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JUST as I have told you that it is impossible to give an exact rule for the bell scale, so I say the same concerning the clappers. Yet, if one wishes the bell to sound well, it is necessary that it have a proportioned blow; for if it is struck with a clapper that is lighter than it should be, it will not give out all the sound that it contains, and if it is struck with a heavier one than it can support, it is forced and the sound is made crude and harsh, in addition to the danger of breaking the bell. Therefore-the clappers must be made so that they bear a certain proportion to the bell, and in order not to proceed by chance, I have diligently tried to find the method as well as possible. I have found that experienced masters [99] have given to bells weighing ten pounds a clapper of one and a half pounds [and, to larger ones, clappers as tabulated on the next page].* Larger numbers than these I have not found because, in truth, few of the extraordinarily large ones are made in our regions. In my opinion, the masters should not be limited to these rules for the differences in clappers but should proceed according to the kind of bell, using a certain discretion for it is not possible to give a definite rule.

Jan 1, 1942

Jan 1, 1951

Jan 4, 1951

HenRy Clay FRick, a pioneer in modern coke and steel industry and, in more recent years, one of the outstanding financiers of America, died on Dec. 2, 1919, at his home on Fifth Avenue, New York. Although he had been ill since election day, when he had an attack of indigestion which developed into ptomaine poisoning, his death was a surprise to all. He is survived by his widow, Adelaide Howard Childs Frick; a son, Childs Frick, one unmarried daughter, Helen C. Frick, and four grandchildren. A quiet funeral service was conducted at the Frick home on Wednesday afternoon by the Rev. Dr. Leighton Parks, pastor of St. Bartholomew's Episcopal Church. This was attended by members and very intimate friends of the family, Trustees of the Metropolitan Museum of Art, Officers of the Links Club, and Directors of the United States Steel Corpn. Henry Clay Frick was born Dec. 19, 1849, in West Overland, Westmoreland Co., Pa. His father, John W. Frick, was a farmer of Swiss ancestG, and his mother, Elizabeth Overholt Frick, a member of an old Mennonite family. Until he was sixteen, he spent his time at school, on his father's farm, and in his grandfather's distillery, where he kept books. He attended Otterbein University, in Ohio, for a year. Frick, learning that coke was an essential of the already rapidly developing steel business, early invested every cent he could get in coking-coal lands. With the help of an associate of his grandfather, he formed the corporation of Frick & Co., coke dealers, and acquired fifty-one ovens in the Connellsville region and 300 acres of soft-coal lands. During the panic of '73, with the help of Judge Thomas Mellon, a Pittsburgh 'banker, he bought out his partners and while coke was selling at 90 cents a ton enlarged his purchases of suitable lands. Later, the price of coke increased until it was selling at $5 a ton. Before he was 30 years old, Frick was rated a millionaire. Association with CaRnegie In 1878, he sold an interest in the business Do E. M. Ferguson of New York, and later a share to Mr. Ferguson's brother. Four years later the business was reorganized into the H. C. Frick Coke Co. with vast coal lands, great banks of ovens, and a capitalization of $2,000,000. Then began his association with Andrew Carnegie. He exchanged a part of his coke interest for shares in Carnegie Brothers of Pittsburgh,

