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By Harrison Schmitt

SINCE the U. S. Geological Survey published the data on the Central Mining District collected by Lindgren and Graton1 and by Paige2 much new information has been obtained by development and mapping, but none of it had been published until recently when Kniffin3 published on Fierro, Lasky4 on the Ground Hog mine, Thorne5 on Santa Rita and Landon6 filed a thesis on the Fierro-Hanover-Santa Rita area at the Uni-versity of Chicago. During the years 1927-1930 much of the writer's time was spent in mapping the geology and ore deposits of this district, particularly in the area of the zinc deposits at Hanover. Some of the data collected are presented here. Previous publications have been freely drawn upon and additional data used that were generously supplied by L. M. Kniffin, Wilfred Wright and Gerald Ballmer. Thanks are due Augustus Locke, Samuel G. Lasky, Kniffin, Wright and Ballmer for suggestions and critical readings of the manuscript, and to the Empire Zinc Co. (a subsidiary of the New Jersey Zinc Co.) for the privilege of publishing material compiled largely at its expense. The relation of the Central. or the Santa Rita-Hanover-Fierro district to the Silver City district is shown on Paige's geologic map in the Silver City folio.7 Granodiorite porphyry and quartz-monzonite porphyry

Jan 1, 1933

By E. B. Hunt

Paraffin deposition has been studied in the laboratory under conditions simulating deposition in well tubing. A theoretical analysis has been made of the cooling of the oil and the precipitation of paraffin from the oil as it flows up the well tubing and through surface flowlines. It is proposed that paraffin deposits are initiated by the precipitation of paraffin directly on or adjacent to the pipe wall and grow by diffusion of paraffin from solution to the deposit. This mechanism is consistent with laboratory and field observations, and has proved useful in the design and interpretation of laboratory paraffin-deposition tests. Tests have been made of the effect of plastic pipe coatings and chemical additives on paraffin deposition. INTRODUCTION Paraffin deposits which form in well tubing and surface flowlines interfere with production and must be removed. Over the years much progress has been made in developing and improving methods of removing these deposits after they form. Much less progress has been made in developing methods of preventing or inhibiting the formation of paraffin deposits. This is due, it is believed, to the lack of knowledge of the mechanism of paraffin deposition, the absence of satisfactory laboratory testing methods and the difficulties in evaluating the results of field tests of preventive treatments. The present investigation was undertaken to elucidate the mechanism of paraffin deposition and to develop suitable laboratory tests for studying the inhibition of paraffin deposition in well tubing and surface flowlines. Current theories on the mechanism of paraffin deposition have been evolved from field observations, from laboratory studies of various factors which might be involved in paraffin deposition, and from laboratory paraffin-deposition tests.1-9 Paraffin deposits have been formed in the laboratory by immersing a cold finger into a hot wax-oil solution and by flowing hot wax-oil solutions through cooled pipe or over cooled plates. These laboratory conditions differ in important features from field conditions, and the observed deposition behavior is not entirely field-like." Thus, there is reason to question the field applicability of the results of these tests. The present investigation was undertaken to determine how to perform and interpret laboratory paraffin-deposition tests to obtain information on the inhibition of deposition in the field. The paraffin problem in the broadest sense encompasses the formation of any predominantly organic deposit in well tubing, surface flowlines and other equipment in contact with crude oil or gas. The present investigation was limited to paraffin deposition involving the precipitation of paraffin wax from solution by cooling and its concentration in a deposit on a cooled surface. This probably excludes its applicability to those problems arising from asphaltic-base crudes, but not those arising from paraffin-or mixed-base crudes. This also excludes its applicability to emulsion and congealing oil problems which are often included as part of the paraffin problem. The phenomenon of cooling appears to be the controlling factor in paraffin deposition involving the precipitation of paraffin wax and its concentration in the deposit. Deposits of this type are usually found in the field only where cooling occurs. Early in this laboratory investigation, it was not found possible to form deposits under constant temperature conditions from a wax-oil slurry, either by steady flow through pipe or by gas-lift up a pipe. Thus, the investigation was limited to situations involving cooling. THEORY The relationships involved in establishing the temperature profiles in an oil stream as it flows up well tubing with a linear (geothermal) pipe-wall temperature distribution or through surface flowlines with essentially constant pipe-wall temperature are presented in the Appendix. The relationship between radial distance in the pipe and the rate of cooling of the oil is then combined with a relationship between cloud point and rate of cooling to develop the pattern of formation of a wax cloud in the oil. The following discussion of paraffin deposition under various laboratory and field conditions is based upon this development which is presented in the Appendix. PARAFFIN DEPOSITION IN SURFACE FLOWLINES The average temperature of the oil coming out of a well is somewhat higher than the ground temperature. Thus, the oil continues to cool on its trip through the surface flowline, and wax deposition can occur. The temperature distributions calculated from Eq. A-4 are given in Fig. 1. As can be seen, almost all the cooling occurs in the first 500 ft from the wellhead. In addition, the radial temperature gradient near the wall decreases rapidly with distance and becomes very small after a few hundred feet. Thus, growth of a paraffin deposit would be expected to decrease rapidly with distance from the wellhead and become negligible after a few hundred feet, since growth is dependent on concentration gradient. Wax precipitation and diffusion of wax to the already

