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By J. E. Owen

A model of a porous body is presented in which the pore space consists of a system of voids and interconnecting tubes. Relationships between porosity and resistivity formation factor are determined partly by calculation, partly by experiment. Con triction effects characteristic of the model are shown to be sufficient to account for high formation factors. It is shown that constriction may be combined with moderate amounts of tortuosity to give model pore systems exhibiting to a first approximation porosity and resistivity properties similiar to those of natural porous bodies. INTRODUCTION The relationship between the electric resistivity of a fluid-filled porous body and the geometry of its pore space is so complex that the calculation of the resistivity of a natural porous rock is a practical impossibility. Both the resistivity of a body and its porosity are measurable quantities, however, and previous successes at relating them have been reached by an empirical approach. Efforts at obtaining theoretically derived formulae relating them have generally been unsatisfactory. One of the reasons for this may lie in the pore geometry that has been assumed. THE TORTUOSITY CONCEPT A Parameter called the formation factor is useful in dis-cussing the resistivity of a fluid-filled porous body. This parameter is the ratio of the resistivity of a fluid saturated porous body to the resistivity of the saturating fluid. Formation factors are often available from measurements on cores or from electric logs, and many attempts have been made to correlate formation factors and porosities of geological formations. Whenever a successful correlation is found, the engineer working with electrical logs has a useful tool for the determination of porsities of pay section?. One of the more successful formulae applicable to these correlations is the familiar equation empirically obtained by Archie.' which F is the formation factor. $ is the porosity, and rn is an exponent called the cementation factor. When the for- mula applies, the cementation factor usually is found to be between 1.3 and 2.2. The values for formation factors experimentally obtained are often higher than simple pore geometry would lead one to expect. In an effort to account for such high values certain formulae have been derived based on a so-called "tortuosity concept." In deriving these formulae a synthetic porous body is usually assumed in which the solid material is an electrical non-conductor. and in which the pore system consists of three sets of fluid-filled tubes of uniform diameter connecting opposite faces of the body which, for convenience, is considered to be cubical in shape. The three sets of tubes account for the whole of the effective porosity of the body, and usually, it is specified that they do not interconnect. By considering that the pore tubes are not straight but tortuous, their resistance to the flow of electric currents can be made as high as needed to explain high formation factors. Such an explanation has some basis in fact, but it appears that the tortuosity concept is often incorrectly applied when other factors are largely responsible for observed high resistivities. Recently, Wyllie and Spangler have recognized that tortuosity as calculated by conventional formulae has little if any physical significance.' RESISTIVITY AND THE CONSTRICTION CONCEPT Any explanation of high formation factors which depends solely on tortuosity of uniform pore paths necessarily ignores the effect that variations in the cross-sectional area of the conducting paths have on the resistivity of a body. Although, as previously pointed out, the calculation of such paths for an actual body is impossible, it will he shown that a synthetic pore network can be devised which will yield to analysis, and lead to results in agreement with the experimental data represented by Equation (1). The porous body to be considered is assumed to be homogeneous and isotropic or, for present purposes, identical in its characteristics in the three directions parallel to its coordinate axes. It will he assumed to be built of identical unit cubes, each of which contains a single pore network connecting all faces of the unit cube. A unit of such a pore network is shown

