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By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By Oscar E. Harder, H. A. Grove

It is now just a quarter of a century since Fred W. Taylor§(23) pub-lished his classical paper On the Art of Cutting Metals, describing his researches in which he, in cooperation with Maunsel White, had developed what is essentially the modern method of heat-treatring high-speed steels. Regarding this research, Dr. Sauveur,(22) in his address on Steel Wizards, Past and Present, at the annual banquet of the American Society for Steel Treating in Philadelphia in 1920 said, "The discovery of high-speed steel, or if you prefer, of the treatment imparting high-speed properties to certain steels by Taylor and Maunsel White I am inclined to consider as our one epoch-making contribution to the metallurgy of steel." It was at about that same time (1900) that Taylor exhibited high-speed steels, heat-treated by the improved process, at the World's Exposition in Paris and attracted much attention by showing that the steels would operate at such feeds and speeds that the tips of the tools were visibly red hot. This observation must have started metallurgists to wondering regarding the relative hardness of the various steels at red-heat temperatures. Considerable work has indeed been done in an effort to measure the hardness of high-speed steels and related materials in the red-heat range, using various methods. The result's, however, have been only partly satisfactory, owing to experimental difficulties. The present investigation had as it's immediate inception an address by J. V. Emmons, of the Cleveland Twist Drill Co., to the Columbus Chapter of the American Society for Steel Treating in 1931, in which he deplored the fact that comparatively little was known with regard to the hardness of high-speed steels at elevated temperatures, in spite

Jan 1, 1933

The Library of the above-named Societies is open from 9 A.M. to 10 P.M. on all week-days, except holidays, from September 1 to June 30, and from 9 A.M. to 6 P.M. during July and August. The Library contains about 55,000 volumes, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library can render valuable service through correspondence; letters requesting information will receive special attention. The Library is prepared to furnish references and copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information as to the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved and the information will be sent more promptly and in more usable shape. The members of the Institute can be of service to the Library by forwarding copies of mining reports, maps privately issued, and similar material, which will be classified, indexed, and made available to other members. Suggestions for additions to the Library, either by purchase or personal solicitation as gifts, will be welcomed. It is hoped that members while in the city will use the Library freely, and assurance is given that most careful service will be rendered to them.

Jan 1, 1915

By W. D. Keller

THE high-alumina clays of Missouri are interesting for several reasons. They are the only sedimentary deposits in North America of first grade (over 70 pct A1,0,) diaspore and boehmite sufficiently large to be mined commercially. Mineralogically, they are composed of diaspore and boehmite in intimate coexistence, but gibbsite, the common hydrated alumina mineral in bauxite and laterite, is absent, or is exceedingly scanty if present.* Therefore, the Missouri high-alumina clays do not represent typical laterization. The physical chemistry leading to their mineral genesis, and the geolbgical setting for their formation, present important problems for scientific study. The origin of the Missouri high-alumina clays has been discussed in earlier reports by Allen1 (1935) and McQueen 8, 9 (1929, 1943). These investigations were made under difficult conditions, however, because no diaspore deposit had been opened where a Paleozoic (Pennsylvanian) rock cover lay undisturbed over the high-alumina clay. The relationship of the clay to only the underlying rocks could actually be observed. Lacking the guidance of critical postdepositional geologic evidence, undue and erroneous emphasis was placed on the postdepositional leaching of the deposits in the theories on the origin of diaspore and boehmite from clay (hydrous aluminosilicates) . With new geologic evidence at hand, a clearer picture can be made for the origin of the Missouri high-alumina deposits. In this paper the geology of a diaspore deposit whose original Paleozoic cover had not been eroded will be described and interpreted genetically. The close relationship of boehmite and diaspore (also with kaolinite and a chloritic mineral), will be established. A theory of origin for the high-alumina clays, consistent with the new data, will be postulated.

