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By Desio S. Oddone, Mark C. Malamphy, Irnack C. Do Amaral

Most igneous rocks, and particularly those of the basic type, contain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anomalies observed during the course of geophysical surveys by the magnetic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemisphere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This convention facilitates comparison with anomalies in the north.

Jan 1, 1940

By Irnack C. Do Amaral, Mark C. Malamphy, Desio S. Oddone

Most igneous rocks, and particularly those of the basic type, contain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anomalies observed during the course of geophysical surveys by the magnetic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemisphere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This convention facilitates comparison with anomalies in the north.

Jan 1, 1940

[Mining Methods Guy N. BJORGE, Chairman CLYDE E. WEED, Vice-Chairman HARLAN A. WALKER, Secretary Alluvial Mining CLINTON BERNARD O. B. PERRY R. B. EARLING C. M. ROMANOWITZ BENERE H. GRANT J. B. STAPLER CHARLES THURMAN Open-Cut Mining Iron G. E. DIEHL P. G. HARRISON EARL E. HUNNER Copper Louis BUCHMAN W. H. GOODRICH J. H. DAVIS WALTER S. LARSH Underground Mining Iron ROY A. BOWEN S. R. ELLIOTT T. C. DESOLLAR W. A. KNOLL GEORGE H. RUPP]

Jan 1, 1940

[PRESIDENT AND DIRECTOR * R. R. McNAUGHTON, '63, Trail, B. C., Canada PAST-PRESIDENT AND DIRECTOR * JOSEPH L. GILLSON, '62, Wilmington, Delaware PRESIDENT-ELECT AND DIRECTOR * LLOYD E. ELKINS, '64, Tulsa, Oklahoma VICE-PRESIDENTS AND DIRECTORS * JOHN S. BELL, '62, Houston, Texas * A. B. CUMMINS, '62, Bound Brook, New Jersey * WAYNE E. GLENN, '62, Houston, Texas * C. C. LONG, '62, Monaca, Pennsylvania * J. S. SMART, JR., '63, New York, New York * J. W. WOOMER, '62, Pittsburgh, Pennsylvania]

Jan 1, 1961

By T. Sterry Hunt

WET processes for the extraction of copper from its ores have of late attracted much attention, especially in Europe, where the use of oupriferous iron-pyrites as a' source of sulphur prevails. These processes present an additional interest, when, as is often the case, the copper-ore's to be treated contain one or both of the precious metals, since the complete separation of these from copper, either in the dry or the moist way, is, as is well known, one of the difficult problems of metallurgy. The principal wet processes hitherto in use for the extraction of copper from its ores, may be included under three classes : I. Those in which the copper in snlphuretted ores is rendered soluble in water by calcining them, after a preliminary roasting which removes the greater part of their sulphur, with a portion of common salt, by which the copper is converted into a chloride (Long-maid and Henderson), or with sulphate of soda, by which sulphate of copper is formed (Monnier). Allied to these is the method by which a portion of the copper is got as soluble sulphate by roasting without addition, a process which is sometimes modified and rendered more complete by re-roasting the lixiviated residues with the addition of a portion of raw sulphuretted ore (Bankart). II. Those methods in which free chlorhydric or sulphuric acid is used to dissolve the copper- from oxidized or roasted ores. These, while simple and efficient, are too costly, except in certain localities where chlorhydric acid is a waste product. Related to them is the plan which consists in exposing the oxidized and moistened ores to the slow action of sulphurous acid mixed with air, by which a soluble sulphate of copper is formed. It has been proposed to decompose the solutions of sulphate or chloride of copper by sulphuretted hydrogen, thus separating the copper as sulphide, and using the liberated acid to dissolve fresh portions of oxidized copper. It is, however, the almost universal practice to throw down the copper from its solutions, however obtained, in the metallic state by the use of iron, either scrap-iron or iron-sponge; although in some instances

Jan 1, 1882

By T. Sterry Hunt

Jan 1, 1882

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some re-maining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By G. A. Beske, P. Hilsch, J. Wulff

