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By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy's law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy's law' has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy's law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.'s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.' To others,' turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy's law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.' In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy's law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy's law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy's law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy's law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy's law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By J. L. Taylor, Pol Duwez

THE present knowledge of the Ti-Al system is limited to the portion of the diagram extending from pure aluminum to the intermetallic compound TiAl3' A preliminary investigation of the titanium-rich Ti-A1 alloys revealed that the solubility of aluminum in titanium is quite extensive and that the transformation temperature of titanium is raised by alloying with aluminum. From an X-ray diffraction study of alloys containing up to 75 atomic pct Al (TiAl3), the phase boundaries at 750°C were located as follows: the a titanium solid solution extends from 0 to about 36 atomic pct Al, a two-phase region exists from 36 to 46 atomic pct Al, and an intermediate phase of varying concentration extends from 46 to 62 atomic pct Al. The purpose of the present paper is to describe the crystal structure of this new phase. The alloys were prepared by melting in a helium arc furnace on a water-cooled copper plate, using a furnace essentially the same as that described in ref. 2. The titanium metal was of the iodide type furnished by the New Jersey Zinc Co., and a piece of pure aluminum (99.99 pct) was obtained through the courtesy of the Aluminum Co. of America. After melting, the samples, weighing approximately 5 g, were sealed in evacuated fused silica tubes and homogenized for 4 hr at 1000°C. The specimens were then held for 10 days at 750°C and rapidly cooled to room temperature. Filings were then taken from each sample, sealed in evacuated vials, annealed at 750°C for 4 hr, and rapidly cooled to room temperature by quenching the vials in water. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using K copper radiation filtered through a nickel foil. Structure Determination The X-ray diffraction patterns of the alloys containing 46, 50, 55. 60, and 62 atomic pct Al were identical, except for a slight shift in the positions of the reflections. The alloy containing 55 atomic pct Al was chosen far structure determination. The powder pattern contained 37 reflections and the a, doublets were well resolved in the back-reflection range. The relatively small number of reflections and the sharpness of the pattern were considered as an indication of a simple atomic arrangement in a relatively small unit cell of high symmetry, and an attempt was therefore made to solve the structure without single crystal work. A satisfactory fit was found on a large scale Hull-Davey tetragonal chart for an axial ratio of approximately 1.45. All the reflections were readily indexed and the tentative unit cell dimensions were computed to be a - 2.81 kX, c - 4.07 kX, and c/a = 1.448. The indices (hkl) and the values of d and sin2 A are given in Table I. The agreement between observed and computed sin2 is quite satisfactory. Once the unit cell was known, the details of the structure were readily found. First, it is obvious that the number of atoms per unit cell cannot exceed two, since more than two atoms would lead to a density greater than that of pure titanium. The next logical step is to assume that the two atoms occupy the corner and center of the cell. If this assumption is correct, the structure may be described as follows: space group D1, - P 4/mmm; one titanium atom in a: 000; one aluminum atom in d: 1/2 1/2 1/2: and no extinctions. Assuming this structure to be the correct one. intensities were computed by means of the usual equation: sin2 0 cos 0 where F is the structure factor; 8, the Bragg angle. and p, the multiplicity factor. The calculated values of intensities are compared in Table I with the visually estimated intensities. The agreement is quite satisfactory and the structure is therefore confirmed. The crystal structure of TiAl just described is the same as that of AuCu ordered. The AuCu ordered

