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1. Healthy and active Local Section organizations are vital factors in promoting the vigor and growth of the Institute. 2. Activity on the part of Local Sections should be recognized and stim¬ulated by appropriation of funds from the Institute's treasury; and these appropriations should be as large as is consistent with the relative needs for other activities. 3. As between different Sections, the amount of such appropriations should be based primarily on the extent of activities as reflected in the number and character of meetings .held and the attendance of the members at such meetings. 4. In making a request for funds for any year, the officers of a Local. Section should submit: (a) a report showing in reasonable detail its income, and expenditures for the preceding calendar year; (b) a statement of the number of. members to whom announcements of each meeting had .been mailed; (c) a record of meetings held, the character of the program, and _ attendance of members at each; and (d) any further facts having a bear¬ing on its financial requirements for the coming year.

Jan 1, 1937

By J. B. Scuffham, G. A. Rowden

The use of ammonia as a leaching agent has been well-documented but only recently have its advantages been fully exploited on a commercial basis. When compared with conventional sulfuric acid leaching processes, the major advantage of ammoniacal systems is their ability to reject iron and many acid consuming gangue materials. Although metallic copper, nickel, zinc, etc. are dissolved rapidly in ammoniacal liquors at ambient temperature in the presence of air the sulfide ores of these metals are more resistant to this treatment. Sherritt Gordon Mines in Canada treats sulfide concentrates at its Fort Saskatchewan plant under pressure with ammoniacal am- monium sulfate solution to solubilize the non-ferrous metal values. Typical leach operating conditions are 80-95°C and 115- 128 psig. Although the metals present in the ammonical solution could be recovered via solvent extraction techniques, Sherritt Gordon Mines currently operates a pressure reduction process using hydrogen to yield metal powders directly from the ammoniacal solution. The basic Sherritt Gordon technology has been applied world wide for the treatment of nickel/cobalt concentrates.

Jan 12, 1973

By Rupert Spivey

Kennecott Copper's Chino mine is one of the oldest copper mines in the United States, having been operated by the Spaniards as early as 1800. At that time haulage methods were indeed primitive. Indians brought the ore up on "chicken ladders" in leather buckets. It was then melted into crude bars and hauled to Chihuahua by mule train. There are still remnants of the old trails near the present pit where the mule hooves cut grooves in solid rock. The mines were worked as underground operations off' and on until open-pit mining was started in 1910 by John Sully and Daniel C. Jackling. Since that time many haulage methods have been used: mule carts, steam and electric trains and finally large haulage trucks, now believed to be the best method for this mine. The general shape of the pit is oval with dimensions of 1% miles by 1% miles. Working benches are 50 ft high, with the bottom bench at 5750 ft and the top at 6450 ft above sea level.

