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By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

Established as a Division February 22, 1928 J J Golden, Chairman M Tenenbaum, Past Chairman Gerhard Derge, Chairman-Elect R W Shearman, Secretary-Treasurer AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1960

On June 1, the offices of the Engineering Division of the National Research Council were moved from Washington to the sixteenth floor of the Engineering Societies Building, 29 W. 39th St., New York City.

Jan 7, 1919

ROBERT F. MEHL, Chairman ALBERT J. PHILLIPS, Past-chairman ROBERT H. LEACH, Vice-chairman E. M. WISE, Vice-chairman W. M. CORSE, Treasurer - Louis JORDAN. Secretary 29 West 39th St., New York, N. Y.

Jan 1, 1938

By T. B. Counselman

AFTER several years study, the Universal Atlas Cement Co. decided to rebuild its plant at Leeds, Alabama. The entire old plant, which was to operate during the new construction, was then to be scrapped with the exception of two kilns. The quarry was to be mechanized, new and larger kilns installed, with the most modern type of equipment all through the plant. Raw grinding operations at all of the Universal Atlas plants were dry. However, the dust hazard of this operation and the growing emphasis on occupational diseases made wet grinding attractive. Coal at Leeds is cheap, so that a slightly higher coal practice was unimportant. Power was cheap, so that waste-heat boilers were not desirable. Since new kilns were to be installed, these could be made long enough to make filters unnecessary. Wet raw grinding could be either the old practice of open-circuit compartment mills or closed-circuit grinding in accordance with metal-lurgical practice. The latter saved power and steel wear and saved initial investment. This had been demonstrated in cement plants. Also, the elimination of tramp oversize was a most important advantage. Ease of chemical control was another factor. Blending in the thickener, with elimination of slurry mixers had been found practicable. Therefore, if wet raw grinding were used at all, the advantages were clearly in favor of closed-circuit grinding. Detailed layouts of the most modern possible closed-circuit dry-grinding plant and of a closed-circuit wet-grinding plant were prepared, and careful estimates were made of initial invest-ment and operating costs. Full consideration of all the factors involved resulted in a decision to install wet closed-circuit grinding.

Jan 1, 1939

By Chester N. Truax

Still another shadow was cast over coal's largest market-the electric utilities-when President Johnson signed into law the Federal Clean Air Act of 1967. Air pollution-sulfur reduction-was thus brought into sharper focus as one of the central problems of the coal industry. Industry executives testified in both Houses of Congress to enable the lawmakers to develop a workable and economic law. The new legislation calls for the Secretary of Health, Education and Welfare to establish air control regions. After the regions are outlined the Department will publish air quality criteria on pollutants. Anticipating this legislation, the coal and utility industries have for the last several years been involved in extensive research programs to develop solutions to the air pollution problem. Even though the coal industry has been under strong attack for its part in adding contaminants to the atmosphere, it is by no means the major contributor.

Jan 2, 1968

Before hostilities between the colonies and Great Britain began in 1775, most of the coal used in the northern colonies undoubtedly came from England, with some supplies for New England coming from Nova Scotia; in New York and Philadelphia the supply came from England with some from the Virginia mines. Table 4 shows data obtained from the Public Records Office, London, for the years 1768-1772. This table supplements Table 3, which records only a few shipments from Richmond in 1768 and 1769; as there was no coal shown in imports coastwise in 1769 in Table 4, and only two small shipments in 1769 in Table 3, there may have been a cessation of shipments then, for some reason not now known. In Table 5 are incorporated all the data in the first two, with a few earlier years, and an attempt is made to estimate the amount used during the period by allowing for coal exported. With the small total tonnages a carryover from one year to another makes a large difference in the annual figures, but over the period the result may be fairly indicative of the amount of coal used before the Revolution. According to present day ideas the quantity of coal used during that war was very small, but apparently it was badly needed for the manufacture of the small amount of munitions made in those troublous days. As Philadelphia was the leading city along the Atlantic coast, and as the southeastern part of Pennsylvania was the leader in making iron, as well as making rifles, it is natural that the first call for coal came from there. At first, procuring supplies such as coal, powder and sulphur was handled by a Committee of Safety, which later became a Council of Safety and later this committee's functions were turned over to a Board of War, functioning with the military organization of the colony. . The organizations of the several colonies were slightly different, but Pennsylvania, Maryland and Virginia followed this scheme generally. Later in the war the Congress began to make arms for the troops, and it is difficult now, with the few records available, to tell when the state functions ceased and those of Congress began. On December 5th, 1775, the Committee of Safety