Jan 1, 1920

By Ralph Hultgren, David W. Mitchell

Magnesium alloys usually are superheated before casting in order to ensure fineness of grain. Superheat temperatures in common use range from 1600" to r 7o0°F.; the casting temperature, which depends upon the mold shape, is usually 200° to 300°F. lower. The process of superhcating requires considerable time and seriously shortens the life of the iron pots used. Recently it has been reported1 that if acetylene, carbon dioxide or natural gas is bubbled through molten electrolytic A.S.T.M. No. 4 alloy at 1400°F. for 5 min., grain refinement equivalent to that of superheating will take place. Addition of certain solids such as graphite or aluminum carbide accomplishes the same results? As will be shown in this paper, it is possible to achieve grain refinement in magnesium casting alloys at low temperatures by mechanical stirring of the molten metal for a short time. This process was developed in the course of research work, supervised by the War Metallurgy Committee under the "Restricted' project NRC-550, for the Office of Production Research and Development of the War Production Board. This paper, based on that work, has been released for publication by the O.P.R.D. Materials and Methods The alloys studied were the most common American sand-casting alloys designated as No. 4 and No. 17 by the American Society for Testing Materials. The magnesiun used in these alloys was of both carbothermic3 and electrolytic' origin. Chemical analyses supplied by the producers are shown in Table I. Each heat consisted of approximately 5 lb. of alloy melted in a Tercod crucible. It was refined by fluxing with Permanente No. 7* refining flux at 1300° to 1350°F. After cooling to 1200° to 1250°F., portions of approximately one pound each, were ladled into iron crucibles contained in an electric furnace at about 1250°F. The molten metal was covered with Permanente No. 21 † covering flux and then heated to the temperature to be investigated. Normally each of the four portions was given a different treatment. In a typical case one portion was stirred vigorously for 5 min., acetylene gas was passed through a second portion for 5 min., a third portion was superheated to 1600°F. for 15 min., then . cooled to casting temperature, and the fourth was held for 5 min. at the temperature of stirring or gassing without other treatment. Each portion was then cast into one-inch diameter cylinders in three "nonturbulent" molds of identical shape. One mold was made of cast iron and the other two of baked sand. The cast-iron mold and one of the baked sand molds were heated to 360°F., the other baked sand mold was at room temperature. The freezing times in these molds were

Jan 1, 1945

By E. Hein, R. A. Dodd

The fatigue softening of prior strain-hardened poly crystalline copper has been determined by measuring changes inflow stress resulting from fatigue treatments. Tensile fatigue does not soften the metal, while the softening due to reversed stress fatigue depends on the extent to which fully reversed stressing is approached. True tensile fatigue is shown to be possible only in the case of long wire specimens. Annealing following fatiguing of strain-hardened metal shows that tensile fatigue is very effective in modifying normal recovery and recrys-tallization. OBSERVATIONS by Ludwik and Scheu,' Kenyon,' Polakowski and Palchoudhuri, Kemsley, and Broom and Ham,596 have shown beyond doubt that strain-hardened metals are softened by reversed-stress fatigue. To some extent the softening might be associated with a rearrangement of dislocations, but the results of Broom and Ham5 on the temperature dependency of the fatigue hardening of annealed copper, and those of McCammon and Rosenberg7 on the partial recovery at 100'C of fatigue-hardened copper suggest that point defects may be involved. Since lattice vacancies are the only species of point defect present in appreciable quantities in thermody-namic equilibrium, most attention has been accorded them in the various theories advanced to explain hardening and softening effects resulting from fatigue. Precise mechanisms remain uncertain, and while some effects may be due to single vacancies, defects arising from vacancy clusters may also contribute to the changes in properties. All types of plastic deformation result in point-defect formation, one frequently invoked formation mechanism involving the nonconservative motion of jogs formed by the intersection of, for example, mixed dislocations. But since fatigue deformation is thought to be a particularly effective way of forming point defects, additional mechanisms peculiar to fatigue must be sought. One possibility is that jogged loops contract during the unloading cycle to give rows of vacancies. A local high-vacancy concentration could conceivably promote polygonization and recovery by climb, and, therefore, could explain the fatigue softening of strain-hardened metals under appropriate conditions of temperature. Conversely, the experiments by Broom and Ham6 on the fatigue hardening of copper single crystals involving subsequent tensile testing of previously fatigued specimens, resulted in the observation of distinctly lowered yield points. This could be due to vacancy atmospheres associated with dislocations, possibly augmented by jogs on dislocations. In addition to the yield-point phenomenon, a post-yield hardening was observed, with a temperature-dependence resembling the friction-hardening of irradiated metals,9 this again suggesting a point-defect mechanism. An important development in this field has been the observation,10 by transmission electron microscopy, of high concentrations of prismatic loops in fatigued aluminum. By analogy with quenched aluminum filmso11 it seems certain that these loops originate in the collapse of vacancy clusters formed during deformation. Metals, such as copper, having a relatively low-stacking fault energy would tend to produce Frank sessile loops (in practice tetrahedral defects with stacking faults on all (111) planes) rather than the glissile prismatic loops observed in aluminum. The manner in which these various defects affect the different aspects of fatigue behavior has not yet been fully investigated. The present work was designed principally to indicate whether tensile fatigue gives rise to hardening and softening effects similar to those associated with reversed stress fatigue, and with the hope of providing additional information on the contribution of point defects to fatigue deformation. Despite the uncertain ty often associated with the interpretation of resistivity data, i.e., the relative contribution of stacking faults and other defects, such measurements are conveniently employed to study point defect pheno-