The effects of the growth precipitates on the su-perconduching properties of an Al- 15 al. pel Zu alloy have been studied using magneization, transition lem-perature, and residual resistivity measurements. Aging at 230C for 1/2 to 11 he produces an increase in Hfp, Ike field of first penetration, and tut increase in trapped flux. The upper critical field, Hc2 remains constant for such aging tunes. Aging at 200°C produces a decrease in Hfp and an increase in trapped flux. The transition temperature remains constant at Tc - 1.227° ± 0.02°K for aging at 220°C for tims of from 1/2 to 10 hr, and for aging at 200°C it remains constant at Tc. = 1.18° i 0.02°K for times from 1/2 hv to 26 hr. The observed behavior indicates that the superconducting matrix when aged at 220°C behaves tike a type U su-perconducior, but when aged at 200°C behares like a type I superconductor. The magnetization changes after aging can be attributed to the growth and clutnge in distribution of the precipitate in a matrix of fixed composition. IT has been realized for some time that the superconducting properties of alloys are highly structure-sensitive. This is evident in the work of Mould and Mapother1 who examined the properties of an aluminum alloy. Precipitation effects have also been briefly mentioned in other studies.2-4 Bonnin and coworkers5 have observed a sharp inc rease in trapped flux in an A1-Mg alloy when the residual resistivity reaches a value that indicates it is a type II superconductor. Recently Blanc, Goodman, and Nemoz5p have reported on precipitation effects in A1-Ag alloys. Detailed studies of precipitation in Pb-Sn and Pb-Cd alloys made by Livingston6 serve to show that the upper critical fields are enhanced by quenched-in solute. Furthermore. at various stages in the precipitation process? the upper critical field is determined largely by the remanent solute. The observed magnetic hysteresis and trapped flux in such alloys result from the interaction between precipitate and the flux filaments in the mixed state. The flux trapping appears to depend largely on the precipitate distribution and is greater if the superconductor is type II than if it is type I. To examine the effect of precipitation in another alloy system, particularly one in which the composition of the superconducting phase does not change significantly during the course of precipitation, the Al-Zn system seems interesting, especially in view of the transition temperature and resistivity studies of Chiou and seraphim.' Furthermore, the recent detailed electron-microscope studies of an Al-Zn alloy by Richards and Garwood8 provide a guide for relating superconducting properties to changes in structure. For these reasons, magnetization, transition temperature, and residual resistivity measurements for varying times of heat treatment at two temperatures were made with a -15 at. pct Al-Zn alloy. The results are reported in this paper. I) EXPERIMENTAL The alloy used was prepared by Cominco Products Inc. from 99.9999 A1 and 99.999 Zn. It was chill-cast, swaged, and drawn to 0.125-in.-diam rod. The analyzed composition was 15.6 at. pct Zn (31.1 wt pct). A jeweler's saw was used to cut the 0.125-in.-diam rod into the 0.875-in. lengths needed for magnetization measurements. The ends of the cylinders were slightly beveled to remove the sharp edges. A portion of the original 0.125-in.-diam rod was drawn into 0.010-in.-diam wire and used for transition temperature measurements. Specimens were suspended from wires within a vertical furnace during heat treatment. All were homogenized at 500°C for a minimum of 3 days and subsequently solutionized for times in excess of 6 hr. The solutionizing temperature was held constant to +3°C. Individual specimens were homogenized, quenched, and aged several times and no effects indicating loss of zinc were noted. The suspended specimens were quenched by cutting the wires and allowing the specimens to fall into a silicone oil bath held at the aging temperature. They were then isothermally transforked by aging in the same bath used for quenching. After aging for the required time (approximately 10 min aging was necessary before the upper critical field reached a fixed value), they were briefly (1 to 2 sec) dipped into an acetone bath at room temperature to remove adherent oil and then immediately transferred to liquid nitrogen where they remained until inserted into the helium bath (usually within an hour). The temperature of the aging bath was held constant to +3°C for longer aging times. The cryostat used for the measurement of superconducting properties consisted of outer and inner dewars for liquid nitrogen and liquid helium, Stokes 6-in. booster diffusion pump and Stokes Model 212 mechanical pump, temperature controller to measure and control the temperature of the helium bath, and a superconducting solenoid with inserted search coils to provide the magnetic field and measure the magnetic moment of the specimens. A schematic diagram of the cryostat is shown in Fig. 1. An ultimate temperature of 0.85°K was reached with this apparatus. The temperature controller used is similar to the one described by Blake and chase.' A 0.5 pct Allen-Bradley carbon resistor and a nichronle heater (200

