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By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

The following is am incomplete list of members and guests who called at Institute headquarters during the period May 10, 1918 to June 10, 1918. Arthur K. Adams, Potrerillos, Chile. J. M. Mahoney, Wilkinsburg, Pa. John Carter Anderson, Tucson, Ariz. Benjamin L. Miller, South Bethlehem, Pa. George S. Blair, Camp Cordon, Ga. Wilbur A. Nelson, Nashville, Tenn. W. A. Deane, Summitville, N. Y. Miles G. Nixon, Chicago, Ill. Charles H. Fulton, Cleveland, Ohio. Walter G. Perkins, San Francisco, Cal. Rudolf Gahl, Inspiration, Ariz. G. M. Ponton, Ottawa, Canada. C. C. Griggs, Eureka, Utah. D. A. Powell, Columbus, Ohio. J. F. Hanst, Potrerillos, Chile. H. W. Reed, Salt Lake City, Utah. Stanley C. Herold, Pittsburgh, Pa. J. C. L. J. Seelig, Padong, East. Indies. Floyd D. James, Boston, Mass. Oberlin Smith, Bridgeton, N. J. Charles Janin, San Francisco, Cal. Harrison Souder, Cornwall, Pa. E. Horton Jones, Copper Cliff, Ont. Stanley A. Spellmeyer, Camp Meade, Md. William Kelly, Vulcan, Mich. Roger S. Sperry, Waterbury, Conn. Ichiro Kitsunezaki, Tokyo, Japan. D. R. Thomas, Toronto, Canada. P. K. Lucke, San Antonio, Tex. Thor Warner, Phoenix, Ariz. E. Francis McCrossin, Birmingham, Ala. L. Douglass Anderson, formerly superintendent of the United States Smelting Co., Midvale, Utah, is now manager of smelters, Intermountain District, United States Smelting, Refining & Mining Co., Salt Lake City, Utah.

Jan 7, 1918

ALABAMA Altoona.-Cain, J. America.-Foreman, J. T. Anniston.-Cowie, L. K. Foster, R. N. Ashland.-Sturdevant, J C Bessemer.-Ball, E. M. McKenzie, W. C., Jr Birmingham.-Abbott, C. E. Aldrich, T. H. Aldrich, T. H, Jr. Ashton, J J. Ball, T. L. Blair, C. S. Brown, T S. Bush, M. W.

Jan 1, 1923

By John J. Cioston

THE steadily rising flood of gold production from all parts of the world has created an avalanche of rumors regarding the stability of the present price of this metal. Markets have been unsettled from Johannesburg to London from New York and Toronto to Melbourne, despite repeated denials from, American and British authorities of any immediate intention to alter the price. Various economists and financial writers have blossomed forth with predictions that the price would be set at the old level of $20.67 per oz.; some have even been so brash as to state That a price of $15 would be necessary to bring production within control. These effusions, based entirely upon monetary theories and with no regard to production costs, serve to confuse rather than clarify the situation.

Jan 1, 1937

By Theodore Simons

I. INTRODUCTION PERMISSION to present this paper at the February, 1915, meeting of the Montana Section of the American Institute of Mining Engineers was liberally granted by W. A. Clark, Jr., President and General Manager of the Timber Butte Milling Co., and by the representative of the Minerals Separation Co. For the many courtesies shown the writer on his visits to the mill and for information supplied, he is indebted to all the officers of these companies, especially to W. N. Rossberg, W. D. Mangam, Hamilton Cooke, Jr., T. M. Owen, T. C. Wilson, R. McGillivary, L. L. Quigley, C. Bartzen and others. The writer takes this opportunity to herewith express to them his appreciation and sincere thanks.