Jan 1, 1964

By R. W. Armstrong, P. C. Jindal

The hardness dependence on grain size for polycrys-talline cartridge brass and a leaded brass has been measured by Brine11 and Rockwell B testing. In each case, the hardness, H, depends on the average grain diameter, 1, according to: H =Ho + kHl-1/2 where Ho and kH are experimental constants. Diamond pyramid hardness values have also been measured as a function of the indentation size and grain size to give additional information on the nature of the hardness test and the dependence of hardness on micro-structure. The hardness of polycrystalline brass depends on its grain size. Bassett and Davis' demonstrated this as early as 1919 by making Brinell hardness measurements on cartridge brass. Since then, the hardness of this type of material has been measured as a function of grain size by making Rockwell,2'3 Vickers,4 and Brinell5 tests. he hardness dependence on grain size has also been measured for other materials. Angus and summers6 investigated the grain size dependence of the Brinell hardness of polycrystalline copper and a Cu-4.5 pct Sn bronze. In other studies, nickel,? Armco iron,Big an Fe-0.07 pct C alloy,I0 and an 0.39 pct C-12.45 pct Cr stainless steel" have been investigated. In some of the preceding cases, the hardness results have been analyzed to show that the hardness varies with the average grain diameter, 1, according to an l-l\4, l-1/4 or I-2 dependence,11-13 The studies of the influence of grain size on hardness have not been based on any theoretical model. This may be because the hardness of a material is itself a complicated property. However, attempts have been made to correlate, experimentally and theoretically, the hardness of a material with its unidirectional stress-strain behavior.14-l6 On this basis, Hall" proposed that the polycrystal hardness dependence on grain size might follow directly from the Hall-Petch18,19 relation for the grain size dependence of the yield stress. Thus, the hardness-grain size relation was given as: H = Ho + kHl-1/2 [1] where Ho and kH were taken as experimental constants. The relation was applied to the measurements on brass,' copper,6 bronze,= and Armco iron.' More recently, this relation was shown by Armstrong and jindal20 to adequately describe the measurements on cartridge brass made by Bassett and Davis' and Babyak and Rhines.5 In this case, the relationship was taken a step further by independently relating the values of Ho and kH to the values of oyand ky, previously reported by Armstrong, Codd, Douthwaite, and petch21 from measurements of the yield stress dependence on grain size for this type of material. In the present investigation, new Brinell and Rockwell B hardness measurements have been made as a function of grain size for a cartridge brass and a leaded brass. In addition, diamond pyramid hardness values were measured as a function of the indentation size. All these results are applied to a further analysis of the hardness dependence on grain size. MATERIALS AND EXPERIMENTAL METHODS Cartridge brass and a leaded brass were selected for this investigation for two main reasons: it was anticipated 1) that these materials could be cold-worked and recrystallized to a wide range in grain size and 2) that the results to be obtained on these typical industrial materials could be usefully compared with previous investigations. The chemical analyses of the actual materials which were employed are given in Table I. The as-received 1/2- and 3/4-in.-thick plates were given various reductions in thickness by cold rolling. The rolled material was heat-treated at various temperatures between 330" and 850°C for differing time periods from 5 min to 9 hr to achieve a variation in the average grain diameter between 0.0339 and 0.000543 cm.22 During heat treatment, the brass was protected from zinc loss by packing it in chips or foils of the same composition material. Reasonably equi-axed grain structures were obtained in each case. The metallurgical grain sizes of the specimens were determined from measurements of the average linear intercept on a random line. Annealing twin interfaces were not counted along with grain boundaries. The

Jan 1, 1970

By F. A. Forward, V. N. Mackiw

The paper relates to the laboratory and pilot plant studies that have been carried out by Sherritt Gordon Mines Ltd., Metallurgical Research Div., in developing the ammonia pressure leach process for extracting copper, nickel, cobalt, and sulphur from high grade nickel concentrate produced from Lynn Lake ores, and describes in some detail the chemistry of the process. IT is well known'.' 2 that copper, nickel, cobalt, zinc, ferrous iron, and a number of other metals combine with ammonia in aqueous solution to form complex ions of the form [Me(NH,)x]"+. The stability and solubility of these ions depend on the concentration of the metal ion in solution, on the amount of NH, present, and on the amount and type of anions present, e.g., OH-, C0;-, NO,, C1-, SO;-. If ammonia is partially or completely removed from such solutions, for example by boiling, the soluble ammines tend to decompose and the metals precipitate as basic salts. These properties of metal ammines have found practical application in the commercial recovery of copper, nickel, and cobalt from a variety of ores. In an operation formerly conducted at Kennecott"" the mill tailing containing 0.80 pct Cu as copper carbonate was leached by percolation with an ammonia-ammonium carbonate solution to dissolve the copper as the ammine. At Calumet and Hecla0-" With a mill tailing containing about 0.4 pct Cu as metallic copper, it has been found necessary to aerate the ammonia-ammonium carbonate leach solutions between stages to oxidize the solubilized copper. At Nicarol"-" where nickel and cobalt occur as oxides and silicates which are not soluble in ammonia, the ore is heated to decompose silicates and to selectively reduce the nickel and cobalt to metal, leaving the iron as Fe,O,, and is then leached with ammonia-ammonium carbonate solution accompanied by aeration to dissolve nickel and cobalt as ammines. In each of these leaching operations, the anion present is CO, and the metals can be precipitated from the leach solution as oxide (copper) or hydroxide and carbonate (nickel and cobalt) by boil- ing off NH, and C02 both of which are recycled to treat a subsequent ore charge. The products-—oxide, hydroxide, or carbonate—can be treated by conventional smelting, calcining, or electrolytic methods to convert them to refined metals. Thus the procedures mentioned utilize the properties of the ammines to extract copper, nickel, and cobalt from nonsulphide ores and separate them from the leach solutions. These processes have the advantage that they can be carried out in closed vessels at atmospheric pressure, that the leaching solutions are specific for the desired metals, that the metals can be recovered as relatively pure compounds by the boiling operation, and that the NH, and CO, can be recycled. Also, as the leach solutions after boiling and filtration are substantially free of metals, NH,, and CO,, they can be discarded, thus facilitating the control of the water balance in the leaching circuit. When, as is the case with Sherritt Gordon concentrates, sulphides are treated with ammonia solution in the presence of oxygen, the leach solution contains SO,--, and an entirely different set of conditions is encountered. The ammine sulphates (of nickel, for example) are more soluble than the carbonates and can be only partially decomposed by boiling. The SO, and NH, in the solutions can not be recovered by boiling. Thus, despite the more favorable leaching conditions resulting from high solubility of the ammine sulphates, the recovery of metals, NH,, and SO, from the solutions must be effected by other means. Sherritt Gordon Nickel Concentrate Treatment The Ni-Cu-Co flotation concentrate produced at Lynn Lake'" contains 12 to 16 pct Ni, 1 to 2 pct Cu, 0.2 to 0.5 pct Co, 33 to 40 pct Fe, 28 to 34 pct S, 8 to 20 pct insoluble, and less than 0.02 oz per ton precious metals. The nickel is present chiefly as pentlandite, the copper as chalcopyrite, and the iron as pyrrhotite and pyrite. Most of the cobalt is thought to be present in pentlandite, although it is known that a small amount occurs as Co-Ni-pyrite.

