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By R. L. Andelin, J. D. Knight, M. Kahn

Self-diffusion in single-crystal tungsten and diffusion of rhenium tracer in single-crystal tungsten have been measured over the temperature range 2660° to 3230°C by direct sectioning and radio-chemical analysis of W185 and Re183 and Re184 tracers. The initial radioactive layer was produced on the diffusion specimens by bombardment with 9.0-mev deuterons. Diffusion heating of the samples in high vacuum was accomplished by induction heating. Temperatures were measured by optical pyrometry, and the system was calibrated ALTHOUGH a considerable body of experimental information has been accumulated on self-diffusion in solids, the major part of the detailed work has by reference to the melting points of tantalum (2996°C), molybdenum (2620°C), niobium (2468°C), and rhodium (1966°C). The diffusion coefficients for the two systems, obtained by least-squares analyses of the data, are well-represented by the equations thus far dealt with relatively low-melting systems. Diffusion studies on the high-melting elements niobium,1 tantalum,2,3 and tungsten4'5 have been limited to polycrystalline material, for which data interpretation and theoretical analysis are sometimes difficult. Only recently, a study has been made with single-crystal molybdenum.6 The present work deals with the measurement of self-diffusion in single-crystal tungsten at temperatures approaching the melting point (3410°c).7 Since the method chosen for producing the radioactive tracer layer-bombardment with deuterons—produced detectable isotopes of rhenium as well as of tungsten, the diffusion of rhenium was measured also.

Jan 1, 1965

By S. Le Fevre

THE application of electricity to the mining and beneficiation of the magnetic iron ores of the Mineville, N. Y., district, on Lake Champlain, has resulted in economies and enhanced quality of product, without which only a comparatively small quantity of the present output could be marketed. The output of the Witherbee, Sherman & Co. mines is about 700,000 tons per annum, and of this about four-fifths is treated by magnetic separation to increase the iron content and reduce the phosphorus. The use of electricity for the magnetic separation of the ore from the gangue is therefore of primary importance, and makes possible the application of electric power for mining and preparing the ore for concentration: The fact which speaks loudest in favor of the application of electricity is this: It is possible for about 25c. per ton of shipping ore to furnish all the power required to put the ore on cars. This includes mining a hard ore underground, from a depth of 900 ft., hoisting to surface, crushing to 4 or s in. in size, and separating from the gangue. This also includes lights about the works, and all miscellaneous power, such as about the shops. The first plant for the generation of electric power for use at Mineville was completed in 1903, and was one of the first for the application of electricity to mining iron ore. This was a Nordberg compound condensing steam engine, direct connected to a 750-kw. alternating-current generator, 3,300 volts, 3 phase, 25 cycles. All the plants added later use the same-current but with higher voltage. The map, Fig. 1, shows the power plants and the transmission system; Figs. 2 and 3 are views of the shaft houses and the mills.

Jan 6, 1914

During the year terminating at the date for the third annual meeting of Engineering Foundation, the Board completed, its undertaking to sustain the National Research Council for one year. Assistance given in the organization of the National Research Council has been amply justified by the results. The Council is now well established in a 4¬story building at 1023 16th Street, N. W., Washington, and has recently secured another similar building near by in order to house its increasing force. The breadth, importance and volume of work done have steadily grown. Foreign offices have recently been established in London and Paris, Dr. H. A. Bumstead being in charge of the former and Dr. William F. Durand of the latter. The total expenditure by Engineering Foundation for the National Research Council was $9,036, derived partly from income of the endowment fund and partly from special gifts from Ambrose Swasey and Edward D. Adams. In May, Walter M. Gilbert was appointed Assistant Secretary of Engineering. Foundation, with headquarters in Washington, his services being contributed by the Carnegie Institution. He also became and has remained to date Assistant Secretary of the National Research Council. In September, resolutions were exchanged between the Engineering Foundation Board and the National Research Council, setting forth a policy of continuing reciprocal relationship, and a conference committee, Chairman M. I. Pupin, Dr. Charles Warren Hunt, and Gano Dunn, was appointed to inform the National Research Council of the readiness of Engineering Foundation to work upon definite problems sug-gested by the Council. No problems have yet been suggested.

