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By F. A. Emmerton

I have used for about two years, in the laboratory of the Joliet Steel Company, a rapid method for the determination of phosphorus in iron, steel, and ores, which possesses one or two features sufficiently novel to warrant description. In general, it is the method described by Mr. Benjamin B. Wright (Transactions, vol. x., p. 197), involving the precipitation of the phosphorus by means of molybdate solution, and its estimation in the yellow precipitate by reduction of the molybdic acid, and titration of the resulting oxide with a standardized permanganate solution, according to the principles laid down by Werncke (Fres, Zeit., vol. xiv., p. 1). In the use of this method, I had difficulty at first in obtaining a yellow precipitate of reasonably uniform composition. It is a well-known fact that, to secure this result, the conditions of precipitation must not vary. The principal condition is temperature; and acidity, concentration, proportion of nitrates and chlorides, and time, are important elements. I am aware that uniformity in these conditions has been obtained to a reasonable extent by many chemists,. so that they are enabled to use with success, methods based on the

Jan 1, 1887

By AIME AIME

A SPECIAL meeting arranged by the Petroleum and Gas Committee of the American Institute of Mining and Metallurgical Engineers was held on Tuesday and Wednesday, Sept. 21 and 22, in the Assembly Room of the American Annex Hotel, St. Louis, Mo. Preceding the first session on Tuesday morning, the members and guests were registered and presented with the usual Institute badges. The morning session was opened at 10:30 by Ralph Arnold of Los Angeles, Calif., Chairman of the Petroleum and Gas Committee. In his opening remarks, he suggested that the petroleum section specialize more and more on the technical problems of the oil industry and that an effort be made to enlarge the membership of the Institute among the technical men of the industry. The following program was presented : OIL FIELDS OF RUSSIA, by A. Beeby Thompson and T. G. Madgwick, of London, England. Presented by H. A. Wheeler; discussed by Arthur Knapp and R. VanA. Mills. This most comprehensive paper was one of what is hoped to be a series to be presented by some of our foreign members. It is by far the best description in English of the world-famous Baku and other fields of Russia.

Jan 1, 1920

By Duane N. Goens, Clifford R. Porter

A 91 kg/h (200 lb per hr) pilot plant was constructed according to "Magnex" design. A non-compliance eastern coal which would generate more than 0.85 kg of S02 per GJ (2.0 lb of SO2 per million Btu.) upon burning was brought into compliance less than 0.52 kg of SO2 per GJ (1.2 lb SO2 per million Btu) during continuous operation of the pilot plant. Approximately 85% of the pyritic sulfur was removed while recovering 90% of the Btu of the feed coal. Pilot plant operation is summarized and preliminary economics presented. Present status of the Magnex design program is reviewed.

Jan 2, 1979

By P. D. Merica, A. N. Finn, R. G. Waltenberg

CeRtain compositions of the light, i.e., aluminum-rich, alloys of aluminum with magnesium and copper have become quite well known within the past ten years under the name of duralumin. These alloys are used for rolling and forging and can be so treated as to develop quite remarkable mechanical properties. Thus a properly heat-treated alloy containing about 4 per cent. of copper and about 0.5 per cent. of magnesium, rolled into sheet or rod, will have a tensile strength of approximately 55,000 1b. per sq. in. (3866 kg. per sq. cm.) with an elongation in 2 in. (50.8 mm.) of about 15 per cent. This alloy, duralumin, was developed by Wilm,1 and its properties more fully described by Cohn.2, The authors considered it worth while to investigate the mechanical possibilities of the light alloys of two somewhat analogous ternary series; namely, of aluminum-magnesium-nickel and aluminum-magnesium-manganese, to study the effect of variation of composition upon mechanical properties within the alumimum-rich group of the aluminum-magne-

