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By HERBERT G. MOULTON

FROM prehistoric times to our own day man has struggled against extremes of climate. Human life, originating in semi-tropical or temperate areas, was unable to progress into the northern latitudes until fire was discovered and some form of clothing provided. It was found possible to maintain life even in the hottest parts of the tropics, but only at a great sacrifice of comfort and efficiency compared with the more temperate zones, or in cooler areas with the protection of clothing and artificial heat. It was no accident, but the natural result of climatic conditions, that efficiency became the greatest and civilization the most advanced in areas where the natural climate was favorable, or in cooler zones where protection against severe cold could be se-cured by relatively simple methods of conserving or producing heat.

Jan 1, 1933

By C. H. Bowen

NDUSTRY needs a generally applicable means of defining average grain size and grain size distribution. Students of sediments hade explored this field, employing methods that might also prove useful in engineering problems. Before attempting to solve specific problems it is well to review the derivation of commonly used grade scales and the reasons for their selection. This aspect of the problem seems largely to have been lost, and a review of basic factors may suggest causes for failures in using size analysis data. Three facts are implicit in selection of a grade scale: 1) Most particulate mixtures are continuous distributions of sizes, and any grade scale that may be employed is an arbitrary means of visualizing that distribution. 2) For purely descriptive purposes, any grade scale, regardless of the rationality of the class intervals, will be satisfactory if it is accepted by a sufficient number of workers. 3) For analytical purposes, class intervals must be small enough to define the continuous distribution accurately. Further, where statistical studies are involved, a fixed relationship should exist between classes or grades. An argument in favor of geometrically related size grades lies in the fact that most particulate mixtures contain such a wide range of sizes that use of an arithmetic diameter scale is practically impossible. Udden, who recognized this fact in 1898,' proposed one of the first grade scales based on a regular geometrical interval. Udden used 1 mm as his basic diameter and a ratio of 2 (or 1/2) between classes. In 1922 Wentworth2 re-examined Udden's grade scale, retaining the same class interval and basic diameter, but extending the scale in both directions and renaming the classes. In 1930 (Ref. 3, p. 82) the American Society of Testing Materials proposed what is now known as the U.S. Standard fine sieve series, also based on the 1 mm diam, with a v2 ratio between sieves. This, then, is a one fourth Udden-Wentworth series in the sizes below the 4 mesh sieve. The U.S. Standard coarse sieve departs from the 1 mm base and uses inches; hence it is not a direct continuation of the fine series. The U.S. Standard series would thus seem to possess all the attributes of a good grade scale, which it is. It has a large number of classes (sieves). in fact too many for practical use in its entirety. This v2 subdivision of the Wentworth grades has led to the common use of two v2 sieve series, the half-Wentworth and the engineers' series. Geologists and sedimentologists favor the half Wentworth, or 18, 25, 35, 45 sieves, etc., whereas the engineers, preferring round numbers, utilize the other half of the U.S. Standard grade scale in the 16, 20, 30, 40 sieves, etc. The fixed geometrical ratio between classes is an advantage in statistical analysis, but the unequal classes cause some complications in calculations. This is especially true when moment measures are used. It was to simplify these calculations that Krumbein in 1934 devised the phi scale. Phi is defined as being equal to —log2 of the diameter in millimeters. Selection of logarithms to the base 2 relate the phi scale directly to the Wentworth grade scale in such a manner that the whole or fractional diameter values 2, 1, 1/2, 1/4 mm, etc., become rational whole numbers, —1, 0,1, 2, etc. Since this is an arithmetic rather than geometric series, calculations are facilitated. When the logarithm is multiplied by —1 the phi values below 1 mm become positive, those coarser than 1 mm negative. Because of its relationship to the Wentworth grade scale (and in turn to the U.S. Standard fine sieve series) it is not necessary to use the transformation equation to calculate the phi value for each individual sieve; this can be done graphically as shown in Fig. 1. It should be noted that this graph may be extended in either direction to include the range of sizes most commonly used by the individual worker. Application to Statistical Analysis Any attempt at systematically relating size analysis data to properties involves a statistical study whether it is recognized as such or not. Since this is true it would seem more logical to use measures and devices related to the general body of statistical theory. Several methods are available for studying particulate mixtures. One of the most commonly employed, and also the most often misused, is the histogram or block diagram. If its limitations are recognized and provided for, the histogram is a very useful tool. According to conventional practice, the bars of equal width are plotted and the values noted in terms of diameters, when in point of fact, log diameter is implied by such notation. Further, the histogram is sensitive to choice of grade scale and size of class interval, either of which may color the result. Grade scales whose classes are not related by fixed intervals are particularly difficult. Another basic weakness of the histogram is that it pictures a continuous distribution as a series of discrete grades.