Jan 6, 1915

By H. G. Schneider

The Smackover oil and gas field lies in Ouachita and Union Counties, Ark., in the south-central part of the state, in T.15 and 16S., R.15, 16, and 17W. It is 10 miles north of El Dorado, the principal business and railroad center in the south-central part of the state, and extends from the town of Smackover in all directions. Productive territory having an aggregate area of nearly 55 sq. mi. has been developed. It extends 6 miles from north to south and 12 miles from east to west. The field may be divided into two parts: the east district, which includes the area east of the town of Smackover, and the west district, which includes the area west of the town of Smackover. In relation to the neighboring productive fields of Arkansas, the Smackover field is 9 miles north of the El Dorado oil and gas field, 8 miles slightly west of north of the East El Dorado oil and gas field, and 16 miles east of the Stephens oil field. Smackover was discovered in May, 1922, when the Oil Operators Tnist drilled well No. 1 on the J. T. Murphy farm, in the southeast quarter of sec. 8, T.16S., R.15W. This well is located almost on the top of the Norphlet dome and was drilled to the Nacatoch sand. It had an initial open flow volume of 30,000,000 cu. ft. of dry gas per day, and a rock pressure of 950 lb. per sq. in. In July, 1922, the V. K. F. Co. completed the first oil well in sec. 29, T.l5S., R.l5W., on the north side of the Norphlet dome, and 3 miles north of the first gas well. This well started the active development of the north and northwest sides of the dome.] The field was extended westwards, when oil was discovered in the Nacatoch sand, during October, 1922, in sec. 4, T.l6S., R.l6W., 51/2 miles west of the original gas well. This opened up the so-called "light oil district," which is located on a structural terrace, for which the name

Jan 1, 1924

By I. J. Jansen

Introduction The Surface Mining Control and Reclamation Act (PL 95-87) lays a new challenge before the surface mining industry by requiring that prime farmlands must be reclaimed to equivalent or higher levels of yield as nonmined prime farmland in the surrounding area (section 510d). We must now evaluate the situation and plan a mining and reclamation program that will achieve that objective. We must recognize that soil and land needs vary with intended land use and climatic setting. Also, various site conditions determine the potential for constructing a productive soil and the best procedures to accomplish that end. It is necessary to plan the land reconstruction program on a site by site basis in order to achieve the best results. Discussion The Prime Land Concept Terms like prime agricultural land have been used loosely for many years to refer to lands that are highly productive and well suited to agricultural use. The concept of what qualified as prime land varied considerably from one geographic area to another and from one person to another. The term prime farmland, as used in PL 95-87, has recently been defined quite

Jan 1, 1982

By ERNEST A. HERSAY

ACCURATE ore-sizing with screens is drawing attention to certain details that now, more than ever before, require attention. There are many tests that must be preceded by careful sizing. The assayer often could profit by a more careful selection of screens. In milling, more attention is given the slimes produced. Cement-manufacturers are pulverizing and screening finer than they formerly did, and others are reducing materials to fine sizes at high cost, with screens used to govern the fine¬ness of the pulverized product. Fine screens are expensive, easily injured by mis-use, are carried in stock sparingly by most dealers, and are handled often by those who know little about them except their designated number. More attention, on the whole, needs be given the actual size of the mesh-openings, and less emphasis placed upon any custom or conventionality in numbering. An effort to classify wire screens, in this respect, leads at once into computations, where one is confronted with details of sizes and standards, of different wires, different gauges, and different customs. There is always uncertainty about the exact working-size of a screen until one gives the matter special attention, and devotes more time to it than its simplicity seems to demand. To know only the number is not sufficient for all uses. Often, in sets, superfluous sizes are used; and sizes are omitted that are of critical importance. In wire screens, the use of different standard sizes of wire makes important differences in dimensions that must be taken into account. The dealer usually grades screens by the number of openings per linear dimensions, regardless of the size of the openings or of the wire. Certain 100-mesh screens in use are found, by measurement, to he actually coarser than others of 90-mesh, a result which is due, of course, to the use of larger