Jan 1, 1956

By W. Spencer Hutchinson

THE purpose of this account is to introduce to other engineers and geologists who use photography a means of interpreting topographic and geologic structure with the stereoscope. Anyone who finds this of sufficient interest to read it at all must cut out the pictures shown and have a good look at them through the stereoscope; there is no other way to appreciate what is meant. Most of us have been disappointed by the flatness of mountain pictures and by the lack of perspective in photographs taken to illustrate topographic and geo- logic features. The use of the stereoscopic principle was suggested by the work of the photographic division of the Air service during the war. Photographs of the battle line, taken from air planes, were mounted for stereoscopic study, with most remarkable development of topography, penetration of camouflage and, by the matching of pictures with a time interval between, sure revelation of new work by the enemy. Thus, two views taken from a plane flying at 10,000 ft., both of the same terrain but from different points, are mounted in proper relation and put into the stereoscope. If the distance between the two positions of the camera was 200 ft., the observer then sees the topographic and military features as though his eyes were 200ft. instead of 235 in. apart.. The result is startling in its revelation of features that are flat and unintelligible when viewed by the unaided eye or in a single photograph. The technic of the work, as developed during the war, was quite complex and

Jan 1, 1921

By William Campbell

In the olden days the making of alloys was an art, and the secrete of the craft were jealously guarded. To-day it has become a science, though the old ideas in regard to the secrets and formulæ are dying hard. Modern progress may be attributed to scientific research and testing of materials, and the substitution of chemical analytical control for " cook-book " methods. We know to-day a great deal about the constitution of alloys, the reasons of the change in structure and physical properties by heat and mechanical treatment; and this new knowledge is due for the most part to the physical chemist and metallographist, who have shown us that alloys are simply solutions, and as such obey definite laws. The application of the theories of solutions and of the phase rule tells us what ought to happen when our alloys are in a state of equilibrium. The working-out of the temperature-composition diagram (thermal diagram) for numerous alloys has thrown a light on the structure and constitution which has dispelled most of the darkness in which we labored before the advent of metallography. The work began with the determination of the freezing-point curves, and here the research of Le Chatelier,' Gautier,2 Roberts-Austen,3 and the other pioneers broke the ground. Next the physical chemists, Tammann,4 Rooseboom,5 Bancroft,6 and their colleagues, showed us the complete thermal diagram and its meaning. Then the researches of Heycock and Neville7 on the Cu-Sn series and of Shepherd 8 on the

