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By B. M. Larsen, L. S. Darken

SOME years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general. our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2-by a high concentration of active (or "free") lime and of manganese oxide dis) solved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. DISTRIBUTION OF MANGANESE BETWEEN SLAG AND METAL AT EQUILIBRIUM On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction [FeO + Mn ;7± MnO + Fe [A] slag metal slag metal] the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as [K" aFPI OFeO ? aMn] where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term aFe may he combined with K" to give a new constant K'. Making these changes.

Jan 1, 1942

By C Macquarie, Maurice Cook

Normally the grain size of cold-rolled and annealed copper sheet is of the order of 0.02 to 0.06 mm., and 0.1 mm., for example, would, for many purposes, be regarded as undesirably large. The occurrence of very large grain sizes in a few isolated cases of copper sheet led the authors to inquire into the causes giving rise to such unusual results. During the course of this work a very large number of experiments have been carried out to determine the effect of varying the conditions of the final and penultimate rolling and annealing operations, as well as of earlier rolling and annealing treatments. A correspondingly large number of observations have been made, but within the space of one paper it is possible only to outline relatively briefly what appear to be the more important of these experiments and observations. The presentation of the results does not follow chronologically the order in which the experiments were carried out and they have been rearranged for the sake of simplicity. In recent years a considerable amount of work has been done in connection with the recrystallization and grain growth in metals arid alloy. that take place on annealing, and a number of generalizations have beell reached. It is known that the crystal size in wrought material in the annealed condition depends on a number of factors, including the time and temperature of the annealing operations and the nature and amount of cold-work to which the material has been subjected. Results. however that are not covered by these generalizations can be obtained, which, in some instances, may even appear to be contradictory to them. Xccortling to these generalizations gradual changes in grain size are effected by progressive variation of the factors involved in annealing or cold-working. The work recorded in the present paper, however, relates to the development of grain sizes which are far beyond those normally encountered in ordinary annealing operations and far in excess of grain sizes which,

Jan 1, 1939

By H Pray, H. W. Russell, Paul D. MILLER

It is known that austenitic chromium-nickel steels that have free carbide in the grain boundaries are subject to intergranu-lar corrosion. It is difficult to detect such a susceptible condition in a fabricated article because present test methods require a sample section for examination and in most cases this is difficult to obtain. The question of the nature and prevention of intergranular corrosion in austenitic stainless steels has been ably discussed by Bain and co-workers1-3 and by other investigator4-10 The present methods of study subject samples to corrosive conditions in such reagents as the Strauss solution, a mixture of copper sulphate and sulphuric acid. Such tests usually require at least 72 hr. to run. Various methods of measuring the degree of sensitization have been employed, such as the measurement of electrical resistivity, magnetic measuremerits, measurement of the degree of cracking produced on bending over a malldrel, and microscopic studies. The detection of carbides at the grain boundaries by metallographic polishing and etching methods is tedious and requires a skilled operator. A recent report on such methods of carbide detection is given by the American Society for Testing Materials Subcommittee VI of Committee A.-1011 and by Arness.12 The present investigation was undertaken to develop a simple test procedure for detecting carbide precipitation or susceptibility to intergranular corrosion. The test is designed for use in the plant and for the testing of fabricated structures. Carbide precipitation, the factor leading to susceptibility to corrosion, is produced by heating the alloy in the temperature range 800° to 1600°F., as in welding, in improper annealing or in service where such temperatures are met. The connection between such precipitation and susceptibility to corrosion has been thoroughly discussed, as has been the use of stabilizing addition elements to prevent precipitation. Experimental Method A small area of the steel under test is subjected to an anodic treatment in a cell that can be 'lamped Onto a a Or an actual structure. The cell and electrical circuit used are illustrated in Fig. I. The cell C is lead, joined to the steel plate D and insulated from it by a short piece of rubber tubing E. The cell is forced tightly against the steel plate by a spring Or clamping device. The seal formed by the rubber against the steel plate is sufficient to retain the liquid bath inside the cell. The spot treated can be made any shape desired, depending on the shape of the rubber gasket. The cell illustrated polishes a circular spot about 3/8- diameter' The bath consists of 60 per cent (by weight) sulphuric acid to which is added 5 ml. per liter of Glycyrrhiza extract (U.S.P.). The cell requires about 2 to 2.5