Jan 1, 1953

By AIME AIME

BY COMBINING the sessions on reduction and refining of copper, lead and zinc it was possible to devote an entire day to nonferrous metallurgy. Four interesting papers were presented at the morning session and four more in the afternoon. In the discussion of papers on copper, F. R. Pyne acted as chairman, with H. M. Shepard as vice-chairman, whereas for those on lead and zinc, F. F. Colcord acted as chairman, with C. R. Hayward as vice-chairman. The paper by P. D. I. Honeyman on the smelting of raw concentrates in the reverberatory furnace was presented by Mr. Pyne and discussed by Messrs. Mazany and Hayward. The interesting paper by E. S. Bardwell, com- paring the use of various fuels in copper-refining furnaces at Great Fails, Mont., was presented by Mr. Shepard and discussed by Messrs. Boggs, Gronningsater and Hayward. That by R. G. Knickerhocker, describing the stationary basic copper converter at Messina, Transvaal, was presented by Mr. Pyne, together with a written discussion by c. R. Kuzell, of the United Verde Copper co. It was an interesting illustration of how well-known processes may sometimes be modified to fit into unusual conditions.

Jan 1, 1932

By B. W. Frazier

At a recent meeting of the North of England Institute of Min ing and Mechanical Engineers, during a discussion upon the com pression of air, attention was called to an apparent anomaly in the phenomena attending the compression. At a subsequent meeting this apparent anomaly was explained by Prof. Herschel, and all the facts observed shown to be strictly in accordance with the laws of thermodynamics. Upon reading the report of the discussion in the published transactions of the society, it occurred to me that an attempt to determine mathematically the amounts of energy (whether in the form of heat or of work) expended and absorbed in compressing air, and causing it to perform work by expansion, might prove of use to some who have not access to any treatise upon the application of the laws of thermodynamics to the compression of air, and who have not the time or the inclination to make such application for themselves. The apparent anomaly noticed was this: If air be compressed, and at the same time, by the sufficient application of a cooling medium, kept at a constant temperature, the indicator diagrams in the

By F. G. Cottrell

AS previously announced, Van. H. Manning has resigned as director of the Bureau of Mines, effective June 1, to become director of research with the newly organized American Petroleum Institute. Doctor Manning has been connected with the Department of the Interior for 34 years, having been civil engineer with the Geological Survey, from 1885 to 1910, previous to his connection with the Bureau of Mines which was organized in the latter year. Doctor Manning was appointed to an administrative position in the new Bureau under Joseph A. Holmes, its first director, and on Jan. 1, 1911, was made assistant director. On Jan. 1, 1914, when Doctor Holmes had to relinquish active

Jan 1, 1920

By R. D. Russell, R. M. Farquhar

ISOTOPIC tracers have become an important aid in following the progress of chemical processes in the laboratory. It has recently been found possible to utilize a system of naturally existing isotopic tracers to obtain information about the geo- logical history of lead ores. Common lead, such as is found in lead deposits, is a mixture of four stable isotopes having atomic weights 204, 206, 207, and 208. Of these, the last three are identical with the lead isotopes produced as stable end products of the radioactive decays of uranium and thorium: the first, lead-204, is not known to be produced on the surface of the earth by any process. Since uranium and thorium occur in the surface regions of the earth in amounts comparable with lead, and since the half-lives of uranium and thorium isotopes are of the same order as the age of the earth, they produce the radiogenic lead isotopes in amounts com- parable to the amount of nonradiogenic lead present. Every significant exposure of a sample of lead to uranium and thorium will therefore lead to the permanent alteration of the lead isotope ratios in that sample.

Jan 5, 1957

H. A. SCHWARTZ, ? Indianapolis, Inc. (written discussion§).-Re-ferring to the very interesting paper on the graphitization of white cast iron, the writer desires to present certain facts and conclusions, entirely, in harmony with those of the authors but which may he not without interest as furnishing additional evidence upon the same subject. The graphitization of white cast iron, being the basis of malleable

Jan 10, 1919

The Institute is desirous of securing the photographs of Adolph Patera and Albert Serlo, two deceased honorary members of the Institute. All resources within the ken of the Secretary have been tried out to secure these photographs without avail. If any, of our members can give us suggestions which will lead to the accomplishment of the desired ends, such suggestions will be much appreciated.