Jan 1, 1968

By Robert Bosworth

THE liability for damages to the surface caused by subsidence is an ever present threat in all underground mining. In ordinary lode mining, this threat rarely materializes into an action, due to the method of mining metalliferous ores, the dip of the veins, and the nature of the ground itself. In the mining of coal, however, this threat is very real. The coal frequently lies close to the surface, in beds underlying large areas of land of which the surface is suitable for agricultural or urban development. Furthermore, the coal is generally mined by the "room and pillar " method and when the pillars of coal are removed, the subjacent support is destroyed. This question of the duty of surface support has now become a very live one in Colorado. What was waste prairie land a few years ago has become valuable agricultural land dotted here and there with growing towns. Frequent references will be made here to Colorado conditions and adjudicated cases, but those conditions and cases and the conclusions to be drawn therefrom are applicable to all coal-mining states. Briefly stated, the question is "Does the owner of the substrata or underlying mineral owe any duty of surface support to the owner of the superjacent strata or surface?" There is no absolute duty of support owed by the mineral owner and this assertion is made with full knowledge of numerous expressions to the contrary by courts of Pennsylvania, Illinois, Colorado and other coal-mining states. Whether or not any duty exists depends upon the circumstances surrounding each case, and since in the nature of things those circumstances are rarely identical, there can be no absolute rule.

Jan 1, 1928

William R. Walker, assistant to the president of the U. S. Steel Corpn., died at St. Luke's Hospital, New York, on Dec. 20, 1922. He was born at LaPort, Ind., Nov. 26, 1857, and his whole career has been closely identified with the iron and steel industry. His first employment was with the North Chicago Rolling Mill Co., Chicago; then he was appointed chemist for the Crown Point Iron Co., at Crown Point, N. Y.; and later he was works superintendent for Spang, Chalfant & Co., of Pittsburgh. He was early associated with Robert Forsyth, the well-known engineer who constructed the South Chicago works of the North Chicago Rolling Mill Company. Prior to 1890, Mr. Walker was works manager for the Union Steel Co., and upon organization of the Illinois Steel Co. he became general manager of its South Chicago works. At the time of the formation of the U. S. Steel Corpn., in 1901, he was appointed assistant to the president, which position he held until the time of his death. Through the technical staffs and committees of the Steel Corpora tion, Mr. Walker had an excellent opportunity to study and direct the development of mechanical methods for coal mining, coal washing, beehive coking, including the collection and recovery of its byproducts, and to interest himself in byproduct coke ovens, and the design and operation of processes for the coking of special coal mixtures. He also brought his experience to bear on the design, construction and operation of the blast furnace and its appurtenances, as well as the bessemer, open-hearth and electric steel processes. Incidentally, he was interested in microscopy and metallography, and was familiar with the manufacture of products related to the iron and steel industry, such as tin, zinc, sulfuric acid and many other substances. Mr. Walker had the remarkable faculty of being able to discuss and conduct investigations in practically any technical branch of the ferrous industry. In the words of President James A. Farrell, "Mr. Wdker was a man of keen mental attainments and possessed an exceptional knowledge of the iron and steel industry, from both the scientific and the practical