Jan 1, 1921

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970

By C. R. Dodson, W. T. Cardwell

This paper presents the results of a theoretical and experimental study of the effect of preperforated liners on well productivity. The analysis concerns the rectangular type of slot, either machine or torch cut, which is common in California. Muskatla treated this problem recently in a mathematical analysis of the flow of oil or gas from natural reservoirs into both gun-perforated and slotted liners. This paper presents additional and simplified analytical considerations and conclusions for the slotted liner, the solutions being applicable in the laboratory as well as in the field. An application of the analytical methods to permeability measurements on mounted core samples is given, to show the effects of sealing wax or other obstructions on the end faces of the cores. Results Fig. I 'Ompares the results of some theoretical calculations with the results of electrical analogy experiments performed in the Standard Oil Company of California's Production Technology Laboratory at La Habra, California. Fig. I indicates that the flux into short, "three-dimensional slots" of the relative dimensions encountered in practice is approximately equal to that into full-length, "two-dimensional slots" having the same open fraction of pipe. (The same numbers of slot rows, and the same radius ratio are also implied.) It can be seen from physical considerations that the closeness of this approximation must improve as the ratio of the external radius to the internal radius increases. Therefore, it is possible to calculate the flow into a slotted liner using a simple modification of the Darcy equation: where N is .the number of slot rows and O is the open fraction of the pipe. Fig. 2 shows the results of calculations . using Eq. 28. The most remarkable features of Fig. 2 are the high flux values for very small open fractions of pipe. For instance, with six slot rows and a radius ratio of 500, 74 per cent of the open-hole flux may be obtained with only o.I per cent of pipe Open. Fig. 2 shows that for a given open frac tion of pipe, the flux is greater, the greater

Jan 1, 1945

By R. C. Ferguson, Harlowe Hardinge

Laboratory and plant data covering 12 different operations show that lower than "standard" ball mill speeds increase grinding efficiency. In the case of high pulp-level mills, the gain is so great that the increase in capital cost of the larger lower speed mill will pay for itself in less than a year's time. THE object of this paper is to show the economic advantage of operating ball mills at relatively slow speeds. Although many operators know that grinding costs are reduced by operating mills at low speeds, they seldom do so for a variety of reasons. When capital is limited, first cost is of primary importance, and installation of the less costly, highspeed mill is favored. When materials are in short supply, as during a war period, capacity rather than economy is the primary consideration. Existing mills are then speeded up to provide the desired increase in capacity, and new mills are purchased without consideration of maximum grinding efficiency. When the mill speed is increased to secure more production, the increase in grinding costs is often obscured by the total benefit derived from the additional output. This increase in grinding cost is seldom recognized as being sufficient to be worth correcting. For these reasons one may be lead to the erroneous conclusion that slow-speed operation is only occasionally applicable. The effect of mill speed on grinding efficiency has been studied in laboratory tests."! The results of some of these tests are given in tables I and I1 and fig. 1. In these tabulations, batch tests using ore charges of 125 to 200 lb were considered comparable to high pulp-level operation and charges of 50 to 100 lb comparable to low pulp-level operation. For the high pulp-level operation, these tests indicate the existence of a maximum in efficiency for operation at a speed of 50 pct of critical, both for the soft (dolomite) and hard (chert) ore. In low pulp-level operation, a decrease in speed increases the efficiency of grinding dolomite; no maximum of efficiency appears in the range of speeds tested. The results with chert were inconclusive. If the performance of large mills is indicated

Jan 1, 1951

By Harlowe Hardinge, R. C. Ferguson

Laboratory and plant data covering 12 different operations show that lower than "standard" ball mill speeds increase grinding efficiency. In the case of high pulp-level mills, the gain is so great that the increase in capital cost of the larger lower speed mill will pay for itself in less than a year's time. THE object of this paper is to show the economic advantage of operating ball mills at relatively slow speeds. Although many operators know that grinding costs are reduced by operating mills at low speeds, they seldom do so for a variety of reasons. When capital is limited, first cost is of primary importance, and installation of the less costly, highspeed mill is favored. When materials are in short supply, as during a war period, capacity rather than economy is the primary consideration. Existing mills are then speeded up to provide the desired increase in capacity, and new mills are purchased without consideration of maximum grinding efficiency. When the mill speed is increased to secure more production, the increase in grinding costs is often obscured by the total benefit derived from the additional output. This increase in grinding cost is seldom recognized as being sufficient to be worth correcting. For these reasons one may be lead to the erroneous conclusion that slow-speed operation is only occasionally applicable. The effect of mill speed on grinding efficiency has been studied in laboratory tests."! The results of some of these tests are given in tables I and I1 and fig. 1. In these tabulations, batch tests using ore charges of 125 to 200 lb were considered comparable to high pulp-level operation and charges of 50 to 100 lb comparable to low pulp-level operation. For the high pulp-level operation, these tests indicate the existence of a maximum in efficiency for operation at a speed of 50 pct of critical, both for the soft (dolomite) and hard (chert) ore. In low pulp-level operation, a decrease in speed increases the efficiency of grinding dolomite; no maximum of efficiency appears in the range of speeds tested. The results with chert were inconclusive. If the performance of large mills is indicated