Jan 1, 1952

By Albert G. Zima

According to recently puhlished statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet. Drill Tools Modern rotary drilling tools are the product of ingenious design and careful selection and adaptation of materials used in their construction. They must withstand terrific abrasion and, because of their compactness, must be designed to resist exceedingly high unit stresses. In bits, core drills and reamers, the bodies are made of either forged or cast alloy steels, heat-treated to develop a combination of high strength and toughness. To provide sufficient strength to the threaded portions and to protect the threads from distortion or damage, the box or pin sections of the tools are hardened to approximately 310 to 330 Brine11 hardness number. Drill and reamer cutters are generally of the movable type; i.e., serrated cones, cylinders or disks, which can readily be replaced when

Jan 1, 1935

By Albert G. Zima

According to recently puhlished statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet. Drill Tools Modern rotary drilling tools are the product of ingenious design and careful selection and adaptation of materials used in their construction. They must withstand terrific abrasion and, because of their compactness, must be designed to resist exceedingly high unit stresses. In bits, core drills and reamers, the bodies are made of either forged or cast alloy steels, heat-treated to develop a combination of high strength and toughness. To provide sufficient strength to the threaded portions and to protect the threads from distortion or damage, the box or pin sections of the tools are hardened to approximately 310 to 330 Brine11 hardness number. Drill and reamer cutters are generally of the movable type; i.e., serrated cones, cylinders or disks, which can readily be replaced when

Jan 1, 1935

By P. Somasundaran

An experimental and theoretical treatment of the depressing effect of inorganic electrolytes on the amine flotation of quartz is presented. Experimental data obtained for the amine flotation of quartz as a function of pH with potassium nitrate as depressant was used to test the models for the effectiveness of inorganic ions as depressants. The validity of commonly used assumptions are examined. The surface tension data obtained for dodecylammonium acetate solutions as a function of KNO3, concentration indicated that the collector adsorption on bubble cannot be neglected in the treatments, since this adsorption changes significantly with the addition of the inorganic electrolyte. It also indicated the possibility of significant changes in the specific adsorption potential of the collector occurring with the addition of inorganic electrolytes.

Jan 1, 1975

By W. C. Meyer, R. R. Klimpel

A physical model of flotation, derived from viewing froth as a kinetic species since it constitutes the carrier of ore particles, not only agrees with and is simulated by engineering mathematical models, but is statistically verified by actual laboratory flotation data. The model couples the mechanical removal of froth using paddles with the more rapid interactions taking place in the bath. It clearly shows that the kinetics of mass removal is dictated by flotation cell dimensions, paddle speed, and, more importantly, froth characteristics. Some conclusions and model predictions are presented.

Jan 1, 1984

By Henry Mulryan

DIATOMS are microscopic aquatic plants of the order Bacillariaceae. They are unicellular plants with skeletons made up of amorphous opaline silica. The skeletons show highly ornate, complicated geometrical designs. Diatoms live in water virtually everywhere. They are found in clean sea water, brackish water, and fresh-water lakes and ponds. When conditions are right, diatoms propagate by subdivision in huge numbers. Alkalinity, temperature, and the presence of high concentrations of silica in the water largely control diatom life. When the diatoms die the skeletons drop to the bottom of their habitat to form oozes of vary-ing thicknesses. DIATOMITES Diatomite, or diatomaceous earth, is composed essentially of the siliceous remains of the diatoms, although other organic skeletons are also present, especially in sea-water deposits where radiolaria, sponges and silico-flagellates are common. Impurities are generally carbonaceous material, fine-grained silt, volcanic ash and dust, and occasional coarse grains of sand. Diatomites are marine, brackish, or fresh-water, depending upon types of diatoms and their method of deposition.

Jan 1, 1939

By Benjamin C. Greene, H. Beecher Charmbury

Water is a most remarkable substance, essential for life of all kinds. As well as needing water to survive, man has always used it for agriculture, transportation, recreation, and many other things. When our country was young and inhabited by few people, the streams, rivers, and lakes were able to provide all the clean water needed by man and take away all the wastes created. However, with our growing population and an ever-increasing demand for goods and services, the public, industry, and government at all levels have become acutely aware of the need to manage the nation's water resources more efficiently. Abundant energy from many sources has helped this nation to become the greatest industrial nation in the world. Coal has contributed a major portion of this energy, generating electricity, running railroads, and maintaining national security during wartime. The result has been the highest standard of living in the world and a time of widespread economic prosperity. The use of water in coal mining is somewhat different from its use in most industries. With the exception of water used in cleaning plants, for underground dust control, and for fire protection, most of the water en- countered in coal mining operations serves no useful purpose. In other words, it is an undesirable element and must be removed, otherwise it will interfere with operations, cause potential water quality problems, and may even stop operations by flooding. In the past, removing water from working areas of most mines was usually a fairly simple matter. Pumps with piping were installed at sumps or low spots in the mine and the water was pumped to the surface or to drainage control facilities constructed for the operation. Ditches were often used to collect and drain the water by gravity to the outside or to main sumps for pump discharge. In either case, the water was allowed to flow into the nearest stream or river. The concept of "water is water'' was generally accepted without too much concern for what was in