Jan 1, 1923

William R. Walker, assistant to the president of the U. S. Steel Corpn., died at St. Luke's Hospital, New York, on Dec. 20, 1922. He was born at LaPort, Ind., Nov. 26, 1857, and his whole career has been closely identified with the iron and steel industry. His first employment was with the North Chicago Rolling Mill Co., Chicago; then he was appointed chemist for the Crown Point Iron Co., at Crown Point, N. Y.; and later he was works superintendent for Spang, Chalfant & Co., of Pittsburgh. He was early associated with Robert Forsyth, the well-known engineer who constructed the South Chicago works of the North Chicago Rolling Mill Company. Prior to 1890, Mr. Walker was works manager for the Union Steel Co., and upon organization of the Illinois Steel Co. he became general manager of its South Chicago works. At the time of the formation of the U. S. Steel Corpn., in 1901, he was appointed assistant to the president, which position he held until the time of his death. Through the technical staffs and committees of the Steel Corpora tion, Mr. Walker had an excellent opportunity to study and direct the development of mechanical methods for coal mining, coal washing, beehive coking, including the collection and recovery of its byproducts, and to interest himself in byproduct coke ovens, and the design and operation of processes for the coking of special coal mixtures. He also brought his experience to bear on the design, construction and operation of the blast furnace and its appurtenances, as well as the bessemer, open-hearth and electric steel processes. Incidentally, he was interested in microscopy and metallography, and was familiar with the manufacture of products related to the iron and steel industry, such as tin, zinc, sulfuric acid and many other substances. Mr. Walker had the remarkable faculty of being able to discuss and conduct investigations in practically any technical branch of the ferrous industry. In the words of President James A. Farrell, "Mr. Wdker was a man of keen mental attainments and possessed an exceptional knowledge of the iron and steel industry, from both the scientific and the practical

Jan 1, 1923

Jan 1, 1913

By Hugh S. Spence

IN MAY, 1930, G. LaBine and E. C. St. Paul, prospect¬ing round the southeastern shore of Great Bear Lake, in the North West Territories of Canada, discovered pitchblende at what is now LaBine Point. At the same time, they also found native silver in a small sheared break on an island lying off the point. Late in 1930, samples of the pitchblende were sent to the Mines Branch, at Ottawa. The material consisted of several fair-sized slabs of botryoidal pitchblende banded with a brownish quartz. A small amount of chalcopyrite was visible as small particles and fine veinlets, and the pieces were rather heavily stained a yellowish-green by secondary copper-uranium salts. Analyses were run in the Mines Branch Ore Dressing Laboratories on two samples, and small-scale concentration tests were made on one of them. The results of this work were published in a Memorandum Series report (No. 48) of the Mines Branch, in March, 1931.

Jan 1, 1932

By Samuel Hoyt

THE writer has long been interested in seeking an explanation of the upper heat effect in the copper-tin alloys over the a + ß range, first described in 1913. These notes are offered, not at all as the final explanation of this heat effect, but rather to indicate certain progress which has been made toward establishing what happens over this temperature interval. While working on the thermal analysis of the copper-rich kalchoids (copper-tin-zinc alloys), it was noted that those alloys containing major portions of tin and minor portions of zinc exhibited two marked heat effects, one at about 520° C. and the other at about 600° C., instead of the single effect which is generally observed in either of the two binary series. This matter was discussed with Dr. Guertler, who suggested that a heat effect at about 600° C. in the pure copper-tin alloys might be expected. This led to a more searching examination of the thermal critical points in the pure copper-tin alloys, with the result that a marked, although somewhat weak, heat effect was located at about 600°. Somewhat later, this upper heat effect was discussed with Dr. Burgess, and it was requested that the Bureau of Standards make heating and cooling curves of one of these alloys for the purpose of removing any possible doubt as to the actual presence of the heat effect. Results obtained by the Bureau are given in Plate I. In an earlier paper1 differential curves were published showing that the heat effect occurred at constant temperature over the a + ß range and increased in magnitude with the amount of a up to a point somewhat above 20 per cent. tin. No heat effect was noticed at this temperature in the eutectoid alloy. The existence of this heat effect seems to require a modification of the present copper-tin diagram in the a + ß field, and it has been the object of the work here presented to secure the evidence upon which such a change should be based.