Jan 1, 1951

By Robert H. Richards

Walter Renton Ingalls recently gave a very interesting talk before the student mining society of the Massachusetts Institute of Technology. In it he showed the present status of mining as he sees it. In the talk he explained that, while discoveries of great mining districts are still pssible, they are being made less and less often; that the great mining companies, although there are large numbers of mines offered for sale, are finding it less and less possible to find new mines that are up to the standard of richness that they wish for purchase. The natural conclusion is that better, cheaper, and more efficient methods of mining, concentrating, and smelting are needed if the lower-grade mines are to be worked at a profit. This is true also if the high-grade mines are to yield their greatest profit. This paper deals only with the concentrating or ore-dressing problem, and gives some thoughts which point towards greater profit. In a paper on The Development of Hindered-Settling Apparatus the writer showed that there were two main lines of work that would lead to greater saving, lower tailing assay, and, therefore, greater profit. The first is the recrushing of middling or tailing products for the saving of the contained values. This is well understood and largely carried out in existing mills. The second is the saving of fine free mineral at the first opportunity. This is a matter less well understood in the mills, and to dwell upon this the present paper is written. The writer is himself convinced and hopes to convince the reader that, for obtaining the above result, not only is better classification needed, but also more classification; that is, there should be more spigots or pockets to the classifier. His attention was recently called to a small mill which had a three-pocket cone classifier fed with from 2 to 0 mm. stuff, supplying feed to four Wilfley tables. The first spigot had about all the

Jan 1, 1914

By E. G. Beinlich

The continuing search for faster, safer, and more economical methods of excavating underground openings has led the staff of the Mather mine of the Negaunee Mine Co. directly to mechanical boring of raises and drifts. The mine is located within the city limits of Negaunee and Ishperning in the eastern portion of the Marquette Iron Range in the Upper Peninsula of Michigan. It is owned jointly by McLouth Steel Corp., Bethlehem Steel Corp., Republic Steel Corp., and The Cleveland-Cliffs Iron Co., who also serves as the operating agent. A total of 2,400,000 tons of iron ore averaging over 60% Fe is mined annually by the block-caving method. This provides feed for the Pioneer pellet plant at Eagle Mills where 1,450,000 tons of pellets are produced yearly with the remaining tonnage being sold as coarse ore. Technical staff of Cleveland-Cliffs have long realized that improved methods of advancing raises and drifts were a necessity if underground mining of iron ore was to survive the transition period in the steel industry's requirements from direct-shipping ore to pelletized ores. For this reason, the Mather mine embarked upon an experimental raise-boring program with a prototype machine in 1961. Improvements since that time in equipment and practice have resulted in the acceptance of mechanical boring of raises as a standard development tool and a vital link in the fulfillment of an orderly development schedule. Advancement of large-diameter openings such as main-level drift headings by mechanical methods in the harder, more competent types of rock has developed more slowly in the mining industry due to the need for more compact and portable machinery and improved bit technology. Many of the obstacles have been overcome by the manufacturers, and in March 1967 it was decided to proceed with a program to bore approximately 4000 ft of 13-ft-diam drift in the Mather graywacke footwall rock.

Jan 1, 1970

By H. W. Camp

In attempting to summarize and pick out the outstanding development,s in refinery engineering during the past 12 or 13 months, one is immediately impressed by the great strides that have taken place. It is, of course, difficult to obtain the proper perspective with the old year so fresh in our minds, and if relatively minor improvements seem to be given equal recognition with those of magnitude, it will be because the nature of the human mind causes us to place the trivial incidents of today with the important things of yesterday. For instance, the Twenly-Second Semiannual Motor Gasoline Survey (December, 1930) of the U. S. Bureau of Mines shows that the total gasoline yield per barrel of crude increased from 39.6 per cent.. in 1929 to 41.99 per cent. in 1930. This latter fact may appear rather confusing since the production of high-gravity crudes has been steadily increasing. However, during the past yew there has been a reduction in gasoline end point of approximately 8" F. which roughly corresponds to about 1.0 per cent. yield from the crude oil. It appears, therefore, that, if the gasoline mere based on a corresponding distillation basis 1930 would show better yields from the crude than 1929. Cracked gasoline increased from 14.83 per cent. in 1929 to 17.46 per cent. in 1930. Percentage of total gasoline from cracking stills has doubled since 192.5, thus indicating the extent to which this phase of refining has advanced over past years. Replacement of the old shell still batteries by a pipe still and single flash system, with an efficient fractionating tower, has proved advantageous both in fuel consumption and in decreasing space required for the installation. Considerable activity has been shown in the field of vapor-phase cracking, with the development of several new types of units. The production of a product with a high antiknock value makes the vapor-phase processes particularly attractive. Cracking equipment has shown a marked advance with the development of corrosion-resisting alloys. Nickel, chromium and vanadium have shown interesting possibilities, but as yet are fairly expensive. Ceramic material for lining reaction