Jan 5, 1918

By J. J. Predali, J. M. Cases

J. J. Predali and J. M. Cases (Attachè de Recherche and Charge de Recherche, respectively, Centre de Recherches sur la Valorisation des Minerais, Institut Polytechnique de Nancy, Nancy, France)-The role of CO, in carbonate flotation is one of the parameters of a complex phenomenon: the adsorption of salts of fatty acids onto minerals. The authors therefore must be congratulated for their work. Their experimental results suggest some questions: 1) Recovery with C02, benzoic acid, or HCl, look very similar [(Fig. 1)] to that with the use of air; however, the recovery decreases very slightly (<10%). But in these two kinds of experiments, two parameters are different: the pH which is near 5.8 (with C02) becomes 9.1(without C02) and the concentration of Ca* I x 10-3 mole per 1 (without C02) becomes 1.9 X 10&apos; mole per 1 (without COO. 2) Adsorption experiments (Fig. 2) permit computing the surface coverage 9 which is 7.4% (without C02) and 8% (without CO_.) for an initial concentration of 12 X 10-6 mole per 1 in sodium oleate. It seems doubtful to us that this small variation can produce large increases of the recovery in flotation. 3) It is difficult to correlate adsoption and flotation experiments because they do not seem to have been done with the same size of particles. The concentration needed to obtain 95% recovery (Fig. 1) is about 3.0 X 10_" mole per l, that is, 1.13 X 10-6 mole for about

Jan 1, 1973

By L. A. Tarshis, H. E. Cline

A stability criterion for a lamellar eutectic interface was derived previously1 assuming that the wavelength, A,. of the perturbation which grows most rapidly is much larger than the lamellar spacing. A. This assumption was required to permit averaging of both the interface temperature and composition over the complicated geometry of a lamellae. If this assumption is invalid, as has been suggested.2,3 then the problem becomes too complicated to solve completely. The first of these analyses1 did not calculate the wavelength. A,. of the initially unstable perturbation. whereas the more recent analysis.&apos; which led to a contradiction of this assumption. did not include one of the key factors for determining this wavelength. To rigorously determine the wavelength, the effect of the curvature of the perturbed interface (not considered by either of the above treatments) must be included. By omitting this term, one would be led to an incorrect conclusion regarding the magnitude of A,. but to an accurate criterion for stability as evidenced by the excellent agreement with experimental observations.&apos; In the case of single-phase alloys. the critical wavelength. A,. for instability can be calculated from the Mullins and Sekerka4 (M.S.) analysis which includes the effects of capillarity. In the following discussion, the M.S. analysis is applied to lamellar eutectics and the critical wavelengths calculated for reasonable growth conditions in Pb-Sn eutectic alloys. In order to apply the M.S. analysis to eutectics. one may substitute i) the effective liquidus slope.1 m*. for the single-phase liquidus slope and ii) the ratio of the bulk alloy composition. C,. to the average interface composition in the liquid (Ci = CE where CE is the equilibrium eutectic composition) for the distribution coefficient to give:

Jan 1, 1970

Discussion of Papers. Meetings of the Institute offer opportunity for social acquaintance and exchange of ideas, for the presentation of papers, and for discussions thereon ; also incidentally for viewing under especially favorable conditions mining operations and industrial establishments, and for hospitals-ties which demonstrate the brotherhood due to kindred interests. Placing sociability prominent is not to be assumed as relegating other features of meetings to subordinate positions; but during about 40 years of membership in the Institute, the value of acquaintances formed (often ripening into close friendship), and the interchange of data, have frequently demonstrated that the social feature of meetings is of great and lasting value to the membership. Of&apos; a roll embracing 4,011 members, resident in all parts of our country, and scattered in various portions of the world, only a small fraction are able to attend meetings, even if the localities selected are alternately widely separated. Hence, the return which most -members receive for their annual assessment of dues is limited to the publications issued, and the credit of being recognized as a member of a great and worthy organization. Tile greater the value of tile contents of our publication, the fuller the return which goes to members. While the Institute disavows responsibility for views or statements made in papers which appear in its Transactions, the fact that these contributions, after passing proper censorship, are accepted by the Institute and spread before the world may properly be received by the writers as endorsements of their (the writers&apos;) ability to present a specific technical or industrial proposition worthy of being carefully read. But the mere presentation and publication of contributed papers falls short of fulfilling one important feature of our meetings. If the purpose is confined to having the writers&apos; views, discoveries, theories, or methods published, this can be obtained through the technical or trade journals and magazines.