Jan 1, 1952

By J. J. Arps, T. G. Roberts

Since the introduction of the relative permeability concept in the middle thirties1,2 various investigators have shown3,10,11,12,15 how the basic equations for the flow of oil and gas through porous media can he utilized to compute the recovery from depletion type or solution gas drive type reservoirs under certain conditions, when the necessary physical data pertaining to the reservoir rock and its reservoir fluids are known. In the study by Muskat and Taylor" in 1945, the effects of viscosity, gas solubility, shrinkage, and the permeability-saturation characteristics of the producing formation on the production histories and the recovery of gas drive reservoirs were analyzed. Each parameter was varied a limited number of times, while keeping the others constant. The work was not carried to the point where the data could be used directly to estimate the primary recovery in those cases where certain rock and fluid characteristics were known or could be assumed. Since the publication of this classic study, the work by Beal in 194616 and Standing in 1952'" has established general correlations of oil viscosity and shrinkage with gas solubility and oil gravity. In addition. a considerable number of relative permeability relationships for different types of reservoir rocks has been published2,5,13,17,19,20. Also, the burden of the numerical work required in the solutions of the differential equation has. during the last few years, been greatly reduced with the availability of modern electronic computing facilities. The purpose of this paper is therefore to present the results of a large number of such recovery computations covering the normal range of variation of the main parameters such as the type of rock, the API gravity of the oil, and the amount of gas in solution. As is to be expected, the ultimate recovery is found to increase with the oil gravity. except for the higher solution gas-oil ratios. Within the normal range of solubilities, the ultimate recovery generally appears to decrease with the amount of gas in solution for the higher oil gravities, and to show a slight increase for the lower oil gravities. Intermediate oil gravities seem to fall between the two trends. The type of reservoir rock, as identified by its relative permeability relationship, appears to have a very pronounced effect on the ultimate recovery. In general, sands and sandstones show higher recoveries than limestones and dolomites, although certain intergranular limestones seem to show a higher theoretical recovery than unconsolidated sand. The recovery from sands and sandstones generally decreases with increasing cementation and consolidation, while the recoveries from limestones and dolomites are highest for the intergranular type and lowest for the fracture type porosity.

Jan 1, 1956

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By N. E. Grosvenor

The present and future activity of western coking coals is discussed. A general description of location, quantity, and quality is used as a basis for discussing development, mining, and marketing problems facing these reserves. As the need for coke from the West increases, solutions to the present mining and transportation problems will be forthcoming. Improved mining and blending technology, coupled with a more economical transportation solution, must precede a rapid development of the West's coke reserves. Ever increasing demands on coke production enhance the prospects of an accelerated development of these reserves.

Jan 1, 1976

By Yap Chu-Phay

IN 1923, when the writer began his studies in metallurgy, he came upon an article by Professor Honda on the, Equilibrium Diagram of the Iron-carbon System, 1 which made a profound impression on him. What interested him most was this sentence: "In the recent diagram of the iron-carbon system, the solidus is usually shown as a curve bending considerably downward. But it can be shown by thermodynamics that if the liquidus is straight or slightly curved, the same must also be true for the solidus. Hence, in my constitutional diagram, the lower portion of the solidus is slightly bent upward." Ever since then the writer has been interested in thermodynamics, especially chemical thermodynamics. The applications of thermo-dynamics to the metallic systems have been, in the writer's opinion, sadly neglected, although we continually use the phase rule in our study of equilibria in the liquid and solid states of metallic alloys. Many investigators, among whom may be mentioned Heycock and Neville, and s Honda and his coworkers, have applied the simple Raoult-van't Hoff law of depression of freezing point, mainly to determine the heat of fusion, but no attempt has been made to investigate the applicability of the thermo-dynamic laws of solution (as opposed to the laws of solution derived from other sources) to metallic systems" showing either limited or complete solid solutions. Perhaps the reason for this neglect is that until recently there have been so few reliable data on the solidus, which is much more difficult to determine than the liquidus. The writer has under way at the present time an investigation of a number of systems, the solidi of which have been more or less reliably determined. Recently, the writer has not only shown the valid applicability of the thermodynamic laws of solution as applied to the system antimony-bismuth but has also suggested a method of attacking problems involving complete and incomplete equilibria.2 In the present paper, the same method of approach is employed. For convenience, we shall divide this paper into two parts:

Jan 1, 1931

By J. V. Richards

(Canal Zone Meeting, November, 1910,) THE Altar district, State of Sonora, Mexico, is for the most part a desert with but little rain-fall and few running streams. On account of this scarcity of water it is necessary for the natives to " dry-wash" the placer-gravel, and the object of the present paper is to describe some of the more common Mexican dry-washing devices. My observations were confined to a property known as Las Palomas placers, 15 miles from the Gulf of California and about 150 miles south of the United States border; a brief description of which property may be of interest as illustrating what is, perhaps, a typical Sonora dry placer. It is said that as long as a century ago the Yaqui Indians discovered rich cement-gravel, known as argo masa, at Las Palomas, and that there has been a more or less steady production of gold from the property ever since. The argo masa is a fairly-coarse gravel, the pebbles being quite firmly held together with a lime cement. Gold is scattered through this cement in particles ranging from fine specks to pieces several grams in weight, and occasional large nuggets are encountered. The contents vary so widely that it is difficult to estimate the average value, but returns of from $10 to $50 per cubic yard are common, and it is doubtful if the Indians considered anything less than from $4 to $5 a yard as "pay dirt." This argo masa occurs in channels varying in thickness from a few inches to several feet, and in width up to 300 ft.. These channels are continuous and are probably ancient stream-beds. They are for the most part covered with an over-burden of a more recent gravel, varying from 30 to 50 ft. thick, and the fact that this over-burden contains values as high as $1.50 per cubic yard, and yet was not worked by the Indians, shows that their idea of what constituted pay-ground was high.

