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By Henry Newton

IT may seem somewhat a work of supererogation to present to the American Institute of Mining Engineers, composed largely of gentle- men with whom the subject is so familiar, a paper on iron ores and their distribution. To many of them, however, it possibly will not be without interest, as there may be some, like myself, who hare nowhere found a connected account of the character of the deposits and the circumstances upon which are founded the great iron-producing centres of the world. This blank I have endeavored to fill,

Jan 1, 1875

By Max W. Ball

THE geologist or mining engineer, whose work takes him into the western United States, whether for the Government or private enterprises, is likely to be called upon to classify public lands as to their mineral character, or to review such classification already made, usually by a Government geologist or mineral inspector. The public-land law covering the matter is clear and logical, and a knowledge of its simpler principles is necessary to intelligent classification work. There are two classes of cases in which a classification of lands as mineral or non-mineral may be required: .first, cases in which lands classified as mineral will be retained by the Government and lands classified as non-mineral alienated; second, cases in which lands classified as mineral will be alienated and lands classified as non-mineral retained.

Jan 1, 1921

By W. Rostoker

A STUDY of the titanium-oxygen system' involved an associated series of measurements of the lattice parameters of the a and TiO phases. The results permit some interesting deductions which are herein reported. A comprehensive survey of the physical PI-operties of the phases in this alloy system has been made by Ehrlich.2 However, only impure titanium was available at that time, so that some revision of his measurements is to be expected. The lattice parameters were calculated from the high angle lines of Debye-Scherrer patterns taken in a 14 cm camera and using filtered CuKa radiation. The specimens were prepared largely by crushing and screening of lump samples which had been quenched from elevated temperatures. Only in the case of low oxygen contents was it necessary to resort to filing and annealing. The results of the lattice parameter studies are graphically presented in Figs. 1 and 2. It will be seen that oxygen produces a pronounced distortion of the c parameter of the a phase (hexagonal close-packed). The trend is in general agreement with Ehrlich's work, although the divergence of actual parameter values strongly suggests that his titanium was very impure. It will be noted that the a phase of titanium can tolerate the unusually high saturation solubility of about 34 atomic pct 0. By virtue of this unique effect, it is possible to make a calculation of the effective atomic diameter of oxygen when dissolved in a lattice with metallic bonding. This has not been possible before. Ehrlich's2 density measurements demonstrated that oxygen occupies interstitial positions in the a lattice and the trend of the lattice parameters would certainly support this. In a hexagonal close-packed unit cell the largest interstitial positions lie at (2/3, 1/3, 1/4) and (2/3, 1/3, 3/4). Accordingly, if both of these positions were occupied, the ratio of titanium to oxygen would be 1:1. The extrapolated c parameter may be taken as between 4.93 and 4.99?. The a parameter appears to reach a constant value of 2.955? at low oxygen contents. The distance of the center of a titanium atom site from the [vc2/16+a2/3-1.448] Then the atomic diameter of the oxygen atom is represented by the function: where the radius of the titanium atom is 1.448A,