Jan 7, 1913

Mr. Raden has described the practical problems associated with fines in phosphate rock beneficiation. In this discussion, a colloid chemical viewpoint is given to the problem of separating phosphate values from phosphatic clay slurries. The phosphatic clays are predominantly colloids of a complex mixture of many minerals (1). The constituents are typically 25% apatite, 40-50% clays, and various amounts of wavellite, quartz, dolomite, fluorite, and other minerals. The clays are montmorillonite, attapulgite, and illite, with some kaolinite. The various mineral colloids in the slurry are heterogeneously coagulated in the as-produced state. Dispersion of the coagulated state is evident from the fact that dispersing agents (certain polyelectrolytes) cause a large reduction in the viscosity of the slurry (2). The as-produced slurry settles from 4 to 8% solids within a week, but thereafter settles much more slowly in the form of a sediment of flocs. The supernatant liquid is often clear because of the cooperative action of the mutual interaction of particles during settling. Mineral segregation during settling has not been observed for the same reason. The initial slow settling rates indicate that the coagulated assemblies are very small. Efforts to separate apatite from the other minerals would be complicated by the heterogeneous coagulation state. Somehow the apatite must be "liberated" from its association with the other minerals before it can be physically separated. One approach for liberating apatite is to disperse the entire suspension. While this is feasible technically, for example by using certain polyelectrolytes (2), the reagent costs based on present

Jan 1, 1979

By W. G. Pfann

Formation and slow solidification of a molten zone in a homogeneous ingot produces a discontinuity in solute concentration at the boundary of the zone and a gradient of concentration within the zone. By using two solutes, one a donor, the other an acceptor, step or graded pn barriers can be produced. EXPLOITATION of the difference in concentration between a molten solution and the solid which freezes from it is continued in this paper. The normal segregation which results from this difference has been used for purification&apos;.&apos;2 and for pn barrier-formation in semiconductors."4 By means of traveling molten zones this difference has been used to effect multistage separations and to eliminate segregation in ingots." a It will be shown here that by means of stationary molten zones this difference can be used to produce discontinuities in concentration. In particular it will be shown that a pn or npn barrier can be made by the simple act of melting and refreezing a portion of a block of semiconductor, provided that the block contains proper concentrations of a donor and an acceptor in solid solution. Assumptions The operation of melting and slow refreezing will be called remelting and the interface between liquid and solid at the start of refreezing will be called the remelt bormdary. While remelting may be done for various shapes of starting crystal and remelt zone it will be assumed that the remelt zone is cylindrical, its length being measured in the direction of freezing, which is normal to the remelt boundary, and

Jan 1, 1955

By F. Weinberg

WHEN impure Zn (< 99.99 pct)&apos;&apos;Z or Zn-Cd alloys3 are progressively solidified, a cell or "corrugation" substructure4 is produced in the solid, with a high impurity or solute concentration along the cell walls. When these materials are polished and suitably etched, etch pits are often observed along the cell walls. For the Zn-Cd alloys these etch pits have been associated with decorated dislocations, present in the corrugation boundaries to accommodate the lattice strain. In the course of an investigation of Zn-2 pct Au alloy, molten metal of this alloy was poured into cold water and the resultant solid pieces were sectioned, polished and etched with a Cr0 ethant. An extremely regular cell pattern was observed on the etched surface, similar in general to the corrugation structure previously reported for impure zinc and Zn-Cd alloys. At higher magnification, regularly spaced pits were observed along the cell boundaries. An example of the regular cell pattern at the center of a specimen is shown in the center and lower portions of Fig. 1; the top of the figure shows the pattern near the specimen surface. Typical etch pits in the cell walls are shown in Fig. 2. It was surprising that a cell pattern as regular as that shown in the center of Fig. 1 was produced at the very rapid solidification rates used (estimated as > 1 cm per sec). In addition, the distribution coefficient for the Zn-Au system is greater than 1. Accordingly, the center of the cells should be rich in solute and should etch