Jan 1, 1931

By Robert Glass Cleland

THE CONNECTING link between Phelps Dodge and the copper mines at Bisbee and Morenci was a Canadian-born mining engineer and metallurgist named James Douglas. Judged by almost any standard, Douglas was an extraordinary man. Like John Muir of the California red- woods, he had in his blood "the heather and bog juices of Scotland," and the rugged virtues of a singularly great race. His father, for whom he was named, was a graduate of Edinburgh University, a member of the Royal College of Surgeons in London, and a man of rash and adventurous spirit. Extremely catholic in his intellectual interests and attainments, he was unusually skilled in his profession, certain-sometimes to the point of disastrous stubbornness--of his own judgments and decisions, careless of life or fortune where duty or moral issues were involved, and always deeply moved by the sufferings and misfortunes of his fellow men. The career of the senior Douglas included a curious medley of novel and adventurous experiences-prolonged hunger and cold while acting as surgeon on a Greenland

Jan 1, 1952

By A. R. Kinkel

The Shasta copper-zinc district of northern California lies in the foothills of the Klamath Mountains at the northern end of the Sacramento Valley. It contains two main areas of base-metal ore deposits, the East Shasta and West Shasta districts shown in Fig. 1. The East Shasta includes the area from the Afterthought mine, near the settlement of Ingot on U. S. highway 299 East, to the Bully Hill mine, on the north side of the Pit River, 9 miles to the north- west. The West Shasta, a well-defined northeast- trending district about 8 miles long and 2 miles wide, west of the Sacramento River, Fig. 2, is the western part of the ore-bearing area formerly known as the Shasta copper belt. Referred to in the older writings as a copper arc, this belt was thought to form a crescent extending entirely around the head of the Sacramento Valley, the convex side to the north. Recent studies by the U. S. Geological Survey in cooperation with the California State Division of Mines show that there are two districts, one at each end of the so-called copper arc, which are distinct in geologic structure and ore occurrences, and that there is only sporadic and unconnected copper mineralization between them.

Jan 2, 1955

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen' with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,' indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina' has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,' 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.' Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison' reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

By Charles C. Upham

Not long ago a few acres of coal-land in the Connellsville region of Pennsylvania were sold at the rate of $1500 per acre. While this was doubtless a " fancy " price, affected by some consideration other than that of the simple value of the coal in the tract. it may fairly be taken as an indication of a progressive and already perceptible diminution in the economically available coal-resources of that famous region. This piesent and prospective development emphasizes the cominercial importance of producing, from the inferior coals of other districts, coke suitable for use in the blast-furnace. Many of the bituminous coals of the United States would meet this requirement if sufficiently freed, before coking, from slate and sulphur, and, so far as the removal of slate is concerned, the problem is not specially difficult. There are many forms of trough-, jig- and gravity-washers which easily and cheaply reduce the slate from as much as 20 per cent. in the coal to as little as 8 per cent. in the coke. But to reduce the sulphur from 4 per cent. in the coal (a proportion sometimes encountered) to 1 per cent. or less in the coke (the proportion demanded by the furnace-manager) is not so easy. It may be safely assumed as familiarly known to members of the Institute interested in this subject that, of the three forms in which sulphur usually exists in coal (hydrogen sulphide, calcium sulphate and pyrite), the pyrite is the one to be removed, RS far as possible, by mechanical treatment before coking. Hydrogen sulphide, being volatile, is expelled in

Jan 1, 1899

By Nicholas J. Grant, Ulf Kalling, John Chipman

D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—I would like to know what evidence you have to prove the MnO was pure MnO. I would also like to know whether you might not explain it on the basis of a temperature reversion; and, was it due to the oxidizing power of MnO? N. J. Grant (authors' reply)—Briefly, we have no proof that pure MnO was used. The manganese oxide was added as chemically pure MnO,. MnO is assumed as the oxide in the reacted slag following standard molecular slag theories, especially under the reducing conditions of these experiments. The noted sulphur reversion cannot by any means be explained on the basis of a temperature reversion since the temperature effect is shown in this paper to be very small. Until a more logical explanation can be offered, backed I hope by some experimental proof, we propose to explain this sulphur reversion as stated in the paper, namely, that it is due to the oxidizing effect of the added manganese oxide. Member—How did the oxygen in the slag give you a reversion of sulphur? What was the mechanism there?