Jan 1, 1981

By R. H. Doremus

From measurements of carbide precipitation rates in a iron it was concluded that the carbides nucleated on dislocations in both strained and unstrained samples, except for the latter at lower temperatures and higher carbon concentrations, where there were more muclei than could form on the dislocations. The equation of Cottrell and Bilby for the segregation of atoms to dislocations was found to be inapplicable to this system. No satisfactory theory for the growth process is available. A study of the rate at which a second phase separates from solid solution can frequently reveal much about the mechanism of separation. There are still many features of the precipitation of carbon from a iron that are not understood, although this system has been examined extensively. To provide more insight into the mechanism of carbide precipitation in a iron, rates of this process were measured at different temperatures, carbon concentrations, and densities of dislocations in the iron. The concentra- tion of carbon in solution was followed from the height of the internal-friction peak; this height is directly proportional to the amount of carbon in solution and is not affected by the growing carbide particles. In this paper these rates are compared with those found by earlier investigators, and the mechanism of precipitation is discussed in light of these results as well as two earlier studies1, 2 and the electron microscopic work reported in the preceding paper. EXPERIMENTAL The amount of carbon in solution was followed by

Jan 1, 1961

By T. M. Gurr

The United States is the world's leading producer of phosphate rock. In 1975 according to the US Bureau of Mines' statistics, 44.3 million tonnes (48.8 million st) of phosphate rock were produced in the United States, l which is 40.6% of the world's production.2 The major phosphate producing areas of the United States are located in [Fig. 1] and the production for 1975 is listed as follows: [ ] All of these areas produce phosphate from deposits which are of marine sedimentary origin. Occurrences of phosphate exist throughout the United States in numerous locations that are of both igneous and sedimentary origins. However, these other phosphate occurrences vary greatly in extent and economic significance. Georgia, South Carolina, California, Texas, Arkansas, Kansas, Iowa, Alabama, Kentucky, and Virginia are but a few of the states in which phosphate is thought or known to exist. The near future expansion will probably continue to be in, or near, existing producing areas, (i.e., Florida and North Carolina).

Jan 1, 1980

By G. K. Burgress, H. S. Rawdon, R. W. Waltenberg, J. J. Crowe

The main objects of this investigation were to determine, from neasurements taken at representative rail mills…

Jan 1, 1915

By Reinhardt Thiessen

UNDER sulfur in coal, is usually understood that form of sulfur which is combined with iron and known as pyrite. It occurs in the form of halls, lenses, nodules, continuous layers, thin sheets, or flakes, both in horizontal planes and vertical cleavage fissures. But pyrites also occur as very fine microscopic particles, or nodules, disseminated through the compact coal. This form has had but very little consideration. Finally, there is sulfur in coal in an amicroscopic form (not visible with an ordinary microscope), probably combined with the organic matter that exists -in tile coal. This form has had considerable attention from a scientific standpoint, but has probably not been recognized enough on the economic side. One or the other, or both, of these two latter forms may comprise the larger part of the sulfur content of coal, especially after it has been washed or otherwise prepared for use.

Jan 9, 1919

By J. R. Long, R. S. Dean, F. S. Wartman, E. T. Hayes

The production of titanium in I5-lb. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,' has provided adequate material for a study of the physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited' and all efforts were centered on fabrication methods for those powders and the proper- ties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. Consolidation of the PowdeR The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at 50 tons per

Jan 1, 1946

By J. R. Long, E. T. Hayes, R. S. Dean, F. S. Wartman

The production of titanium in I5-lb. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,' has provided adequate material for a study of the physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited' and all efforts were centered on fabrication methods for those powders and the proper- ties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. Consolidation of the PowdeR The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at 50 tons per