Jan 1, 1962

By Roshan B. Bhappu, Ronald J. Roman, Dexter H. Reynolds

The reaction between manganese dioxide and molybdenite in a water- sulfuric acid medium was studied at atmospheric pressure and from 25° to 103°C. Both solids are dissolved to give, as final products in solution, Mo(VI), S(VI), and Mn(II). Stoichiornetric relationshifis are most simply represented by the equation MoSz + YMnO2 + 15H+ - HMoO-4 + 2HSO-4 + 9Mn++ + 6H20 The rate of this reaction was found to be dependent on temperature, manganese sulfate concentration, acid concentration, and, in a complex way, the surface areas of both manganese dioxide and molybdenite. Both the total amount of manganese dioxide and tnolybdenite and the ratio of manganese dioxide to molybdenite played a part in determining the over-all rate of the reaction. The effect of acid concentration on the rate was also dependent on the ratio of manganese dioxide to molybdenite. SEVERAL reports in the literature describe reactions using manganese dioxide in water-sulfuric acid media as an oxidizing agent. Nearly all previous work describes interactions between an ion and manganese dioxide, such as the oxidation of ferrous to ferric iron,' or the interaction between a molecule in solution and manganese dioxide, such as the oxidation of toluene to benzaldehyde.2 Only a few references describe the use of solid manganese dioxide to oxidize another solid in sulfuric acid. One report3 states, "Manganese dioxide in dilute sulfuric acid solutions had no beneficial effect (in leaching copper from chalcopyrite), but in more concentrated acid solutions the rate of solution was about the same as that for permanganate." In 1902 a German patent4 described a process which used manganese dioxide in strong (50°Be') sulfuric acid for oxidizing chromite ores to soluble iron and chromium salts. The process consisted of mixing the sulfuric acid with the finely ground ore and manganese dioxide. The pulp was then heated to about 120°C and an electric current passed through it. The manganese dioxide apparently dissolved in the strong, hot acid solution, oxidized the iron and chromium and itself was reduced to manganese 11! then was oxidized at the anode back to manganese dioxide, and the cycle repeated. An extensive study5 of the kinetics of the oxidation of pyrite with manganese dioxide indicated that in dilute sulfuric acid solutions (about 0.1 N) and at elevated pressures the dissolution of the pyrite was brought about by air oxidation of the iron to ferrous sulfate, followed by manganese dioxide oxidation of the ferrous sulfate to ferric sulfate. The mechanism proposed by the authors involved the oxidation of the iron at the surface of the manganese dioxide. Also! the oxidation of sulfide sulfur to sulfate was credited to the oxygen in the air, not to the manganese dioxide. Since the metallurgical literature is lacking in information concerning the use of one solid to oxidize another solid. the current investigation was under-