Jan 1, 1953

By C. F. Jenkins, G. V. Smith

Serrated plastic flow in stable austenitic alloys based on Fe/Ni has been shown to be related to the presence of carbon and/or chromium in the systems. Strength peaks and plateaus in the serrated-flow temperature region for a commercial alloy correlate with an increased dislocation content, arising, presumably, from enhanced multiplication as a result of a strong interaction between dislocations and solute atoms. The data generally support a mechanism controlled by migration of vacancies, with the energy for vacancy motion being modified by the presence of chromium. Chromium atom -dislocation interaction is responsible for effects above 500°C, whereas the defect interacting with dislocations between 200" and 500°C is suggested to be a carbon-vacancy Pair. ThE phenomenon of jerky flow, serrated flow, or the Portevin-le Chatelier (P-C) effect in austenitic stainless steels is usually attributed to substitutional at1,2 mospheres1,2 or to precipitates&apos;-4 which form at dislocations during plastic deformation. On the other hand, evidence exists which supports a direct inter-stitial-dislocation interaction mechanism for serrated flow in fcc Ni-C,5,6 Ni-H7-9 and in nickel-austenites containing carbon." The present work consists in a study of serrated plastic flow in stable austenitic al-loys. The effects of carbon and of chromium were investigated separately, and a commercial stainless steel with different levels of interstitial impurity concentration was studied in an attempt to delineate the combined effects of the alloying elements. EXPERIMENTAL TECHNIQUES a) Materials and Fabrication. A commercial AISI 330 stainless steel and several specially prepared aus-tenitic alloys have been studied. The experimental alloys were prepared by arc melting the constituents under purified argon. Analyses of the materials are given in Table I. The commercial alloy was obtained as 5/8 in. bar stock and rolled to 0.092 in. sq, with several intermediate anneals. At this stage some of the material was annealed in Pd-purified hydrogen at 1100°C to establish different levels of interstitial content. All other heat treatments were in vacuum (10-5 torr). The "pure" alloy ingots were swaged to 0.120-in. rod and annealed in Pd-purified hydrogen at 1100°C. The analyses for these conditions are also contained in Table I. Following the above treatment, the final wire sizes Table I. Chemical Analyses of Test Materials Hrin Hydrogen at Cr, Ni, Alloy 1lOO°C wt pct wt pct C, ppm* N, ppm* Type 330 As-received 14.78 33.25 430 300 Type 330 64 14.78 33.25 40 50 Type 330 200 14.78 33.25 27 21 Fe/35 Ni 72 - 35.10 <10 62 Fe/35 Ni 200 35.10 <I0 44 Fe/35 Nil15 Cr 72 14.95 34.94 <I0 61 Fe/35 Ni/15Cr 200 14.95 34.94 <10 45 Fe/35 Ni/C $ 35.OM 380 *Sensitivity: N t 5 ppm Ct10ppm. f Nominal Ni content. % A master NiC alloy was used in preparation of this material; courtesy of D.E. Sonon. were obtained by either swaging or cold drawing. The test results did not vary with these techniques. b) Specimen Preparation. Two sizes of specimen and two gripping systems were used. i) 0.070-in. wire with a chemically milled gage section: 0.75 in. long, 0.060 in. in diam. These were fastened into grips containing tapped grooves. ii) 0.050 in. wire, gage length 1.5 in. Ball bearings were welded to the ends of the wires and the gage length was taken to include all material between the welds. Socket-type grips were used with these specimens. With specimens of type ii), joining was performed in a specially constructed brass jig, under argon, and automatic timing was utilized in the procedure. No adverse effects of welding were noted. Specimens were encapsulated and solution treated for 1 hr at temperatures selected to produce the same average grain size, -50 µ. Annealing twin boundaries as well as normal crystal boundaries were counted. The temperatures used are listed in Table 11. Table 11. Specimen Size. Temperature of Heat Treatment and Resulting Grain Diameters for Test Materials Recrystallization Resulting Material Condition Temperature Grain Sue AISI 330 Not H purified 0.070 120O°C 45 to 55µ in, wire AlSl 330 H , pure, 0.070 in. 1150°C 45to55µ wire Fc/35Nil15Cr Pure, 0.070 in. wire 1000°C 45tossp Fe/Ni Pure. 0.070 in. wire 775°C 45 to 55µ Fe/Ni/C Pure, 0.050 in. wire 850°C 10 to 20p AlSl 330 Not purified, 0.050 1150CC 45to55p in. wire AlSl 330 ti, pure, 0.050 in. 1150°C 45to55p wire