Jan 1, 1963

By D. L. Katz

A PHASE diagram showing boundary curve and quantity of liquid in the two-phase region was determined for a mixture of natural gas and natural gasoline in the region of its critical conditions. The tempera-tures and pressures of phase measurements were in the range of 85° to 212° F. and 1300 to 2600 lb, per sq. in., respectively, with the critical conditions at 169.5° F. and 2615 lb. per sq. in. abs, Color phenomena were observed in the region of the boundary curve from 102° to 192° F. Approximate densities of the single-phase and two-phase regions and analysis of the system are included. Boundary curves between the single-phase and the two-phase regions have been determined for several binary mixtures containing hydro-carbons. 2,3,4,6,7,10,11,12,14 These investigators did not report the relative amounts of liquid and vapor within the two-phase region. The equilib-rium values obtained from the dew-point and bubble-point data can be used to compute the lines showing percentage of liquid on the pressure-temperature phase diagrams but the positions of the lines near the critical temperature and pressure are uncertain. Relative amounts of vapor and liquid were obtained for a gasoline and a naphtha&apos; within the two-phase area but not in, the region of the critical temperature and pressure. The bubble-point and dew-point lines, as well as the percentage liquid lines within the two-phase region, were determined by visual observations in glass apparatus.

Jan 1, 1939

Forty-three years ago a record for low cost was made at the Spanish mine, in Nevada county, California. In 22 days of September, 1887, there was mined 2796 tons of ore at a cost of 37.5 cents per ton, of which 32.4 cents was for labor and 5.1 cents for supplies. The mill treated this ore for 23 cents per ton, of which 12.3 cents was for labor and 10.7 cents for supplies. Thus the total operating cost was 60.5 cents per ton. The yield was $1.16 in gold per ton, leaving a profit of 56 cents per ton, or 48 per cent of the yield. The mine was an open-cut in a schist formation on a hillside and the work was done by Chinese laborers that were paid $1.40 per shift. The ore was soft, and could be ground effectively in four Hunting- ton mills, supplemented by silvered amalgamating plates.* The engineer in charge was F. W. Bradley, a student from the University of California. As has been indicated, the conditions were unusually favorable in respect of softness of ore, accessibility to the mill, metallurgic simplicity, with cheap labor and power, but even at that the results were so remark- able as to attract general attention, which, as might be expected, was magnified, for advertising purposes, by the manufacturers of the Huntington mill, the firm of Parke & Lacy, at San Francisco. The record made at the Spanish mine therefore found its way into many textbooks on mining published at that time. The editor of the &apos;Mining and Scientific Press&apos;† (at that date, Charles G. Yale) evidently took a warm interest in. the

Jan 1, 1932

By George E. Moore, B. K. Miller

The Missouri fire clays are here divided into plastic and semiplastic clays occurring as widespread bedded deposits in east central Missouri and flint and diaspore clays occurring as isolated "sink-hole" deposits in the north central Ozark region. Visual inspection was the first method used in clay prospecting. Thin overburden, hard sandstone "rimrocks," and the occurrence of diaspore float made this method particularly applicable in the flint and diaspore fields. The first drilling tool used was a hand auger. One man can drill 25 to 50 ft. per day at a cost of about 35 cents per foot. Holes can be drilled to a depth of 150 feet. Spud drills are often used where the overburden is hard. This drill uses a slotted earth socket bit. A two-man crew can drill about 100 ft. per day at a cost of about 35 cents per foot. Mechanically powered auger drills have been used extensively in wildcat drilling in the past few years. This type of drill furnishes a continuous set of cuttings. The practical depth limit with this drill is 50 to 60 ft. Two men can drill 300 ft. per day at a cost of about 20 cents per foot. Core drilling is used mainly to prove a known &apos;lay deposit. A A crew with a No. 22 Sullivan drill can drill about 30 to 40 ft. per day in soft clay, at a cost of about $1.25 per foot. Introduction Because of the geological variations in the Occurrence of the several types of fire clay mined in Missouri, it is necessary, when discussing the prospecting methods used for discovering and proving these clays, to divide these operations into two classes, one including plastic and semi-plastic fire clays, the other flint and diaspore clays. The plastic and semiplastic fire clays in the east central and St. Louis districts are generally classified as Cheltenham clays. This formation is a more or less continuous deposit and is found Over a large area in east central Missouri. There are variations, however, in the quality and thickness of the clay, which necessitate detailed prospecting in order to determine deposits of economic value. The nature of the overburden (Fig. 1), which consists of Pennsylvanian limestone and shale beds of varying thicknesses, and a mantle of glacial drift, regu1ates the methods and equipment used in prospecting for these clays. The district in which these clays occur is a gently rolling upland region, characteristic of most of northern Missouri. Along the southern fringe of this area there are numerous deposits of flint clay lying as masses or lenses in depressions at the base of the continuous and widespread Cheltenham formation, or as outlying "sink-hole" deposits in the area marginal to that formation. South of the Missouri River in the north central Ozark region, there are high-grade flint and high-alumina clays, commonly referred to as burley and diaspore clays in sink-hole type deposits. The overburden On these deposits is thin, consisting chiefly of soil and hard-pan, which varies from a plastic