Jan 1, 1942

By R. H. King

This paper describes the results of an underground coal mine trial installation of a shielded trailing cable. The cable was a three conductor, round, type SHC-GC and was installed on a shuttle car in a conventional room-and-pillar mining section. The purpose of the study was to evaluate proposed legislation that would require shielding on low-voltage trailing cables. Such legislation would require machine modifications to cable reels, packing glands, and couplers; increase cable splicing complexity; and necessitate additional splicing materials and training. Furthermore, fault location might be more difficult. Even though shielding will cause some problems for the mine operator, it can reduce electrical shock hazard to mine workers. This paper presents information that mine operators can use to solve most of the problems encountered if they are required to install shielded cables. The in-mine evaluation was funded by the US Bureau of Mines; however, the views and conclusions in this paper are those of the author and should not be interpreted as necessarily representing official policies of the US government.

Jan 1, 1982

By Oswald J. Heinrich

At the Baltimore meeting of the Institute in February, 1879, Mr. Eckley B. Coxe, then president of the Institute, called attention in his address to the subject of Secondary Technical Education, and

Jan 1, 1881

ALBERT SAUVEUR, Chairman. A. A. STEVENSON, Vice-Chairman. HERBERT M. BOYLSTON, Secretary, Abbot Bldg., Cambridge, Mass. John Birkinbine, William Kelly, J. S. Unger, William H. Blauvelt, Charles Kirchhoff, Felix A. Vogel, James Gayley, Richard Moldenke, Leonard Waldo, Henry D. Hibbard, Joseph W. Richards, William R. Walker, Henry M. Howe, C. F. W. Rys, William R. Webster, Robert W. Hunt, E. Gybbon Spilsbury, Frederick W. Wood. J. E. Johnson, Jr., The innovation of a special meeting under the auspices of the Iron and Steel Committee was well justified, if we accept as a criterion the number of papers presented at the meeting held on Oct. 16 and 17 in New York and the attendance at that meeting. Twenty-four papers were read, and most of these were widely discussed orally, while doubtless the written discussions will be even larger in extent. Discussions will be received up to Dec. 1, 1913. The attendance at the meeting of 106 members and 75 guests is an evidence of the wide anti growing interest in the Institute of men interested chiefly in iron and steel. It is especially interesting to note this large attendance at a meeting where very little of a social nature was introduced into the program. An informal dinner for the men at the Engineers' Club closed the meeting. At this dinner were present about 70 members and guests. One of the Vice-Chairmen and the Secretary of the new Committee on Petroleum and Gas told of the important plans in prospect of that Committee. Brief impromptu speeches by a considerable number of the members and guests were enjoyed. Professor Marburg reiterated his previous assertion that he believed that the Institute and the American Society for Testing Materials, as well as some of the other technical societies, were all fighting for one good cause; that there was room in the field for all of these societies with their various points of view; and that they should march shoulder to shoulder. The success of this dinner was due largely to the efforts of Mr. Johnson who had the affair in charge.

Jan 11, 1913

By L. D. Muller, C. P. Sayles

When minerals are mined in arid or semiarid areas where water is at a premium, dry processing is a natural route to take for concentrating or classifying the values. Until recently though, dry processing technique were limited by the lack of suitable equipment. With the advent of the pneumatic pinched sluice at Warren Spring Laboratory, Stevenage, Hertfordshire, England, a new tool emerged to fill this gap and it has the potential of providing industry with a high output concentrator or preconcentrator for dry natural ores and secondary materials. The pneumatic pinched sluice gives every indication of fulfilling these requirements with the added advantage that with homogeneous materials-such as crushed limestone or quartzose sands-it may alternatively operate as a high throughput dry classifier or sizing device. An industrial version of the equipment is now being manufactured by Dryflow Separators Ltd., as sole licensee for the National Re- search Development Corporation.