Jan 1, 1970

By W. S. Owen, T. Bell

The variation ox the M, temperature with nitrogen concentration has been determined experinzentally. The free-energy difference between martensite and the parent y Phase at the M, temperature,is computed for Fe-C and Fe-N alloys using recent solubility data fm the Fe-N system and new data for the variatim of the activity of the interstitial solute in the y phase with concentration. The "geometric model" is considered also, and the importance of Zener ordering is noted. It is shown that, although at any chosen concentration the M, temperature and the activity are significantly different in the two alloy systems, the free-energy duference is the same within the limits of experimental error, thus Providing further evidence of the very close similarity between the martensite transformations in Fe-C and Fe-N alloys. TO estimate the free-energy change accompanying the martensite transformation in binary interstitial alloys it is necessary to know the variation of the Ms temperature with interstitial solute concentration and some thermodynamic data. To date, only the Fe-C system has been discussed because this was the only system for which relevant experimental measurements had been made, but even in this case the data available are insufficient to permit the free-energy change to be calculated without the assumption of a thermodynamic model for the y and a solid solutions. The last comprehensive discussion of the topic was by Kaufman, Radcliffe, and Cohen in 1.960.&apos; Since that time Ellis, Davidson, and Bodsworth2 have redeter mined the activity of carbon in y iron as a function of carbon content and Atkinson3 has measured the activity of nitrogen in Fe-N austenite. The M, temperature of Fe-N is reported in the present paper. Thus, it is now possible to assess the free-energy change accompanying the martensite transformation in Fe-N alloys on the same basis as that used to assess the change in Fe-C alloys. This comparison is of interest because it has been shown recently4 that the structure of the martensite formed in Fe-N alloys changes with nitrogen content in a manner exactly parallel to the changes in structure in the Fe-C series and that the strain associated with the distortion of the iron lattice in either the y or the a phase by a nitrogen atom is the same as that produced by a carbon atom. The work to be described tests whether or not this close similarity between the two systems extends to the thermodynamics of the martensitic transformations. THE Ms TEMPERATURES FOR Fe-N MARTENSITE Bose and Hawkes5 found the M, temperature of a eutectoid Fe-N alloy (2.35 wt pct N) to be 35°C. This single determination appears to be the only reported measurement of the M, temperature of an Fe-N alloy. In the present work a series of more than fifteen different specimens containing between 0 and 2.7 wt pct N were prepared by controlled nitriding of pure iron wire 0.010 in. diam. The iron was supplied by B.I.S.R.A. and was designated ACN2. The nitriding procedure, all aspects of which are critical, has been described in detail elsewhere.&apos; Each specimen was quenched from the austenitizing temperature into brine at 20°C without removing the specimen from the ammonia-hydrogen atmosphere in which it was ni-trided. Alloys containing up to 0.7 wt pct N were fully martensitic. More concentrated alloys contained progressively more retained austenite. At 2.34 wt pct N the specimen was completely austenitic after quenching to 20°C. The M, temperature of specimens with M, temperature above 20°C (those containing less than 2.35 wt pct N) was determined by a thermal arrest technique. For the more concentrated alloys (2.35 to 2.70 wt pct N) the variation of electrical resistance with temperature down to -196°C was used. Unlike Fe-C alloys, Fe-N alloys cannot be reaus-tenitized in vacuum or in an inert atmosphere because excessive loss of nitrogen occurs, even in short times, at high temperatures. Consequently, the alloys were reaustenitized in the ammonia-hydrogen mixture corresponding to nitrogen equilibrium at the temperatures used. The specimens were quenched in a blast of cold hydrogen gas and the temperature, measured by a thermocouple welded to the 2.5-in.-long specimen, was recorded on a high-speed recorder. In the first experiments 0.002-in.-diam chromel-alumel wire thermocouples were used but it was found that these gave erroneous readings due to contamination by nitrogen pickup. Pt-Pt 13 pct Rh wires of 0.002 in. diam were found to be satisfactory. Further details of the experiments are available in the original thesis.7 The cooling rate was controlled between 400° and 4000°C per sec by adjusting the hydrogen pressure. At least three cooling curves were obtained for each composition. Each specimen was analyzed for nitrogen after quenching. To aid in the accurate location of the martensite arrest points a series of cooling curves of 0.010-in.-diam platinum wire were recorded and these, which did not contain an arrest, were used as comparison standards. Four specimens, each in the form of a 3-in. loop, were prepared from each of the four alloys containing more than 2.35 wt pct N. One specimen was used for nitrogen analysis, one for X-ray diffraction, and two for resistance measurements below 20°C. The latter specimens were quenched from 20°C into constant-temperature baths at selected lower temperatures.

