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By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By W. H. Emmons

Many mineral veins occupy faults, and movements on certain warped fault planes have resulted in openings. On normal faults the steeper parts have the widest openings, and on reverse faults the flatter parts have the widest openings. Theoretically the width of the opening is the sine of the angle of deflection times the amount of movement on the fault plane, but actually the widths of some of the openings are probably less because of readjustments of walls along joints or of other readjustments. The first treatment of the subject seems to have been in a book on mineral veins by John Leithart, published in Newcastle, England, in 1838. Later the subject was treated in various texts published in Germany, in England, and elsewhere. The subject was not given much prominence in the earlier American literature on economic geology, but has interested several workers in that field in the past decade. In this paper examples of districts showing ore shoots on warped faults, with relations noted, are described. Fault veins of the three depth classes of veins are noted. Many epithermal veins are in normal faults, and commonly the larger ore shoots are in their steeper portions. Many mesothermal veins are in reverse faults and, many others are in normal faults. The flatter parts of veins in reverse faults are commonly wider than the steeper parts, although they are not always as rich as the steeper segments of the veins. There are not many hypothermal veins in faults of measured displacement. Introduction When faults are followed along dip or strike, many of them are found to have curving or warped surfaces, and cross sections through them in most directions show sinuous or waving intersections. Openings are formed where one wall moves away from the other (Figs. I,2). Where there is a bend in the fault, movement in any directions except along the axis of the bend will

Jan 1, 1949

By W. H. Emmons

Many mineral veins occupy faults, and movements on certain warped fault planes have resulted in openings. On normal faults the steeper parts have the widest openings, and on reverse faults the flatter parts have the widest openings. Theoretically the width of the opening is the sine of the angle of deflection times the amount of movement on the fault plane, but actually the widths of some of the openings are probably less because of readjustments of walls along joints or of other readjustments. The first treatment of the subject seems to have been in a book on mineral veins by John Leithart, published in Newcastle, England, in 1838. Later the subject was treated in various texts published in Germany, in England, and elsewhere. The subject was not given much prominence in the earlier American literature on economic geology, but has interested several workers in that field in the past decade. In this paper examples of districts showing ore shoots on warped faults, with relations noted, are described. Fault veins of the three depth classes of veins are noted. Many epithermal veins are in normal faults, and commonly the larger ore shoots are in their steeper portions. Many mesothermal veins are in reverse faults and, many others are in normal faults. The flatter parts of veins in reverse faults are commonly wider than the steeper parts, although they are not always as rich as the steeper segments of the veins. There are not many hypothermal veins in faults of measured displacement. Introduction When faults are followed along dip or strike, many of them are found to have curving or warped surfaces, and cross sections through them in most directions show sinuous or waving intersections. Openings are formed where one wall moves away from the other (Figs. I,2). Where there is a bend in the fault, movement in any directions except along the axis of the bend will

Jan 1, 1949

Jan 1, 1894

By Granville S. Borden

This brief is a reconnaissance report on some prospects in the field of taxation which can safeguard our Mineral Resources. The brief is a prospectus soliciting help and enthusiastic cooperation in the common task of developing these prospects in a manner which will be most beneficial to all parties-the owners, operators, employees, tradesmen, the federal and state governments, and the people of this nation.

Jan 4, 1950

By H. A. Kuhn

The Pittsburgh coal field in Western Pennsylvania is conceded to be the most important in the world.

Jan 1, 1915

By Jerome Alexander

The object of this paper is to show that many of the important phenomena of metals and alloys are due to the facts that, at some stage, metals and alloys, or some of their constituents, are in a colloidal state and that a portion of the metal or alloy tends to remain in this state. The so-called amorphous phase in pure metals is an isocolloid, consisting of colloidal groups of metal molecules that may be dispersed in still more finely subdivided metal; these colloidal particles are not truly amorphous, but may consist, in part, if not entirely, of ultramicroscopic crystals; as a result the expressions amorphous phase and amorphous theory might he replaced by the expressions colloidal phase and colloidal theory. Any substance is in the colloidal state when the constituent particles consist of molecular or atomic groups, whose size varies approximately from about 100 down to about 5pp, that is from just below the limit of microscopic resolvability to the dimensions commonly ascribed to the larger molecules. Colloidality involves no assumption as to the shape, internal structure, or orientation of the colloidal particles; size alone is the critical factor. A colloidal system may therefore contain crystalline groups, or amorphous groups (non-crystalline, random or haphazard clusters), or a mixture of the two. All colloids consist of at least two phases, the subdivided substance, or dispersed phase, and the substance into which this is subdivided, the dispersion medium. It is not necessary that there be any chemical difference between the dispersed phase and the dispersion medium. As molecular forces are extremely powerful, their application may produce marked changes in the physical properties of metals. It is doubtful whether metal in the interior, especially of large masses, possesses the same properties as that on or near the surface, which alone is open to inspection.