Jan 1, 1941

By Leslie W. Austen

ROTARY kiln operators will agree that some of the most severe conditions a refractory must stand occur in the hot zone of a kiln burning Portland cement, dead burn dolomite, magnesite, peri-clase, and similar materials. Frequently the operator is faced with factors beyond his control which drastically shorten the life of refractories. Shutdown due to mechanical failure can be serious if the period is of sufficiently long duration to cause the dropping of coating or the loosening of the lining. A change in slurry can affect the coating and cause ring buildup. A change in type of fuel and its effect upon the flame can cause a shift in location of the hottest zone. Weekend shutdowns or any other interruption can cause the operator trouble and may damage the refractories, since stopping and starting a rotary kiln is certainly more difficult than stopping and starting a motor. Some operators have tried to set an estimate of damage for each shutdown in equivalent days of running time. Conditions affecting the refractory may be roughly grouped in four classes: chemical attack, mechanical stress, thermal shock, and abrasion. Chemical Attack: The drive to obtain maximum production through a kiln demands maximum operating temperatures, temperatures which are limited more by the ringing up or melting of the clinker. This can cause interface temperatures at the junction of coating and refractory which require the use of a basic kiln block to withstand the chemical attack. Chemical changes take place within the refractory itself, especially in chemically bonded or unburned kiln blocks. These changes cause the formation of the ceramic or burned bond. Migrating liquids or fluxes from the kiln charge have an effect within the refractory and lead to mineral or glass formation. The alkalies, sodium and potassium, migrate into the refractory as silicates, chlorides, sulphates or other salts. They may move under capillary action or may be caused to move by volatilization with condensation in the cooler portion. Mechanical Stress: Concentrated stress may be caused by several factors or combinations thereof. I—The rings of refractories must be kept tight and rigid within the kiln, and this alone demands considerable force to hold the blocks in place. So that the force will not be concentrated, the blocks should fit the circle as perfectly as possible, with the faces in contact overall. 2—As the kiln is heated, thermal expansion takes place at the hot end of the kiln block. Since this disturbs the plane face it too can cause a concentrated stress at the two ends of the block, and shearing stress can be set up within the brick itself because of the difference in expansion between the two ends. 3—If a lining becomes loose and moves in the shell very severe stress can be set up, and as the kiln rotates this load changes and gives the effect of repeated loading. Permanent expansion of the refractory can also cause severe loading. 4—Not least important, flexing of the kiln is frequently the cause of concentrated stresses. Thermal Shock: Thermal shock, the result of heating and cooling too rapidly, occurs on starting and stopping or when a large patch of coating drops, exposing the bricks. Again, its destructive effect is often the result of phase change, liquid to solid or the reverse; dense refractories loaded with glass-forming impurities are particularly susceptible. Thermal shock is a. problem with refractories set in the wall or roof of a stationary furnace, and becomes even more serious in a rotary kiln, the tendency to spa11 being magnified with movement and concentration of stress. Uniform rate of feed and loading insures both better coating and a more uniform stress. Abrasion: If the refractories do not take a coating, abrasion can become a most destructive factor. Movement of the lining in shell or movement of loose blocks causes abrasion, which is also most destructive if the refractories do not take a coating. An analysis of the problem of basic lining for the hot zone reveals, therefore, a number of desirable characteristics: high refractoriness, basic chemical reaction, resistance to spalling, good strength at all stages, ability to take coating, true sizing, volume stability, and abrasion resistance. Increased demand

Jan 1, 1953

By P. B. Baxendell, R. Thomas

Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poett-mann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 BID in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 BID for 27/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of % 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approxirnately ± 10 per cent clown to flow rates as low as 300 B/D in 27/8-in. tubing. INTRODUCTION Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert,' but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results cliscouraging. In 1952 a paper was published by Poettmann and Carpenter' which proposed a new approach. Their method was also based on an energy-balance equation. but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional 1osses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields" This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was 1 set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather 1imited data derived from low-rate observations in 23/8- and 27/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist—due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus. it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La. Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen. To obtain full pressure gradients, a special tubing string was installed which was equipped with electronic surface-recording pressure measuring devices,

ARTICLE I Name and Object Sec. 1. This Division shall be known as the Institute of Metals Division of the American Institute of Mining and Metallurgical Engineers. Sec. 2. The object of the Division shall be to furnish a medium of cooperation between those interested in the field of physical metallurgy; that is, the nature, structure, alloying, fabrication, heat treatment, properties and uses of metals; to represent the AIME insofar as physical metallurgy is concerned, within the rights given in AIME Bylaw, Article XI, Sec. 2, and not inconsistent with the Constitution and Bylaws of the AIME; to hold meetings for the discussion of physical metallurgy; to stimulate the writing, publication, presentation and discussion of papers of high quality on physical metallurgy; to accept or reject papers for presentation before meetings of the Division. ARTICLE II Members Sec. 1. Any member of the AIME of any class and in good standing may become a member of this Division upon registering in writing a desire to do so, but without additional dues. Sec. 2. Any member not in good standing in the AIME shall forfeit his privileges in the Division. ARTICLE III Funds Sec. 1. The expenditure of the funds received by the Division shall be authorized by the Executive Committee of the Division. ARTICLE IV Meetings Sec. 1. The Division shall meet at the same time and place as the annual meeting of the AIME, and at such other times and places as may be determined by the Executive Committee subject to the approval of the Board of Directors of the AIME. Sec. 2. The annual business meeting shall be held within a few days before or after the annual business meeting of the AIME. Sec. 3. At a meeting of the Division, for which notice has been sent to the members of the Division through the regular mail or by publication in the Journal of Metals at least one month in advance, a business meeting may be convened by order of the Executive Committee and any routine business transacted not inconsistent with these Bylaws or with the Constitution or Bylaws of the AIME. Sec. 4. For the transaction of business, the presence of a quorum of not less than 25 members of the Division shall be necessary. ARTICLE V Officers and Government Sec. 1. The officers of the Division shall consist of a Chairman, a Senior Vice-Chairman, a Vice-Chair -man, a Secretary and a Treasurer. The office of Secretary and Treasurer may be combined in one person, if desired by the Executive Committee. Sec. 2. The government of the affairs of the Division shall rest in an Executive Committee, insofar as is consistent with the Bylaws of the Division and the Constitution and Bylaws of the AIME. Sec. 3. The Executive Committee shall consist of the Chairman, Senior Vice-Chairman, Vice-Chairman, past Chairman, Secretary, and nine members, all of whom shall be nominated and elected as provided hereafter in Article VII. Sec. 4. The Chairman, Senior Vice-Chairman and Vice-Chairman shall serve for one year each, or until their successors are elected. Each member of the Executive Committee shall serve three years. The Chairman shall remain a voting member of the Executive Committee for one year after his term as Chairman. Sec. 5. The Treasurer of the Division shall be invited to meet with the Executive Committee, but without ex-officio right to vote. He shall be appointed annually by the Executive Committee, from the membership of the Executive Committee or otherwise. Sec. 6. The annual term of office for officers of the Division shall start at the close of the Annual Meeting of the Institute and shall terminate at the close of the next Annual Meeting. ARTICLE VI Committees Sec. 1. There shall be standing committees as follows: Programs Committee. Finance Committee, Membership Committee, Annual Lecture Committee, Technical Publications Committee, Mathewson Gold Medal Committee, Nominating Committee, Education Committee and such other Committees as the Executive Committee may authorize. Sec. 2. It shall be the duty of the Programs Committee to secure the presentation of papers of appropriate character at meetings of the Division. Sec. 3. It shall be the duty of the Finance Committee to inquire into and examine the financial condition of the Division and to consider proper means of increasing its revenue and limiting its expenses. The Finance Committee shall audit the accounts of the Division and report to the Executive Committee prior to the Annual Meeting of the Division. It shall render a budget to the Executive Committee estimating receipts and expenses for the ensuing year so that action can be taken on same at the first meeting following the Annual Meeting.

