sands in the Morrison estimated at 15,000,000 cu. ft., and at 3242 ft. an oil sand was encountered in the Sundance. Initial production from this horizon was 2575 bbl. in this well. This structure previously was only productive of water in the sands of the Dakota group but has been producing shale oil from horizons in the Benton. The second well completed by the Midwest Refining Co., No. 18 SD in Sec. 23 was also productive of gas in the Morrison and made an initial of 300 bbl. from sands in the Sundance. By the end of the year three other wells wrrc nearing the completion stage but none of them indicate that they will be as big producers as the discovery. To date the productive area has

Jan 1, 1928

By W. E. Crawford

The Fresnillo Company's mill at Fresnillo, State of Zacatecas, Mexico, treats oxide ores from the Fresnillo mine, dump ores and underground ores from the Plateros district, company leases and custom ores from the Zacatecas district, custom ores from other districts and tailings from old dumps at Fresnillo. The normal capacity of the mill is approximately 2600 dry short tons per 24 hours (a ton of 2000 lb.). The final product of the mill is a precipitate containing gold and silver, which is smelted and shipped as doré bullion to the refinery of the Compania Minera de Penoles, S.A., at Monterrey, State of Nuevo Leon, Mexico. The geology of the district was described in 1923, by T. C. Baker,' from whose paper the following data have been taken: The mineralization of the district was effected in the Tertiary period, following the intrusions and preceding the appearance of the flows. The area within which productive veins have been found is 1 mile long by 1/2 mile wide. The important units of each of the four general fracture systems meet in the central portion of Proano hill, which is an outcrop of graywacke, and where the rock was also intensely fractured by subsidiary movements, resulting in a shattered zone 1200 ft. long by 400 ft. wide. The mineralization was more intense in the immediate vicinity of the principal channels through which the solutions rose. The valuable metals are silver and gold, the ratio by weight of the former to the latter being 1000 to 1.5. Argentite is the predominant silver mineral, and is associated with pyrite and manganese mineral. The sulfides are primary throughout. A slight secondary action is represented by small quantities of native silver and silver halides, principally cerargyrite, which are found in the upper part of the mine. Oxidation has penetrated with great thoroughness to the lowest horizon so far exposed, this being 420 ft. below the present ground-water level. The shattered mass within the central portion of the hill and near the surface was sufficiently mineralized to produce a large stockwork

Jan 1, 1935

[NORTH AMERICA UNITED STATES ALABAMA ADAMSVILLE U. S. Steel Corp. Neason, James E. ALBERTVILLE Thompson Floral Co. Loudermilk, E. L. ANNISTON No Data Supplied Bonnichsen, Bill BESSEMER U. S. Steel Corp.-TCI Div. Beck, Adolph W., Jr. Boyle, James R. Cofield, William H. *Evans, James D. F., II *Guyton, Jesse C. Johnson, Leland H. Tetley, Albert L. No Data Supplied Crockard, F. H. Fisher, Joe T. Griffin, Joseph M. McFarland, E. A. Mohr, Henry E. Neal, George M. Walker, Wilber D.]

Jan 1, 1961

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

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

W. M. PEIRCE, Chairman J. L. CHRISTIE, Past-chairman E. H. DIX, JR., Vice-chairman ALBERT J. PHILLIPS, Vice-chairman E. M. WISE, Secretary International Nickel Co., Bayonne, N. J. W. M. CORSE, Treasurer Executive Committee W. H. BASSETT, JR. R. H. LEACH' D. K. CRAMPTONR. F. MEHL J. A. GANN W. E. REMMERS G. O. HIERS H. J. ROAST JEROME STRAUSS Finance Committee J. L. CHRISTIE, Chairman W. M. CORSE C. H. MATHEWSON T. S. FULLER H. S. RAWDON

Jan 1, 1934

NEW MEMBERS The following list comprises the names of those persons who became members during the period Oct. 10 to Nov. 10, 1914: Members ADDAMS, CHARLES EDWARD, Asst. Supt.. . Ray Consolidated Copper Co., Ray, Ariz. ALEXANDER, HARRY H., Asst. Mgr. and Mgr., American Smelting & Refining Co., Maurer, N. J. ALLING, MARK,N., Min Engr Downieville, Sierra Co., Cal. ANDERSON, LESLIE DOUGLASS, Supt U. S. Smelting Co., Midvale, Utah. ATKINS, WILLIAM, JR., Sec'y Kingwood Coal Co., Howesville, W. Va. BLAKE, TRUE WALTER, Min. Engr Rombauer Coal Co., Novinger, Mo. BRACKETT, GEORGE SYLVESTER, Supt... Pittsvein Coal Co., Flemington, W. Va. BRAINERD, HOWARD STANFORD, Met Ingersoll-Rand Co., Phillipsburg, N. J. BROWN, THOMAS J., Genl. Supt., Nova Scotia Steel & Coal Co., Sydney Mines, N. S., Canada.