Jan 1, 1968

[Pumps: oil-well: plunger: essential parts, G26, 130; 74, 828 improved type, 74, 846 leakage, 74, 837 operating cycle, 74, 833 Uren design, G26, 145 sucker-rod failures, G26, 136 sucker-rod stress, 74, 835 sucker rods, 74, 830, 832 tubing, 74, 833 tubing difficulties, G25, 138; 74, 836 Olivite, 73, 337 valve and seats, 74, 832 Punching: Monel metal, 78, 86 nickel, 78, 86 Punjab. See Indian Empire. PUPIN, M. L biography, M26, 113 John Fritz medalist, 1931, M81, 499 recipient of Washington Award, M28, 155 PURDY, R.: Discussions: on Relative Efficiencies of Domestic Fuels in Relation to Their Costs and Their Advantages 108, 353 on Uses on Coal in the Ceramic Industry, 108,389,398]

Jan 1, 1936

By D. W. Fuerstenau

On page 1243, column 1, the first line of the author&apos;s reply should read "D. W. Fuerstenau (author&apos;s reply)---," rather than D. E., as printed. In the sentence immediately preceding the first equation (page 1243, column 2)&apos; the word "none" was omitted. The sentence should read: "However, if enough ore is put into the mill [so] that none of the energy put into the mill is wasted on metal-to-metal impact, then the product should have size modulus determined by the relation: ..."

Jan 1, 1961

By E. J. Whittenberger

OVER the past two decades, the Cr-Ni stainless steels, popularly termed 18-8 steels, have been used in ever increasing amounts in the aircraft, automotive, chemical, transportation, and building industries.&apos; The contribution of nickel to these steels is associated with its strong austenite forming tendencies which assure good hot and cold forming characteristics, and with its beneficial influence upon corrosion resistance, especially in oxidizing acids. The adjustment of the chromium and nickel contents has been used advantageously in controlling the rollability and the response of the mechanical properties of these steels to cold reduction. With the advent of the jet age and the government stockpiling of nickel, considerable emphasis has been placed upon the development of satisfactory low nickel or nickel-free substitute austenitic stainless steels, especially for nonmilitary applications.2 Fer-ritic 17 pct Cr (AISI Type 430) stainless steel has been effectively substituted for the austenitic grades in applications with mildly corrosive exposure. However, the limited formability and ferromagnetic behavior of this grade do not permit its satisfactory use for many applications. To achieve better formability in a nenmagnetic steel and conserve nickel, a number of low nickel substitute austenitic grades of stainless steel have been developed in recent years. In most of these steels, manganese and nitrogen have been substituted for a portion of the nickel content, for example, 17 pct Cr-4 pct Ni-6 pct Mn (AISI Type 201), 18 pct Cr-5 pct Ni-8 pct Mn (AISI Type 202), and 16 pct Cr-1 pct Ni-17 pct Mn, all of which contain approximately 0.15 pct N.1 The precipitation of ferrite when large ingots of these Cr-Ni-Mn-N steels are heated to temperatures high enough for conversion to slabs on conventional universal slabbing mills has seriously affected the hot workability of these steels. This has been especially true in the case of the 16 pct Cr-1 pct Ni-17 pct Mn (sometimes referred to as 15 pct Cr-1 pct Ni-15 pct Mn) composition." Because it is possible that little, if any, nickel will be available for nonmilitary stainless steel applications in the event of a national emergency, a need has existed for a nickel-free austenitic stainless steel containing hot and cold forming characteristics similar to 18-8 steels and corrosion resistance at least comparable to the 17 pct Cr ferritic steel. The aforementioned deleterious effect of ferrite upon the hot working characteristics of the 16 pct Cr-1 pct Ni-17 pct Mn, steel indicates the importance of establishing the austenite-austenite plus ferrite phase boundaries as the first step in the development of nickel-free or low nickel substitute steels. This paper presents the data collected in an elevated temperature constitutional study of the Cr-Ni-Mn-N system at the South Works of the United States Steel Corp. Experimental Procedure The 300 compositions used in the investigation were melted in a 26 Ib induction furnace and cast in 3 14 in. diam by 18 in tall hot-tcpped ingot mo1ds.