THE CHAIRMAN (EDWIN LUDLOW, Lansford; Pa.).-Mr. Wang's paper reminded me that some years ago I was asked if I would not go into the Tien Tsin district and take charge of Americanizing a Chinese mine. They said the trouble was that, while wages were only 9 c. a day, the coke cost $2 a ton delivered to the cars. Reading Mr: Wang's paper would indicate the need of a little Americanization in the Manchurian field. Wages are only 40 c: a day, yet the cost is $3.60 a ton. An efficiency engineer would have an excellent opportunity in that field. T. T. READ, New York, N. Y.-It is always true that low-priced labor is inefficient, wherever we find it; for example, in Japan, where wages are low, but not so low as in Manchuria, working costs are not relatively much lower than ours. Mr. Padshah, describing his experience in India, once told me that, while wages were only about one-fifth as high

Jan 4, 1918

By J. P. Zannaras

If we assume that testing of the model started at time C, that time t2 was the instant at which the elastic limit of the material was passed at the points of the maximum stress, and that at time t3 the failure of the model was completed as shown in the typical photograph (Fig. 1), then actually the photograph shows the final results of what took place between time t2 and t3. By the principle of similitude all conclusions drawn from the behavior of the model were applicable and valid for actual mine roofs up to the time t, after time t, motions and friction came into play during the destruction of the model. The events between t2 and t3 and the photograph itself are not representative of the events expected in an actual mine roof unless corrections imposed by the principle of similitude are made.

Dec 1, 1956

By J. B. Nau

A short time ago some interesting experiments concerning a new steel-making process in the open-hearth furnace were made by the writer at the Croton magnetic mine, N. Y.

Jan 1, 1892

By A. F. Buddington

INTRODUCTION EVER since a genetic connection between many ore deposits and magmas began to be widely recognized, some two-score years ago, there has been much discussion of the complex and intricate problem of the genetic association of specific kinds of mineralization with specific kinds of igneous rocks. General discussions of the latter problem and pertinent data have been given by S. F. Emmons, Kemp, Lindgren, Niggli, Rastall, Spurr, Vogt, and others. In this paper no attempt is made to deal with mineral deposits genetically associated with volcanic rocks, but only with those presumed to be related to exposed intrusive masses. The writer is indebted to E. S. Bastin, F. F. Grout, Edward Sampson, and to the members of the committee in charge of the preparation of the volume, for a critical reading of the manuscript and many worth-while suggestions.

Jan 1, 1933

Jan 1, 1892

By D. R. Mitchell

MEETING for the thirteenth time in New York as part of the five-ring circus known as the Annual Meeting A.I.M.E., the Coal Division experienced a wartime boom in attendance. Technical sessions were crowded and whereas 65 seats were set up for the annual luncheon meeting of the Division over 100 members showed up, many of whom had to be fed elsewhere. Possibly the Coal Division should adopt "13" as its lucky number. Discussions at technical sessions, formal and informal, were lively. Those papers containing material directly concerned with the war, or containing information that might be usable for war industries, were enthusiastically received. Some criticism was made in regard to the present method of handling discussions and it was suggested that better success would be had in getting discussions in the record by the use of hired reporters. This is being considered by the executive committee of the Coal Division.