Jan 1, 1921

By L. H. Ketchum, T. L. Theis, W. H. Engelmann

The use of a suspended growth system of Thiobacillus ferrooxidans attached in a film to individual particles of bentonite and operated as a sequencing batch reactor is shown to be a practical way of oxidizing ferrous iron in acid mine drainage. This component, followed by limestone neutralization, is both a technically and economically feasible approach to treating these waste waters, compared to existing and other proposed methods. The advantages, in addition to less expense, are greater safety, acceptable treatment at a lower pH, lower solids buildup, less danger of overtreatment, and greater flexibility in operational characteristics. In this paper, data on the continuous bench scale operation of the system under a variety of conditions shows sustained levels of oxidation in excess of 98%. Capital and operating costs are projected to be $80/1000 m3 ($80 per 35, 000 cu ft) of waste water.

Jan 1, 1985

By Robert E. Hoffman, John B. Hudson

The self-diffusion coefficient of pure lead has been measured at five pressures between atmospheric and 40 kb. over a temperature range of about 150°C near the melting point at each pressure. Measurements were made using a radiotracer technique, samples being sectioned electrochemically after the diffusion anneal to determine the diffusion penetration curve. Pressure was applied in a "belt" type pressure device similar to that used by Hall et al., in the diamond synthesis. The self-diffusion coefficient, D, can be represented by an equation of the form at constant pressure, and an equation of the format constant temperature. An apparent correlation between the effects of pressure on self-diffusion and on the melting point of the material observed by Nachtrieb et al., at pressures below 10 kb. was found to be only approximate as measurements are carried to higher pressures. OVER the course of the past 30 years a large number of studies1-' of the rate of atom movements in solid metals have been carried out. These studies have in general been aimed at increasing the understanding of the detailed atomic process by which atom movements in metals can take place. The largest portion of these studies consisted of measurements of the self-diffusion coefficient, D, as a function of temperature. From such studies con- siderable information regarding the energetics of the motive process has been deduced. Recently such measurements have been extended to the pressure dimension. However, the existing work in this area is scanty and has in the past been limited to the pressures attainable in oil or gas bombs—i.e., up to about 10 kilobars (kb). In the present work, the self-diffusion behavior of pure lead has been investigated using the "belt" type high-pressure apparatus designed by Hall7 over a pressure range from atmospheric to 40 kb at temperatures extending over about a 150°C range close to the melting point at each pressure.

Jan 1, 1962

By L. D. Jaffe, D. C. Buffum, F. L. Carr

SINCE the temper brittleness of steels is generally considered to be a grain-boundary phenomenon¹,² it would be expected that austenitic grain size would affect temper brittleness. Several investigators"" reported that temper brittleness, as measured by room-temperature impact tests, increased as the austenitiz-ing temperature was raised. It was subsequently pointed out that conclusions as to temper brittleness based upon room-temperature impact tests are likely to be misleading.1,6 Hurlich7 used a range of testing

Jan 1, 1954

By Stephen Taber

A VEIN may be defined as an aggregation of mineral matter, more or less tabular or lenticular in form, which was deposited from solution and is of later origin than the inclosing rock. This definition differs from the one found in many text-books in that no assumption is made as to the origin of the space occupied by the vein or the manner in which the mineral matter was deposited. In the present paper the writer purposes to discuss the mechanics of vein formation, and does not wish to begin by begging the question. The origin of ore deposits has been diligently investigated in recent years, but, while much has been written concerning the chemistry of the process, the physical side of the question has received less attention. The source of the ore minerals; the chemical composition of ore-hearing solutions; the relative importance of magmatic and meteoric waters as agents of concentration; and the causes of mineral precipitation have all been discussed at length. On the other hand, little has been written concerning the mechanics of vein formation, and the theories given in text-hooks today are essentially the same as those developed by the early Cornish and Saxon miners. Early investigators often regarded both veins and dikes as igneous in origin, but today the theory that vein minerals have been deposited from solutions, either liquid or gaseous, is firmly established. The latter view is supported by the fact that many vein-forming minerals are not found in unaltered igneous rocks; by evidence obtained in the laboratory regarding the solubility of minerals; by the presence of many ore minerals in hot-spring waters; by the occurrence of some veins in regions consisting exclusively of unaltered sedimentary rocks; by evidence as to the temperature at which some minerals are formed; and by the absence of mineral segregation due to difference in specific gravity. There is still, however, much difference of opinion as to whether certain tabular-shaped 'masses should be classed as veins or as dikes. Some of