Jan 1, 1958

By NEWTON C. MARSHALL

AS every school boy knows, the Andes mountain range forms the backbone of South America, extending the full length of the continent along its western edge and fairly close to the Pacific coast. But in Colombia these mountains are divided into three distinct ranges known as the Western, Central and Eastern ranges of the Andes. United at the southern end, they spread out like three fingers in a northerly direction across the Republic of Colombia. These great natural barriers have only in recent years been tarried by railroads or wagon roads, and they have had their effect upon the history of the country, both political and ethnological. Each of the three ranges dies out and dwindles away before reaching the boundary of Colombia on the Caribbean Sea. When I studied my geography as a youngster 1 used to think that the

Jan 1, 1935

By Thomas T. Read

The purpose of the following research, as originally planned, was to investigate the influence of temperature upon the plate¬amalgamation process. In order to consider the amalgamation process intelligently, it was first necessary to learn the nature of an amalgam. In the performance of this task it was found necessary to consult a large volume of literature and to perform experimental investigations. The conceptions of the nature of amalgams thus obtained have so important a bearing on the amalgamation-process as a whole, as well as upon the possible influences of temperature, that it was advisable to include them in the treatment of the subject. The broader title is therefore used, even though some features of the amalgamation process have been treated very briefly and others entirely omitted, there being nothing new to present regarding them and their development not required for a clear presentation of the matter in hand. I. HISTORICAL INTRODUCTION. Gold was one of the earliest metals known to man. Occurring in the metallic state, it could be picked up in nuggets or washed, as gold dust, front the sand and gravel of streams. Interesting descriptions of the processes employed in early times for the recovery of gold may be found in Pliny&apos;s Natural History and in the treatise by Agricola on ores and minerals. But little progress in the treatment of the ores of gold was possible until efficient -crushing machines were devised. This want was supplied by the introduction, about the beginning of the sixteenth century, of the stamp mill to treat the ores of Saxony. Blanket strikes, or similar devices, were used to catch the

May 1, 1906

Henry LOUIS, London, England (communication to the Secretary) : Prof. Richards&apos;s paper has impressed me as highly valuable. Without entering upon any discussion of it as careful and thorough as it deserves, I venture to mention one or two points which a perusal of it has recalled to my mind in connection with my own study and practice of ore-dressing. I always mentally divide jigging into two phases: 1. A particle at rest on the jig-bed is lifted and carried upwards by the rising current of water, at an increasing velocity, which tends to a maximum. When the upward current is stopped, the particle continues to rise with rapidly diminishing velocity until it comes to rest. This completes the first phase. 2. In the second phase, the particle falls from its position of rest with an increasing velocity which tends again to a maximum, and continues to fall until the rising current of water has reduced its velocity to zero. This completes the second phase. The second phase will evidently be greatly modified by the effect of suction, as Prof. Richards shows; but I do not see that his experiments very clearly imitate the action of the second phase. And the brief intervals at the end of each phase, when the mineral particle, by reason of its acquired velocity, is still moving, though in opposition to the water-current, yet remain to be investigated. I feel especially, in Prof. Richards&apos;s paper, a difficulty which I have felt with regard to all similar previous investigations, namely, that the experiments deal with particles falling a long distance, when the velocity becomes uniform. I question whether this uniform maximum velocity is attained in actual jigging-practice. If so, it is certainly for a comparatively very small proportion only of each stroke. It seems to me that an investigation like that of Prof. Richards, but confined to the first 6 or 8 inches of fall only, and carried out with suitably delicate recording-apparatus, is what we