Jan 1, 1913

By Roy Moore

THE Tom Reed Extension and Big Jim mines of United Eastern Mining Co. are situated in the Oatman district, Mohave County, Ariz., about 28 miles southwest of Kingman, the nearest railway point. Articles descriptive of the mine surface plant, mill construction, and plant operations have been written by Otto Wartenweiler1, the designing engineer; Wheeler 0. North,2 when he was assistant general manager for the company, and Earle M. Bagley, mill superintendent.3 The last article covers average costs for the full time the mill was operated. The geology of the mines is described by F. L. Ransome4 of the United States Geological Survey. Production was started in January,. 1917, and the known orebodies were exhausted in May, 1925, showing a life of seven years and five months. On account of the comparatively short life and the fact that stoping operations were confined to two orebodies, little experimenting was done with mining methods. The two orebodies were in what is generally called the Tom Reed-United Eastern vein, which occupies a fault fissure having a normal displacement of several hundred feet. Seven or eight very productive ore shoots were mined along this vein in a distance of 1 ½ miles, the two worked by the United Eastern being 1 mile apart. The maximum dimensions of the Tom Reed Extension ore shoot were height, 750. ft.; length, 950 ft.; thickness, 48 ft. The vein structure varied from a solid quartz-calcite filling to a series of parallel stringers separated by andesite. From this body, 511,976 tons of ore were mined. (Fig. 1.)

Jan 1, 1928

GEO. F. COMSTOCK,* Niagara Falls, N. Y. (written discussion?).-In this exposition of experimental data, the author infers, indirectly at least, that by the Charpy test information was obtained that led to the improve-ment of certain ordnance parts and that this improvement could not have been attained without the Charpy test. On examination of the data, however, it appears that the important point of the whole matter was that while the material had been accepted from the results of longitudinal tensile tests, it was really transverse ductility that was desired. The writer has no desire to attempt to detract from the value of the paper or to discredit the Charpy test in any way, but he would like to ask the author if he will not give more clearly his reasons for preferring the Charpy impact test for investigational and control work of this kind, over the more usual tensile test made in a transverse direction. The tensile test pieces are more cheaply made than the square notched impact bars; and from the former the limit of elasticity and the ultimate strength as well as, the ductility are obtained, while in the Charpy test only one property is measured. It does not seem that the author has shown a sufficient reason for favoring the latter test, when both it and the trans-verse tensile test served his purpose equally well in indicating the proper metal and treatment required for his special forging, and it is hoped that this reason will be given more clearly as a matter of useful general information.

Jan 11, 1919

By Robert Richards

Introduction. 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 possible, 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.

Jan 9, 1913

By Edward C. Morse

The metallurgical history of Republic has been completely reviewed in a paper presented at a previous meeting of the Spokane Local Section by Professor Thomson;' therefore, the present paper will be confined to matters directly pertaining to the San Poil mill: When I came to Republic last fall to look over the situation there was a plant in operation successfully treating the tailings from one of the earlier mills in the camp. I refer to the mill of the Rathfon Reduction Co. This mill was operating in accordance with modern cyaniding practice, and I was given to understand that the work was very satisfactory and profitable, else it would not have been continued as long as it was. At that time I obtained much metallurgical information of value from Harry W. Newton, Superintendent of the mill of the North Washington Power & Reduction Co. I took a number of samples from the San Poil mine, with the view of determining if Mr. Newton's experience with the ores from the other mines applied to the San Poil ores. I made a large number of tests under a variety of conditions, and found that it was possible to extract as high as 98 per cent, of the values from San Poil ore by the laboratory-tests when the ore was pulverized to 200-mesh and treated with a solution of a strength of 5 Ib. of KCN to the ton. A fairly strong solution was required because of the proportion of silver in the ore, which makes it, from a metallurgical point of view, practically