Jan 5, 1919

By J. Burns Read, S. Tour

It is the purpose of this paper to summarize, as far as possible, the metallurgical information and experience gained by the Ordnancc Department, during the war, in the manufacture of artillery cartridge cases, to describe the tests to which artillery cartridge cases were put, and to summarize the knowledge and experience gained in this testing. The authors wish to acknowledge the aid given by manufacturers, army officers, and civilian employees of the Department in obtaining data. Artillery cartridge cases are cold drawn from circular disks punched from strips of rolled brass. The rnanufacture involves from 25 to 30 main operations, which are done almost entirely on a punch press. Descriptions of the operations have appeared in various periodical:: and, therefore, will not he given here. After each cupping, or drawing, operation, except the last, the cases are annealed at from 540" to 650" C. (1000" to 1200°F.), to remove all the hardening stresses set up in the metal and to allow complete recrystallization. After each annealing, the cases are pickled in niter cake or sulfuric-acid solution and then washed in water to remove all traces of acid. In some instances, the cases arc then immersed in a cyanide-salt solution, and afterwards rinsed in water, to remove the thin layer of copper that forms on the surface of the cases during the acid pickle. The last cold-drawing operation is followcd by the heading operation which, by flattening the head of the case on the outside, causes the metal to flow on the inside to approximately the proper finished dimensions. The mouth, or open end, is then annealed at 430" to 450" ('. 1800" to 900" F.) by immersion in a salt bath or by gas flames. After being washed, the eases are tapered, when they arc ready for machining, inspection, and testing. Cartridge-case Disks Good disks of proper composition and physical properties are essential to the production of good cartridge cases. The Ordnance Department

Jan 1, 1923

By J. Burns Read, S. Tour

It is the purpose of this paper to summarize, as far as possible, the metallurgical information and experience gained by the Ordnancc Department, during the war, in the manufacture of artillery cartridge cases, to describe the tests to which artillery cartridge cases were put, and to summarize the knowledge and experience gained in this testing. The authors wish to acknowledge the aid given by manufacturers, army officers, and civilian employees of the Department in obtaining data. Artillery cartridge cases are cold drawn from circular disks punched from strips of rolled brass. The rnanufacture involves from 25 to 30 main operations, which are done almost entirely on a punch press. Descriptions of the operations have appeared in various periodical:: and, therefore, will not he given here. After each cupping, or drawing, operation, except the last, the cases are annealed at from 540" to 650" C. (1000" to 1200°F.), to remove all the hardening stresses set up in the metal and to allow complete recrystallization. After each annealing, the cases are pickled in niter cake or sulfuric-acid solution and then washed in water to remove all traces of acid. In some instances, the cases arc then immersed in a cyanide-salt solution, and afterwards rinsed in water, to remove the thin layer of copper that forms on the surface of the cases during the acid pickle. The last cold-drawing operation is followcd by the heading operation which, by flattening the head of the case on the outside, causes the metal to flow on the inside to approximately the proper finished dimensions. The mouth, or open end, is then annealed at 430" to 450" ('. 1800" to 900" F.) by immersion in a salt bath or by gas flames. After being washed, the eases are tapered, when they arc ready for machining, inspection, and testing. Cartridge-case Disks Good disks of proper composition and physical properties are essential to the production of good cartridge cases. The Ordnance Department