Jan 12, 1918

By Alan Morris

Brass rod for use in automatic screw machines is one of the major products of the brass mills. A large tonnage is consumed each year in the manufacture of an endless variety of finished articles and parts for assembly into other products. The machines that do this work have been developed to a high degree of efficiency, and their manufacturers are still striving for higher production speeds. This development has brought with it a demand for brass rod to meet the increasingly difficult machining conditions. This paper is a report of the results of tests undertaken in an effort to obtain a measure of the effects of such variables as lead content, microstructure and cold work on the machinability of brass rod. It is realized that the term "machinability" has never been well defined. Power, finish and tool life all should have a place in such a definition. In practice it is sometimes found necessary to sacrifice some of these in order to obtain a rod that will not tend to throw up a burr, or will give a burr which is easily tumbled off. Again a specially stiff rod may be necessary because of long overhang from the chuck or a rod of special characteristics is needed to take a given broaching operation without chattering. It is only through an understanding of the effect of basic mill operations on the machinability of the rod that such problems as these may be solved most economically. It is hoped that this paper, together with the discussion it may evoke, will prove to be a basis for such an understanding. Testing Apparatus The testing apparatus used was of the single-tooth milling cutter type, in all respects sirnilar to that first used and described by Airey and Oxford1 and again by Boston. The machine used in the present test is shown in Fig. 1. It is an ordinary milling machine in which a heavy pendulum has been substituted for the pulley on the arbor. If the pendulum is raised

Jan 1, 1932

By D. Kuhlmann-Wilsdorf

A new theory of work hardening is developed which rests on only a few simple principles and is applicable to a wide variety of materials and dislocation structures. It explains, qualitatively, the general characteristics of the three-stage shear stress-shear strain curve of fcc metals, as well as the most important features connected with easy glide. The value of, the work-hardening coefficient in stage 11, is derived quantitatively, from first principles, and is shown to be insensitive to many changes in detailed dislocation behavior. The low rate at which energy is stored during mechanical working in stage 11, the dependence of slip line length on stress, and the so-called Cottrell-Stokes law are explained. Although the theory is primarily developed for fcc metals and alloys, it is largely applicable also to some other materiuls, and in particular apparently to poly crystalline simple steels in theh linear range of hardening. FOR pure fcc metals and alloys, after many different pretreatments and under a great variety of testing conditions, the well-known three-stage work-hardening curve is commonly observed. Moreover, the work-hardening coefficient in stage 11, 011, bears an almost constant relationship to G, the modulus of rigidity, such that K = G/Brr" = 300, within a factor of about 2 either way. The very fact that the three-stage curve and the value of K are so very persistent, can hardly be understood except on the assumption that some quite simple phenomena are responsible. In this light all available theories of work hardening must be judged unsatisfactory: Each of them is based on some quite specific dislocation model, while it is known that metals with similar values of K may have widely different dislocation structures, for example, dislocation tangles in the case of pure fcc metals, and piled-up groups of dislocations in a-brasstype alloys. Thus, while a particular theory might conceivably represent a special case with a reasonable degree of accuracy, it cannot possibly have illuminated the underlying principle. Another severe criticism applying to the presently most widely discussed theories is that they employ empirical or even quite unexplained parameters in order to arrive at a numerical value of K. This indicates that some vital aspect of the work-hardening process has remained unexplained. In the present paper, a new theory of work-hardening is developed which does not suffer from the above shortcomings. It is derived from first principles, and is founded on the realization that the underlying causes for the three-stage work-harden- ing curve and for the persistence of the numerical value of O,, must be few and simple. As a first step it is shown herein that the experimental oklservations on "easy glide" can be explained on the assumption that in this stage dislocations multiply, beginning in a number of restricted area:;, and from there penetrate into crystal regions still substantially free of glide dislocations until a quasi-uniform dislocation distribution has been established. During "easy glide", the resistance to the movement of the foremost dislocations, advancing into still largely a dislocation-free regions, is believed to control the flow stress. This resistance is determined by various factors, among them the reaction of the dislocations against bowing-out into loops, which is due to their line tension. Without such bowing-out no dislocation multiplication would occur, but the corresponding contribution to the flow stress stays practically constant all through stage I. According to the present theory, stage TI begins as soon as there are no more areas left into which newly formed dislocations have not yet penetrated, i.e., as soon :is a quasi-uniform dislocation density has been attaned. Regardless of how, in detail, the dislocations should happen to be arranged at the end of "easy glide", whether in pileups or tangles, on one glide system or on several, the stress necessary to overcome the line tension of the segments must now increase, because the dislocation density increiises while the average free dislocation length decreases. It is argued that all other contributions to the flow stress stay at about the same level as in stage I, and that the said increase in the stress necessary to bow out dislocation segments into loops is responsible for the major part of work hardening in stage 11. Stage TII of the stress-strain curve is explained by largely follouing the ideas of Seeger and his co-workers; however, it is pointed out that the start of stage m may on occasion indicate the onset of "conservative climb" instead of cross slip. Indirect evidence indicates that linear work hardening persists even under the profuse action of cross slip, but at a lower rate. Only when, in addition to cross slip, climb operates extensively, does the work-hardening rat,. drop sharply, ultimately down to zero. BRIEF SURVEY OF EXPERIMENTAL EVIDENCE The stress-strain curve of crystals of many different substances are qualitatively similar. No significant permanent plastic deformation takes place below the so-called "critical resolved shear stress". As the applied stress is raised beyond this level. yielding occurs with little or no work hardening and