Jan 1, 1943

By Arne Westgren

ONLY in exceptional cases can the ordinary methods of chemistry be used for determining the constitution of compound metallic substances. Recourse has therefore been taken to special methods, the main expedients of which are, as we know, thermal analysis and metal microscopy. To these may be added-though more accessory-the determination of electric conductivity, specific volume, hardness or other properties. The information obtained by these methods has been compiled in equilibrium diagrams. Naturally, the technically most important alloys, such as steel, bronze and some others, have been subjected to very close study, and many investigators have devoted themselves to the solving of their problems of constitution. The equilibrium diagrams of these systems are therefore known today with a comparatively high degree of accuracy, even though it must be admitted that many details regarding their transformation reactions still remain to be completely explained. The equilibrium diagrams of the other alloys as a rule have not been determined so accurately. Most of them are based only on approximate determinations of the homogeneity ranges of the various phases. Thus extensive, detailed studies remain before these diagrams may be considered as established. Unfortunately, it must also be admitted that many of the alloy diagrams given in the present handbooks are as a whole very dubious. As a matter of fact, many of them may really only be viewed as the results of rather superficial, orientating investigations. In fact, there also seems to be a general opinion prevailing in our day that much work still remains to be done before the equilibrium conditions of the alloys may be considered as fully explained. At present, in almost all institutes for research on metals, as well as in many university laboratories, investigations to this effect are being carried out. As a rule, the classical methods of metallography, the thermal analysis and metal microscopy are applied.

Jan 1, 1931

By W. H. Bassett, C. H. Davis

The late J. P. Sparrow, chief operating engineer of the New York Edison CO., carried out a series of practical tests on condenser tubes of several copper alloys and reported on the results to the Association of Edison Illuminating Companies at its meeting in September, 1913. In the preparation of these tubes the senior author had the pleasure of cooperating. Copper-zinc alloys in the proportions of 60-40,70-30,80-20, 90-10, and Admiralty metal, which is in effect 70-30 with 1 per cent. of tin, were tried. Monel metal and several copper-nickel alloys, and 8, 5, and 3 per cent. aluminum bronze were also tried. At the time of this report, the aluminum bronze had been in service for 4 1/2 years and seemed to be giving especially good results but later it began to fail and showed no substantial improvement over Admiralty metal. Monel metal was unsatisfactory and the nickel alloys apparently did not give better service than the Admiralty alloy. Previous to the publication of the report, and after considerable discussion, it was agreed that a test where tubes of different kinds could be under laboratory observation would be advisable, so the apparatus described here was set up in The American Brass Co.'s Waterbury Laboratory. This was fitted with tubes of copper, brass, bronze, nickel silver, cupro-nickel and other alloys, and the test started on Oct. 11, 1912. Salt water from East River, New York harbor, was barrelled and transported to the laboratory for the test. A fresh supply, completely replacing the water in service, was obtained at the end of each six months period. Plan of Procedure In general, the procedure was to inspect the tubes at short intervals and to remove those that had begun to leak. The tubes removed were carefully examined and a photographic and microscopic record of the

Jan 1, 1925

NEW MEMBERS The following list comprises the names of those persons who became .members during the period of Jan. 10, 1918, to Feb. 10, 1918. ANTISELL, TONER, Min. Engr.; Supt., Great Falls Mine of Maryland, Chevy Chase, R: F. D. No. 4, Washington, D. C. BAKER, RAYMOND FRANK, Geol:, The Texas Co., Producing Dept., Box 362, Tulsa, Okla. BERTON, ADRIEN, Chief Engr., Corocoro United Copper Mines, Ltd., Corocoro, Bolivia. Buck, WILMER EARLE, Met., Curtis & Co. Mfg. Co., Hamberger & Kienlein Aves., St. Louis, Mo. BUELL, WILLIAM H., Asst. Director, Experimental Station, E. I. duPont de Nemours & Co., Wilmington, Del. CARDENAS, FEDERICO F., Mgr., Cia. Minera Nazareno y Alicante, S. A., Allende, No. 112, Saltillo, Coah., Mexico. CHEVALIER, JEROME A., Pet. Geol., The Carter Oil Co.; Exchange National Bank Bldg., Tulsa, Okla. CLEAVES, DANIEL LUNT Supt., St. Joseph Lead Co., Herculaneum, Mo. CLOTHIER, GEORGE A., Resident Min. Engr., Province of British Columbia,