May 1, 1906

By K. E. Nelson

The effect of thorium and zinc variations on the strength and 100-hr creep characteristics of Mg-Th-Zn-Zr alloys was investigated. Optimum resistance to creep at 650° and 700°F are attainable within a certain range of thorium and zinc contents. This range does not conform to that which develops maximum tensile properties. RAPID advances have been made during the last few years in the development of magnesium alloys for elevated temperature applications demanding high resistance to creep. The beneficial effect of rare-earth metals on the creep resistance of magnesium alloys has been emphasized by a number of publications1-13 and such alloys are now in commercial production. The use of thorium as an alloying ingredient in magnesium was mentioned by McDonald and also in two Alien Property Custodian patent applications.10,17 The initial observation of Sauerwald that thorium contributes still higher creep resistance to magnesium than is attainable with rare-earth metals has recently been substantiated.'" " In fact, it has been demonstrated that the useful temperature range of magnesium alloys is appreciably extended by the use of thorium. In all cases, it was observed that zirconium must be included in the alloys in order to render them fine grained and more readily castable. Several recent publications:2-27 indicate that a still further improvement in creep resistance and a further extension of the useful temperature range can be realized by the addition of zinc to alloys. The primary purpose of this paper is to present the results of a comprehensive study of the effect of zinc on the strength and creep characteristics of Mg-Th-Zr alloys. Compositions covering the range of thorium content from M to 6 pct and zinc content from 0 to 5 pct have been investigated. The creep characteristics at 650" and 700°F reported in this paper are based on results of tests of 100-hr duration. It is appreciated that creep tests of 100-hr duration might not yield adequate data for design purposes for parts with much longer expected life. However, for the purposes of the present discussion, it is felt that the combination of stresses and temperatures used in the 100-hr creep tests have yielded a clear representation of the compositional variation of creep resistance at the temperatures investigated. Creep tests of 1000-hr duration are now in progress on a few of the most promising alloys. Preparation and Testing of Alloys The alloys studied in this intensive investigation were prepared in 25 lb capacity mild steel crucibles. The thorium, zinc, and zirconium were alloyed and poured as described in earlier publications The thorium was introduced into the melt in the form of a Mg-Th hardener," the zinc added in the metallic form, and the zirconium alloyed in the form of the commercial hardener containing magnesium and 30 to 50 pct Zr.10, 26 Fluxing practices for melting and refining were the same as for magnesium-rare-earth metal-zirconium alloys. The melts were sampled for analytical determinations and poured into separately cast 1/2 in. diameter standard tensile bars. The test bars were given a precipitation treatment of 16 hr at 600°F in laboratory furnaces. It has been shown by other tests that a high temperature solution treatment followed by an aging treatment is unnecessary for the development of optimum properties in Mg-Th-Zn-Zr alloys. The selection of 600°F as the aging temperature was based on an attempt to achieve metallurgical stability without coalescence of the undissolved phases and the attendant loss in strength. The thorium, zinc, and zirconium contents of each melt were determined chemically. The zirconium contents are reported in two parts, "soluble" and "insoluble," referring, respectively, to the portions present in the alloy which are soluble and insoluble in dilute HCl acid. Distinction is being made between these two components of the zirconium content in the alloys because it has been found that only that portion of the zirconium content which is soluble in dilute inorganic acids affects the structure and properties of the alloys. The usual impurities consisting of copper, iron, manganese, and nickel were determined spectroscopically. The analysis for each melt is listed in Table I. A description of the methods of tension and creep testing has been detailed in earlier papers. The tests were performed with the cast skin re-

Jan 1, 1954

Oct. 8-13, 1917 COMMITTEE ON ARRANGEMENTS H. A. BUEHLER, Chairman, W. E. McCOURT, Secretary, C. J. ADAMI, Southeastern, J. A. CASELTON, Entertainment, F. W. DEWOLF, Book, , E. F. GOLTRA, Finance, L. L. HUTCHISON, Tulsa, E. McAULIFFE, Transportation, P. N. MOORS, Reception, MRS. P. N. MOORE, Ladies, J. D. ROBERTSON, Publicity, VICTOR RAKOWSKI, Joplin., H. A. WHEELER, Excursions, A. THACHER.