Jan 1, 1965

By T. F. Mueller, P. A. Witherspoon

For the case of an infinite radial system operating at constant terminal rate, the reservoir engineer often uses the "point source" solution of the diffiusivity equation to study pressure interference effects. At early times and at short distances from the inner boundary these solutions are invalid. The amount of error is often not precisely defined because of mathematical difficulties. Work presented here shows that, if dimensionless time is defined appropriately, previous solutions of the pressure equation can be displayed .as a family of curves on one chart. These solutions include the point source solution (referred to in the field of hydrology as the Theis solution) and other solutions obtained with digital computer methods. With these curves, an exact evaluation of the pressure drop within a reservoir or an aquifer can be made by the engineer. Examples of field problem solutions are presented. In most reservoirs the error involved when the Theis solution is employed is often negligible; whereas, in the calculation of interference effects in an aquifer, a substantial error can occur through such an approach. INTRODUCTION Flow equations are used in petroleum engineering to study the behavior of individual wells and reservoirs. In the case of wells, the pressure response at the wellbore face is the major point of interest; whereas, in the case of reservoirs, the pressure response at the interface of the aquifer boundary is sought. To aid in such studies, the flow equations have been solved in terms of the behavior at these two inner boundaries. Only limited work has been published in regard to the pressure conditions away from these points, i.e., within the reservoir or aquifer. Theis and Mortada are among the few who have reported on this problem. The Theis approach employs the exponential integral and is valid for pressure conditions that occur some distance away from the flow disturbance. It is derived from the concept of a point source, as opposed to a flow across some finite area. The Mortada results, on the other hand, are valid at all points within the reservoir or aquifer. They are presented in terms of dimension less ratios of the radius where the pressure is desired to the radius where the flow rate is measured. Their main use, in the past, has been in aquifer studies. The published results are presented in the form of graphs that are limited to a maximum radius ratio of 64. These graphical results are cumbersome to interpolate at non-integral radius ratios, so that one may be forced to utilize a rather involved analytical expression presented by Mortada. BASIC EQUATIONS The solutions of Mortada and Theis are both based on the diffusivity equation as applied to the case of an infinite radial system subject to a constant terminal rate. The equation is obtained by combining the material balance equation with Darcy's flow equation. The assumptions implicit in the use of this equation are as follows: (1) a single fluid is present that occupies the entire pore volume; (2) the reservoir is horizontal, homogeneous, uniform in thickness, and of infinite radial extent; (3) compressibility and viscosity of the fluid remain constant at all pressures; and (4) fluid density obeys the equation Using the diffusivity equation in situations where the above conditions do not hold will result in errors. These errors (not discussed here) but only the errors which arise in the solution of the equation itself. The diffusivity equation for the homogeneous reservoir conditions cited above can be written in cylindrical coordinates, as To obtain a dimensionless equation, so a single solution can be used for applications of different porosity, permeability and fluid properties, the following transformations are usually made: After these transformations are made, Eq. 3 .can be written in dimensionless form, as MORTADA SOLUTION One solution of Eq. 6 has been given by Mortada.

Jan 1, 1966

By John V. Beall

Copper production in the. United States in 1972 amounted to 1,658,000 tons according to the USBM. This figure is up over 1971 but falls below 1970 production of 1,719,101 tons. This report is essentially about the status of copper mining operations in the U.S. and is an update and expansion of the report "Southwest Copper-A Position Survey" published in [A=], October 1965. At that time, the trend was toward using larger equipment to mine lower grade ore and toward the expansion of dump leaching practice. That trend continues today but, it is overlain by intensive activity to comply with existing environ¬mental legislation and uncertainty over proposed revisions of venerable laws governing mining. In the U.S. today there is, practically speaking, no excess smelting capacity so that expansion of copper production through the startup of new mines is inhibited. Owners of a large undeveloped orebody would have to decide before going into production whether to sell the concentrates offshore, which has many problems, whether to try one of several unproved chemical processes for producing refined metal from concentrates or embarking on the construction of a traditional pyrometallurgical plant in the face of considerable uncertainty over the pollution standards that eventually must be met. The situation is such that not only is the present rate of U.S. copper production threatened but the ability to meet projected increased demand in the years ahead may have been severely retarded.

Jan 4, 1973

By A. J. Carlson, G. M. Marincel, M. L. Hovland, J. H. Healy

Research personnel of Erie Mining Co., a pioneer taconite mining firm on the Mesabi Range, have invented a new method to make an effective 325 mesh separation at high tonnage rates over stationary screens. The company regards this development as historically significant in that it represents the first successful method to commercially screen large tonnages of ore at fine sizes. Erie, which is now completing an expansion program at its plant site near Hoyt Lakes, Minn., has incorporated this screening method as part of that expansion. When completed, the concentration plant will produce 10.3 million tons of iron concentrate, all of which will have been efficiently screened at 325 mesh.

Jan 4, 1967

By H. N. Wolcott

Among the many cases of replacement of one mineral by another, that of quartz or silicates by pyrite, or even other sulphides, is not uncommon, but the reverse of this process does not appear to have been recorded, even if it has been observed. It seemed to the writer, therefore, that the case described below was worthy of record. Fig.1. GROUndALass of chalcopyrite (C) containing Rounded GRAINs of TYRITE (P) SHOWING DEFFERENT DEGREES OF REPLACEMENT BY QUARTZ (($), AND ALSO QUARTZ VEINLETS CUTTING THROUGH THE PYRITE. (PHOTOGRAPHED BY REFLECTED LIGHT.) The specimens described in this paper were obtained by R. B. Morton of Idaho Springs, Colo., from the Old Town mine, in Russell, Gulch, and ;re in the collection of Cornell University, where the writer studied them. In the rough, the specimens appeared to consist largely of chalcopy-rite. with some grains of tetrahediite. The polished surface of some of