Jan 1, 1923

By Huey-Lin Luo, T. R. Anantharaman, William Klement

Two new metastable phases have been obtained in Au-Ge alloys by rapid cooling from the melt. One is of the hep structure with near-ideal axial ratio and may be considered a Hume-Rothery phase. The other has a complex tetragonal structure (a = 11.627Å and c = 22.191Å for the Au60Ge40 alloy) and may be looked upon as a superlattice made up of forty-four fee unit cells. Alloys with the tetragonal phase are charactevized by marked preferred orientation. The metastable constitution of the Au-Ge alloys is discussed with reference to the rate of cooling from the melt. THE Au-Ge equilibrium diagram features a rather deep eutectic near 27 at. pet Ge with a maximum solid solubility of 3.2 at. pet Ge in gold and is similar to the Ag-Ge, Ag-Si, and Au-Si diagrams.' The present study of the effects of rapid cooling from the melt on the structure of Au-Ge alloys constitutes an extension of similar investigations2-8 in this laboratory on alloys of noble metals with germanium and silicon. Nonequilibrium hep structures have so far been obtained by quenching Ag-Ge2, 3 and Ag-Si4, 5 alloys from the melt; an Au-Si alloy of approximately eutectic composition has been found6 to solidify in a noncrystalline state. EXPERIMENTAL PROCEDURES Twenty-nine alloys prepared from gold of 99.9+ pet and germaium of 99.999 + pet purity were investigated. The method of alloy preparation, the technique of rapid quenching from the melt, and the X-ray diffraction procedures were similar to those described previously.3, 4 Essentially, small sections (-20 mg) of thin alloy rods (-1 mm diam) were rapidly heated up to 1200°C in a graphite crucible under argon and the liquid alloy ejected by a helium blast onto a polished copper strip held on the inner periphery of a rotating wheel. The resulting thin foils were examined with or without the copper substrate in a G.E. X-ray Diffractometer or in a 114.6-cm-diam Debye-Scherrer camera. RESULTS Table I gives the constitution of liquid-quenched Au-Ge alloys, as estimated from intensities of X-ray reflections from the corresponding phases, viz., a (fee solid solution), ß (hep phase), ? (tetragonal phase), and diamond-cubic (dc) germanium. Despite unavoidable variations in the quenching rates, the proportions of the phases in different alloys were generally reproducible and stable at room temperature. There was no evidence of quenching strain, since the a doublets were well-resolved in high-angle Debye-Scherrer reflections in all cases except where stacking faults in the a fee and ß hep structures contributed to X-ray line broadening. The ß and ? metastable phases showed signs of decomposition to the equilibrium a phase and germanium only after a few hours annealing above 100°C. A few alloys around the eutectic composi-

Jan 1, 1965

By G. T. Higgins

PREVIOUS workers1,2 have found evidence of exaggerated grain growth or secondary recrystallization on annealing sponge zirconium at temperatures high in the a, phase field, but no details of the orientation relationship between the secondary grains and "as-recrystallized" matrix were reported. In other hexagonal metals, namely dilute Mg-A13 and Cd-zn4 alloys, secondary recrystallization has been observed in which the secondary grains are related to the primary recrystallized structure by rotations about the c axis. These rotations are thus comparable with the rotations about the (111) axis observed in the secondary recrystallization of fcc metals. In the current work secondary recrystallization has been observed on annealing iodide zirconium at 800°C and the associated changes in crystallographic texture have been examined. The material employed was arc-melted iodide zirconium of the following composition: Impurity O H Fe Hf Pb I Ni C1 A1 ppm by wt 130 5 230 98 23 28 200 39 30 This was received as 0.25-in. plate, and, prior to the annealing studies, was cold-rolled to 0.040 in. Specimens 1 in. sq were chemically polished and annealed for various times at 800°C in a vacuum better than 5x 10-6 Torr. For metallographic examination specimens were first chemically polished and then anodized8 to enhance contrast between the grains when examined under polarized light. Changes in crystallographic orientation associated with the development of secondary grains were followed by (1011) and (0002) pole-figure determinations using a conventional Schulz goniometer in reflection. Filtered Cr Ka radiation was employed and great care was taken to avoid spurious re- sults due to the close proximity of the Bragg angles for the (1011) and (0002) reflections. Figs. 1 and 2 illustrate the change in grain structure on annealing at 800°C. After 24 hr the structure has ceased to be equiaxed due to the development of certain grains in preference to others. It is notable that the secondary grains do not grow to the extent observed in sponge zirconium.1,2 This appears to be due in part to the fact that normal grain growth is inhibited in the less pure sponge zirconium, with the result that the driving force for secondary recrystallization remains high, while at the same time the number of grains able to develop in the presence of the impurities is also smaller. As a consequence, in sponge zirconium those grains that do develop preferentially are able to grow into the fine -grained matrix without impingement, while in iodide zirconium the preferential growth of many grains leads to early impingement. The pole figures determined for specimens annealed for 5 min and 24 hr at 800°C are illustrated respectively in Figs. 3 and 4. These indicate that the dominant feature of the initial recrystallized texture consists of basal planes at an angle of 321/2 deg to the sheet surface, with a (1120) axis lying parallel to the