Apr 1, 1911

By AIME AIME

THE convention which met in Washington at the call of the Joint Conference Committee was called to order at ten o'clock on Thursday morning; June 3, by Richard L. Humphrey, temporary chairman, member of the American Society of Civil Engineers, who made a brief statement of the reason for the meeting. Lieut. Col. Charles W. Kutz, Corps of Engineers, U. S. A., and Engineer Commissioner of the District of Columbia, then welcomed .the engineers composing the convention on behalf of the District of Columbia and, the Washington engineers. Although an elaborate program had been prepared on which were many well-known speakers on interesting and important topics, , it was voted to intersperse this to fill in the usual and unavoidable hiatuses in the business program of such a convention[ Calvert Townley, president of the American Institute of Electrical Engineers, was elected permanent chairman, and J. C. Hoyt, of Washington, was elected secretary of the convention. The following committees were appointed: Consti¬tution and by-laws, Richard L. Humphrey, chairman; resolutions, Philip N. Moore, chairman; and program, F. H. Newell, chairman. Then, Gardner S. Williams, member of the, A. S. C. E. and the Grand Rapids Engineering Society of. Grand Rapids, Mich., and one-time member of the American Association of Engineers, offered the following resolutions:

Jan 1, 1920

By Allen V. Heyl

This old district is a major zinc and lead source and minor copper and barite source. Ores are chiefly in the Galena Dolomite and in limestones and dolomites of the Decorah and Platteville Formations, all of Middle Ordovician age. Locally, deposits have been mined from Lower Ordovician dolomites and Upper Cambrian sandstones. Small deposits of lead, zinc, and iron sulfides have been found in Upper Ordovician Maquoketa Shale and in Lower and Middle Silurian Edgewood, Kankakee, and Hopkinton Formations. No post-Precambrian igneous rocks are known in the region, and the granitic and metasedimentary Precambrian basement rocks unconformably underlie the district at depths of 1500 to 2000 feet. The strata are gently flexed and faulted, probably largely the result of gentle compressive and rotational adjustments in the underlying crystalline basement, especially along lineaments between basement blocks. Folds of three orders ·of magnitude are recognized, and many related reverse, strike-slip, and normal faults of small to moderate displacements are present. Zinc-lead deposits are commonly linear, arcuate, or elliptical in plan. Most ore occurs as vein fillings in fractures and as breccia fillings and lining vugs, but some is in bedded replacements and impregnations of wall rocks. The ore is in shears, small reverse and bedding- plant faults, joints, and solution-slump structures related to intermediate and small folds. The main primary minerals in their general sequence of deposition are quartz, illite, dolomite, pyrite, marcasite, cobaltite(?), sphalerite, galena, chalcopyrite, millerite, barite, and calcite. Wall-rock alterations include solution of the carbonate rocks, silicification, dolomitization, clay alteration, and sanded dolomite. Oxygenisotope, trace-element, lead-isotope, and sphalerite- stratigraphy studies are in progress. Fluid inclusions in sulfide and gangue minerals are filled with concentrated brines at 120° to 40°C. Sulfides are directly replaced by supergene minerals above the water table at 50 to 100 feet in depth. In this relatively cool climate and limestone environment, smithsonite is in pseudomorphs after sphalerite; solution transport and redeposition of supergene minerals are rare. Ore genesis is postulated by rising hot-water solutions-a mixture of heated connate, magmatic, and meteoric waters.