Jan 1, 1953

By D. H. Forbes, I. B. Cadoff, H. M. Manasevit

Single-crystal silicon films have been obtained on several natural crystal faces of BeO using the thermal decomposition of silane and the hydrogen reduction of silicon tetrachloride. From an analysis of X-ray diffraction data it was determined that the following film-substrate orientation relationships exist: (111) Si 11(0001) BeO, (111) Si 11(1011) BeO, (100) Si 11f1010) BeO. and (110) Si 11(1010) BeO. An analysis of the crystallographic relationships between the film and substrate indicates that a match occurs between the silicon atoms in the film and the berylliuni ion sites in the substrate. This correspondence is in agreement with previous work on the deposition of silicon on sapphire.1-3 silicon on spinel: and tungsten on sapphire. The high resistivity, thermal conductivity, and radiation resistance of beryllium oxide make it an important substrate material for the deposition of thin films of silicon or other semiconductors. The importance of semiconductor-insulator composites to the field of integrated microelectronics has been well-documented in the case of silicon on sapphire.'-' The successful growth of large-area single-crystal silicon on an insulator, sapphire, was first reported in 1963.1,2 Since that time studies have been made of the crystallographic relationships between the deposited film and the sapphire substrate. On the basis of the observed relationships, a model has been proposed relative to the crystallographic requirements for epitaxy between the semiconductor film and the metal oxide substrate.3 It is proposed in this model that epitaxy is the result of a match between atoms of the deposited film and the metal ion sites of the substrate plane. This match is not limited to a 1 to 1 correspondence between sites in the two lattices. Sub- sequent studies of the deposition of silicon on spinel4 and tungsten on sapphire5 have yielded data which support this model. On the basis of this previous work it was felt that silicon on BeO should also fit this model. In the present study, the choice of substrate orientation was limited to the natural faces of synthetic BeO crystals. Of the faces available, the (0001) plane seemed the most favorable for epitaxial growth. EXPERIMENTAL PROCEDURE Silicon films were deposited from silane and silicon tetrachloride in the apparatus shown in Fig. 1. The hydrogen ambient gas was purified by passage either through a DEOXO unit, molecular sieves, and a liquid nitrogen cold trap, or through a heated Pd-Ag thimble. The gas was then mixed with the silicon source materiai and passed over the substrate which lies on a spacer above an inductively heated silicon pedestal. The following deposition conditions were used: a hydrogen flow rate of 3 liters per min with silane and silicon tetrachloride concentrations of 0.2 mole pct and a pedestal temperature of 1175" * 5°C as observed with an optical pyrometer assuming an emissivity of 1.0. Deposition was preceded by a 15- to 30-min hydrogen-etch period conducted at a temperature of 1275°C (obs). Adherent silicon films from 2 to 10 u were grown on the various BeO faces. The substrates were synthetically grown beryllium oxide single crystals ranging from 5 to 10 mm in