Jan 3, 1918

James DouGlas, New York, N. Y. (communication to the Secretary*):—In my paper on the Conservation of Natural Resources, I referred to the slow replacement of bee-hive ovens by the by-product ovens as a most notable instance of waste. And I quoted from Mr. Parker's report for 1906 an explanation given by him in accounting for the small production of by-product coke. It was that the market for the by-products of the coke-ovens was so limited that some of the ovens constructed were out of operation. His report on the manufacture of coke in 1908' does not record an improvement, and attributes the strange fact that we alone, of all the industrial peoples, delay the adoption of this cardinal improvement from the continuance of the same almost inexplicable cause. To quote again from his report, he says (p. 241): "The year 1908 was not marked by any notable gain in the construction of byproduct coking plants, though some new work was done. There was a net increase

Jan 1, 1910

By W. Kennedy

THROUGHOUT northeastern Texas we have an extensive series of iron-ore deposits, occupying portions of nineteen counties and having approximately an actual ore-covered area of 1000 square miles. The existence of these ores has long been known. Kennedy* says: "Iron-ore is distributed in profusion throughout Texas, being found almost everywhere except in the level region of the coast." Before this, C. Newell† had mentioned the existence of these ores thus: " Iron is found in abundance in the eastern, northern and middle portions of Texas;" and in 1849 Edward Smith‡ said: " We met with immense hills of iron which were said to be, and appeared to be, of excellent quality, in Cass and Titus counties.. . .. It is well known that Texas abounds with iron of first-rate quality." In 1859, Dr. Shumard? reports that detailed surveys had been made in several counties, and says: " Our labors have demonstrated the important fact that we have a vast iron-region in the eastern part of the state, embracing considerable areas in Cass, Harrison, Rusk, Panola, Smith, San Augustine and Shelby counties. The ore-deposits belong to the Tertiary era and consist chiefly of hematites and limonites, of which there are several varieties. We have also found in this district extensive beds of carbonate of iron." Dr. Shumard gives no very exaggerated description of Cass county§ as it then existed when he says : " Cass county alone is capable of supplying a number of furnaces with an abundance of excellent iron-ore for many years." Of Rusk county he says: "Our de-

Jan 1, 1895

Jan 9, 1951

By A. W. Ambrose

THE underground losses of oil exceed by hundreds of thousands of barrels all the oil that has been lost in storage, transportation, or refining. The quantity lost is, of course, indeterminate; but when it is considered that the contents of an entire oil field have been excluded from recovery by invading waters, some idea of the amount wasted may be gained. Similarly, enormous quantities of gas have been lost underground. Conservation of the oil, therefore, should start before it is brought to the surface rather than after it is placed in storage tanks. Water is one of the most important causes for underground losses and the operator should give as serious consideration to an underground flood of water as he would to a destructive surface flood. The best insurance, of course, is to have the wells drilled in such a manner that water has no access to the productive oil and gas horizons, and on abandonment the wells should be properly plugged. The encroachment of edge water and the occurrence of water in the base of an oil sand present a very serious problem to an oil company; sooner or later these waters are bound to cause considerable damage, if they do not entirely destroy the possibilities of further production. Too often, however, a field has been considered to be in a hopeless condition, whereas wells in as bad a condition in other areas have been repaired and the life of the field appreciably lengthened. The corrections are very often suggested by technical study. Very successful results have been accomplished by detailed underground work in the California oil fields, in Cushing, Oklahoma, and in other areas.