Jan 1, 1968

By Henry S. Mackay

The interesting paper recently submitted by Messrs. Tobelmann and Potter1 shows that chemical problems have developed which are of great interest in this new and important branch of metallurgy. Those who realize what a process of this kind really involves will agree that it deserves a better name than '(leaching process." The word leaching conveys the idea that the copper is simply leached out of the ore with acid and then precipitated on iron; the chemistry of such a process would be of little interest. As, however, during the first year's operation of this plant 24,400,532 lb. (11,067,837 kg.) or about two-thirds of the produce, was electrolytic copper, while 7,992,033 lb., or about one-third, was cement copper, it would seem more appropriate to term the process electrochemical. It further appears, from the particulars given, that efforts have been made to have the entire production in the form of electrolytic copper. This could be done if the chemistry of the problem were kept in balance, so that it would not be necessary to discard any solutions that carried copper and acid of commercial value. A process, such as that under consideration, in which the copper is precipitated from solution by electrolysis, the solvent being at the same time regenerated, is one that requires special chemical and electrochemical knowledge and experience if all the copper in solution that has been extracted from the ore is to be successfully and economically produced as electrolytic copper. The object of this paper is to discuss, from the practical and theoretical standpoints, the chemical and electrochemical problems involved in the working of a process of this kind, and which must be solved to keep it in chemical and electrochemical equilibrium. In such a process, if the chemical balance is maintained, a solution can be used alternately as a solvent for the copper in the ore and as an electrolyte of high efficiency for the precipitation of the copper. To maintain the chemical equilibrium and so attain this result, the process must be so controlled that the solu-

Jan 1, 1921

By J. G. Savins

Certain types of macromolecules added to water and salt solutions flowing in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these materials. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89-in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a I-in. water line yields a throughput capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion. INTRODUCTION This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe f1ow.I Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required* to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd,3 Agoston et al., Bundrant and Matthews, Robertson and Mason,6 Ousterhout and Hall,7 Daily and Bugliarello~ Lummus, Anderson, and Fox. 9 That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels,l0 Dever, Harbour, and Seifert.11 One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver12 and Dodge.13 However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction-. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabulal5 and Granville.16 Along somewhat different lines are the drag reduction studies of Kramer.17118 He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne,19 Cess and Sparrow,20'21 Sparrow, Jonsson, and Eckert.22 Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merri11,23 Dodge and Metzner, Clapp,25 and Thomas.26

Jan 1, 1965

One of the best known of the early mining districts of Nevada was that at Eureka, where gold was first produced in 1864. While the most productive period for the district was during the early 1900s, production was maintained until World War II. During this time it is said that the Eureka district produced as much as $200 million from over 3,200 km (2,000 miles) of tunnels and workings. The Windfall Mine was discovered in 1902; and a 100 ton cyanide plant was operated there during the periods 1907 to 1912 and 1932 to 1940. Since 1974, however, Windfall Venture has been operating a unique heap leaching facility on the site of the old Windfall Mine. Gold at the Windfall occurs primarily in the Cambrian Hamburg dolomite which has been "sanded" and in which the original cementing material has been destroyed. The gold is micron sized and is accompanied by anomalous amounts of arsenic and mercury; however, the ore is low in base metals which distinguishes it from the typical Eureka district ores. Mining the ore causes it to break down into very fine sizes, approximately 50% minus 150 microns (100 mesh). Conventional heap leaching by spraying proved to be impossible; and extensive test work on alternate methods, aided by the United States Bureau of Mines, was conducted using 9 m (30 ft) high columns and then large tonnage heaps. The leaching procedure adopted was to build 10.6 m (35 ft) high heaps on a 50 mm (2 in.) asphalt pad covered with a layer of gravel for drainage assisted by perforated pipe drains and gravel-packed sumps. A berm is constructed around the top of each pad and cyanide solution is allowed to “pond” on top of the heap. The resulting percolation is at the rate of 24 liters per sq m per hr (0.6 gal per sq ft per hr), a figure about 2.4 times the average used in other heap leaching operations. The dolomite furnishes its own protective alkalinity and no lime or caustic is used in the solution which contains 0.4 kg per mt (0.8 lb per st) of NaCN. Pregnant solution from the heaps averages about 0.7 g Au per mt (0.02 oz per st) with a cyanide content of about 0. 2 kg per mt (0.4 lb per st) and a pH of plus 9. Addition of NaCN brings the pH of the leach solution up to 11 to 12. Carbon adsorption of the gold was originally done in six enclosed columns mounted in a trailer but five conventional columns have been substituted as the size of the operations has increased. Carbon stripping is with hot caustic, cyanide and 10% ethanol solution. The