Jan 1, 1948

By B. K. Miller, George E. Moore

The Missouri fire clays are here divided into plastic and semiplastic clays occurring as widespread bedded deposits in east central Missouri and flint and diaspore clays occurring as isolated "sink-hole" deposits in the north central Ozark region. Visual inspection was the first method used in clay prospecting. Thin overburden, hard sandstone "rimrocks," and the occurrence of diaspore float made this method particularly applicable in the flint and diaspore fields. The first drilling tool used was a hand auger. One man can drill 25 to 50 ft. per day at a cost of about 35 cents per foot. Holes can be drilled to a depth of 150 feet. Spud drills are often used where the overburden is hard. This drill uses a slotted earth socket bit. A two-man crew can drill about 100 ft. per day at a cost of about 35 cents per foot. Mechanically powered auger drills have been used extensively in wildcat drilling in the past few years. This type of drill furnishes a continuous set of cuttings. The practical depth limit with this drill is 50 to 60 ft. Two men can drill 300 ft. per day at a cost of about 20 cents per foot. Core drilling is used mainly to prove a known &apos;lay deposit. A A crew with a No. 22 Sullivan drill can drill about 30 to 40 ft. per day in soft clay, at a cost of about $1.25 per foot. Introduction Because of the geological variations in the Occurrence of the several types of fire clay mined in Missouri, it is necessary, when discussing the prospecting methods used for discovering and proving these clays, to divide these operations into two classes, one including plastic and semi-plastic fire clays, the other flint and diaspore clays. The plastic and semiplastic fire clays in the east central and St. Louis districts are generally classified as Cheltenham clays. This formation is a more or less continuous deposit and is found Over a large area in east central Missouri. There are variations, however, in the quality and thickness of the clay, which necessitate detailed prospecting in order to determine deposits of economic value. The nature of the overburden (Fig. 1), which consists of Pennsylvanian limestone and shale beds of varying thicknesses, and a mantle of glacial drift, regu1ates the methods and equipment used in prospecting for these clays. The district in which these clays occur is a gently rolling upland region, characteristic of most of northern Missouri. Along the southern fringe of this area there are numerous deposits of flint clay lying as masses or lenses in depressions at the base of the continuous and widespread Cheltenham formation, or as outlying "sink-hole" deposits in the area marginal to that formation. South of the Missouri River in the north central Ozark region, there are high-grade flint and high-alumina clays, commonly referred to as burley and diaspore clays in sink-hole type deposits. The overburden On these deposits is thin, consisting chiefly of soil and hard-pan, which varies from a plastic

Jan 1, 1948

By E. L. Dougherty, J. W. Sheldon

A numerical method for computing the dynamical behavior of fluid- fluid interfaces is described. Results of studies made to assess the accuracy and economy of the method on a computer are reported. It is concluded that it is practical to obtain digital computer solutions for fluid- fluid interface problems with two space dimensions. PROBLEM DEFINITION We consider two-dimensional flow in a rectangle as shown in Fig. 1, where a fluid-fluid interface divides the rectangle into two regions. The pressure is specified along the lower boundary (the injection boundary) and upper boundary (the withdrawal boundary). There is to be no flow of fluid across the side boundaries, which are walls of symmetry for the flow, and px = 0 along these boundaries. The fluids are incompressible, the absolute permeability and porosity is constant, and each fluid has its own constant mobility. Thus, the pressure satisfies Laplace&apos;s equation in each region. Across the interface, pressure is continuous and the normal component of fluid flux is 1. These conditions are shown in Fig. 1. The velocity of a point on the interface in the direction of the normal from Fluid 1 into Fluid 2 is U,/ Q, where Un is the normal component of volumetric flux at the point on the interface, i.e., For brevity, we call the problem defined above "Problem A". Problem A is a simple example of a dynamical fluid-fluid interface problem. However, the same numerical methods which we use to solve Problem A can be extended to the solution of a large number of fluid-fluid interface problems which are mathematical models for various oil recovery processes,l hence our interest in Problem A. We define the interface by prescribing the x, y coordinates of a finite set of points. These points are called "interface mesh points" and are illustrated by triangles or asterisks in the figures. Fig. 2 is a procedural (flow) chart displaying the main steps in the solution. We comment briefly on some of these steps in this section and then give further details in subsequent sections. For mobility ratio greater than one it is well known that Problem A is unstable.*2 Small amplitude,