Jan 1, 1967

By Theron Wasson

The year 1942 in Michigan was devoted largely to the development of fields discovered in 1941 but was also characterized by a great increase in prospecting for new productive horizons below the Dundee limestone. Some new fields were discovered but as yet these have shown few signs of being of major importance. Michigan's total production for 1942, of 21,754,000 bbl. of oil, as reported by the U. S. Bureau of Mines, was second only to the record year of 1939 when 22,799,000 bbl. of oil were produced. All important fields were prorated throughout the year, and it is obvious that without proration a new all-time high would have been established for the state this year. From 1925 to the end of 1942, Michigan has produced annually the following amounts of oil: Year Barrels Source 1925 4,000 1926 94,000 1927 435,000 1928 592,000 1929 4,641,000 1929 Michigan Geological Survey 1930 3,928,000 3,785,000 1932 6,925,000 1933 7,942,000 1934 0,603,000 1935 15,776,000 U.S. Bur. Mines, 1937 1936 11,928,000 U.S. Bur. Mines, 1938 1937 16,628,000 U.S. Bur. Mines, 1939 1938 19,211,000 U.S. Bur. Mines, 1938 1939 22,799,000 1940 19,764,000 1941 16,361,000 1942 21,754,000 Total 183,170,000 This tabulation shows the steady growth of the industry in Michigan since the first discovery of oil in 1925. Maes A map of the oil and gas fields of Michigan in 1941, published in the report for 1942, shows the main producing areas and should be referred to if information in regard to their location is desired.* The main producing zones were shown in the columnar section in the same publication. Development in Fields Reed City Field.—During 1942 the Reed City field, which ended 1941 with 112 producing oil wells, added 70 new producers to bring the total at the end of the year to 182 wells and 4700 proven acres. A south extension of the field developed during the year was in large part responsible for the increase. Approximately 9,000,000 bbl. of oil was produced from the field during the year, bringing the total accumulated production to the end of the year to roughly 11,750,000 barrels. Headquarters Field.—The Headquarters field, which started the year with ro producing oil wells, ended the year with 41 wells aid 1240 proven acres. Approximately 2,300,000 bbl. of oil was produced in 1942. Kawkawlin Field.—Although not a 1941 discovery, the Kawkawlin field has been actively developed on the 40-acre spacing plan during the last year, 42 producers having been completed, bringing the total number of wells at the end of the year to 77. Nearly 500,000 bbl. of oil was produced during the year.