Jan 9, 1920

By E. Marburg

Most ingots complete solidification vertically rather than transversely. This conclusion is based on complete solidification patterns of big-end-up and big-end-down ingots developed from dumped and split ingots. New mechanisms for segregation in ingots are proposed. Internal soundness in ingots is found to depend upon adequate width of vertical core. A LTHOUGH it has long been recognized that the A internal soundness of ingots is principally been recognizedthatthedependent on the process of solidification, knowledge of this process is still only fragmentary. The mechanisms causing the several types of segregation in ingots, which mechanisms are necessarily related to the solidification process, are not well understood. In absence of a better conception of the solidification process, it seems hardly surprising that mold design varies widely. Guiding principles for mold design are needed. At stake in the improvement of ingot quality are not only improved properties of steel but also appreciably higher yields of sound steel, which would considerably decrease manufacturing costs. In the present study, following a general description of the several types of segregation in ingots, Fig. 1, complete solidification patterns of a big-endup and a big-end-down ingot, including the zones of accelerated solidification, have been reconstructed. In both ingots, a core of vertical solidification extends from the base cone to the hot-top junction. Based on the finding that ingots complete solidification vertically rather than transversely, as has been previously assumed, new mechanisms for segregation in ingots are proposed. Internal soundness in ingots is found to depend upon the width of the vertical core, which in turn depends principally upon the width to height (w/h) ratio of the ingot. Solidification patterns of ingots are of three general types: 1—those in which vertical solidification does not reach the top, 2—those in which vertical solidification just reaches the top of the ingot, and 3—those in which vertical solidification reaches the top some time before transverse solidification would reach the middle of the ingot, so that a vertical core of definite width at the top of the ingot is developed. Axial defects vary characteristically with the solidification pattern. Examples of ingots of each type are presented. Dumped ingot data reported by Nelson' have been used in developing families of curves of transverse and vertical solidification, and in deriving the effect of the w/h ratio upon the solidification pattern. Photographs of many ingots split at Homestead and at Duquesne Works, United States Steel CO., as well as those published by the British Iron and Steel Institute,' have been studied and analyzed. In the interest of brevity, only typical ingots of each type or classification from the above sources have been reproduced. Segregation in Ingots Segregation in ingots falls into three principal classifications: 1—lamellar segregation, as revealed in sulphur prints (Figs. 2 and 3); 2—zone segregation, or broad variations in composition; and 3— interdendritic, or microsegregation. The last class, of minor importance, is not considered here. When liquid metal cools, according to the theory of differential or selective solidification,2 metal of relatively high purity selectively solidifies first. Liquid segregates (principally carbon, phosphorus,

Jan 1, 1954

By J. G. Richardson, K. H. Coats

During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and high rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leuerett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas. INTRODUCTION In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of the gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating — for given aquifer characteristics and fluid properties — the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formula1 and Buckley-Leverett2 method have some applicability to the problem; Woods and comer3 reported one-dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer.4 Douglas, Peaceman and Rachford5 presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek,6 Blair and peaceman7 and Goddin.8 Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here. One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques might reasonably be applied. However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability, porosity, reservoir thickness and dip angle.

By P. R. Kalischer

IN the production of alloys by powder metallurgical processes it is often necessary or desirable to include one or more components that tend to form very stable oxides Included in this group of metals are aluminum, manganese, magnesium, silicon, and a few others In many cases it is not necessary for the sintered compact to have full density and the other physical characteristics of a cast alloy and in that event no undue precautions need be taken If, however, it s required that the sintered part be entirely homogeneous, and have maximum density and physical properties, some method must be found to reduce the surface films of oxide, which are always present on the metals, and for the metals mentioned above this is always extremely difficult, if not impossible Since the production of high-density alloys is of particular interest to powder metallurgists, some experiments were undertaken to devise methods of reducing the refractory oxides For this work, alloys of iron, nickel, and aluminum were chosen because aluminum oxide is one of the most stable oxides and because these alloys in the right compositions form excellent permanent magnets All of the pertinent properties of the magnets could be accurately and delicately measured by density measurements and magnetic tests of sufficient scope to give a complete demagnetization curve From such a curve the maximum coercive force, residual magnetism, and energy products could be obtained and compared with the same properties for a cast material Any lack of homogeneity, density, or solid diffusion would be immediately apparent as a decrease in the magnetic properties NATURE AND REMOVAL OF SURFACE BARRIERS The early work of the present investigation was based upon published processes In the published information it was claimed that by intimately mixing iron, nickel, and iron-aluminum alloy (50 per cent Fe, 50 per cent Al) powders, compressing such a mixture into the desired shape and size, and then sintering (heating to a temperature below the melting point of the component metals) in hydrogen at 1200ºC or higher, a sound, homogeneous article could be made having the desired physical size, shape, and strength, and good magnetic characteristics However, this early work showed clearly that something in the powder compress was inhibiting diffusion and the process was almost entirely unworkable In the initial phase of the investigation samples of iron powder, nickel powder, and iron-aluminum alloy powder were pressed into separate bars and sintered in hydrogen Both the iron and nickel powders sintered