Jan 1, 1895

By W. A. Anderson, R. F. Mehl

RECRYSTALLIZATION of cold-worked metals has long been known to proceed by a process of nucleation and growth.1 When a cold-worked metal is heated to a temperature at which recrystallization will ensue, nuclei of new grains, essentially strain-free, appear and grow. As the process proceeds, nuclei continue to appear and to grow, until the cold-worked matrix has been entirely consumed and recrystallization has been completed (Fig. I). Conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time, yields an isothermal recrystallization curve, showing the time course of the recrystallization process (Fig. 2).2 Evidently, then, the rate of recrystallization is determined by the rate at which nuclei form and the rate at which they grow. The rate of nucleation N is the number of nuclei that form in unit time in unit volume of the unrecrystallized matrix, and the rate of growth G is the increase in radius of the recrystallized grain per unit time. In recent years attempts have been made to determine N and G as these vary with the well-recognized variables affecting recrystallization: time, temperature, degree of deformation, etc.&apos; Such studies yield information that is more fundamental than that conveyed by the conventional recrystallization diagram,&apos; since the rate of recrystallization is thus analyzed into its two component rates.2 Methods are now available by which N and G can be measured, and analytical expressions have been developed for the interrelationships among N, G, the isothermal recrystallization curve, and the final grain size, which greatly facilitate analysis.2-4 The application of these methods has been demonstrated recently for the recrystallization of silicon ferrite.2 Data on N and G in dependence upon the recognized recrystallization variables are, however, very fragmentary;* values of N and G have been determined for some metals, but the effect of temperature, which would yield the fundamentally important activation energies, has been too little studied. Thus far there has been no detailed study of the recrystallization of any one metal in terms of N and G over appreciable ranges of the variables time, temperature, degree of deformation, and original grain size. It is the purpose of the present paper to provide such a study, employing aluminum.

Jan 1, 1945

(Under this heading will be published notes sent to the Secretary of, the Institute by members or other persons introduced by members.) Development and production. Member open for engagement. Past year in war mineral field work, operation and production. Ten years&apos; thorough experience in both subordinate and executive positions, gold, silver and copper in the United States, Mexico, and South America. Age 37, married. Minimum salary $3600. Interview. South or East. A-577. Engineer and executive. Captain U. S. Army, age 36, expects discharge before July 1. Seven years&apos; mining and metallurgical experience. Six years with large technical college as assistant professor of mining and directing extensive experimental work. Desires position as executive or research engineer with reliable company or as professor of mining with first-class college. A-909. Mining engineer. Twenty-five years&apos; experience including mine and works operation, construction, plant installation, and mine examination. Speaks Spanish. A-1173. Metallurgical engineer. Twelve years&apos; laboratory and operating experience, covering copper blast furnace, roasting, reverberatory smelting and latest Cottrell treater practice on copper dust and zinc dust. Technical graduate. 36 years of age, married. Highest recommendations. Open for immediate engagement. A-2354. Mining engineer. Junior Associate. At liberty about July 1. Captain Heavy Artillery. Single, age 24. Go anywhere. Best refer-ences. A-2843. Engineer. Age 26, single, graduate Missouri School of Mines, B. S. in Mis. Met. E. Desires position with oil or metal company in any capacity. Location immaterial. At present engaged, desires change. A-2844.

Jan 7, 1919

By S. H. Penn

One of the more challenging aspects of the unfolding age of space travel centers about the opportunity for man to use the natural resources of other worlds. The first of the extraterrestrial worlds to be exploited will be the moon. After only a scant few thousand years of scratching the earth&apos;s crust, man will embark upon a venture that for centuries has excited the imagination of many (while staggering that of most) and may become a reality within the next decade. There has never been a time when so much money and effort will have been expended to exploit an area about which so little is known. Paradoxically, this effort combines much of the detached objectivity so typical of our analytical time with the proverbial optimism of the indefatigable prospector. As the earliest manned lunar missions will be brief and exploratory in nature, astronauts will not be expected to attempt to exploit any of the possible lunar natural resources. In later missions, with a more extended period of time available for the astronauts to stay on the moon, it may be desirable or even necessary to "live off the land". The resulting exploitation of lunar resources will be intended primarily to reduce the dependence of manned missions upon terrestrial logistic support and to reduce the cost of maintaining lunar bases.