Jan 1, 1967

By Arnulf Muan, Hobart M. Kraner

Ferromanganese alloys react with aluminu-silica brick in blast furnace hearths and cause the formation of new phases with low refractoriness and consequent failure of the refractory lining. The nature of these reactions is explained on the basis of petrographic observations, thermodynamic data, and Phase equilibrium considerations. Animproued hearth design resulted from these findings. The production of ferromanganese in blast furnaces presents many problems which are not encountered in the production of iron in the same furnaces. One of the most serious of these problems is the rapid failure of refractories caused by their reaction with the ferromanganese metal. The present paper describes such a "hearth attack", its symptoms, causes, and cure. Following an introductory discussion of operating practice in ferromanganese blast furnaces, results are presented of a petrographic examination of samples from a furnace which had to be shut down because of refractory failure. The causes of this failure are then analyzed on the basis of petrographic observations combined with thermodynamic and phase equilibrium data available in the literature. The latter type of data were subsequently used as a guide in recommending improvements in hearth designs which have since proven themselves successful in practical operations. I) FERROMANGANESE BLAST FURNACE PRACTICE It is considered good practice to blow in a furnace on iron and operate it in this way for a period of time preliminary to producing ferrornanganese. During this time, iron generally penetrates the bottom refractories six or more feet below the original working surface of the hearth. Not only does this metal pervade the joints to these depths, but the pores of the refractories are usually also filled by molten iron. The high throughput of the iron furnace provides ample heat to maintain a high temperature in the hearth refractories. This, together with a high ferrostatic pressure, causes porous clay brick of the hearth to shrink. During subsequent use of such a furnace in ferromanganese production, the iron in the pores of hearth brick if; replaced to some extent by ferromanganese. The replacement is usually not complete. This is probably due to the lower metal throughput and lower prevailing temperatures resulting from this in the brick of the hearth bottom. When the ferrornanganese furnace is banked—or when the temperature in the furnace falls due to a furnace delay—-manganese oxidizes even though the atmosphere is largely CO. Considerable expansion accompanies this oxidation of manganese from metal to oxide. The hearth refractories are then subjected to the disintegrating forces of the volume expansion. These forces may in extreme cases be large enough to lift the furnace off its mantle supports as was described in a previous paper.' When cooling takes place slowly, however, and the temperature remains at a fairly high level, the refractories undergo fluxing action by the MnO. This latter reaction and the reduction of SiO2 of the clay brick is the general subject of the present paper. The observations to be described herein were made on a ferromanganese furnace located at the Johnstown plant of Bethlehem Steel Co. The furnace was lined entirely with clay refractories and had operated on iron for 266 days and on ferromanganese for 96 days prior to being taken off because of a hearth wall failure. II) PETROGRAPHIC EXAMINATION AND CHEMICAL ANALYSIS The photograph reproduced in Fig. 1 shws a cross section of the upper part of an 18 by 9 by 4-1/2 in. bottom block removed from the blast furnace. This brick came from a depth of approximately 6 ft below the original working face of the bottom. It will be noted that the 4-1/2 in. dimension is almost the same as when the brick entered the furnace. Three characteristically different zones marked I, II, and III on the print of Fig. 1 are apparent. Results of chemical analyses of the original brick and samples from each of these zones are listed in Table I. Petrographically the various zones were characterized as follows: The central zone marked I was essentially un-reacted brick. The microstructure consisted of fine needles of mullite, and the pores in this entire area were filled with iron. This is characteristic of

Jan 1, 1962

By F. W. Jessen, John C. Miller

In many areas where carbonate rocks form important parts of the stratigraphic sequence, stratigraphers have experienced varying degrees of difficulty in differentiating and correlating limestone and dolomite units in both surface and subsurface work. With early Paleozoic rocks of the Mid-Continent, insoluble residues yield a remarkable amount of strati-graphic data and relatively good correlations may be carried over broad distances.' Unfortunately, neither such information nor electric logs and radioactive logs have been particularly helpful in interpreting the limestone sections of the Permian Basin of West Texas. This is because: (1) the variations in the sections may be very slight; (2) no completely satisfactory method of interpretation has been developed; and (3) the measurements themselves are not sensitive enough for small variations. Also, such logs are influenced by the fluid content. Paleontology and micro-paleontology remain the ultimate arbiters. As a routine tool, however, paleontol-ogical examination is slow and tedious. Chemical analysis may be used, but this, too, is extremely slow. Although rocks are not classified according to chemical composition, there is considerable variation with rock types. Correlation by chemical composition has two advantages, first, the characteristics determined are subject to minimum human error and interpretation, and secondly, the lithologic changes are not masked by fluid content as in the case of electric and radioactive logs. Some fossils concentrate certain elements which tentatively might be used to date rock units.' Rapid chemical analysis by spec-trographic means could be used as an adjunct to other means employed in correlation work, or might, in itself, present a suitable method. PURPOSE OF THIS INVESTIGATION Sloss and Cooke' have published data concerning spectrographic analysis of limestone rocks specifically for purposes of direct correlation of a single formation. These authors found satisfactory evidence that differences in percentage of four elements (Mg, Fe, Al, and Sr) in the Mississippian limestones of northern Montana were useful in carrying out correlation of this formation over a distance of approximately 50 miles. It was concluded from the preliminary work that the spectrochemical method offered possibilities of solution of some problems of correlation heretofore not possible. Since the work of Sloss and Cooke' was confined to one particular limestone zone, extension of the use of the method to examine two or more geologic formations would aid materially in the over-all problem of correlation of such rocks. Equipment is now available commercially with which very rapid spectrographic analyses may be made, and hence the problem was to determine whether the variations existing in the minor constituents of limestones were sufficient for use in possible correlation. Qualitative and semi-quantitative investigations were made to determine whether significant changes in the chemical condition occurred. It was a further purpose to investigate the geologic time-boundaries to see whether significant chemical variation could be found corresponding to the paleontological breaks. It was desirable to attempt correlation of a thick section of limestone or dolomite rock and to have as much information as possible on the section. Furthermore, it was felt that examination of formations more difficult to correlate by other means would enhance the value of the method should definite points of correlation be found. Samples were chosen from the Chapman-McFarlin Cogdell No. 25 well in the Cogdell field, Kent County, Tex., and from the General Crude Oil Co., Coleman No. 193-2 well in the Salt Creek field, Kent County, Tex. These fields belong to the famous series of "Canyon" reef fields of West Texas. Cores from the above wells were available from the United States Geological Survey, Austin, Tex. THE SPECTROGRAPHIC METHOD The choice of procedure to be followed in this investigation was based on the anticipated requirements peculiar to the problem. Since the problem was primarily to investigate the possibilities of applying the spec-trograph to problems of correlation in thick carbonate sections, a precise quantitative analysis did not appear necessary. A qualitative analysis to show the possible absence of presence of any element, or a semi-quantitative analysis of the elements present to show the relative changes in magnitude of selected elements was required. Both types of analysis were employed. The two most widely applied methods of semi-quantitative estimates are those of Harvey and of Slavin4,5 though various other procedures have been described.6 while the Harvey method has been modified by Addink,7 this refinement did not seem necessary to the present problem. Essentially, the procedure employed is a variation of the total energy method of Slavin with two exceptions: (1) stressing matrix effect, and (2) using densitometer measurements. As measured by a densito-