Jan 1, 1943

By Theron Wasson

The year 1942 in Michigan was devoted largely to the development of fields discovered in 1941 but was also characterized by a great increase in prospecting for new productive horizons below the Dundee limestone. Some new fields were discovered but as yet these have shown few signs of being of major importance. Michigan's total production for 1942, of 21,754,000 bbl. of oil, as reported by the U. S. Bureau of Mines, was second only to the record year of 1939 when 22,799,000 bbl. of oil were produced. All important fields were prorated throughout the year, and it is obvious that without proration a new all-time high would have been established for the state this year. From 1925 to the end of 1942, Michigan has produced annually the following amounts of oil: Year Barrels Source 1925 4,000 1926 94,000 1927 435,000 1928 592,000 1929 4,641,000 1929 Michigan Geological Survey 1930 3,928,000 3,785,000 1932 6,925,000 1933 7,942,000 1934 0,603,000 1935 15,776,000 U.S. Bur. Mines, 1937 1936 11,928,000 U.S. Bur. Mines, 1938 1937 16,628,000 U.S. Bur. Mines, 1939 1938 19,211,000 U.S. Bur. Mines, 1938 1939 22,799,000 1940 19,764,000 1941 16,361,000 1942 21,754,000 Total 183,170,000 This tabulation shows the steady growth of the industry in Michigan since the first discovery of oil in 1925. Maes A map of the oil and gas fields of Michigan in 1941, published in the report for 1942, shows the main producing areas and should be referred to if information in regard to their location is desired.* The main producing zones were shown in the columnar section in the same publication. Development in Fields Reed City Field.—During 1942 the Reed City field, which ended 1941 with 112 producing oil wells, added 70 new producers to bring the total at the end of the year to 182 wells and 4700 proven acres. A south extension of the field developed during the year was in large part responsible for the increase. Approximately 9,000,000 bbl. of oil was produced from the field during the year, bringing the total accumulated production to the end of the year to roughly 11,750,000 barrels. Headquarters Field.—The Headquarters field, which started the year with ro producing oil wells, ended the year with 41 wells aid 1240 proven acres. Approximately 2,300,000 bbl. of oil was produced in 1942. Kawkawlin Field.—Although not a 1941 discovery, the Kawkawlin field has been actively developed on the 40-acre spacing plan during the last year, 42 producers having been completed, bringing the total number of wells at the end of the year to 77. Nearly 500,000 bbl. of oil was produced during the year.

Jan 1, 1943

By E. T. Turkdogan, P. Grieveson, J. F. Beisler

Experimental results are given for the rate of reduction of silica from silicate melts by paphite-saturated iron in the presence of carbon monoxide. It is shown that, when gas bubbles are present at the slag-metal interface, the interfacial chemical reaction is the rate-controlling process in the transfer of silicon from slag to metal. From the silicon-concentration profiles in the metal sample, the diffusivity of silicon in paphite-saturated iron is found to be (5.4 * 0.4) x 10 sq cm per sec at 1600°C. Some consideration is given to the transport of oxygen from the slug-metal interface to the walls of the gvaphite metal container as becoming the rate-controlling process in the absence of gas bubbles at the slag-metal interface. ATTEMPTS were made by Fulton and chipman1 to investigate the kinetics of reduction of silica from calcium alumino-silicate melts by graphite-saturated iron in an atmosphere of carbon monoxide. In these experiments with 400 to 500 g of metal and slag, both phases were stirred in such a manner that the interface was essentially undisturbed. Initially, the graphite-saturated iron contained about 15 pct Si and, after about 8 or 10 hr of reaction time at 1600°C, the silicon content of the metal in- creased by about 0.2 pct. In a written discussion on this paper of Fulton and Chipman, schuhmann2 pointed out the possibility that this observed slowness of the reduction of silica could be due to the transport of oxygen across the liquid metal boundary layer at the slag-metal interface. Although this explanation of Schuhmann is quite feasible for the experimental data of Fulton and Chipman on silica reduction, such a reasoning should not be extended to other rate data on slag-metal reactions unless sufficient evidence is available satisfying the boundary conditions for such a transport process. The hydrodynamics of stirred liquids are very complex and even for a simple method of stirring there is no exact mathematical solution which will predict the mass transfer coefficient accurately. The best available solution of this problem is that given by Lewis' and later modified by mayers~ for a two-liquid system where liquids are stirred by counter-rotating stirrer blades without disturbing the interface. In such a system the mass transfer coefficient is estimated from an empirical relationship using the data on viscosity and density of the two liquids, rate of revolution, the length of stirrer blades, and the diffusivity of the element which is transferred from one phase to the other. It was found in these investigations' that the estimated and observed mass transfer coefficients, in systems containing two immiscible aqueous solutions, agreed within *40 pct. Although this is not considered to be an unreasonable error for the study of industrial processes, uncertainties of this magnitude cannot be tolerated in any theoretical study of reaction kinetics. In view of the complexity of the