Jan 8, 1918

Jan 1, 1902

By William G. Schultz

Sylvite’s potash mine probably ranks as one of the most highly mechanized and automated mining operations in the world. Employing, on a normal 10-hr production shift, one supervisor and a crew of seven operators, Sylvite is able to mine at an average rate in excess of 600 tph. The ore is produced by two Marietta miners weighing 258 tons, making them the largest and heaviest piece of equipment ever taken underground. The ore produced by these two Marietta miners is conveyed to the shaft area, cycled through a 15,000 ton storage system and hoisted to surface completely automatically. The operation of all equipment in the mine can be monitored and controlled from a central control panel located underground.

Jan 7, 1972

By Eugene Guccione

FOREWORD-At the SME-AIME meeting in Las Vegas this year, the SME Publications Board and the MINING ENGINEERING Committee decided that a fitting way of celebrating the United States' bicentennial would be to publish an article in ME covering the great men in American mining. After some discussion as to the inclusion of financiers -men such as William Randolph Hearst, J. Pierpont Morgan, etc.-the group agreed that the feature should be restricted to the "nuts-and-bolt people," e.g., mining engineers, geologists, mineral processing engineers. Thus, from the AIME All Institute Honors roll and from the SME Awards list, the group chose these 11 historical figures: Herbert Hoover, Daniel C. Jackling, Henry Krumb, James Douglas, Rossiter W. Raymond, Hal W. Hardinge, Seeley W. Mudd, Erskine Ramsay, Howard N. Eavenson, Robert A. Richards, Arthur F. Taggart. What follows is an account of each of these great miners' achievements and the problems they faced, and an assessment by some of today's mining leaders of the challenges that lie ahead.

Jan 7, 1976

By Ionel I. Gardescu

Natural gas influences the movement of oil through reservoir rock by affecting the physical properties of the oil and the pressure within the reservoir. The presence of gas bubbles changes the laws of flow and the distribution of forces. The problem of flow of oil and gas through a porous rock is complex, and most authors, in order to analyze their problems, have found it necessary to make or accept certain generalized assumptions. Some of these assumptions, particularly the ones dealing with capillary phenomena and moleculnr forces, have not received sufficient attention and by lack of understanding have often been misinterpreted. Herold1 has called attention to the resistance offered by gas bubbles in capillary spaces and has drawn some interesting conclusions with regard to the action of natural gas in a reservoir rock. He has duplicated an experiment of the French physicist Jamin, has interpreted his findings in terms of molar mechanics, and, from experimental observations, has made a number of assumptions which he later applies in discussing problems of natural flow and recovery of oil. The Jamin action is an assumption because it lacks a physical proof and has never been determined quantitatively. Tickel12 attempts to develop a formula expressing the work performed by a distorted bubble. H. A. Wilson, in the recent publication of the American Petroleum Institute on the function of natural gas, discusses the phenomenon in terms of classical physics. Both contributions are incomplete and offer no experimental data. This paper includes a study of the static condition of equilibrium of gas and liquid bubbles confined to capillary spaces. In order to avoid any possible confusion, it is proposed to restrict the term "Jamin action"