Jan 1, 1962

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Jan 1, 1961

By FOSTER HEWElT

THE scope of this paper is the description of two districts in Peru in which deposits of vanadium have been found, and the consideration of much laboratory-work that I and others have done to determine the nature of these deposits. It is with regret that I present some of the data in a state of evident incompletion, particularly the analyses of a few of the minerals, which leaves some doubt as to whether the true nature of the minerals is understood. I make no apology, however, since in this case, as in many others referring to ore-deposits, conclusive opinions cannot be stated until a great amount of work has been done, and the deposit has been thoroughly exploited. I believe that the data and the tentative conclusions here presented indicate a unique and interesting condition which may assist others in work along similar lines; and further, what is of more practical importance, stimulate a search for a metal which, though long considered rare, is probably so merely because proper care has not been taken to recognize it. An excellent bibliography on the occurrence of vanadium in nature is given by F. W. Clarke in his paper, Data of Geo-chemistry;1 and in the preparation of this paper I have consulted many of the references contained in the Bibliography of the Chemistry of Vanadium, by M. Moissan.2 A brief review of the subject having special reference to the metallurgy of vanadium is contained in the small book by P.. Nicolardot.3 One of these vanadium-deposits has already been briefly

Mar 1, 1909

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957

By W. O. Philbrook, R. H. Spitzer, F. S. Manning

A generalized mathematical model has been developed to describe the kinetics of the gaseous, topo-chemical reduction of porous hematite spheres. Gas-solid reduction is permitted at each of three advancing interfaces and is controlled by a complex series-parallel sequence of chemical and transport steps. Despite the fact that transport resistances are significant to the advance of each interface, little deviation from linear advance is predicted for the first 98 pct of reduction. Calculations to predict the movement of magnetite /wustite interface by a solid-state diffusion mechanism have been incorporated into the earlier dense-pellet model.' The porous-pellet model is found to give a better description than the dense-pellet one for McKewan's measurements2 of interface movements in dense polycrystalline hematite reduced in hydrogen-water vapor mixtures. THIS paper reports a continuation of work"3" directed toward the better understanding of gas-solid reactions and the development of mathematical models that may be helpful in the design or control of ore-reduction processes. Laboratory studies of the reduction of single oxide samples in tube furnaces normally employ an abundant excess of pure reducing gas. Reduction may appear to be adequately described by a model assuming gas-solid reaction solely at the iron/wustite interface.''' However, when iron ore is reduced in either a fixed bed or an efficiently operated counter-current column, there are portions of the bed where the partially spent gas is no longer capable of reducing wustite to iron. Nevertheless, the formation of the intermediate reaction products, wustite or magnetite, can and does continue. In order to account for this aspect of the reduction of beds of particles, three semiempirical mathematical models were devised.' One of these was for the limiting case of completely dense particles, and two alternatives were provided for porous particles. For purposes of the analysis, a dense pellet was defined as one in which the wustite and magnetite layers were impervious to the reducing gas when the atmosphere was capable of forming iron. In a porous pellet, the intermediate product layers were assumed to be sufficiently permeable to allow reducing gas to penetrate beyond the iron/wustite interface to form wustite and magnetite by removal of oxygen as a gaseous product rather than by a solid-state redfiction mechanism. Further progress required a better understanding of the reaction of the individual particles with the gas stream. A comprehensive mathematical treatment was developed' to describe the continually changing interplay of transport and reaction steps

Jan 1, 1967