Jan 1, 1918

By Denton R. Wieland, Harvey T. Kennedy

The frequency of bubble formation is measured for oils from the East Texas field and the Slaughter field in cores from these fields. East Texas oil was also tested in a Slaughter core. The data checked previous results in that a definite supersatrtration may exist without the formation of bubb1es in periods of observation totaling 158 hours. Measured frequencies varied from zero at supersaturations below 14 psi to 3.1 bubbles/sec/ cu ft of rock at 40 psi supersaturation INTRODUCTION The formation of bubbles is essential in a solution gas-drive reservoir in the displacement of oil. In formations where the basic pore structure consists of fine pores or fractures connected to larger pores or crevices, bubble formation in the fine pores may be the most effective means by which the oil may be displaced, even if secondary methods are applied. The most efficient oil displacement would occur where at least one bubble would form in every pore. As the pressure decreased, the bubbles would expand, due to the gas diffusing into the bubbles, and displace the oil toward the lower pressure area around the wellbore. Kennedy and Olson' have shown that the total number of bubbles formed in a reservoir is primarily dependent upon the rate of pressure drop, the rate of diffusion of gas through oil, and surface area of the rock. The surface tension of the liquid and other characteristics of the rock may also exert an important effect, which would give a different frequency to different rocks and oils and various combinations of different rocks and oils. The purpose of this paper is to present frequency measurements on two rocks and two oils. A hydrocarbon liquid is at equilibrium with gas when it contains the maximum volume of gas in solution that it can have at the prevailing temperature and pressure. If the temperature is maintained constant and the pressure is reduced below the equilibrium pressure, the liquid is supersaturated to the extent of the difference in the two pressures until the gas comes out of solution as a free phase. As shown by previous work, and confirmed in the present investigation, the number of bubbles formed per second increases with an increase in supersaturation. Kennedy and Olson showed that a tenfold increase in the rate of pressure decline resulted in a tenfold increase in the number of bubbles formed per cubic foot of reservoir rock, e.g., for decline rates of 0.1, 1, and 10 psi/day, the number of bubbles formed per cubic foot would be 40, 400, and 4,000, respectively. For another hypothetical system, Stewart, Hunt, and Berry' estimated that for pressure declines of 0.1, 1, and 10 psi/day, the number of bubbles formed would be approximately 10, 100, and 1,000 cu ft of reservoir rock. Their value of bubbles formed is lower than given by Kennedy and Olson; however, the order of magnitude agreed satisfactorily. The rate of diffusion will also affect the number of bubbles formed. If the diffusion coefficient is high, the gas in solution in the oil surrounding a single bubble will tend to diffuse into the bubble rather than forming other bubbles. On the other hand, the formation of more bubbles will tend to occur if the diffusion coefficient is very low. In his thesis dated Aug., 1953, Wood" reports on the frequency of bubble formation in a system consisting of oil and rock from the Rangely field. In the present work, the apparatus of Wood was redesigned to allow greater precision, especially at low supersaturations, where bubble growth is slower, and detection is more difficult.