Jan 1, 1963

By N. A. Gokcen

EQUILIBRIA in the reactions between gases and liquid metals have been the subject of many interesting investigations. The experimental realization of true equilibrium, however, is questionable in certain cases due to the lack of conclusive studies in reaction rates. It -will be shown here that a systematic interpretation of rate studies with the analysis of prevailing experimental conditions leads to valuable practical information. The reactions of particular interest are: H2(g) +S(inFe) - H2S(g) [1] H2(g) +O (inFe) =H2O(g) [21 2H2(g) + SiO2(s) = 2H2O(g) + - (inFe) [3] The usual and perhaps the most convenient method of investigation may be illustrated with reaction 1. A stream of gas mixture consisting of H2 + H2S is passed over or bubbled through the liquid metal at constant temperature. The ratio of H2S/H2 in the entrant mixture is fixed in each experimental run, and, therefore, the composition of melt varies until the establishment of equilibrium. The purpose of this paper is to derive a formula expressing the minimum time required for the establishment of equilibrium and to compare the calculated values from such a formula with the available data. Equations Reaction 1 is used for the purpose of illustrating the derivation. Let E represent the equilibrium and X the nonequilibrium sulphur in weight percent at any time t in minutes. For the sake of simplicity, it is first assumed that E > X although the results are of general applicability without restriction. It has been shown by Morris and Williams' that within a difference of 1 pct S or less, i.e., E-X5 1.00, the value of K'1 = Ph2s/Ph2.S% is very nearly constant. The maximum ratio of available Ph2s/Ph2 = H,S/H,, from which sulphur can be absorbed by metal, is equal to H2S/H2 in equilibrium with E (which equals H2S/H2 in the entrant gas), minus H,S/H, in equilibrium with X. Thus: Available H2S/H2 = EK'1 - XK'1 [4] Eq. 4 expresses that sulphur can be absorbed by metal from the H2S/H2 in the entrant gas until the gas leaving the metal assumes a value of H2S/H2 which is in equilibrium with the dissolved sulphur X at that time. H,S constitutes up to approximately 1 pct of the gas mixture. Its disassociation into H2 and SL is about 1 pct at 1600°C, hence, the H2S/H2 impinging on the surface of metal is very close to that in the entrant gas. The rate of flow of hydrogen entering the reaction chamber is kept constant experi-

Jan 1, 1954

AS provided in Article VIII, Section 4 of the By- laws, the Papers and Publications Committee has formulated the following, rules of pro-cedure and submitted them to the Board of Directors for consideration and approval. In preparing these rules the committee, and an active subcommittee con-sisting of Messrs. Norris, Sharpless; Fohs and Wither-ell, have kept in mind the desirability of codifying the practice that has grown up through the now sev-eral years of experience of the committtee, without casting them in a mold so rigid as to be hampering. The problems of the Institute change from year to year and the methods of publication must change also to meet each new situation as it arises. "The estab-lishment of divisions and special volumes devoted to the papers. read before each required certain changes from former practice. These rules have been framed with this in view. The committee suggested, however, in its letter of transmittal, that the system will be made all the more workable if the Board will, as far as practicable, in making appointments to this committee, arrange for representation from each of the professional divisions and technical committees. It is understood that the chairman of the committee will be named by the Board. The rules regarding spe-cial volumes have been framed, keeping in mind the present policy of distribution, as already approved by the Directors under which the special volumes go only to the special. groups except on request. The committee has not attempted to provide rules governing consideration of any appeal made to the Board from one of its decisions, but its services and files will necessarily be at the full service of the Board in any such event. The rules which were ap-proved by the Board at its meeting on March 30, 1928, are as follows: Signed by C. S. Witherell, Chairman. (A) The authority of. the Committee on Papers and Pub-lications, hereinafter called the Committee, is defined in Art. VIII, Sec. 4 of the By-laws of the Institute, which reads as follows: "Papers and Publications: The Committee on Papers and Publications shall consist of the Secretary of the Institute, and at least twelve members of the Institute, to assist in passing on all papers offered for publication. They shall be appointed annually by the Board of Direc-tors, on recommendation of the President, and shall have authority, subject to appeal to the Board, to accept or reject papers for publication in the Transactions and Technical Publications of the Institute. The Commit-tee shall formulate a set of rules of procedure which, when approved by the Board, shall have the force of By-laws until revoked or amended." The policy of the Committee will be to uphold the ob-jects of -the Institute as set forth in the Constitution (Arti-cle 1, Sec. 2).