Jan 1, 1957

By A. E. Bellis

THE CHAIRMAN (ALBERT SAUVEUR, Cambridge, Mass.).-Any information likely to throw light on the constitution and proper treatment of high-speed steel in order to obtain maximum results, should surely he welcomed. All users of high-speed steel, I believe, will agree with the authors that, in order to obtain satisfactory results, it is not sufficient to heat all brands of high-speed steel to one and the same temperature; apparently very slight differences of chemical composition seem to call for marked differences in temperature. I think that all of us agree that a properly treated piece of high-speed steel should have a fine austenitic or polyhedral structure and that an appreciable quantity of free carbide may be present in the case of very high tungsten steels. What we seem to lack is a satisfactory method, quick and reliable, of ascertaining when the proper structure has been obtained. I think Mr. Bellis' paper is a step in the right direction. To the untrained eye, however, it is not an easy matter to select from some of his photomicrographs the one representing the best structure; for instance, in the case of steel A, we wonder why temperatures of 2,250 and 2,300 do not yield the same results, seeing that both structures are apparently alike, and the same might apply to some of the other samples. I have no doubt, however, that the experienced observer is capable of detecting structural differences that are not made plain here and by which he is able to select the proper quenching temperature. COLIN G. FINK, East Orange, N. J.-On page 68 the authors say that the use of a barium chloride bath to eliminate this difficulty has the disadvantage that the surface of the tool becomes decarbonized." I would like to ask whether they actually found that the surface was decarbonized, or whether they base this conclusion on softening alone? A. E. BELLIS, Springfield, Mass.-No, we have never demonstrated that it was a decarbonization, it is just the softening of the steel. The addition of ferrocyanide to the ferrochloride bath has been suggested. I think that is not altogether satisfactory, because the ferrocyanide bath changes composition very rapidly at these high temperatures, and it would be just a question of luck whether or not it had too much or too little ferrocyanide in the bath giving equilibrium with the carbon content.

Jan 4, 1917

By K. R. Garr, D. Kramer, A. G. Pard

EXPOSURE of steels to a fast-neutron flux results in helium generation by (n,a) reactions. The elements Fe, Ni, Cr, and N are major participants in the (n,a) reaction and helium concentrations of up to 5 x 10"5 atom fraction could accrue in fuel clads after a year of service in proposed fast reactors.' Such concentrations of helium can severely reduce the ductility of alloys at temperatures of reactor service. The phenomenon of helium embrittlement has been studied in austenitic alloys which were irradiated with particles as a rapid means of producing significant helium concentrations.2-5 The pres-ent work is a continuation of those studies and is concerned with helium effects in a ferritic stainless steel. I) EXPERIMENT Small sheet tensile samples with a gage length of 0.50 in. and a cross-section of 0.009 by 0.040 in. in the gage length were punched from cold-rolled type 405 stainless steel. The composition of the steel used in this work is given in Table I. Prior to helium injection, the samples were annealed 24 hr at 760°C which caused complete recrys-tallization with a resulting grain size of 40 u. This treatment rendered the alloy completely ferritic and carbide particles, 0.5 to 2 uin size, were present at a density of 1 x 1011 cm-3, Fig. 1. These carbide particles were probably a mixture of the M7C3 and M4C types.6 Helium was injected into the samples by irradiation with a particles from a cyclotron, which produced uniform concentrations through the center two-thirds of the sample thickness. Details of this procedure were previously described.' The average helium concentration, as measured on a gas-source mass spec- 11) RESULTS A) Tensile Tests. The results of the tensile tests are given in Table I1 where the values shown are averages of two samples. There was no significant effect of helium on either the yield strength or tensile strength at 550" or 650°C but an increase in both is apparent at 750°C. Samples with helium showed a 20 pct loss in total elongation at 650°C which increased to a 55 pct loss at 750°C. The uniform elongation is not affected by helium at 550" or 650°C but shows an increase at 750°C.