Jan 1, 1958

By L. W. Fagg

The purpose of this paper is to present in a convenient form data and examples necessary in making dynamometer card analyses; also to outline a procedure of well weighing. Many articles and papers have been written delving into the mathematical considerations relative to the shape and characteristics of dynamometer cards. However. it is recognized that there are too many unknown factors involved in such calculations to assure a workable degree of accuracy. For this reason the accepted procedure is to take dynamometer cards on wells in question rather than try to calculate the load curve. The polished rod dynamometer is now recognized as a necessary tool for measuring loads, torque, and horsepower. It is also used to determine pump action and trouble-shoot for any seemingly abnormal pumping condition. The apparently infinite variety of a = maximum load (height x scale constant) b = minimum load. Range of load is difference between maximum and minimum load speed—taken with stop watch stroke —measured at polished rod c = beginning of down stroke in direction of arrow. (End of up stroke) d = beginning of up stroke. (End of down stroke). Polished Rod Horsepower = (Area of card) x Scale const. x Stroke x Length x spm (Length of card) 33000x 12 1.35 1.35------x5300x 24 x 12 2.53 --------------------------= 2.06 23000x12 Appraximate Peak Torque: Upstroke = (2390) (12) (1) = 28,700 in. Ib Downstroke = (1 860) (12) (.866) = 19,300 in. Ib Counterbalance should be increased to make up stroke and down stroke peak torque equal. FIG. 1 dynamometer cards that can be obtained is one reason for the general lack of usage of the dynamometer as a control instrument rather than a means for making routine measurements of leads and horsepower. When it is considered that the dynamometer card is a record of the resultant of all forces acting on the polished rod at any particular instant during the pumping stroke. the problem is then one of breaking down this resultant into its various components. As a means of a quick review we shall consider the examples shown in Figs. 1 to 9: and Tables I and II and then proceed to the interpretation of variously shaped cards caused by some abnormal operating condition. In Table 11, when we were considering the factors involved in calculating the peak polished rod load, it can be seen that the factors involved greatly oversimplify the problem. Certain assumptions are made which may or may not he even close to the actual field conditions, such as the specific gravity of the fluid generally considered as one; that the crank has constant angular velocity; that the down-hole friction is zero; and that the fluid lift is from the pump. In the following examples we shall see what a variation in fluid weight and friction can do to the general shape and magnitude of the dynamometer card. (Figs. 10 to 22.) MAKING THE WELL STUDY It is obvious that it would be impractical to consider in detail all of these factors each time a well study is made, inasmuch as each well study job could conceivably be extended into a research project rather than serve the practical requirements of finding the answer to a specific problem. For this reason it is important that some objective be established previous to the time the well study is made. Load at TU = 3070 Ib Crank angle when polished rod is at position TU = ? ? = 30° Maximum counterbalance effect at polished rod = 2760 Ib Torque at TU = (Load at TU — Max. counterbalance effect-lbs) sin 0 x Length of Stroke 2 = (3070-2760) .5 x 24 = 1860 in. 15 2 Torque at TD = (Load at TD — Max. counterbalance effect-lbs) sin ? x Length of Stroke 2 = (530 - 2760) sin 330' x 24 = 13,400 in. Ib 2 Note: sin 0 from c to d on UPSTROKE will be positive value. sin 0 from c to d on DOWNSTROKE will be negative value Torque at c and d is zero because 0 is zero. FIG. 2 —APPROXIMATE METHOD FOR CALCUlATlNG TORQUE

Jan 1, 1950

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 S. K. Kawatra, R. A. Seitz

Various mathematical models and expressions to describe the behavior of a hydrocyclone have been presented in the literature (Lynch and Rao, 1977; Plitt, 1976; Plitt and Kawatra, 1977). Two of these models, by Lynch (1977) and by Plitt (1976), have been extensively used for process control studies (Kawatra and Thayer, 1879; Seitz and Kawatra, 1984). However, neither of these models relates the fineness of grind in a hydrocyclone overflow to the corrected efficiency curve of a hydrocyclone. If such a relationship were available, then one could relate fineness of grind to the operating variables using equation (1) or (2). A plant metallurgist is interested in knowing the fineness of grind rather than the dso(c) of a hydro- cyclone. As a consequence, several empirical relation- ships between fineness of grind and hydrocyclone operating variables are available. These relationships (Fewings, Wickham, and Wiseman, 1979; Manning, 1978; Watson, Cropton, and Brookes, 1970; Watts, Thompson, and White, 1978; Wiegal, 1973) have only a limited relationship with each other and have met with varying degrees of success. The object of this paper is to develop a fundamental relationship between fineness of grind and the efficiency curve of a hydro- cyclone