Jan 1, 1965

By F. A. Hill

Coal mining in the State of Washington offers many interesting problems for the mining engineer, due to the varied physical conditions occurring in different fields, and often in, the same mine. The different coal seams worked in the same mine commonly require different mining and transportation methods for economical operation. The coal measures have inclinations ranging from 5° to vertical, and in the same mine the dip of the coal may vary from 30° to 50°. In all fields, the seams are extensively faulted, folded, and sheared. The quality of the coal produced ranges from brown lignite to bituminous- coking coal, the following being typical analyses: Lignite Sub Coking Coal bituminous Moisture 23.5 14.30 0.57 Volatile hydrocarbon 31.0 33.03 23.57 Fixed carbon 37.4 41.30 65.55 Ash 8.1 11.37 10.31 100.0. 100.00 100.00 Very little of the coal contains as much as 0.75 per cent. sulphur. The brown lignites occur mostly in Lewis and Thurston Counties, and, as a rule are very cheaply mined. This coal has been successfully used in locomotives of the Oregon & Washington Railroad, after equipping them with specially designed fireboxes. The sub-bituminous coals occur in all the coal-mining counties. Their cost of production varies widely, according to the character of the formations, the pitch, and the wall conditions. This makes a fairly good steam coal, but the lump is used mostly for domestic trade, after grading into lump, nut, and pea.

Jan 4, 1918

By David R. Poirier

THE activity of carbon in Fe-C-Cr liquid solutions has been measured by Richardson and Dennis,1 Fuwa and chipman,2 and Goto et aL3 Fuwa and Chipman2 have presented their data along with data of Richardson and Dennis1 and utilized an interaction parameter. However, the interaction parameter is only valid for dilute solutions of carbon, because, as indicated, the same interaction parameter does not apply to more concentrated solutions of carbon (i.e., the effect of chromium on the saturation of graphite in liquid iron). Ohtani4 has attempted to account for the effect of carbon concentration on the interaction parameter; however even his analysis does not apply to the saturation data. Also, the effect of temperature on interaction parameters must be taken into account. Therefore, in any process where the concentration of carbon and/or the temperature changes (such as solidification), the use of an interaction parameter is not adequate to know the activity of carbon. The purpose of this communication is to make use of the existing data on the effect of chromium on the activity of carbon in liquid iron solutions in such a way that the activity can be described as a function of both composition and temperature. The method is an extension of Rist and chipman&apos;s5 analysis for the binary Fe-C solutions. As in Rist and Chipman&apos;s analysis, the activity coefficient is assumed to obey the relation: log y1 = at(l -X1)2 + It [1]

Jan 1, 1969

By L. G. Schulz

THE possibility of using reflected X-rays to produce images of crystals was explored by Barrettl who developed simple experimental procedures for X-ray microscopy and who showed by numerous examples the great range of information that could be made available. In his method characteris radiation is used to produce an image of a limited area of the sample on fine-grained film, this image subsequently being enlarged approximately X100. A somewhat different method will be described here;&apos; white radiation from a fine-focus X-ray tube-"&apos; is used to produce an image of a relatively large area of a single-crystal surface. part of the sample; therefore, white radiation is needed. The resolution in the image formed on the photographic film will depend on the size of the focal spot of the X-ray tube. If the sample is made

Jan 1, 1955

By K. E. Beu

THE integrated intensity X-ray method of meas-uring retained austenite concentrations in hardened plain carbon or low alloy steels as proposed by Averbach and Cohen1,2 has the advantages of being a highly sensitive and precise quantitative method. The various phases of this method have been studied and several modifications have been developed which aid not only in reducing the time required per determination, but which also increase the possible accuracy of the method. A fundamental step in the original calculation procedure is to plot V.A(?) curves for austenite and martensite and to obtain VM/VA ratios from these curves.&apos; In taking this ratio the absorption factor A (8) drops out since it is constant for a. given diffraction angle 8. The reason for eliminating A(?) in this manner is because it is apparently assumed