Jan 1, 1941

By E. S. Davenport

WHEN annealed carbon, or low-alloy, steels are suitably heated the ferrite (alpha iron solid solution) and the carbide, of which they are composed, react together to form a single solid solution of carbon (and other elements) in gamma iron (austenite). This reaction may begin only at a certain minimum temperature called the eutectoid temperature. The first ferrite and carbide thus to react together do so in definite proportions known as the eutectoid composition. With further heating the original constituent that is present in excess is dissolved in the austenite until exhausted. Whether the excess constituent be ferrite (hypoeutectoid steels) or carbide (hypereutectoid steels) the procedure is much the same, and upon slow cooling the homogeneous austenite expels the excess of either (proeutectoid ferrite or carbide) until the eutectoid composition is reached. Thus the reaction upon heating is strictly reversed upon cooling and accordingly an equilibrium diagram of this process may be constructed. Such an equilibrium diagram concerns itself only with the tempera¬tures involved and with the proportions and compositions of the phases developed under conditions that suffice to permit equilibrium. Specifically it has no concern for the type or mode of distribution of these constituents nor with any extra-equilibrium conditions such as undercooling, which is almost universally encountered in metals. Actually, however, of great importance is the sluggishness toward equilibration caused by the not inconsiderable time involved in diffusion. Thus instead of the theoretical transformation point AE, we find for a certain rate of heating or cooling the use of the designations Ar and Ac (transformation temperature found on cooling and upon heating). These figures obviously have no particular meaning except as measured and expressed for a definite heating or cooling rate, and represent the apparent temperature displacement caused by an inadequate time allowance. In this paper are presented the results of a study of the time required for' the transformation of austenite to ferrite and carbide at a variety of temperatures and also of the time required for the reaction austenite ?martensite at the temperatures at which this reaction occurs instead of

Jan 1, 1930

By V. Koump, R. H. Tien, W. J. Kim

This paper presents an approximate solution of the problem of freezing of a binary alloy. he alloy is in the form of a one-dimensional slab of finite thickness. The surface temperature of the slab is assumed to be constant and lower than the solidus (or eutectic) temperature. The densities of the liquid and the solid are assumed to be equal. For a given binary alloy system, initial concentration of solute and surface temperature, the solution yields a) the temperature distribution in the solid skin, b) the temperature, concentration, and solid fraction distribution within the solid-liquid region, and c) the positions of the liquidus and the solidus (or eutectic) fronts as a function of time. The results of calculation for Fe-C and Fe-P systems are presented. In this investigation we are considering the problem of solidification of a binary alloy. The alloy is in the form of a one-dimensional slab of finite thickness. The molten alloy is initially at liquidus temperature. At time zero the surface of the slab is reduced to a temperature T, < Te,, where Te, is the solidus (or eutectic) temperature and T, is a constant. The densities of solid and liquid alloys are assumed to be equal and independent of temperature and composition. A qualitative picture of solidification of an alloy, under these conditions, is illustrated in Fig. 1. During the initial stage of solidification, before liquidus front reaches the center of the slab, freezing proceeds by propagation of two isothermal fronts, the liquidus front and the solidus (or eutectic) front. The fraction of solid at the liquidus front is zero; the fraction of solid at the solidus front is unity, The solid fraction and the temperature distribution between the two fronts and the width of the solid-liquid region change with time. During the later stage of freezing, after the liquidus front reaches the center of the slab, the liquidus front disappears. The solid fraction and the temperature at the center of the slab, as well as throughout the solid-liquid region, are now changing with time. The solidification is completed when the fraction of solid at the center of the slab reaches unity. In solution of this problem we seek to determine a) the temperature distribution in the solid, b) temperature, concentration,

Jan 1, 1968