Jan 5, 1928

By F. S. McNicholas

IN the writer's opinion the term "block caving" has been rather loosely applied to a general principle of mining, and therefore detailed classification of caving methods and draw, together with the characteristics required for each method, will fill a desired need. Selection of caving method should be made only after a study of all governing conditions, such as size of orebody, lateral and vertical extent of ore-body, attitude, treatment demands, possible resultant pressures, and cost and profit comparison of methods. Successful caving methods can be classified under six main headings: (1) Full-protected block caving, (2) semi-protected block caving, (3) unprotected block caving, (4) full-panel caving, (5) half block-panel caving, (6) block-panel caving. The methods and factors governing choice of method are shown in Table I. Full-protected Block Caving Full-protected block caving consists of develop-ing, undercutting, and drawing to exhaustion a block of ore of predetermined size without coordination of mining or draw with adjoining areas. The block is mined and drawn as an independent unit (Fig. 1). Full-protected block caving demands that mining and draw cannot be done against unconsolidated capping in adjoining caved and exhausted blocks. Two sides of block are against solid. Caved capping must be allowed to consolidate for a suitable period, usually not less than one year. Pillars may be left in lieu of consolidated capping (Fig. 2). The advantages of full-protected block, caving are: (1) A definite area is developed, mined, and drawn as a unit so that all work may be completed, the block drawn to exhaustion in the minimum length of time, and the area then abandoned. (? Production is not restrained because of coordina1, on with adjoining areas. (3) Records of draw and caved reserve of ore are good. Upon abanwnment of the block, accountability for production is closed out with no carry-over to adjoining areas. The disadvantages of full-protected block caving are: (1) Side dilution from the draw adjacent to the consolidated capping may be serious, particularly where capping does not consolidate sufficiently in the allotted time. (2) Boundary weakening is needed on the solid sides of the block except in weak rocks. (3) Maximum cantilever and compression effect to aid caving and fragmentation may not be secured since the draw should proceed from the solid to the consolidated capping to minimize side dilution. However, undercutting from the loose (caved capping) to the solid with a slight initial draw in the same manner will develop cantilever effect. (4) A period of at least one year, more is usually desirable, must be allowed for caved capping ,to consolidate before mining the adjoining block, depending upon the characteristics of the capping. (5) Capping may not consolidate sufficiently in the time that can be allowed. Full-protected block caving is indicated where: (1) The ground is weak and heavy and workings

Jan 1, 1952

AALL,Christian H.,(M '49), Asat.Research Dir , Phosphate Div Monsanto Chem.Co.,Monaanto, Tenn. AAMOT,Olav Crone, (M '29), Dir of Tech., Chromium Min. & Smelt. Co Ltd Box 6215, Hillyard, Spokane, Wash. AARING, Floyd Daniel, (J '48), Prod. Engr., Canadian Gulf Oil Co., 8035 - 102nd St., Edmonton, Alta., Canada AASE, Glenn D., (J '40), Met Engr Western Research Div. ,Amer. Smelt. & Refin. Co., Selby, Calif ABADIE, Henry G (M '43), Senior Prod Engr., Long Beach Oil Dev Co., 255 S Santa Clara Ave Long Beach 2, Calif. ABBOTT,Clarence E (M '04), Civil Engr., 901 Insurance Bldg., Raleigh, N.C. ABBOTT, John, H., (M '46), Resident Mgr., Hickman, Williams & Co., Rm 2205,230 N Michigan Ave., Chicago 1. I11.

Jan 1, 1952