Jan 1, 1970

By S. J. Hruska

Rate expressions for the formation of two-and three-dimensional nuclei on foreign substrates are developed, taking into account previously neglected contributions to the standard Gibbs free energy of formation of critical nuclei. The temperature dependence of critical super saturation data predicted using these expressions is in accord with data for cadmium on copper and sodium on CsCl. EXPERIMENTAL data on the heterogeneous nuclea-tion of metal crystals from the vapor phase1&apos;2 exhibit the temperature dependence predicted by a nucleation rate equation derived by Pound et al.3 In their treatment, the critical nuclei are visualized according to the Volmer4 model as cap-shaped (three-dimensional). Accordingly, it seems desirable to compare these data with a nucleation rate equation which is derived on the assumption of disk-shaped (two dimensional) nuclei. Further, Lothe and Pound5 have recently shown that the standard Gibbs free energy of formation of these critical nuclei contains a contribution which has heretofore been neglected. Thus it is necessary to re-examine these nucleation data using a rate equation which contains this contribution. The van&apos;t Hoff isotherm relates n(i), the concentration of nuclei of critical size i (i = number of atoms), to nil), the concentration of adsorbed single atoms: where standard Gibbs free energy of formation of critical nuclei given by is temperature insensitive and is the bulk free energy change/volume of transformed material], T = substrate temperature and k = Boltzmann&apos;s constant. Previously,3 was determined by considering only the contributions of bulk and surface free energies in transforming i atoms from the population nil) to a cluster of i atoms. It has been shown5 that this procedure does not take into account the free energy contribution arising from the multiplicity of sites, q, where the clusters can be situated. If this contribution, -kT In q/n(l),is added to iG3 [Note that this increases n(i) by a factor q/n(l).] Since the above does not affect the remaining terms in the rate expression of Pound et al., the details are referred to their paper. The resulting nucleation rate is If the experimental AGV and T values at some common value of are employed, a plot of vs T(ln C3/l + In p&apos;) should yield a straight line of slope k/B<p and intercept . The corresponding plots for / = 1 nucleus per sq cm sec and C3 = 1018 are shown in Figs. 1 and 2 for cadmium on copper1 and sodium on CsCl2 and the values of obtained therefrom are entered in Table I. It is apparent that the data yield reasonable straight lines with about the same scatter as found using the equation of Pound et al. When the configuration of minimum free energy for a nucleus is a circular monatomic layer, the standard free energy of formation is

Jan 1, 1963

AGGLOMERATION U.S. 4,067,727 - In the sintering of a charge of iron oxide ore, a fuel and a flux on a travelling grate machine, the dust problem is minimized by providing a plurality of cooling zones and by directing heated dust-laden air from a first cooling zone to the sintering zone wherein the dust is filtered from the air by the material being sintered. Air from a further cooling zone can be exhausted directly to the atmosphere. Dust removal in the cooling zone is improved by using a purging zone in which higher pressure air agitates the dust in the sintered material. This patent is a division of U.S. Patent No. 3,973,762, dated Aug. 10, 1976. F. Cappel, assigned to Dravo Corp. Jan. 10, 1978. 6 pp. (75-5). Filed: 4-1-76 (672,748).

Jan 1, 1979

By R. F. Miller

DUE to wartime secrecy restrictions a large part of the technical information developed by government and industrial laboratories was withheld from distribution. Much of this information has now been released or "declassified" and reports of technical work carried out during the war in allied and enemy countries are also becoming available. Information on the latter subject has been augmented by the work of the Technical Industrial Intelligence Corps of the U. S. Army. Through the Joint Chiefs of Staff, rep¬resentatives of this Corps co-operated with the British Combined Intelligence Observations Subcommittee, and some of the observations were made by combined personnel of both groups. The U. S. Government has undertaken the indexing and abstracting of all of this information in the Bibliography of Scientific and Industrial Reports, a weekly bulletin which appeared first early in 1946. Other publications, such as the Bulletin of the British Iron and Steel Institute and The Metals Review of the American Society for Metals, provide abstracts of domestic and foreign magazine articles and papers presented to technical societies. However, they do not cover the industrial and government reports recently released by the Government nor the reports of the Army investigators hence the new bibliography is a welcome addition to our metallurgical library.