Jan 1, 1913

By James Douglas

At this last meeting of our Institute for the year 1899, it is appropriate that we should look back at the past. To review the century's progress in the exact sciences and the resulting arts that fall within the scope of our labors is beyond my ability. But I wish to draw your attention to some phases of that progress, almost as important, which lie within the zone of sociology, touching at so many points the domain of applied technology. One of these is suggested by the library of technical literature which this century has produced —not the least important contribution to which is our own Transactions. The nineteenth century has witnessed the beneficial spread of democracy in politics. Under the impulse, to no small degree, of the same spirit, there has grown up a brotherhood of fellow-workers and a sense of fellow-ownership in the secrets of nature. Though the Patent Office has assumed such proportions as to hare become a source of national revenue, and a multitude of inventors, great and small, are seeking through its agency to secure some pecuniary profit from their devices, there is even greater eagerness among both interested and disinterested workers in the field of technology to publish their observations, and even their discoveries, and to give them to the world without remuneration. The motives influencing the great body of writers who, without any pay, use the technical journals and such media of communication as our Transactions, in order to give to the brethren of their craft the results of

Jan 1, 1900

By C. S. Barrett

THE crystal imperfections known as faults in stacking (stacking disorder) are of importance to both fundamental and applied science and are receiving increasing attention. On the theoretical side there have been recent advances in the analysis of diffraction patterns in terms of stacking faults, and on the experimental side it has been found that certain metals develop a faulted structure on cooling through a phase transformation. Beyond this, little is known of what may be called the physical and mechanical metallurgy of faulting, although there has been no lack of discussion and conjecture as to the presence of faults in metals and the effect of faults on mechanical properties and microstructures. In the close-packed metals the nature of faults can be described very simply. Face-centered cubic (FCC) crystals consist of close-packed layers of atoms, (111) planes, stacked above each other in a definite manner. If one layer is designated as the A layer, the next must be a B or a C layer; that is, every atom of the second layer lies not above the atoms of the A layer, but nestles in the hollows between these, using the hollows designated as the B positions, or the equivalent hollows designated as C. If the sequence of layers is ABCABC...., so that layers three spacings apart are directly over each other, the crystal is FCC; if CBACBA ... it is an FCC crystal that is a twin of the former; if ABAB........or BCBC..it is hexagonal close-packed (HCP). A fault is a break in the sequence, such as ABCABABC .. . which has the effect of inserting an HCP lamella into an FCC crystal. Regularly spaced faults spaced two layers apart would convert an FCC crystal entirely to HCP, or an HCP to FCC. A fault in an FCC crystal is also equivalent to creating an FCC twin of minimum thickness; in fact, the entire crystal would be converted to its twin if faults were introduced regularly. (In HCP crystals, however, twinning does not occur on the basal plane and a fault on this plane is not identical with a thin twin). Faults are one of the possible causes for annealing twins,' for the strain markings that are brought out by etching deformed metal,'," for the altered X ray reflecting power of metal at slip bands that is revealed in X ray reflection micrographs,' for the extinction of Kikuchi lines in electron diffraction patterns, and for the hardening of latent slip planes.' Since other explanations of these effects are also available," there has been no direct proof of faults from deformation; yet it has appeared likely that they would occur. Faults resulting from phase transformations in metals, however, have been clearly revealed by diffraction in cobalt" and lithium. It is to be expected that the faulting tendency is greatest

Jan 1, 1951

Jan 1, 1912

By Smith, George Otis

THE matter that I have on my mind this evening is engineering's need of an open forum. Our fathers of three centuries ago were pro-testanta for freedom of speech and thought in matters religious; later, our fathers were revolutionists for freedom of speech in matters political; until today freedom of speech has become so universal throughout the land that even in the sanctuary of our homes, at times, we have to turn off the loud-speaker. Talk is not always a condition of progress, but light is everywhere necessary to growth, whether the growing thing is a blade of grass, a baby chick, or a young idea, and we must regret anything that tends to shut out the light from the operations of business and industry. Of course, I realize there is little that is novel in what I am saying. Indeed, I have found that Dr. James Douglas-a name we love to honor in our Institute-as long ago as 1907, gave an address at the Toronto meeting that any of us would be proud to be author of twenty-one years after. Dr. Douglas at that time spoke on secrecy in the arts and the text then taken by this leader in metallurgical technique and in the constructive management of big business was "the dangerous temptation to adopt secretive methods by very large corporations." In both thought and language Dr. Douglas was direct and vigorous and he needs no internreter. He advocated the wide open door for ideas on two counts: advancement of technical knowledge and education of public opinion. A few sentences will serve not only to prove the vision of James Douglas, but also, I hope, tempt you to hunt up his address in the Institute's TRANSACTIONS, and thus get his whole thought first hand.