Jan 1, 1971

By Michael J. Messel

THE critical shortage of asbestos fiber in the world today brings to the foreground the question of locating and developing new deposits. The object of this paper is to discuss some of the more important factors which should be considered in the examination and valuation of a new asbestos enterprise. Some of the more important uses of asbestos fiber are for textiles, heat insulators, building materials, filters and a series of other uses. The properties of this mineral, such as fibrous structure, color, strength, silkiness and flexibility, coupled with resistance to fire, certain chemical action and decay make its application unique for certain industrial uses which consume over 500,000 tons annually. These same unique properties which make this mineral so valuable also make a deposit one of the most difficult to appraise accurately, because of the many undeterminable and varying factors which must be considered before a deposit can properly be termed commercial. The majority of the asbestos fiber today, having the above mentioned properties, is sold by grades which are based on fiber length. Present day fiber prices vary over a wide range from $800 to $225 for crude fibers and $300 to $20.00 per ton for milled grades. For valuation purposes a careful study should be made of existing fiber prices and markets. EXAMINATION OF DEPOSITS In carrying out prospecting and examination of a deposit, considerable caution is required to get the necessary information in the form that will have the most value for the final determination. There are two main classes of asbestos fibers, chrysotile and the amphiboles, the chrysotile being, by far, the most important both in abundance and uses. This paper will stress mainly chrysotile deposits, however, the amphiboles have many important uses, especially amosite and crocidalite. Their valuation presents special problems as other factors may be involved, especially as they are not graded according to any well defined and adopted standard but usually according to the use for which they are being supplied. Most chrysotile deposits occur in two main types of rock, (I) mainly in basic igneous, such as dunite and peridotite, (2) to a lesser extent in sedimentary rocks, such as dolomite and limestone. All of these require a certain degree of metamorphism to be favorable to asbestos formation. Approximately 90 pct of the asbestos deposits are derived from serpentinization of dunite or peridotite, whereby the magnesiumsilicate olivine was altered to hydrous magnesium-silicate serpentine. Under certain favorable geological conditions, this serpentine takes a fibrous form having a definite crystal structure, probably due to molecular rearrangement, and is known as chrysotile. The fiber veins are usually ir-

Jan 1, 1947

By JAMES J. DOUGHERTY

THIS paper is a general discussion of developments in our reverberatory smelting practice during the past five years. It deals briefly kith changes in furnace types ; changes in furnace feed ; de- crease in the amount of slag produced; relation of slag assays to copper loss in the slag; increase in the grade of matte and furnace capacities. The reverberatory is but one unit in the copper plant ancl 'any discussion of it must be considered with reference to the other units and to the plant as a whole. A change in the grade of concentrates at the concentrator puts an entirely new aspect on reverberatory smelting and, likewise, a change in the grade of matte at the reverberatory affects the rate and cost of converting. The introduction of differential flotation in 1927 had a very marked influence on all smelting operations and its effect will be noted

Jan 1, 1930

By Albert F. J. Bordeaux

INTRODUCTION. THE following general survey of the character and present condition of the silver-mines of Mexico, though not offered as a detailed treatise, has been prepared with care, is believed to he generally up-to-date, and is offered as a summary which may be found useful by mining engineers. Mexico has ranked for several centuries first among the silver-producing countries. It is now second as copper-producer, and seventh as gold-producer, with a fast-increasing output every year. The total amount of capital invested in its mining- and smelting-works is more than $250,000,000, while the yearly metallic production is $160,000,000. There are more than 20,000 recorded mining properties. The silver-mines of Mexico represent deposits of three principal classes: (1) veins and stock-works in eruptive rocks; (2) fissure-veins crossing the crystalline schists, granite, diorite, etc. ; and (3) veins and replacement-deposits in limestone. The true fissure-veins in some districts contain (in value) more gold than silver. In other deposits, the silver is decreasing in depth, leaving galena and zinc-blende as the principal ores.