Jan 1, 1956

By Z. Moser, W. Ptak

The experiments were carried out by the method of measuring the electromotive force of concentration cells having zinc as a reference electrode, the second electrode being the liquid alloy Zn-Sn-Cd-Pb. The electrolyte consisted of liquid chlorides and had zinc ions. The measurements were made for seventy -five alloys of different mole fractions within the temperature range of 714° to 877°K. The experimental results enabled the calculation of the activity of zinc in tested solutions. The activities of zinc were calculated by means of Krupkowski's formulas.3 In addition, the formulas for coefficients of activity of zinc, tin, cadmium. and lead as the function of composition and temperature were given. Activity of zinc was compared with the values obtained from experimental results, and good agreement has been observed. On this basis it can be stated that the theoretical formulas are suitable for determining the thermodynamic properties of liquid quaternary metal solutions. IN the metallurgical processes being carried out at present multicomponent liquid metal solutions take part. For the thermodynamic analysis of these processes it is necessary to know the thermodynamic properties of these solutions. Therefore, many experimental and theoretical papers deal with this problem. The theoretical papers are generally based on the assumption that the structure of liquid metals is similar to their structure in the solid state. In this manner the model of liquid solution, consequently described by means of statistical thermodynamics, has been accepted. This method is being lately developed, especially for solid solutions. Statistical thermodynamics was applied among others by Guggenheim 1 for describing the thermodynamic properties. Unfortunately, the formulas of statistical thermodynamics are often not suitable for the interpretation of experimental results. Attention should be drawn to the relations obtained by means of formulas of phenomenological thermodynamics which always have constants derived with the aid of experimental methods. In the case of the multi-component solutions which contain some additions of impurities besides the basic metal, wagner2 introduced interaction parameters. Equations for the relationship between the activity coefficients and composition were also given by Krupkowski." he application of these formulas requires a good knowledge of the thermodynamic properties of the corresponding binary systems. In these formulas, as in Wagner's, there appear constants which should be determined from ex- perimental data. Nowadays, different experimental methods are applied for evaluating the thermodynamic functions of solutions, for instance: vapor pressure measurements, calorimetric methods, and the measurements of electromotive force of concentration cells. In the present paper this last method for evaluating the thermodynamic properties of four-component systems, Zn-Sn-Cd-Pb, was applied. For instance in the case of Zn-Sn solutions Alabyshev and Landratov, 4 Fiorani and Valenti, 5 and ptak6 performed the investigations. The Zn-Pb system was worked out by Kleppa 7 and Cd-Pb and Cd-Sn by Elliot and chipman.' This method was also applied for determining the activity of zinc in ternary solutions. 1) EXPERIMENTAL METHOD The experimental arrangement with detailed description is given in Fig. 1. It consists of resistance furnaces, one serving for melting samples and the other containing the flat-bottomed, measuring quartz tube with the liquid electrolyte. Liquid metals and alloys are in glass supremax tubes, which have an opening in their lower part above the metal level. This opening allows the filling of the tubes by the electrolyte. In these tubes tungsten wires are placed which by means of suitable conductors are connected with a potentiometer. It is assumed that tungsten dissolves Fig. 1—Schematic diagram of the experimental arrangement for the investigation of the thermodynamic properties of liquid metal solutions: 1, resistance furnaces; 2, autotransfor-mers; 3, galvanometers; 4, regulator of temperature; 5, gas purifier with concentrated H2SOP; 6, U-tube with P2O5; 7, thermostats; 8, steel block for thermostating; 9, supremax tubes for alloys; 10, tungsten electrodes; 11, inlet and outlet of argon; 12, measuring quartz tube; 13, tube for melting samples; 14, tube for thermocouple; 15, cover of quartz tube; 16, rubber seal; 17, bottom cover; 18, outlet of electrodes to potentiometer; 19, outlet of thermocouples to potentiometer; 20, upper view of the quartz tube cover; 21, orifices for cover screws; 22, orifice for argon inlet; 23, orifice for thermocouple; 24, orifices for tubes containing liquid metals; 25, inlet for water-cooling system.