Jan 1, 1947

By David B. Reger

The year 1936 in West Virginia was characterized by increased activity in natural gas. The number of actual completions was only slightly increased but many more wells were drilling than at the end of 1935 and there was almost feverish activity in taking new leases. This pronounced revival is partly due to the fact that the extremely cold winter of 1935-1936 showed that additional supplies of gas would be desirable and partly to the hope of finding new pools in the deeper sands. No new pools have actually been found, but the Oriskany sand (L. Dev.) development of Kanawha County, which was already assured by the end of 1935, was greatly extended into wider and richer territory. The Middle Devonian shale (Childres sand), reached incidentally by Oriskany exploration as well as by direct design, has been productive of gas in much wider areas of Boone, Lincoln, Putnam and Kanawha Counties than heretofore known. Routine drilling to the upper sands in dehed territory, also, was greatly increased, although not yet much reflected in completions. Thc supply of marketable gas, however, has been substantially enlarged. In preparation for further exploration there has been an extensive leasing campaign throughout the entire territory where gas seems at all probable, or ever possible. Exact figures are lacking, but new leases have certainly been taken on more than 1,000,000 arres. One operator estimates that 500,000 acres have been leased in the Appalachian geosyncline alone between Parkersburg and Charleston. Exploration, both for shallow and deep-sand gas, on some of these new leases is now under way. There was little activity in oil. No special search for new pools was made and none was found, but the usual routine drilling in old pools occurred. One major gas pipe-line enterprise was undertaken and completed. Operating technology was much the same as usual. In certain localities repressuring for oil has become a matter of routine, and in others the use of acid in treating small wells in calcareous beds has been continued. Financially, the year has been eventless. Some attempts to buy and

Jan 1, 1937

By Don Blackmar

THE production of non-ferrous secondary metals has become a large and important industry in the United States, and deals with practically every type of manufacturing concern. Its business is unique in that it generally buys from its customers as well as sells to them, whether they are individuals, cities, corporations, or the United States government. Its operations are of vital importance to the success and prosperity of many of the nation&apos;s most important manufacturers; yet there are few industries about which less is generally known by those outside it, whether concerning the magnitude of its operations or the details of its actual technique. The industry itself is to blame for this meager publicity, because its technical men have made few attempts to openly exchange ideas, in spite of the excellent examples set by the iron and steel or the copper and brass industries. Whether this is due to the ancient shroud of secrecy generally supposed to cover smelting operations, or because its technical men actually felt that the industry was too puny to be interesting, is hard to say. This paper will consider its subject in a general way, attempting to show something of the size and importance of the industry, as well as its fitness to do its work well. Attention will be called to the sound economic reasons for the handling of non-ferrous wastes by specialists, and to the often unseen losses of metals and labor which occur when manufacturers reclaim their own metallic wastes.

Jan 1, 1928

By Francis P. Sinn

LOW prices have made 1938 a difficult year for the zinc industry of the world. Particularly in the United States, output had to be radically curtailed to bring production into line with consumption. Despite these unfavorable conditions, some additional plant construction is contemplated. In Jugoslavia, through co-operation with the Government, Trepca Mines is lo build a zinc plant to produce 10,000 metric tons annually, the plant to be ready for operation in July, 1941). Cerro de Pasco is proceeding with its plans for an electrolytic plant in Peru. A pilot plant, to be ready next summer, is under construction. In eastern Canada an electrolytic plant is planned in Quebec to treat concentrates from Yoranda and other mines but no defi-

Jan 1, 1939

Jan 1, 1944

By Young C. Kim, Francis Martino, Ish Chopra

For the past two and one-half years, various emission control strategies were jointly developed by the University of Arizona and the Homer City Owners to com- ply with the clean air requirements at its Homer City Power Plant. Some of the available options for the SO2 emission control by the Homer City Owners were:l)cleaning of run-of-mine coal,2) scheduling of mining operations at its captive mines, 3) blending the captive mine coal with externally purchased low sulfur coa1,and 4) placing a partial FGD system. This paper describes two specific emission control strategies developed and implemented. These are: 1) production scheduling at the mining face to minimize sulfur variability, and 2) external purchasing of low sulfur coal for further blending. The main objective of this paper is to share our experiences on implementing the developed strategies. This paper emphasizesthe need for proper mine planning on a short-term basis, if the power plant is to meet the desired objective.