Jan 1, 1981

By J. R. Long, C. E. Armantrout, A. H. Roberson, T. R. Graham

The preparation and fabrication of copper-manganese-zinc alloys and the evaluation of their engineering properties have for some time been an integral part of a research program of the Federal Bureau of Mines. In this project, the use of electrolytic manganese, along with high purity copper and zinc, has permitted the preparation of alloys which contain a minimum of impurities which are capable of producing detectable effects in the properties studied. The initial work on the physical properties of wrought alpha solid solution alloys and a general outline of the alpha solid solution area for alloys containing up to 40 pct manganese have been presented in previous reports. 1,2,3,4,5 The evidence accumulated in these investigations clearly showed that additions of manganese to the copper-zinc alloys improve the strength properties of the brasses without seriously reducing their characteristic ductility and that considerable quantities of manganese could be added to the copper-zinc alloys without exceeding the mutual solubilities of manganese and zinc in copper. In continuation of these studies, additional data have been obtained in a more extensive investigation of the phase relationships of the copper-manganese-zinc ternary system. The present report delineates the solid phase boundaries of the ternary system from the copper-zinc binary to the manganese-zinc binary for alloys containing up to 50 pct zinc. Summary The alloys used in this investigation were conditioned by working schedules designed to homogenize the structures prior to heat treatments required for the equilibrium phase sludy. The treated alloys were examined by metallographic methods including hardness and X ray data for confirmation. The composite data of the investigation are summarily presented in a series of isothermal sections of the ternary system at 1100, 1200, 1300, 1200, and 1500°F. The salient features of the system as outlined by these data are: (1) the continuous alpha solid solution which extends across the diagram to the gamma-manganese phase of the manganese-zinc system at temperatures of 1200°F and higher, (2) the beta phase of the copper-zinc system similarly forms a continuous solid solution with its counterpart the beta field of the manganese-zinc binary, (3) at 1100°F (593°C) these alpha and beta fields are greatly restricted by complications arising from the allotropic transitions of manganese and the decreasing solubility of manganese in the alpha solid solution. The alpha + beta fields intersect the alpha + alpha manganese field to produce the beta + alpha manganese field and two adjacent three phase fields consisting of alpha + beta + alpha manganese and gamma + beta + alpha manganese. Typical microstructures representative of the various phase areas at each temperature are also presented. Review of Previous Work The copper-manganese-zinc alloys have periodically been the subject of numerous investigatioris of both prac-