Jan 1, 1969

By T. F. Mueller, P. A. Witherspoon

For the case of an infinite radial system operating at constant terminal rate, the reservoir engineer often uses the "point source" solution of the diffiusivity equation to study pressure interference effects. At early times and at short distances from the inner boundary these solutions are invalid. The amount of error is often not precisely defined because of mathematical difficulties. Work presented here shows that, if dimensionless time is defined appropriately, previous solutions of the pressure equation can be displayed .as a family of curves on one chart. These solutions include the point source solution (referred to in the field of hydrology as the Theis solution) and other solutions obtained with digital computer methods. With these curves, an exact evaluation of the pressure drop within a reservoir or an aquifer can be made by the engineer. Examples of field problem solutions are presented. In most reservoirs the error involved when the Theis solution is employed is often negligible; whereas, in the calculation of interference effects in an aquifer, a substantial error can occur through such an approach. INTRODUCTION Flow equations are used in petroleum engineering to study the behavior of individual wells and reservoirs. In the case of wells, the pressure response at the wellbore face is the major point of interest; whereas, in the case of reservoirs, the pressure response at the interface of the aquifer boundary is sought. To aid in such studies, the flow equations have been solved in terms of the behavior at these two inner boundaries. Only limited work has been published in regard to the pressure conditions away from these points, i.e., within the reservoir or aquifer. Theis and Mortada are among the few who have reported on this problem. The Theis approach employs the exponential integral and is valid for pressure conditions that occur some distance away from the flow disturbance. It is derived from the concept of a point source, as opposed to a flow across some finite area. The Mortada results, on the other hand, are valid at all points within the reservoir or aquifer. They are presented in terms of dimension less ratios of the radius where the pressure is desired to the radius where the flow rate is measured. Their main use, in the past, has been in aquifer studies. The published results are presented in the form of graphs that are limited to a maximum radius ratio of 64. These graphical results are cumbersome to interpolate at non-integral radius ratios, so that one may be forced to utilize a rather involved analytical expression presented by Mortada. BASIC EQUATIONS The solutions of Mortada and Theis are both based on the diffusivity equation as applied to the case of an infinite radial system subject to a constant terminal rate. The equation is obtained by combining the material balance equation with Darcy's flow equation. The assumptions implicit in the use of this equation are as follows: (1) a single fluid is present that occupies the entire pore volume; (2) the reservoir is horizontal, homogeneous, uniform in thickness, and of infinite radial extent; (3) compressibility and viscosity of the fluid remain constant at all pressures; and (4) fluid density obeys the equation Using the diffusivity equation in situations where the above conditions do not hold will result in errors. These errors (not discussed here) but only the errors which arise in the solution of the equation itself. The diffusivity equation for the homogeneous reservoir conditions cited above can be written in cylindrical coordinates, as To obtain a dimensionless equation, so a single solution can be used for applications of different porosity, permeability and fluid properties, the following transformations are usually made: After these transformations are made, Eq. 3 .can be written in dimensionless form, as MORTADA SOLUTION One solution of Eq. 6 has been given by Mortada.