Jan 1, 1983

Jan 1, 1944

By G. B. WATERHOUSE

THE year 1929 was exceedingly busy and prosperous for the iron and steel industry in the United States. The lake shipments of ore were approximately 65,000,000 tons, steel ingots produced were about 57,000,000 tons. Plants were very active. operating for many months well over their rated capacity, slowing down during the last quarter following the severe break in the stock market. The ore tonnage mentioned above was the greatest ever shipped by lake from the Lake Superior region. The trend at the ore mines has been to supplement manual labor by mechanical appliances as much as possible. Mining methods have been greatly improved along the lines of safety as well as to increase the percentage of ore recovery. Crushing and grading of iron ores continued to gain in popularity inasmuch as remarkable blast-furnace operations and records were obtained with sizing and uniformity of raw materials. Progress was made along other lines. The Bradley process for the separation of manganese osicle and iron oside from siliceous manganiferous iron ore was cleuelopecl; also considerable work was clone on a process for the beneficiation of the Cuban laterite ores. Sintering of ores and concentrates increased in popularity. A new analytical method for the deter- mination of sulfur in iron ore was worked out which reduced the time required appreciably. The ore re- serves of the Lake Superior district continued to receive considerable attention and played an important part in the recent mergers which have taken place in the iron ancl steel industry.

Jan 1, 1930

By M. T. Hepworth, T. P. Papazoglou

Hydrogen diffusion in hcp and bcc titanium in the temperature range 610° to 900°C was measured by reacting cylindrical specimens of high-purity titanium at constant temperature with small constant pressures of hydrogen of the order of a few Torr. In the range 0 to 6.7 at. pct H in hcp titanium, the diffusion coefficient D in sq cm per sec is given by: where T is in °K and R in cal per g-atom OK. Only three measurements of diffusivity in bcc titanium were made: at 900&apos; : the diffusivity in ß titanium was found to be 1.8 x 10-4 sq crn per sec. McQUILLAN1 has studied the constitution of the Ti-H system and reported the concentration of hydrogen as a function of pressure of hydrogen and temperature. He found hydrogen absorption was reversible and rapid at temperatures above 500°C in both crystallographic modifications, the a (hcp) phase and the ß (bcc) phase, with the latter phase stabilized by hydrogen additions. Wasilewski and Kehl 2 measured the diffusivity of hydrogen in hcp and bcc Ti-H alloys. For bcc alloys, they reacted cylindrical specimens of titanium with hydrogen gas at 1 atm pressure. They measured the rate of absorption of hydrogen isothermally on specimens ranging from zero hydrogen content when above the transformation temperature to hydrogen contents sufficient to stabilize the bcc phase when below the transformation temperature. By integrating Fick&apos;s second law for a cylindrical geometry, assuming a diffusion coefficient independent of composition, they calculated diffusivities as a function of temperature. In the range 650" to 1000°C their results in bcc titanium yielded the expression: where D is in sq cm per sec, T in OK, and R the gas constant in cal per g-atom-OK. Their studies on the hcp a phase were conducted by exposing long cylindrical titanium specimens to hydrogen at a sufficiently high pressure to establish a surface layer of fl phase 80 to 120 u thick for the duration of an isothermal experiment. Concentration profiles were then determined by hydrogen analysis from chips obtained upon machining quenched specimens. The diffusivity of hydrogen was then calculated yielding the expression: The present investigation was undertaken principally to redetermine the diffusivity data on a titanium by a direct absorption from the gas phase at sufficiently low hydrogen pressures to avoid the presence of a surface bcc phase and also to check the diffusivity data at low hydrogen concentrations in the bcc stmcture. EXPERIMENTAL PROCEDURE High-purity electrolytic sponge titanium (99.9 pct) of BHN 91 was arc-melted, forged, rolled, and machined into cylinders of final hardness, upon annealing, of BHN 92. Cylindrical specimens of two sets of dimensions were used: 1.524 by 2.931 cm and 1.905 by 3.663 cm diam and length, respectively. The experimental apparatus used for annealing specimens and for admitting known amounts of hydrogen at constant pressure is shown in Fig. 1. In a typical experiment, a specimen was lightly abraded with fine-grain silicon carbide, washed with water and detergent, and then thoroughly degreased with reagent-grade tri-chlorethylene and acetone. The specimen was suspended by a Chrome1 wire in the center of a quartz furnace tube, without contact with the tube, and heated to 925°C (as measured by a thermocouple adjacent to the specimen, outside the tube) for a period of at least 4 hr under a vacuum of from 10-6 to -7 Torr as measured by an ionization gage. The furnace temperature was then adjusted to the temperature chosen for the particular diffusion study and the specimen allowed to equilibrate thermally. Hydrogen was then ad-