Jan 9, 1908

The American Petroleum Institute, 250 Park Ave., New York, N. Y. Lacey Walker, Secretary. A complete price list of publications will be sent upon application. The American Petroleum Institute issues a variety of publications; in addition to the Daily Oil Digest ($25 per year) and a weekly Statistical Bulletin ($12.50 per year to nonmembers), a Quarterly is published ($4 per year to nonmembers). Books published by the Institute: American petroleum supply and demand, $3; A series of "Petroleum facts and figures" for each of the years 1928, 1929, 1930 and 1931, $2 for each copy; Function of natural gas in the production of oil, $1; Bibliography of organic sulphur compounds, $4; and "Oil" (Oil Industry Series in one volume), 50 cents per copy. Volumes of the first six annual Meeting Proceedings are out of print, but the Proceedings for the 7th annual meeting in 1926

Jan 1, 1933

By P. A. Beck

In the course of work on grain growth in high purity aluminum a simple optical method was developed for detecting the presence or absence of preferred orientation in annealed specimens. The specimens were prepared by grinding, polishing and "deep etching." The etching reagent used for high purity aluminum has been described.* The resulting etch pits produced selective

Jan 1, 1949

By C. E. Sims, F. W. Boulger, H. A. Saller

Most of the data on equilibrium constant and the deoxidations potentialities of those elements, considered to be stronger deoxidizers for steel than is silicon, have been calculated from thermodynamic data. The reason for this is, primarily, the obvious difficulty of obtaining direct experimental evidence of equivalent accuracy. This is an excellent use of the principles of thermodynamics and has given valuable data not otherwise available. Such results, of course, can be no more accurate than the physical constants used in the calculations, and one can never be sure that the basic data are either complete or accurate. In fact, as in the case with silicon,1 there are not only discrepancies among the calculated theoretical values of the equilibrium constant for deoxidation of steel but also between the theoretical and experimental values. It is highly desirable, therefore, to obtain experimental values for checks on calculated results whenever possible. If they disagree, both cannot be right, but if there is good agreement, their value is enhanced. The present work was done in an effort to obtain experimental evidence in regard to some of the common alloying additions but more particularly the so-called "strong" deoxidizers for steel. The method used was to determine the minimum concentration of the deoxidizer that would effect a certain definite degree of deoxidation in steel. The criterion of deoxidation was the change from the large globular Type I sulphide to the eutectic Type II as described by Sims and Dahle.2 This change is sharp and definite, and inasmuch as it can be produced with equal facility by aluminum, zirconium, and titanium, it is considered a manifestation of a certain degree of deoxidation and not an alloying effect. Ostensibly such a procedure could give only a comparison of deoxidizing powers and no absolute values. Nevertheless, repeated observations have shown that, when increasing increments of aluminum are added to a steel, the residual aluminum content begins to increase simultaneously with the appearance of Type II inclusions. Thus it seems warranted to postulate that the Type II inclusions appear coincident with the virtual elimination of FeO as an active constituent of the steel. Experimental Procedure The data obtained were primarily from the microexamination of polished and unetched specimens and from chemical analysis. Experimental heats weighing 200 to 250 lb were made in a basic-lined high-frequency induction furnace. The base composition was nominally that of a medium-carbon casting steel to which the appropriate additions were made. Specimens were poured into sand-cast ingots 3 in. in diam as shown in Fig 1. Sand-cast ingots were used to prevent chilling and to allow sufficient time in freezing for normal inclusions to form of a size large enough to be studied readily. In the first few heats, the tapered wall ingot was used, but in the majority, the extra large riser was used to prevent piping in heavily deoxidized steels. Specimens for microexamination were taken from the location shown in Fig 1, and drillings for chemical analysis were taken from a similar location. The procedure was to melt the base composition and deoxidize with the usual manganese and silicon additions and then to pour an ingot. The furnace was then tilted back, and the first increment of strong deoxidizer or special alloy was added and allowed to disseminate through the melt, with enough power on to hold the temperature constant, for 45 sec. Then a second ingot was poured. After this, another increment was added, and after the same holding time another ingot was poured. In this way from 9 to 12 ingots were poured from each heat, each successive ingot having progressively larger total additions of alloy. Eighteen heats were made altogether, and the range of alloys used and additions made are outlined in Table 1. The three principal types of sulphide inclusions found are illustrated in Fig 2. The globular Type I sulphides are characteristic of silicon-killed steels, the eutectic Type II are characteristic of steels deoxidized with a small amount of aluminum, while the larger, angular Type III are usually found in steels with a residual aluminum content above about 0.02 pct. In all specimens studied, the transition from Type I to II either did not occur at all or was very abrupt and clear cut. There never was any doubt as to just which increment produced the change, although the individual additions were small, in the order of 0.01 pct. The change from Type II to Type III was considerably less sharp, and, in some cases, both types were found together. Inasmuch as the formation of Type III sulphides is apparently not a deoxidation phenomenon, they will not be discussed here.