Jan 1, 1966

By E. V. Kleber, V. F. Novy, R. C. Vickery

The constitutional diagram for the gadolinium-cobalt system has been determined. Seven intermetallic compounds have been found at compositions corresponding to the follwing gadolinium-cobalt ratios: 3:1, 1:1, 2:3, 1:2, 1:3, 1:4, 1:5. The GdCor compound has a congruent melting point above 1600°C. whereas the remaining compounds melt incongruently. Eutectics exist at 16 wt pct Co and 84 wt pct Co, with melting points of 620° and 1260°C, respectively. PREVIOUS papers'" have recorded constitutional data for systems of gadolinium with iron and nickel. This paper presents data obtained on alloys of gadolinium with the remaining 3d transition element-cobalt. voge13 found that cerium forms, with cobalt, the intermetallic compounds; Ce3Co, CeCo, CeCo2, CeCo3, CeCo4, and CeCo5 Other workers4-' found the 1:2 compound in this series to exist in a C-15 (face-centered cubic) structure and the 1:5 compound to exist in a hexagonal crystal system. Comparison of earlier data with that now reported will be made subsequently. EXPERIMENTAL Methods of alloy preparation, annealing procedures, and experimental techniques have been previously reported.' The cobalt content of alloy specimens was determined volumetrically. RESULTS Microstructure—The alloy containing 10.5 wt pct Co corresponds closely to the composition of the first intermetallic compound Gd3CO. In Fig. 1 the microstructure is essentially single phase composed of Gd3Co which formed peritectically. The globular areas are remnants of the peritectic reaction which did not quite go to completion. A eutectic occurs between Gd3Co and the next higher compound GdCO, which is followed by a series of peritectic compounds. Fig. 2, an arc-cast alloy containing 20.2 wt pct Co, shows large primary crystals of GdCo etching either white or black (depending on crystallographic orientation), embedded in the eutectic. Similarly, in Fig. 3 at 31.2 wt pct Co, a compound, probably GdCo3, has separated from the melt. Subsequent peritectic reactions were almost completely by-passed as the alloy cooled, the residual liquid freezing as a fine eutectic. In the 47.5 wt pct Co alloy, Fig. 4, the high melting point compound, GdCO4, has solidified as massive, white-etching grains, which reacted with the liquid to form GdCo3 as the second phase. The microstructure of an arc-melted alloy containing 60.5 pct Co is complex, Fig. 5, and presents some difficulty in interpretation. The grey etching matrix is probably primary GdCO4. The dappled phase represents grains of GdCO5 which have separated from the melt on cooling. The discrete spots in this phase are eutectic liquid. Small light etching crystallites are probably GdCO5 formed by the incomplete high-temperature peritectic reaction. GdCO4 is retained in arc-melted specimens containing 70.5 wt pct Co, Fig. 6. White areas of this compound are held in a matrix of GdCO5 the appearance of which is mottled slightly by inclusions of the second eutectic in this system. The development of the spheroidized eutectic at high cobalt contents is depicted in Fig. 7 (80.3 wt pct Co) in which the white massive crystals are GdCO5 compound. Further development of this eutectic is seen in Fig. 8, the primary white phase here being pure cobalt. Thermal Studies—Differential thermal analyses and melting point determinations have yielded the data shown in Fig. 10. The high gadolinium eutectic, indicated by microscopy, was confirmed at about 16 wt pct Co, melting at 620°C . A eutectic also occurs at about 84 wt pct Co melting at about 1260°C. The thermal arrests at 8803 960°, 1060; and 1210°C,

Jan 1, 1962

By Elmer Weber, W. M. Baldwin

Solid lead obeys a single parabolic weight increase vs. time law. In contrast, liquid lead undergoes three successive parabolic weight increases vs. time laws, the first of which has a low constant relative to the latter two. The conversion times for the change from one parabola to the next decrease with increasing temperature. IN recent reports on the subject,1,2 it was noted that zirconium and titanium scale in air by a complex mechanism. The scale first forming on the metal is protective to the extent that it gives a low constant, K, for Tammann's, and Pilling and Bedworth's parabolic equation: w² = Kt [1] relating weight increase, w, due to chemical reaction of the metal with the air, and time, t. After hundreds of hours of apparent stability in some cases the first scale yields to another that offers little protection to the metal. This transition from one scale to another, from a slow parabolic oxidation reaction to a fast one, was not due to impurities in the atmosphere or incidental effects (changing environment, etc.) but was a specific behavior of the metal itself, the transition occurring at definite times (dependent on temperature) and showing other reproducible traits. In view of this behavior how can long-time service behavior be predicted from short-time laboratory tests, not only in the case of these metals, but in any case? Certainly a systematic study of the type of scaling behavior described above—wherever it is found—would help to answer this question. The present paper is a report on the behavior as it is found in lead—the only metal to the authors' knowledge for which the behavior has been described at all, if inadequately, for our present purpose.* At least four oxides of lead are known, of which one occurs in two allotropic forms. They are ß (red) tetragonal PbO stable up to 486°C;8 a (yellow) orthorhombic PbO stable from 486°C up to its dissociation temperature in air at about 2300°C;9 minium or Pb3O4 which from the dissociation pressure data given in Fig. 1 decomposes to PbO at 540°C in air; lead sesquioxide or Pb2O3,; and lead dioxide or PbO2 which, according to Fig. 1, decomposes in air at 400°C to minium. In view of the high dissociation temperature of PbO, lead will scale up to at least its boiling point. Further, it is known that oxygen is almost insoluble in liquid lead.'V his implies a fair probability that an oxide scale would not dissolve in the molten metal and would afford the same protection to lead in the liquid state as in the solid. All of the oxides of lead for which specific gravity data are available are more voluminous than an equivalent weight of metal or a lower oxide from which they might form, hence the scales will be in compression. Lead oxides are known to be ductile, so it would be anticipated that they would form coherent nonporous scales. It is not surprising to learn, then, that both solid and liquid lead scale according to the Tammann, and Pilling and Bed-worth law.14,15 (Gruhl states that at 600°C and above lead oxidizes linearly with time because of "spitting" of the scale.) The parabolic constants K reported by various investigators3,14-16 are badly scattered, however, as shown in Fig. 2. The oxides formed on solid lead were described as being reddish-brown but were not chemically identified by Pilling and Bedworth.15 Gruhl's descripdin³ of the appearance of the scales On his liquid samples indicates that a (yellow orthorhombic) PbO is formed initially on the specimens but gives Way eventually—at least at temperatures below 486 °C— to .ß (red tetraunal) PbO, and that below 540°C minium—Pb3O4 :is firmed at an even later time as an overlay on either the red or yellow PbO. Fig. 3 is a graphical interpretation of Gruhl's description. Gruhl does not indicate any change in the parabolic scaling rate as yellow PbO converts to red. He does indicate that minium reduces the scaling rate, al-