Jan 1, 1953

By G. H. F. Gardner

The boundary conditions F = 1.0 and 4 = 1.0 (100 per cent) are dictated by the definition of F in the equation 1/F = aFp. These conditions have physical significance as the "limiting conditions" for the observed behavior in systems of dispersed particles. The other boundary conditions, cited by Gardner in his Eq. 3 as applying to this system, have no significance in the systems we studied. Maxwell&apos;s equation (Eq. 2) cited in Gardner&apos;s comments was developed for and limited to a regular, rather than random, dispersion of spheres which are sufficiently removed from each other so that they do not interfere with current flow about their neighbors. These restrictions also apply to Rayleigh&apos;s analysis. The title of Rayleigh&apos;s paper cited by Gardner is "On the Influence of Obstacles Arrayed in Rectangular Order upon the Properties of a Medium". He is not discussing randomly dispersed spheres. It might be inferred from Gardner&apos;s comments that Rayleigh specifically considered the differential equation (Gardner&apos;s Eq. 3). This is not the case. Mathematically, Gardner&apos;s Eq. 3 is exactly true for the system to which it applies, however, as both Rayleigh and Maxwell note that their equation for F in terms of F is not for randomly dispersed spheres. At the time we wrote our paper, we were aware of the work of Wyllie and Gregory as cited by Gardner. We cited their work in Ref. 5 of our paper. Our comment on page 287 of the paper about the validity of an m value of 1.3 for spheres with a porosity of 38 per cent remains as our answer to Gardner&apos;s question on this point. Our data, at 38 per cent porosity, show that the condition a = 1 and m = 1.3 holds for spheres near 40 per cent porosity.

By A. Heim, M. Gondouin

Invasion experiments were run on Berea sandstone cores to get laboratory measurements of resistivity and saturation profiles characteristic of water and oil sands invaded by mud filtrate. Injection rates were as low as 1.13 cm/D, and the cores were 30 to 36 in. long, cut parallel to the bedding planes. In the water-sand case, the resistivity profiles revealed the existence of an extensive transition zone between flushed and uncontaminated zones. In the linear geometry of the experiment, the width of the transition zone increased as the square root of the injected fluid volume. For the oil-sand case the core was prepared by displacing the formation water with kerosene to minimum water saturation. During the subsequent invasion experiment. oil saturation was measured directly by means of an oil-soluble radioactive tracer, and resistivity profiles along the core were taken at the same time. These data were interpreted in terms of an oil-water front, followed by a formation water bank, a zone of mixed waters, and finally, invaded mud filtrate near the borehole. Micro-fingering and capillarity seemed to affect considerably the resistivity profiles observed in the invaded oil-sand experiment. Beyond the regular conductive annulus or "low zone", it was found that a resistive "anti-annulus" could also be formed. As a result of these experiments, some simplified invasion profiles have been accepted and are being used in Grand Slam* interpretations. INTRODUCTION The importance of the mud filtrate-invaded zone in interpreting electrical logs has long been recognized.&apos;,* In trying to account for its effect, only very simple models of the resistivity profiles in the radial direction from the borehole have been used. In fact, most log interpretation charts have been based on resistivity models consisiting of two media of uniform resistivity (R, and R,) abruptly separated at the diameter of invasion. Such a clean separation of the media of different resistivities seems unrealistic, since flushing may not be perfect and may vary with radial distance into the formation.3** The nature of the transition zone, when it is within the radius of investigation of the surveying devices, may affect the log readings. Campbell and Martin&apos; verified that a conductive annulus containing a high percentage of formation water may be formed when mud filtrate invades an oil-bearing sand. Interpretations which are to include the effect of such an annulus require the addition to the model of a conductive zone located at the outer rim of the invaded zone.&apos; Using the Buckley-Leverett relations,6 aturation profiles may be derived, from which resistivity profiles can be calculated. Results of such computations by K. S. Kunz and J. H. Moran were given in a paper by Dumanoir. Tixier and Martin,7 and led to the construction of log interpretation charts which were based on a representation with three media of resistivities R, R0 and R1. Fig. 1 shows a schematic representation of a resistivity profile which includes an annulus. Campbell and Martin realized that, during the invasion of an oil sand, both capillarity and mixing would contribute to rounding of the profile shown in Fig. 1. Capillarity tends to draw some of the formation water from the annulus into the uncontaminated (Rt) zone, whereas mixing of the mud filtrate with formation water of the

Jan 1, 1965