Jan 1, 1950

By Henry Wurtz

Jan 1, 1880

By E. S. Bumps, M. Baeyert, W. F. Craig

SOME time ago during a study of impact properties of tempered martensite,1 it was postulated that the consistently good ductility of tempered martensite might be caused by its relatively small and peculiarly shaped ferrite grains. The fer-rite grains of tempered martensite have approximately the same size and shape as the martensite "needles." Thus they form an interlocking mass of needle-shaped grains quite different from equiaxed or lamellar ferrite grain structures. When the common mechanical test methods are applied to steel, variations are often observed in the ductility of specimens that have closely similar hardness and tensile strength values. The ductility so measured appears to be structure dependent. When steel from the same heat has been heat treated to produce different structures with the same hardness, the elongation and reduction of area values from the tensile test and the transition temperature determined by the notched-bar impact test vary according to whether pearlite, tempered martensite, or other structural constituents were produced by the heat treatment. It has been widely recognized that tempered martensite gives a consistently good performance, when tempered to the same hardness as many other structures with which it has been compared. In recent years the isothermal transformation of austenite to specific structural products and the quantitative evaluation of the character of these products with respect to their nature and response to deformation has received considerable attention. The objective of the present study was to pursue somewhat further the dependence of ductility upon structure; specifically, it was desired to ascertain whether ferrite grain structure, including both shape and size of the grains, can account for the consistently good performance of tempered martensite in the notched-bar impact test. It was thought that a simple experiment would indicate whether the ferrite grain structure plays any part in the good ductility exhibited by tempered martensite in contrast to other steel structures with different types of ferrite grains. By determining the impact transition temperature, it was proposed to compare spheroidites having similar carbide particle size and spacing but obtained in such a manner that their ferrite grain structures would be very different. Spheroidite obtained by tempering martensite, with its small, needle-shaped grains, was to be compared with spheroidite from pearlite. If the latter is produced by sub-critical annealing, the ferrite grains correspond to the pearlite colonies. Thus, if the pearlite was not too coarse, the ferrite grains of spheroidite from pearlite are equiaxed in contrast to the needle-shaped grains of spheroidite from martensite. It was thought that the ferrite grain structure of spheroidite from martensite might depend to some extent upon the grain size of the prior austenite. The austenite grain boundaries limit the maximum attainable size of the martensite needles and thus of the ferrite grains in the derived spheroidite. In order to evaluate any possible influence of prior austehite grain size, spheroidites were to be prepared from martensites that had been formed from fine-grain austenite and also from coarsened austenite. As the carbide particle size and distribution were to be essentially alike in the various spheroidites, the difference would be in the ferrite grain size and shape. Thus any marked difference in transition temperature could be attributable to the character of the ferrite grain structure. There are certain considerations in assuming that these spheroidites would be equivalent in all respects except ferrite grain structure, and an attempt was made to take them into account. One of the considerations was the choice of the carbon content of the steel. An approximately eutectoid steel was selected for two reasons. First, the pearlitic structure would contain no proeutectoid ferrite which might complicate the picture by producing a non-uniform ferrite grain structure in the resulting spheroidite. Then, too, the high-carbon content would inhibit ferrite grain growth during the sub-critical treatment. Another factor to be taken into account was the choice of an alloying element to assure a martensitic structure throughout on quenching the impact specimens. Nickel was chosen, because it is a common alloying element and resides in the ferrite both upon its formation from austenite and throughout tempering. The formation of alloy carbides, or even a large solubility of the alloying element in cementite, would have complicated the interpretation by changing the composition of the ferrite .during spheroid-ization. The possibility of temper brittleness was minimized insofar as possible by using a tempering temperature as high as consistent with the 1 pct of nickel in the steel, namely, 1150°F. While it certainly is not claimed that no difference other than ferrite grain structure could exist between the spheroidites, nevertheless, reasonable precaution has been exercised within the limits of steel metallurgy. It is believed that any large difference in transition temperatures would reflect the difference in ferrite grain structure and that relatively good ductility in the spheroidites from mar-

Jan 1, 1951

By J. R. Linney

APPROXIMATELY 5,788,000 long tons of crude ore was produced by the Eastern magnetite industry in 1946, or a drop of 26 per cent compared -with 1945. Decrease in production -throughout the industry varied from :8 per cent for the mine with the lowest reduction to 49 per cent for the mine -with the highest reduction. At the Chateaugay mine, operated by :the Republic Steel Corp. at Lyon Mountain, N. Y., 426,900 long tons of crude ,ore was produced, yielding 129,500 long tons of concentrates or a reduction of 46 per cent compared with the previous year. Owing to a strike the mine was closed down from Jan. 21 to July 29. At the Mineville mines, also operated by Republic Steel, output was 755,000 long tons of crude ore or a reduction of 49 per cent compared with 1945. The yield from the crude ore production consisted of 51,500 long tons of lump ore and 380,000 long tons of concentrates. The Mineville plant did not operate from March 17 through July 28, on account of the strike. The Fisher Hill mine, which produced 93,000 long tons of crude ore, included in the above figures, has not operated since March 17, 1946.