Jan 7, 1917

By C. E. Birchenall, R. H. Condit

THREE surface activity procedures are in com--L mon use for the determination of diffusion coefficients in solids. In the oldest of these' the activity observed at the original surface is compared before and after diffusion, where all the activity is in a thin, plated layer on the surface before diffusion. Partial absorption of the radiations from active atoms which have diffused below the surface reduces the effective activity after diffusion. The formula employed to calculate the diffusion coefficient is where F, is the ratio of final to initial activity at the surface, measured with identical counting geometry; Z=u3Dt, where D is the diffusion coefficient; t is the diffusion time; and u is the absorption coefficient for the radiation in the solid as defined by Lambert's law. This absorption law implies that all the rays are parallel to each other and normal to the specimen surface. This assumption of a collimated beam used by Steigman, Shockley, and Nix has been adopted by all other investigators and, although it gives results which are approximately correct under restricted physical conditions, it does not represent many actual circumstances. It is the purpose of this paper to show the importance of the divergent rays and to indicate a procedure for taking them into account. In the residual activity method the activity is determined on a series of surfaces ground on the specimen at progressively greater depths in the diffusion layer parallel to the initial surface. Gruzin2 has de- rived a formula for this procedure, which may be put in the form where I is the ratio of the activity measured at a newly ground surface at distance k below the initial surface to the activity at the initial surface measured after diffusion, and K= k/2p Dt. A third procedure involves the autoradio-graphic determination of activity on a plane ground at a small angle to the initial interface through the penetration zone. Aut oradiography can be particularly sensitive to the oblique rays. Unlike most counters which detect essentially all ß particles or X-rays which enter the active volume as a single event, the photographic emulsion may be thin enough so that oblique rays with longer path length in the emulsion produce more darkening than rays which move normal to the film plane. Consider a plane containing a source of radiation uniformly spread over a circle and a point counter located on the perpendicular through the center of the circle. As the counter moves along this line, the total angle 6, at the counter subtended by the specimen will vary. For a fixed counter distance, let 6 be angle between the counter axis and the line connecting the counter to a point P on the active plane. If an absorber of thickness X is interposed parallel to the source between counter and source, the ray from point P to the counter will pass through an absorber thickness X secant 6. Exponential absorption is assumed to hold for all rays. If r, is the ratio of intensity at the counter with absorber to the intensity without absorber and a = pX, 1 00 The behavior of this integral, evaluated numerically,

Jan 1, 1957

[NORTH AMERICA UNITED STATES ALABAMA Birmingham Cord, Richard H. Dlsmukes, Edward B. Hunter, Robert A. Citronelle Perrin, Huey P. Fairfield Pagel, Herbert Ervin Fairhope Ruffles, William R. Huntsville Eng, Harvard Kelley, Dean W. Waggoner, J. B. Weber, Thomas C. Mobile Hankins, James D. Horner, William L. Petroutson, Peter C. University Cudworth, James R. Jones, Walter B. Mason, William L.]

Jan 1, 1961

ROBERT H. LEACH, Chairman ROBERT F. MEHL, Past-Chairman D. K. CRAMPTON, Vice-Chairman E. M. WISE. Vice-Chairman W. M. CORSE, Treasurer LOUIS JORDAN, Secretary 29 West' 39th St., New York, N. Y. Executive Committee 1940 1941 ARTHUR PHILLIPS W. P. SYKES L. E. SCHUMACHER E. A. ANDERSON CARL E. SWARTZ D. L. COLWELL 1942

Jan 1, 1939

University of Alabama University, Alabama Mining and Metallurgical Society Meets first and third Mondays each month JOHN MACLEOD MCKEE, President WILLIAM L. ALLMAN, Secretary J. R. CUDWORTH, Faculty Sponsor RICHARD L. BOWRON, Counselor University of Arizona Tucson, Arizona Millers' Society LA MONT WEST, President AL WALLACH, Secretary J. B. CUNNINGHAM, Faculty Sponsor B. R. HATCHES, Counselor