Jan 12, 1914

NEW MEMBERS The following list comprises the names of those persons who became members during the period May 10 to June 10, 1914. Members ABE, ASAKA, Chief Min. Engr., Yamagano Gold Mine, Satsuma-Gori, Satsuma, Japan. ANDERSON, FRANK M., Geol Cartagena Refining Co., Cartagena, Colombia, S. A. BACON, MAURICE W., Genl. Mgr Stewart Mining Co. Butte, Mont. BACON, RAYMOND F., Chem Director, Mellon Institute, Pittsburg, Pa. BAKER, HAMILTON WALLACE, Min. Engr Fernley, Nev. VON BAYER, AUGUST HECTOR, Supt Kentucky Solvay, Coke Co., Ashland, Ky. BISHOP, WHEELER SCOTT, Research Chem Care Braden Copper Co., Rancagua, Chile, S. A. BOWEN, CHARLES GILMAN, Timekeeper 208 School St., Grass Valley, Cal. BOYER, SAMUEL L., Mine Operator, Mgr., Mike. Horse Min. Co., W. 2808 Boone Ave., Spokane. Wash.

Jan 7, 1914

By John S. Johnson, Thomas Fraser

SIZING is the process of separating mixed particles into groups of particles all of the same size, or into groups in which all particles range between certain definite maximum and minimum sizes. In coal preparation, sizing is generally accomplished by passing the coal over screens. Separation by differential settling in air or water currents has been adapted to the special field of separating very fine sizes, and these processes are in commercial use to a relatively small extent in the coal industry. Separation with screens is a very old industrial practice. Agricola described the use of screens for ore treatment in the middle ages. In the literature of the British coal industry references were made to the screening of coal as early as 1589, but the practice of extensive sizing for the market did not become general until the last half of the nineteenth century. In America, the practice of sizing developed first in the Pennsylvania anthracite region, beginning with the use of rakes' in the mine working places to recover coarse coal. This mining procedure left the fines in the mine. Preparation outside the mine started with the installation of station¬ary cast-iron plates with 4 to 6-in. square holes. The run-of-mine coal was dumped upon the platforms, the large pieces of rock were picked out by hand, and the large lumps of coal were broken with hammers. The term "breaker," which still applies to the anthracite-preparation plant, originated with this practice, but the term is no longer descriptive of the entire function of the plant. In 1884, the first power-operated anthracite coal breaker' was erected by Gideon Bart at his colliery at Wolf Creek near Minersville, Pa. This plant utilized a system of rolls for breaking the coal and revolving screens for sizing. The plant was driven by a steam engine. It 'could handle

Jan 1, 1943

By John S. Johnson, Thomas Fraser

SIZING is the process of separating mixed particles into groups of particles all of the same size, or into groups in which all particles L range between certain definite maximum and minimum sizes. In coal preparation, sizing is generally accomplished by passing the coal over screens. Separation by differential settling in air or water currents has been adapted to the special field of separating very fine sizes, and these processes are in commercial use to a relatively small extent in the coal industry. Separation with screens is a very old industrial practice. Agricola 1 described the use of screens for ore treatment in the middle ages. In the literature of the British coal industry references were made to the screening of coal as early as 1589, but the practice of extensive sizing for the market did not become general until the last half of the nineteenth century. In America, the practice of sizing developed first in the Pennsylvania anthracite region, beginning with the use of rakes2 in the mine working places to recover coarse coal. This mining procedure left the fines in the mine. Preparation outside the mine started with the installation of stationary cast-iron plates with 4 to 6-in. square holes. The run-of-mine coal was dumped upon the platforms, the large pieces of rock were picked out by hand, and the large lumps of coal were broken with hammers. The term "breaker," which still applies to the anthracite-preparation plant, originated with this practice, but the term is no longer descriptive of the entire function of the plant. In 1884, the first power-operated anthracite coal breaker3 was erected by Gideon Bart at his colliery at Wolf Creek near Minersville, Pa. This plant utilized a system of rolls for breaking the coal and revolving screens for sizing. The plant was driven by a steam engine. It could handle

Jan 1, 1943

By J. C. Fisher

C. S. Smith has described a method for measuring the relative values of different solid-solid and solid-liquid interfacial tensi0ns. When a polyphase alloy is held at an elevated temperature, individual particles of each phase adjust their shapes and minimize the interfacial energy. Wherever three interfaces meet, the dihedral angles are such that the three interfacial tensions, considered as forces, are in equilibrium. When the angles between three forces in equilibrium at a point are known, it is possible to determine any two in terms of the third. In this way ratios of interfacial tensions have been .obtained. The value of a given interfacial tension ratio was found to be independent of the alloy system from which it was determined. Smith also has employed the method when one of the phases is liquid. When equilibrium is reached with respect to In the course of work on grain growth in high purity aluminum a simple optical method was developed for detecting the presence or absence of preferred orientation in annealed specimens. The specimens were prepared by grinding, polishing and "deep etching." The etching reagent used for high purity aluminum has been described.* The resulting etch pits produced selective

Jan 1, 1949

[ ]

Jan 1, 1938

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