Jan 1, 1986

By J. Pinto, F. Galasso

THE current emphasis in preparing boron fibers by reduction of gaseous boron compounds on a resistively heated metal wire substrate has renewed interest in the borides of those metals which have relatively high melting points and are available as fine wires. A knowledge of the structures and properties of the borides, which are formed when boron diffuses into the metal core during boron deposition, can be of assistance in the understanding of the boron fiber formation process and the fiber properties. Many of these borides are well-known and their properties have been measured. However, when an unidentified boride is found in the core, it may be difficult to establish its composition because of the small amount of material available, the preferred orientation effects on the reflections in its X-ray pattern, and the possible overlap of X-ray reflections if several borides are present in the core. For example. the proper indexing of the X-ray pattern of WB4, which was formed in the tungsten substrate core during boron fiber formation, was accomplished only after small single crystals of this boride were grown and X-ray precession investigations were conducted.' This note presents the results of a study of the phases formed in the core when tungsten, tantalum, and molybdenum metal wires were used as substrates in the boron fiber preparation process with particular emphasis on the identification and characterization of a higher boride of molybdenum analogous to WB,. Boron was deposited on resistively heated stationary 0.0012-in.-diam tantalum, tungsten, and molybdenum wires at 1050°C for various times up to 60 sec using boron trichloride and hydrogen as the reactant gases. After 60 sec of boron deposition the fibers were approximately 0.006 in. in diam. Examination of photomicrographs of fiber cross sections showed that the boron had diffused nearly to the center of the tungsten and molybdenum cores in 15 and 30 sec, respectively, and only halfway to the center of the tantalum core in 60 sec. X-ray diffraction photographs of the fibers indicated that it was also after 15 and 30 sec deposition times that the tungsten and molybdenum metal reflections, respectively, had disappeared from the X-ray patterns of the fibers. The patterns of the boron fibers produced using tantalum wire as a substrate showed that amorphous boron, TaB2, and tantalum metal were present after a few seconds deposition time and remained even after deposition times of 60 sec. Until a deposition time of 15 sec was reached, the tungsten substrate fibers contained amorphous boron,273 6WB, W2B5, and WB4 as well as tungsten metal, while the molybdenum substrate fibers contained amorphous boron, MoBa, Mo2B5, and molybdenum metal for deposition times up to 30 sec. Just before the molybdenum metal pattern disappeared, a pattern similar to that of WB, appeared, suggesting that a phase, MOB,, isomorphous with WB,, was present in the fiber. This same pattern was obtained from the product formed by heating a mixture of molybdenum metal and excess boron powder in a boron nitride crucible at 1960°C in an argon atmosphere. As was the case with the WBn pattern, this pattern could best be indexed on the basis of a hexagonal unit cell rather than the tetragonal unit cell Chrktien and Helgorsky reported for ~0~4,~ see Table I. The unit cell parameters for MoB4 were calculated to be a, = 5.214A, co = 6.358A. Assuming the space group P63/mmc and positions5 2M01 in 2b and 2MoII in 2c found for tungsten in WB~,' a logical structure for MOB, was determined using geometrical considerations to place the boron

Jan 1, 1969

By Lewis A. Delano, Harold Rabling

It has been generally recognized that, owing to the extreme friability of galena, fine grinding has a tendency to cause excessive sliming of the mineral, so operators of lead mills have attempted to avoid this condition by commencing concentration at as coarse sizes as any mineral is freed. Jigging has been the basis of the milling process, making a clean coarse concentrate and a large amount of tailing, which was considered sufficiently low-grade to be rejected. However, developments and improvements in concentration processes are everywhere changing the low-grade tailing of yesterday into material worth re-treating today. Investigations of the work of the Hancock jig on the Bonne Terre ore have shown that the best results to be expected will give a tailing assaying 0.75 per cent. lead; the average for all conditions and grades of ore will be between 0.80 and 0.90 per cent. By crushing the jig tailings in ball-mills and retreating by tables and flotation, a tailing of considerably lower grade can be made; the problem then becomes an economic one of increased crushing costs versus higher recovery. In considering the entire elimination of jigging, the increascd smelting charges due to a greater amount of slime galena will be counterbalanced by the lower operating cost, increased recovery, and the many advantages of a simpler flow sheet. In developing these problems in the Bonne Terre mill of the St. Joseph Lead Co., a long series of tests has been carried out covering every stage of crushing and concentration, and a large number of possible flow sheets were considered and tried. Only the final results and a few comparisons will be given here. At the same time, a careful and detailed cost-keeping system has enabled us to compare milling costs with the various Bow sheets, and to calculate the economics of the problem with great accuracy. Concentration Problem The ore occurs as widely scattered deposits of galena disseminated through limestone; it has a specific gravity of 2.8 and the following composition: Pb, 4.00 per cent.; Fe, 3.00 per cent.; Zn, 0.32 per cent.; S, 3.10 per cent.; MnO2, 0.73 per cent.; SiO2, 4.20 per cent.; Al2O3, 3.20 per cent ; CaO, 28.60 per cent.; MgO, 16.85 per cent.; CO2, 36.00 per