Jan 1, 1928

By O. W. Ellis

THE writer has dealt with the effect of various methods of melting copper upon the gas content of the metal.1 The copper referred to in his in his earlier paper was melted in the foundry both in the oil furnace and the electric furnace. As the metal, did not measure up to conductivity FIG. L -INGOT OF OVERPOLEP COPPER. standard, the term "casting copper" was applied to the material in the title of the paper. It was thought that some information in regard to the gases in a sample of overpoled copper might also be of interest, and through the courtesy of C. R. Stevens, superintendent of the copper mill of the Westinghouse Elec. & Mfg. Co., such a sample was obtained. The metal was chill-cast in the form of an ingot about 7 in. long, 2 ½ in. deep (from the base to the raised surface of the ingot) and from 1 3/8 to 1 7/8 in. wide. A photograph of part of the ingot is shown in Fig. 1. The effect of overpoling on the surface of the metal is here quite clearly shown.

Jan 1, 1929

By M. B. Kahle, A. D. Pernichele

Four types of slope failures in waste dumps are recognized debris flow, foundation failure, edge slump, and blowout. The first three types, although at times causing considerable damage to property and interfering with mine operations, are not usually dangerous to personnel because of their slow rate of movement. The fourth type, the blowout, is the most dangerous because of its explosive mode of failure and lack of forewarning. The December 1969 failure at Verona dump is presented as an example of a blowout. Data from piezometer holes indicate that the blowout was due to perched leach solutions near the face of the dump. The level of water in this zone is very closely related to the rate of leach water application on the dump. A detailed analysis of core samples indicates that the impounded water was perched on a zonal accumulation of jarosite which is associated with a buried dump surface. Drain holes proved successful in controlling perched leach solutions in the critical zone near the face of the dump. Monitoring of the water level in the perched zone is considered essential in preventing blowouts. The use of drain and piezometer holes has allowed an increase in the rate of water application on the dump while preventing additional failure.

Jan 1, 1972

By Paul W. Zimmer, Carl E. Dutton

Iron ore in the Menominee district is mined from two iron-formations of middle Precambrian age. The older formation is present in the northeastern part; is composed mainly of hematite, magnetite, quartz, and minor silicates; and contains about 34 per cent iron. The rock has been so coarsened by meta- morphism that concentration of magnetite and hematite is feasib!e, and pellets containing more than 60 per cent iron are being produced. The older formation is also present in the southeastern part where it has 1:een only slightly metamorphosed. Ore containing more than 50 per cent iron was formerly mined from local residual concentrations of iron oxides from which silica had been sufficiently leached, or replaced by iron oxide, or affected by combinations of these processes. The younger iron-formation occurs in the western part of the district and, if unaltered, is interlayered siderite and chert. The ore in this area also contains more than 50 per cent iron and formed as local residual concentrations but in two stages. The siderite was converted to iron oxides (hematite and "limonite"), and silica was contemporaneously or subsequently removed by leaching, or replacement, or combinations of these processes.

Jan 1, 1968

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 AIME AIME

BEGINNING Thursday, July 16, the National Broadcasting Co. is broadcasting from 6:30 to 6:45 p.m., over its nationwide network and possibly also by short wave a series of eleven radio programs dealing with the contributions of engineers to the prosecution of the war. The series is being arranged and sponsored by a committee of representatives of the national engineering societies, R. L. Sackett, chairman. The committee began its deliberations before Pearl Harbor and had scripts under way on blackouts, bombs, and damage to structures. The declaration of war emphasized the importance of the proposed radio program. The National Broadcasting Co. and the Office of Civilian Defense enthusiastically endorsed the committee's proposal and have been generous in their help and approval of scripts so far submitted. Controversial matters are included in the broadcasts and changes will be made when requested by O.C.D. up to the minute that a program goes on the air. In this way the latest and authoritative information will be given.

Jan 1, 1942