Jan 1, 1950

By C. A. Doh, R. Q. Fields, M. Lebourg

A formation tester run on logging cable is now available to the oil industry. It offers a method of safely and rapidly testing possible producing formations in uncased holes. These tests can be made up the hole after running the electric log. Reservoir pressure data is continuously recorded at the surface as the fluid sample is extracted. The tester may be assembled with a reservoir of 1-, 2.75-, or 5.5-gal capacity. A retaining pad on the body of the tool is expanded against the wall of the hole at the exact depth desired; this depth is determined by electrical log control. Two bullets are then fired through the center of the retaining pad which create a connection between the formation and a flow line to the sample chamber. When the chamber is filled, a valve is closed and the fluid sample sealed at maximum pressure. The tool is retracted to minimum diameter and brought out of the hole. Electrical circuits permit a complete recording at the surface of the mechanical operations of the tool as well as the formation pressure build-up and the hydrostatic mud pressure. The tool was introduced commercially during the latter part of 1955 in the Gulf Coasts of Louisiana and Texas. Over 1,000 operations have been made to date (Sept. 1, 1956); 50 per cent of which resulted in successful tests. Failures have been due mostly to ineffective sealing in unconsolidated sands. One major company had 41 successful tests out of 80 attempts with 23 ineffective pad seals. Results for this company were very gratifying as to pinpointing gas-oil ratios, indicating productive permeabilities and aiding in determination of fluid content where electrical log and side-wall coring information were inconclusive. Eight typical pressure curves are discussed (including misruns). Six types of fluid recoveries are interpreted. Eight actual field examples of electric logs, showing the problems solved by the formation tester, are illustrated. The present applications of the tool are discussed: 1. Determination of productive fluid—varticularlv differentiating between gas and oil. 2. Determination of reservoir pressure as an aid to: (a) safety in completion technique, (b) reduction in drilling costs, and (c) reservoir analysis. 3. Determination of minimum gas-oil ratios. 4. Location of gas-oil or oil-water contacts. 5. Recovery of samples for examination and analysis: oil (gravity); gas (hydrocarbon content); water (salinity). Additional applications envisioned for the future are also given: (I) subsurface exploration based on accurate pressure, (2) recovery of fluid samples from the undisturbed reservoir for PVT work, and (3) possible quantitative study of permeabilities or productivity index. Running the formation tester requires no special pre-cautionary measures. Because full hydrostatic mud pressure is maintained at all times, well depth is no problem. Thus, the method allows safe, economical testing in wells which heretofore could only be tested by setting casing. INTRODUCTION A new method of safely and rapidly testing possible producing formations in uncased holes is achieving considerable success. The method offers promise of further advances in reservoir study. Called the formation tester, the new instrument is unique in that it operates on logging cable. It thus offers all the advantages of wire-line operations and becomes an important adjunct to present logging and side-wall coring services. The tester is operated against the wall of the hole at any depth desired. Zones to be tested are usually determined by a study of the electrical and the micro-caliper surveys. Reservoir data, as well as the operating cycle of the tool in the hole, are continuously recorded at the surface during the operation. The tester, as it was originally designed, was capable of recovering a 1-gal sample of reservoir fluid per trip in the hole. Tools with reservoirs of 2.75- and 5.5-gal capacity are now available. The 5.5-gal reservoir is equipped with a segregating system, set before going in the hole, so that the last portion of the recovery (usually 1 gal) is automatically separated from the first portion. This makes it possible

Jan 1, 1958

By C. Ernest Birchenall, Robert F. Mehl

Application of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion cocfficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner¹ derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smith5 on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 Activities in Brass9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by

Jan 1, 1947

By C. Ernest Birchenall, Robert F. Mehl

Application of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion cocfficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner¹ derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smith5 on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 Activities in Brass9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by

Jan 1, 1947