Jan 3, 1966

By C. M. Brinckerhoff

Safety work in mining at the Andes Copper Mining Company, Potrerillos, Chile, is divided into three parts: (1) accident prevention, (2) fire prevention and protection, and (3) silicosis prevention and control. In the company&apos;s operations a steady campaign has been waged to reduce accidents and silicosis, and to prevent fires. In the following pages the safety record for the past twelve years will be examined and the methods explained by which the accident rate was reduced. Table 1 contains yearly data pertaining to the scale of the mining operations and the accident record. Block caving is used for all ore production and the tonnage mined has aver- aged 30,000 short tons per day for the past seven years. Table 2 classifies 44 fatal accidents which have occurred since 1935. The leading causes of accidental death are transportation of ore and use of explosives, followed in order by per- sons falling, falls of ground, and by asphyxiation. In the case of serious accidents, however, the greatest cause is falls of ground, followed, in turn, by ore

Jan 1, 1949

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By J. J. Friel, E. S. Erickson

Dolomite-fluxed pellets of various compositions were made from magnetite concentrate, hematite concentrate and a concentrate containing a natural mixture of both. Physical properties and reduction test results were used to ascertain proper compositions and firing temperatures. These pellets were subjected to physical tests and to reduction tests. Petrographic and electron microprobe examinations were made to evaluate the effect of composition and fining on the phase assemblage. We interpreted our test results in terms of chemistry and microstructure and related these to properties. This approach enabled w to determine the composition best suited to each of the three concentrates. Compared with acid pellets, dolomite- fluxed pellets of the optimum compositions had similar physical properties but swelled less, softened at a higher temperature, and reduced faster and more completely.

Jan 1, 1983

The Institute has prepared a list of Societies&apos; publications, magazines, . etc., which were duplicates and were discarded at the time of the consolidation of the libraries of the three Founder Societies. These books will be disposed of about March 1, 1916 by the Board of Directors of the Institute through the Library Committee. If, meanwhile, members who have incomplete sets of these books, or for any other reason desire to secure some of them, they are asked to communicate immediately with the Secretary, as this is in unusual opportunity to secure books at a very low price. American Gas Light Journal, viols. 31 to 39. American Institute of Electrical Engineers, Transactions, vols. 5 to 26. American Machinist, vols. 3 to 20, 22 to 29. American Society of Civil Engineers, Transactions, vols. 2 to 10, 21 to 24, 26 to 33, 39 to 49, 52, 55, 58, 74. Index, viols. 1 to 21. American Society of Mechanical Engineers, Transactions, vols. 1 to 28. Index, vols. 1 to 20, vols. 1 to 25.

Jan 1, 1916

By John B. Hastings

THE occurrence of such a large amount of gold in the Hartsel granite, even though the surmised existence of similar areas is not new, brings freshly to mind the pegmatite type of magmatic differentiation lately brought again to attention by occurrences at Silver Peak, Nev., described by Spurr; and in Alaska, described by both Spurr and Brooks. In both localities graunitic rocks or dikes are thought to pass into metalliferous quartz-veins. An interesting association in this connection is the occurrence of diamonds in residual pegmatitic clay of San Juao de Chapado, Brazil, described by Derby :1 (P. 142) "Bodies of pegmatite are quite common in the older rocks of Brazil, both in the. diamond regions and elsewhere, occurring not only in the gneiss and granite, but in the schistose series as well. Those that have been examined are dike-like in their mode of occurrence and granitic in composition." (P. 143) "The question of the eruptive or secretionary origin of pegmatites has long been a subject of discussion among geologists. . . . The recent studies . . . seem to have clearly established that most if not all of them are essentially eruptive masses, though possibly modified in some way by aqueous agencies. Even before becoming acquainted with the literature of the subject this view had seemed to me to be the only acceptable one as regards the typical pegmatites of Brazil." What is pegmatite ? J. F. Kemp says ". . . veins or dikes-it is an open question which is the more correct term-are met formed of very coarsely crystalline aggregates of the same minerals that constitute granite. These are called pegmatite and in them is the home of graphic granite, the curious intergrowth of quartz and feldspar, such that a cross fracture of the blades of quartz suggests cuneiform characters. . . . In regard to the larger veins or dikes it seems improbable that true igneous fusion could have afforded such coarsely crystalline aggregates, and so we are forced to assume such abundance of steam and other vapors, i.e, mineralizers, as to almost, if not quite, imply solution."

Jan 5, 1908