Jan 1, 1952

By C. S. Land

Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water - wet rocks for both two- and three - phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. INTRODUCTION Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. 1 and by Osaba et a1.2 Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems.3 Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by snel14 as 11, ID, DI and DD. I and D refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis5 published three-phase curves for unconsolidated sand, and Snell4 reported results of several English authors for both drairrage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et a1.3 for increasing water and gas saturations (ID). Corey et a1.6 reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean7 and Sarem8 calculated three-phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three-phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (11) are those of Naar and Wygal.9 These curves are based on a theoretical study of the model of Wyllie and Gardner 10 as modified by Naar and Henderson.11 Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids.12 Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term.13 The works of Purcell and Burdine were combined by Corey14 into a form that has

Jan 1, 1969

By P. K. Foster, C. M. Payne, A. McNabb

Some measurements of the rate of loss of hydrogen from cylinders of iron and steel are analyzed in terrns of a trapping theory. The apeement is encozcraging and gives rise to estimates for the density of traps in the metal. Furthermore, the results appear to be consistent with the assumption that the diffusion constant D for the steady flux of hydrogen through iron lies on the extrapolation of the linear curve (log D us 1/T) obtained at higher temperatures. IT has been shown in a previous paper1 that the literature relating to hydrogen diffusion in steels contains sufficient evidence to invalidate the application of Fick's laws to hydrogen diffusion in steel at low temperatures. To account for the deviations from simple diffusion behavior a trapping theory was developed, and the fundamental laws modified accordingly. In the present paper, new data on the evolution of hydrogen from long cylinders are presented, and together with some published data are examined in terms of the requirements of the theory.' Properties of solutions of the basic equations derived previously1 and appropriate to the present experimental conditions are outlined in the first section as they determine the form in which the experimental data must be presented for a comparison of theory and experiment. Two new solutions not previously reported have been derived as described in the Appendix. The experiments and treatment of data are then given in Sections 2 and 3 and the results are discussed in Section 4. 1) THEORETICAL CONSIDERATIONS The hydrogen-diffusion theory1 applied in this paper postulated that lattice-dissolved hydrogen at a concentration C diffuses randomly in accordance with Fick's first law, but that the lattice contains a uniform density N of traps which can capture and delay hydrogen atoms. kC atoms are trapped per second in a region containing unit concentration of vacant traps while p are released per second in a region containing unit concentration of occupied traps. On this basis it was shown (Eq. [30] of Ref. 1) that, when local changes in the lattice-dissolved concentration C are slow enough for equilibrium to be established with the traps, the system is represented in dimensionless form by the equation:

Jan 1, 1965

By H. H. Haung, J. D. Miller, E. F. Pereira

The chemistry of copper extraction from ammoniacal solutions by hydroxyoxime extractants was studied Equilibrium measurements were made by shakeout experiments with subsequent analyasis of the aqueous and/or organic phases The kinetic experiments were carried out in a single drop reaction cell in order to establish the details of the intrinsic reaction kinetics for this system. Equilibrium measurements Indicated that the extraction involves complete displacement of ammonia ligands from the coordination sphere of the cupric ion by the extractant molecules The extraction reaction has the following stoichiometry

Jan 1, 1981

R. B. BrinSmade, Ixmiquilpan, Hgo., Mexico (written discussion*).—While agreeing with Mr. Gibson that his net-profit tax is the fairest and best for mines, I believe that the tax he describes can be more accurately defined by another name. In accounting, net profits are usually considered to be the residual of the gross income after operating expenses and the annual charge for upkeep of plant have been deducted. Even the necessary interest on bonds or mortgages should not be subtracted in this calculation, for this interest represents merely that fixed portion of the net profits going as a return to that fraction of the total property value owned by the bondholders. Applying this method of calculation to the gross income of a mining property, we should onIy deduct operation expenses and upkeep of plant to get the net profits on its whole property value. So Mr. Gibson in deducting a further sum, to cover the interest and amortization of the capital expended in mine development and equipment, really arrives at something quite differen't from net profits; which can properly only be defined as the annual value of the mineral in the ground, or the royalty value in miners' parlance. From one viewpoint, Mr. Gibson's first principle, which assesses taxes, "proportionate to the benefits received by the person or property taxed," is identical with his third principle wbich assesses "with reference to the extent and value of the natural resources enjoyed." With one exception, everything of use around a mine represents a cash expenditure, or its equivalent in human labor, and state action has not added an iota to its value. The one exception is what makes the enterprise possible and it includes the mineral deposits and their associated surface; water and other landed rights. These natural resources are origin2!1y the gift of tile people acting through their agent, the state, and it is evident that a tax laid on whatever profits may arise from their enjoyment will be exactly "proportionate to the benefits received by the person or property taxed." Mr. Gibson is mistaken in his belief that the general property tax of the United States has the same incidence as his system of taxing profits, because the general property tax falls not only on land1 value—as does

Jan 1, 1920