Jan 1, 1930

By S. F. Shaw

THE Sierra Mojada mining district is situated in western Coahuila, about 8 km. east of the Chihuahua state line, and about one-half way from the northern to the southern extremity of the state. It is at the terminus of the Mexican Northern R. R., 125 km. northeast of Escalón, Chihuahua; also about 240 km. due west of Monclova, Coahuila. The altitude is approximately 1500 m. above sea level. The Sierra Mojada valley is about 10 km. long, from east to west, with a width of 1 to 2 km. It is approached from the east through the Puerto del Oro, where the Mexican Northern R. R. enters the valley; the slope from west to east is gentle. The Sierra Mojada, of which about. 300 m. is an almost vertical wall, bounds the valley on the south side; on the north side, the slope to the crest of Sierra Planchada is more gradual, rising only 200 or 300 m. above the valley. Water is relatively scarce in the district, and there are no running streams. The rainy season, usually beginning at the middle of June, lasts through July, and occasionally into August or September. In some years the rains fail entirely. The slope of the ground is such that nearly all the water immediately runs off. The arroyos along 'the flanks of the mountains are not very deep, but in heavy rains, sometimes approaching cloudbursts, a tremendous volume of water rushes down them, carrying large boulders. A certain amount of seepage collects in the agglomerate, lying below the conglomerate, and is retained in the local fractures. Some shallow wells have been sunk in this agglomerate, and one well over 150 m. deep was sunk on, the Volcan ranch, supplying about 76 1. (20 gal.) per min. A considerable supply of water is collected in large earth reservoirs in and below the town of Esmeralda. In ordinary years this supply will last until January or February, after which the Volcan well has to be depended on until the next rainy season.

Jan 8, 1922

By R. E. Grace, H. W. Schadler

DARKEN1 has established the theoretical relation between the self-diffusion coefficients and the Boltzmann-MatanO Or interdiffusion coefficient: D is the Boltzmann-Matano or interdiffusion coef-

Jan 1, 1960

By L. G. Westgate

PART I.-AREAL GEOLOGY§ PIOCHE lies 240 mi. southwest of Salt Lake City, in southeastern Nevada, 19 in. west of the Nevada-Utah line. It is at the end of a branch line (33 m.), which connects at Caliente with the Los Angeles and Salt Lake division of the Union Pacific System. Its commercial relations are with Salt Lake City and Los Angeles, chiefly with the former. The surrounding area is part of the Great Basin, an arid region of alternating mountain range and intermont plain, the latter floored with outwash from the mountains. About Pioche the plain varies between 4700 and 6000 ft. above sea level. The town lies in a valley at the east base of a low northwest-southeast range (the Pioche Hills) 12 miles in length, which rises about 1000 ft. above the adjacent flat. West of the. Pioche Hills is a higher north-south range consisting of two parts: to the south the Highland Range, between Bennett Pass and Stampede Gap; to the north the Bristol Range, from Stampede Gap to Bristol Pass. This double range reaches altitudes of 8000 to 9000 ft., or more, (the highest point, Highland Peak, is 9395 ft.) and rises some 2500 ft. above the surrounding plain. It is continued in lower hills to north and south. Smaller ranges rise from the flat west of the Highland and Bristol ranges. The area studied and shown on the map (Fig. 1) is covered by 3 one inch to the-mile topographic sheets: the Highland Range, the. Bristol Range, and the Panaca, the latter mapped in part only. The sedimentary rocks of the district include Paleozoic limestones, sandstones and shales, Pliocene tuffs, and modern wash. Igneous rocks are represented by intrusive dikes and stocks and by extensive lava flows of mid-Tertiary time.

Jan 1, 1927

By Howard A. Smith

OF late considerable experimental and theoretical interest has been shown in the rates of transformation from a single phase, usually a supercooled solid solution, into one or more phases. Such reactions may involve both diffusion and transformation of the major constituent, as in iron alloys, or it may simply involve diffusion, as in superstructure formation and in age-hardening systems. Most of the work has been confined to ferrous alloys1-9† although two investigations have been made on copper alloys 10-11. That such work may be of considerable practical importance has been demonstrated by Bain12, by the workers at the Kaiser Wilhelm Institut für Eisenforschung13, 14, and by the everyday use of precipitation and age-hardening principles15. Experiments in this country have generally followed Davenport and Bain's technique of rapid supercooling followed by isothermal treatment. In Germany16, 17 the work has been extended to the study of the influence of accurately controlled and measured rates of cooling. The work on steel indicates that there are two subcritical temperature ranges where reaction starts sooner after quenching and proceeds at a more rapid rate than at other temperatures. At subcritical temperatures above Ar" where reaction is dependent upon atomic migration there is a period of time of which the length depends upon the alloy content and the temperature, before which no reaction has been detected. Davenport and Bain1 find that different sorts of atoms in solid solution in gamma iron affect the length of this "prereaction" period differently, manganese

Jan 1, 1935

By J. H. Wernick, E. E. Thomas

THE etch-pit technique for revealing dislocations in bulk samples allows one to determine dislocation densities and to study their behavior under various mechanical and thermal treatments. We have developed a chemical polish-etch for the development of etch pits on the (1100) plane of Cd which appear to

Jan 1, 1961