Jan 1, 1939

[Billings Petroleum Section: Fraser M. Burback, chairman; N. J. Matthews, first vice-chairman; Charles B. Evans, second vice-chairman; and lion M. Madden, secretary-treasurer. Meets 3d Tues., Petroleum Club. California Coastal Section: Jack R. Severns, chairman.; Gilbert L. Jemmott, vice-chairman,- Jack A. Biren, secretary; and Robert L. Richardson, treasurer. Meets 3d Thurs.] [ ]

Jan 1, 1961

By Coolbaugh, Franklin

CRUSHING of Climax mine-run ore is carried out in two plants: No. 1 plant (flowsheet in Fig. 1) has a capacity of approximately 5000 tons per day. It is used as a stand-by except when maximum production is required. No. 2 plant (Fig. 2) has a top capacity of approximately 17,000 tons per day. The No. 2 crusher is more efficient to operate on reduced tonnages regardless of the wide variation in peak capacities. The system of crushing is similar in both plants: Mine ore, of a size which can be drawn through 48 by 96-in. slusher openings underground, is dumped into the crusher bins from ten-ton mine cars and fed into 48 by 60-in. Buchanan jaw crushers by means of chutes and Ross chain feeders. The jaw crushers are set to discharge at approximately 9-in. size. Jaw crusher discharge is conveyed to 7-ft. Symons standard cone crushers where it is broken to minus-2-in. size,

Jan 1, 1946

By B. G. Reisdorf

This paper describes the microstructural changes that occur when quenched ultrahigh-strength steels containing OA pet C and various amounts of nickel, silicon, and cobalt are tempered. The changes that occur in hardness, yield strength, and martensite diffraction-peak widths when these steels are tempered are related to the precipitation of the carbide phases. An unea$ectedly high silicon content (about 30 pct) was found in the E -carbide phase in a steel containing only 1.5 pct Si. TEMPERED martensitic steels have such wide-spread utility that they have been the subject of numerous investigations, and a sizable amount of literature has developed on this subject.M This investigation, which is a part of a larger program to correlate microstructure with mechanical properties at a variety of strength levels, is limited to the microstructural changes that occur when a quenched 0.40 pct carbon steel (USS Airsteel X-200 steel) is tempered, and to the effects of the alloying elements—nickel, cobalt, and silicon—on these microstructures. Used in this investigation were electron microscopy, electron-diffraction identification of the carbide phases, electron-probe micro-analysis of the carbides, X-ray determinations of retained austenite, and measurements of martensite X-ray diffract ion-peak widths. MATERIALS AND METHODS The chemical analyses of the eight heats examined eats No. 30 through 37) are shown in Table L Heat No. 30 has the chemical com~osition of Airsteel X-200, and the remaining seven heats contain various amounts of nickel, chromium, cobalt, and silicon. The heats were air-melted in an induction furnace and cast into 8 by 8 in. ingots that were subsequently heated to 2300 and rolled to 1-in.-thick plate. Oversize 0.505-in.-diam tensile specimens were rough-machined from the plates and austenitized in air at 1700° F for half an hour and oil-quenched. The specimens were then tempered in air at temperatures of 400° to 1000 for tempering times of 1, 4, and 16 hr, and finish-machined to 0.505-in.-diam tensile specimens. Electron micrographs were prepared from Formvar replicas of the midthickness of tensile-specimen shanks that had been electrolytically polished and etched in nital. Electron-diffraction patterns were obtained from carbon-extraction replicas. The replicas were prepared by etching the sample surface in the same manner as for microscopy, evaporating carbon on the etched surface, and re-etching the sample to free the carbon film and the precipitate particles. Electron-probe microanalysis was performed on some of the extraction replicas. To obtain adequate fluorescent X-ray intensities, several thicknesses of replica were exposed to the electron beam so that the results represent an average composition of the extracted particles rather than an analysis of single precipitate particles. The retained austenite contents of the specimens were determined by an empirical X-ray diffraction