Jan 1, 1969

By B. W. Gonser

SOFT solders are used principally in the automotive, can-making, building construction and electrical industries, but their field of usefulness extends well beyond these principal users to a vast list of miscellaneous applications where metal joints are required. The most common soft solders and the only ones considered in this discussion are those com-posed of lead and tin, with or without various relatively small percentages of impurities or additions. A small amount of antimony is often pur-posely added. As an indication of the importance of these lead-tin solders, 8620 long tons were consumed in 1934 in the U.S., and during most of 1935 from 900 to 1000 long tons were used each month. A great many factors influence the properties of joints made with soft solders. Fluxes and the fluxing procedure used to prepare the surfaces to be joined in order to give a true metal-to-metal contact are among the most important of these factors. The temperatures used, cleanliness of the work and general soldering technique have their effect, but when results are unsatisfactory they are usually attributed to the metallic solder itself and the raw materials from which it is made. Some-times criticism of the solder is justified. The wrong composition may be chosen for a given job, impurities may be present that ruin certain desired qualities, or uniformity may be lacking. A solder may even be looked upon with suspicion because of its ancestry, regardless of its true composition and behavior. To clarify the effect of slight differences in composition as found in commercially refined solders, a comparison of properties of solders grouped according to their origin has been undertaken. This investigation seeks to give practical information on the proper-ties of tin-lead solders produced from virgin metals, from commercially

Jan 1, 1936

By I. E. Rosenzweig

GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula p — 2rca-j [1] where 1 C = -------------------------------------- a a 1 a a [2]

Jan 1, 1940

By I. E. Rosenzweig

GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula p — 2rca-j [1] where 1 C = -------------------------------------- a a 1 a a [2]

Jan 1, 1940

By G. B. Gould, F. M. Gibson

IN DECEMBER, 1934, the joint Committee on Fuel Values, of the American Institute of Minim and Metallurgical Engineers and the American Society of Mechanical Engineers, submitted a preliminary report, which briefly stated its conclusion that it was not possible to devise any formula for the valuation of coal, based upon the various physical and chemical properties, that would be generally applicable. That report also listed those chemical and physical properties of coal that are generally recognized to have some effect on its use in steam plants, and those physical characteristics of steam plants which affect, in one way or another the relative importance of the properties of coal used in them. Since then, the Committee has considered and discussed in greater detail the interrelationship of the properties of coal and plant characteristics. The conclusions of the Committee are summarized below, with certain recommendations regarding engineering procedure, which will promote the collection of more easily correlated observations with respect to this subject, and thus advance more rapidly the accumulation of data capable of general application.

Jan 1, 1936

By S. E. Szasz, E. J. Moore, B. F. Whitney

An accurate value of formation water resistivity R, is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where R, has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate R, from the chemical analysis of the formation water. INTRODUCTION It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating R, from the chemical anaylsis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ions, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na&apos; and C1-. Dunlap and Hawthorne&apos; have proposed to convert the concentration of all other ions to equivalent Na&apos; and C1-concentrations by means of constant multipliers; e.g., 0.95 for Ca"; 2.0 for Mg"; 0.27 for HCO 3-; 0.5 for SO, -, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. The Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of R, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp.&apos;s Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples. FUNDAMENTAL CONSIDERATIONS The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na&apos; or C1- always carry the same charge. Compounds of polyvalent ions, however. may show incomplete dissociation, e.g., NaSO; + Na&apos; instead of SO,-- + 2Na&apos;. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaC1, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy. The Dunlap method, on the other hand. is too simple because it askmes that at any concentration the contrih-

Jan 1, 1967