Jan 1, 1947

By T. Reed Woodbridge

The object of this paper is to bring to notice a method in use at the Cedar Point laboratory of Witherbees, Sherman & Co., for determining the phosphorus in the ore mined at Mineville, N. Y. This ore is magnetite, with a gangue containing crystals of apatite. In 1886, Mr. H. F. Dawes, then head chemist at the works, suggested that as all the phosphorus seemed to be in the apatite, it could be obtained in solution by dilute nitric acid. After some experimenting the following method was adopted, and has proved invaluable for rapidity and ease; half a dozen determinations requiring very little more time or trouble than one. From + to 10 grammes of ore are weighed into a 150 c.c. beaker; 50 C.C. hot water and 10 c.c. strong nitric acid are added; the beaker is covered and the contents are boiled for 1/2 hour (10 minutes sometimes proves sufficient; but 4 hour is safer). The bumping which ensues if more than & gramme is used need cause no trouble. The hot solution is filtered into a 250 C.C. beaker. The filtration and washing (with hot water) proceed rapidly, as the magnetite itself is but slightly acted upon. After the addition of 15 C.C. ammonia and 15 c.c. nitric acid, the solution is cooled to 45' C., and from 15 to 40 C.C. of molybdic acid solution is added and stirred vigorously. In 5 minutes the precipitate will be down, and the determination can be finished by any good method. At Cedar Point the method more commonly used is weighing as yellow salt. Good washed filter-paper is used, No. 0 Swedish being preferred; and dozen 3 1/2-inch filters are numbered and dried and weighed at 110°C. These are always kept in stock. The yellow salt is filtered on one of these, washed with dilute nitric acid (2 per cent. by volume); dried for 1 hour at 110' C., and then weighed, 1.63 per cent. of weight being calculated as phosphorus. The filters vary in the two weighings from

Jan 1, 1889

By Michael B. Bever, Barton Roessler

The effects of deformation by wire drawing at 78OK on initially ordered and initially disordered specimens of the alloy Cu3Au were investigated. The resistivity, stored energy, drawing force, and microhardness were measured as functions of strain; microstructural changes were observed. The results are interpreted in terms of the structural imperfections and the changes in atomic configuration resulting from deformation. A few experiments on the effects of room-temperature annealing after deformation at 78°K were made; they suggest vacancy-promoted ordering in disordered alloys. BARTON ROESSLER, Junior Member AIME, formerly Graduate Student and Alcoa Fellow, Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Mass., is with Westinghouse Research Laboratories, Pittsburgh, Penn. MICHAEL B. BEVER, Member AIME, is Professor of Metallurgy, Massachusetts Institute of Technology. Based in part on o thesis by B. ROESSLER submitted in October, 1959 to the Massachusetts Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Science. Manuscript submitted April 6, 1961. IMD AN investigation of the effects of deformation at room temperature on the alloy Cu3 Au was reported in a recent paper,' which included a review of the literature on the deformation of order-disorder alloys. In general, plastic deformation of ordered alloys reduces the degree of long-range order and causes corresponding changes in their properties. Deformation of disordered alloys changes their properties in a manner characteristic of solid solution alloys; these changes can in part be attributed to the destruction of short-range order. The effects of deformation on solid solution alloys are of two kinds: 1) generation of structural imperfections, which occurs as a result of deformation in any metallic system including pure metals, and 2) changes of atomic configuration, which are characteristic of solid solutions and particularly of order -disorder systems. These two types of effect are not independent of each other and the state of a deformed solid solution alloy is determined in a complex manner by the way in which the structural imperfections cause changes in atomic configuration both during and after deformation.

Jan 1, 1962

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By Henry Wurtz

HERACLITUS, a sage of antiquity, called the dark philosopher, who refused a throne, preferring a hermit's cell, propounded, twenty-four centuries since, the maxim : [ ] War (or strife) engenders all things. This, though probably intended by Heraclitus to apply especially to the internal forces of nature, is often said, with equal reason, of the affairs of men. Controversial strife, whether fortunately or unfortunately, is a crucible through which all new discoveries in science, and all technical applications of science must pass-a test which they must all endure before they can become so vitalized as to germinate, so to speak, take root in the human mind, grow tip, and overspread the earth. The greater the number and the power of the elements arrayed against such a growth, and of the influences hostile thereto, the greater should be the inherent vitality of the germ, the more strenuous, skilful, and persistent its cultivators and upholders. During the decade last past we have had, in spite of the severe stringency of the times, an active growth of this kind in progress, whose prospective importance it would now be difficult to overrate. This is the movement which has for its motive the idea that, generally speaking, fuel should be gaseous in form, and which has for its goal the introduction into general public use of gaseous products, made by cheap and rapid processes and on a gigantic scale, distributed throughout our cities and towns in distribution-systems which shall be proportionately gigantic, and sold at prices which will bring such fuel within the means of the poorest householders. Personally, for ten years past, the writer has never failed, on occasions public or private, to urge his belief that the realization of this idea, deemed by him a certainty of the future, will bring about

Jan 1, 1880