Jan 1, 1963

By G. M. Willis, F. L. Hennessy

The oxygen pressure in equilibrium with silver and Ag2O-B2O3 melts has been measured between 800' and 900°C, to obtain the thermodynamic properties of the liquid. The compound Ag20. 4B20:1 appears to exist in the liquid, which shows marked heat content and entropy effects. A KNOWLEDGE of the thermodynamic properties of binary liquid silicates, borates, and phosphates would be of considerable assistance in the interpretation of the behavior of multi-component metallurgical slags. However, the literature contains comparatively few studies of the thermodynamics of binary slags. The system Ag20-B,O, attracted our attention as it was known to give a single liquid phase,',' in which high contents of silver could be obtained (up to 61 pct Ag according to Foex2). Further, it would be expected that the partial pressure of oxygen over melts in equilibrium with metallic silver could be used to determine the activity of Ag2O in the Ag,O-B,O, system. In many respects, it may be expected that the reaction of a basic oxide with boric oxide would be analogous to its reaction with silica. Liquid immiscibility frequently occurs in both borate and silicate systems. With B2O3 and SiO reaction with a basic oxide presumably involves a breakdown of the three-dimensional network of the acid oxide by reaction with oxygen atoms common to more than one silicon or boron atom. Ag2O-B2O3 was therefore investigated as a model of a slag system in the hope that its thermodynamic properties would assist in understanding those of other systems. Several methods for determining the activity of a component in a slag have been described in the literature. Chang and Derge" used high temperature electromotive force measurements to obtain the activity of SiO2 in CaO-SiO2 and Ca0-Al203-Si02 slags, but the cell reaction in their work is not clear. low has used rate of volatilization and vapor pressure measurements combined with phase diagrams to obtain activities in the systems KO-SiO,, Na,O-SiO, and Li,O-SiO," and PbO-SiO26 Taylor and Chipman7 extrapolated their results for the distribution of FeO between liquid iron and CaO (+Mg0)-FeO-SiOl slags to obtain the activity of FeO in the binary FeO-SiO2 system. In principle, one of the most direct methods for obtaining the activity of a metallic oxide in a phase is by comparison of the equilibrium oxygen pressure for the system metal-pure oxide with that of metal oxide-containing phase. Schenck and othersa have studied the stabilization of Ag2O on combination with other oxides (MO,) in the solid state by measurements of the oxygen pressure in systems of the type Ag-Ag,O-xM0,-MOy-0, (gas). Schuhmann and Ensio" have determined the activity of FeO in iron silicate slags in equilibrium with solid iron, using CO/CO2 mixtures to establish known partial pressure of oxygen. Although the method gives the activity of FeO without ambiguity, the slag is not a binary system, and interpretation of the results in terms of the hypothetical binary system FeO-SiO, is not possible. If a metal is solid at temperatures at which the properties of the slag containing its oxide are to be studied, this method has the considerable experimental advantage that the metal can be used as the container for the slag, and contamination by contact with refractories is avoided. In this work, crucibles for Ag2-B,O, melts were made from silver, and the liquid brought to equilibrium with definite pressures of oxygen gas. The oxygen pressure PO, thus fixes the activity of Ag20 in the liquid silver borate. For the reaction at a given temperature. is substantially constant, is directly proportional to the square root of the equilibrium oxygen pressure. Varying the oxygen pressure changed the silver oxide content of the liquid and it was possible to obtain the activity of Ag2O over a range of composition. Experimental Procedure In principle, the method consisted of bringing melts in silver crucibles or boats to equilibrium at a fixed temperature under a definite pressure of oxygen and analyzing the glass after solidification. Materials: B2O3 glass was prepared from A.R. quality boric acid by fusion in platinum. The silver