Jan 1, 1946

By Stephen Taber

INTRODUCTION THE term asbestos, as commonly used, includes half a dozen minerals all having a well-developed fibrous structure, but differing in chemical composition and in some of their physical, properties. In its strict application the name is limited to the fibrous varieties of the monoclinic amphiboles. Commercially, however, the most important of the asbestiform minerals is chrysotile, a fibrous variety of serpentine. About 95 per cent. of the asbestos used in manufacturing is chrysotile, and it commands a much higher price than any of the other fibrous minerals now on the market. Although the production of asbestos has increased rapidly in recent years, comparatively little has been published concerning its origin. The present paper is preliminary in its nature, and therefore does not pretend to exhaust the subject. The ideas herein developed are the result of field investigation, laboratory experiments in the growth of fibrous

Jan 10, 1916

By W. R. Crane

THE support of roof in mines is dependent largely on the character of the top rock and its occurrence. The formations overlying the orebed in the Birmingham district are sandstone and slate. The sandstone occurs in beds of sufficient thickness to constitute important elements in the system of support; the slate is relatively strong but is thinly stratified. The alternating beds of sandstone and slate furnish an excellent combination in that the former are strong and the latter are impervious; however, their continuity is broken by jointing or slip planes. The thickness, and consequent weight of the overlying formations, is important in so far as the size and arrangement of pillars are concerned but may be relatively unimportant, temporarily at least, as a factor in the support of the roof. The position of the respective beds of sandstone and slate, their relative thickness, and their inherent weakness because of the occurrence of faults and folds, may exert a predominating influence on their support in place, which is affected only in part by the weight of the cover. The only mine in this district that operates under a cover of approximately 2000 ft. (1900 ft.) is the Shannon so-called "twin slope," situated 14,000 ft. southeast of the portal of the No. 7 mine of the Tennessee Coal, Iron, & Railroad Co. The conditions in this mine indicate what may be expected in other mines when the same depth is attained; in fact the effect of pressure is shown in several mines that have not reached two-thirds of that depth. It is evident then that conditions affecting the support of roof will not improve but rather will become more difficult with the extension of the mines into the valley under a constantly increasing weight of cover. Further, the difficulties will probably be augmented by the occurrence of faults and other disturbed ground, the presence and position of which at present are largely unknown.

Jan 9, 1924

By Dwight Farnham

Description of Quarry THE shale used at the Renton plant of the Denny-Renton Clay Coal Co., for the manufacture of vitrified paving brick occurs in a hill rising from 200 to 300 ft. above the level of the valley in which the plant is situated. The shale deposit, which is of unknown thickness pitches about 10° to the southeast. The 150-ft. face worked extends approximately east and west, so that the clip, as shown by the photograph, is to the left and into the hill. The shale is overlain with about 50 ft. of gravel, 70 ft. of clay, and 30 ft. of mixed loam and gravel, making altogether from 125 to 150 ft. of overburden. Disposal of Overburden The overburden is removed by sluicing. For this purpose a No. 2 Joshua Hendy giant is used, throwing a 12-in. stream', and having 60 lb. pressure at the nozzle. The water is drawn through an 8-in. pipe from Cedar river, about 1,000 ft. distant, by means of a Worthington four-stage centrifugal pump, direct connected with a 100-h.p. motor placed just south of the factory, and 1,500 ft. from the nozzle This plant handles the material satisfactorily to a height of about 75 ft. above the level of the top of the shale. When the higher levels are worked, an auxiliary plant consisting of a four-stage Byron Jackson centrifugal pump with a 100-h.p., belt-connected motor, is thrown into the system. This plant is situated on top of the shale and can be discerned at the extreme right of the trestle work in Fig. 1.

Jan 9, 1914

The Library of the above-named Societies is open from 9 A.M. to 10 P.M. on all week-days, except holidays, from September 1 to June 30, and from 9 A.M. to 6 P.M. during July and August. The Library contains about 55,000 volumes, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library can render valuable service through correspondence; letters requesting information will receive special attention. The Library is prepared to furnish references and copies of articles on mining and metallurgical subjects; to determine the existence of mining-maps, and to furnish general information as to the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be .of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape. The members of the Institute can be of service to the Library by forwarding copies of mining-reports, maps privately issued, and similar material, which will be classified, indexed, and made available to other members. Suggestions for additions to the Library, either by purchase or, personal solicitation as gifts, will be welcomed. It is hoped that members while in the city will. use the Library freely, and assurance is given that most careful service will be rendered to them.

Jan 9, 1914