Jan 1, 1922

By C. S. Desai

INTRODUCTION Behavior of joints in rock and interfaces in structures and geological media subjected to static and cyclic loading play an important role in analysis and design of structures founded on rock and soil foundations. The objectives of this paper are (1) to describe a device that can permit laboratory testing of joints and interfaces under translational and torsional motions, (2) to present procedures for constitutive modelling of joints and interfaces with a typical example of modelling of a concrete-sand interface, and (3) to give brief details of the proposed research plans for cyclic testing and modelling of joints in concrete as a simulation of joints in rock. The subject of testing and modelling of interfaces and joints is wide in scope, and in view of space limitations, it is not possible to provide a comprehensive review herein. Hence, only a few references, particularly relevant to the ongoing research by the authors and co-workers are included; a review of the subject can be found in (Desai, 1981) and (Heuze and Barbour, 1982). Although there can be (minor) differences in modelling for the behavior of joints and interfaces, the basic procedures can be considered to be essentially similar. Now onwards in this paper, the term joints will be used to imply both joints and interfaces. TESTING DEVICE Appropriate laboratory (or field) testing is an important and indispensable ingredient for constitutive modelling of joints. A new device has been developed for static and cyclic testing of

Jan 1, 1984

By M. Semchyshen, G. A. Timmons

P. A. Beck (University of Illinois, Urbana, 111.)—An interesting result of this work is the fact that in cold rolled molybdenum sheet complete loss of work hardening is obtainable on annealing, without change in texture. The retainment of the cross-rolling texture on soft-annealing is particularly significant, since this is essentially a single orientation texture, where texture retainment could be achieved by only one of the two niechanisms which produce this effect in aluminum,16 namely by recrystallization in situ. Recrystallization in situ was originally discovered by Collins and Mathewson (1940) and by Crussard (1944) as a phenomenon taking place on annealing in relatively mildly deformed single crystals of aluminum. It now appears to be a major (in many cases the major) mechanism of annealing of severely cold rolled poly-crystalline material, not only in aluminum,le but in metals as different in character as beryllium," tita- nium,'" and molybdenum. All these data now confirm the general validity, at least for more or less pure metals, of the interpretation of the annealing process given a few years ago by Smith.'" The whole question of recrystallization is now reopened. Indeed, it appears that recrystallization, as defined traditionally, may not occur at all, since at the time "deformed material" is absorbed by "recrystallized grains," it has already become completely strain free by recovery and "recrystallization in situ."

Jan 1, 1953

By T. D. Yensen

Discussion of the paper of T. D. YENSEN, presented at the New York meeting, February, 1916, and printed in Bulletin No. 110, February, 1916, pp. 483 to 512. JOHN A. MATHEWS, Syracuse, N. Y.-Concerning the critical composition of the steel containing 2.50 per cent. of silicon, I may say that 12 or 13 years ago we made some of these alloys. They. were not as pure as the alloys made by Mr. Yensen, nor were they melted in vacuo, but one of them contained exactly 2.50 per cent. silicon, and about 0.25 per cent. carbon. It gave us no trouble whatever in hammering to a billet or rolling into bars, nor even when rolling into ¼ -in. wire rods. The steel in question was practically free from everything except carbon or silicon and contained no manganese sulphur or phosphorus worth mention. The alloy containing 2.50 per cent. of silicon worked perfectly well, as well as one containing 0.5 per cent. silicon, and it seems to me that further work should be done by Mr. Yensen on the physical properties of alloys at this seemingly critical change point. W. E. -RUDER, Schenectady, N. Y.-We -have made silicon steels of practically every composition and have never obtained any material under 5 or 6 per cent. of silicon which was brittle. This may be due, of course, to the presence of carbon, in some of the 'commercial materials, and I presume that Mr. Yensen would argue that the: presence of this carbon might prevent inter-granular brittleness. However, all of our silicon steels, up to 5 per cent. of silicon, by treatment in hydrogen at temperatures near the melting point, can be made to show inter-granular brittleness. Furthermore, the material made brittle in this way could be restored by treating at the same temperature in hydrogen containing a hydrocarbon vapor. I discussed this matter some years ago in a paper on inter-granular cement. It therefore appears likely to me that Mr.

Jan 5, 1916