Jan 1, 1954

By T. Watanabe, S. Karashima, H. Oikawa

Creep tests of a! iron and its solid-solution Fe-Mo, Fe-Co, and Fe-Si alloys with bcc structure were conducted under constant stresses in ferromagnetic and paramagnetic temperature regions above 0.5T,(T, is the absolute melting temperature). It was found their high-temperature creep behavior changed in the vicinity of the magnetic transformation temperature, that is Curie temperature, TC. In the ferromagnetic region below the steady-state creep rates were lower than those expected from the extrapolation of the data in the paramagnetic region, the amount of decrease being affected by solute addition. Also, activation energies for steady-state creep were different in the two temperature regions. The observed changes were concluded to be due to the effect of ferromagnetism on diffusion. It is well-known that plastic deformation of metals and alloys in the temperature region where mobility of atoms becomes high enough is controlled by atomic diffusion." Many experimental results394 on fcc and hcp materials have been reported to confirm this view. In bcc metals and alloys, not much basic investigation of creep deformation has been performed. In particular, experimental work on iron5-&apos; and its alloys, covering a quite wide temperature range is extremely scarce. On the other hand, the effect of ferromagnetism on diffusion has recently been demonstrated in a iron and its alloys;&apos; it has been made clear that diffusion rates in ferromagnetic temperatur~e region are significantly lower than those expected from diffusion measurement in the paramagnetic region. Therefore, it is concluded that the magnetic effect influences the high-temperature creep behavior in a! iron and in its alloys. The present authors have conducted creep experiments on a iron and its solid-solution alloys over a very wide temperature range, and have demonstrated the magnetic effect. A part of the result has already been reported elsewhere.26 In this paper, the experimental results will be described in detail. While the manuscript was in preparation, a similar magnetic effect on creep deformation of a iron was reported by Ishida . Though their experiments covered an extremely wide temperature range, the creep stresses varied from several thousand psi to several ten thousand psi with decreasing temperature. Consequently, it may be said that there remain some questions concerning their results. I) EXPERIMENTAL PROCEDURE The materials used in the experiments were pure iron and its alloys; they were prepared by vacuum melting (10"" mm Hg) electrolytic iron (99.9 pct), molybdenum powder (99.9 pct), ultrapure silicon, and cobalt pellet (99.5 pct) in alumina crucibles. The ingots were hot-forged to plates 10 mm thick and 50 mm wide, and then were hot-rolled at about 700°C into sheets 1 mm thick. Creep specimens, 5 mm in width and 15 mm in gage length, were machined from the sheets. They were annealed at temperatures which were well above their respective recrystallization temperatures. The chemical compositions of the metal and alloys are shown in Table I together with their heat treatments. High-temperature creep tests by the use of a lever-type creep testing machine were carried out in argon atmosphere under constant tensile stress. In order to keep &eep stress constant within about *0.5 pct, stress change due to specimen elongation was compensated by tensile force of a stainless-steel bellows which was inserted between the loading lever and lower specimen grip with the assumptions of a linear relationship between change in cross section and strain and uniform strain along the section. Beyond the limit of compensation by the bellows, small amounts of load were removed after appropriate strains. The testing temperatures were maintained to within i2"C of the reported values. Creep deformation was auto-graphically recorded at the upper (moving) specimen grip using a linear differential transformer which was held by a stainless-steel rod mechanically connected to the lower specimen grip. It was also directly measured with a dial-gage reading to -& mm. 11) EXPERIMENTAL RESULTS AND DISCUSSION 1) Creep Curves of a Iron and Its Alloys. Creep curves of a! iron, Fe-Si, Fe-Co, and Fe-Mo (<2 at. pct Mo) alloys usually consisted of three stages, that is transient (primary), steady-state (secondary), and accelerating (tertiary) stages. An example is illustrated in Fig. 1 for a! iron. However, in Fe-Mo alloys with more than 2 at. pct Mo, an inverse transient creepZ8 was observed as indicated in Fig. 2. The inverse behavior, which varied with the amount of molybdenum, may be due to the substructure* in the annealed specimen as was sug-

Jan 1, 1969

By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966