Jan 1, 1953

By R. E. Cook

This work presents the development and application of equations of the form developed by Martin1 to describe gravity segregation performance during natural depletion. One-dimensional depletion analyses are applied to several hypothetical reservoirs. Considerable attention is given to the changes in saturation distribution in the dip direction resulting from depletion at various rates. Vertical gas saturation distribution within a sand having vertical permeability is studied to illustrate conditions which provide For low gus-oil ratio production from wells selectively completed away from sand tops, as observed from well performance. Results of performance calculations are shown graphically and illustrate the rate sensitivity of the gravity segregation mechanism and the influence of reservoir geometry and withdrawal distribution. It is shown that for sufficiently high depletion rates gas saturation distribution in the dip direction is characterized by the formation of two discontinuities, or saturation "fronts"; the updip front being the gas-oil contact of the secondary gas cap and the downdip front occurring at a position dependent upon the reservoir depletion rate, withdrawal distribution and reservoir geometry. The gas saturation in the region between fronts is shown to continually increase with time, while that downdip from the lower front remains very low and relatively stable. The effect of increased depletion rate is to reduce the region of stable gas saturation and thus enlarge the portion of the reservoir producing with continually increasing gas saturation. Special attention is given to the performance of reservoirs having sufficient vertical permeability to permit liberated gas to segregate vertically within the sand section before proceeding in the updip direction. It is shown that reservoirs of this type are far less sensitive to depletion rate due to the mechanical control of producing gas-oil ratios afforded by selective well completions away from sand tops. It is shown that gravity segregation performance is adversely af- fected by decreasing reservoir cross-section area in the updip direction. It is also shown that down-dip withdrawal concentrations can restrict gas segregation rates in the dip direction. INTRODUCTION The natural depletion performance of several large producing reservoirs in Western Venezuela has unmistakably shown the significant role that gravity forces play in governing the gas-oil ratio behavior of individual wells and the over - all pressure-production performance of the reservoirs. Analysis and prediction of the natural depletion performance of these reservoirs is of great importance in determining the economics of pressure maintenance operations. In 1957, a method for the analysis of pressure maintenance performance was presented by Martin1 which, in the original and more general form of the equations involved, provides a physically sound basis for the analysis of one-dimensional gravity segregation performance during natural depletion. The work reported herein is an application and extension of Martin's outstanding developments to a series of hypothetical reservoirs in an attempt to explain the general behavior of the gravity segregation mechanism and the influence of such parameters as depletion rate, reservoir geometry and withdrawal distribution. The study considers two types of flow: "distributed flow", where vertical permeability in the reservoir is zero and fluids flow only in the dip direction while uniformly distributed over the sand thickness; and "segregated flow", where vertical permeability is sufficient to permit gas to segregate against the sand top before proceeding updip. This latter type of flow has been recognized as an important mechanism active in the massive sand reservoirs of Western Venezuela. ANALYSIS OF ONE-DIMENSIONAL DISTRIBUTED FLOW SYSTEMS For an inclined reservoir having zero vertical permeability, the velocities of oil and gas flow at any point in the reservoir can be derived from Darcy's equations as

By R. Schuhmann, J. Th. Overbeek, P. L. De Bruyn

THE technique of concentrating valuable minerals from lean ores by flotation depends upon the creation of a finite contact angle at the three-phase contact, mineral-water-air. If the mineral is completely wetted by the water phase, contact angle zero, there is no tendency for air bubbles to attach themselves to the mineral. However, when the contact angle is finite, the surface free energy of the system, water-air bubble-mineral particle, can be diminished by contact between the bubble and the particle, and if not too heavy the mineral will be levitated in the froth. With a few exceptions, all clean minerals are completely wetted by pure water. Thus the art of flotation consists in adding substances to the water to make a finite contact angle with the mineral to be floated, but to leave the other minerals with a zero contact angle. The contact angle concept and experimental measurements of contact angles have played important roles in flotation research for several decades.'-" Nevertheless, there remain unanswered some basic questions as to the scientific significance of the contact angle and the nature of the processes by which flotation reagents affect contact angles. The contact angle is a complex quantity because the properties of three different phases, or rather of three different interfaces, control its magnitude. Considering the interfaces close to the region of ternary contact to be plane, the relation among the contact angle and the three binary interfacial tensions is easily derived. The condition for equilibrium among the three surface tensions, Fig. 1, or the requirement of minimum total surface free energy leads to Young's equation, Eq. I: ysa — ysl = yLA cos 0 [1] According to this equation, the contact angle has one well-defined value. Actually it is found in many experiments that the value of the contact angle depends on whether the air is replacing liquid over the solid (receding angle) or the liquid is replacing air (advancing angle). The receding angle is always the smaller of the two.4 Two explanations have been offered for this experimental fact. According to some investigators,5-8 roughness of the surface causes apparent contact angles that are different for the receding and the advancing cases although the actual local contact angle may be completely determined by Eq. 1. The other explanation involves the hypothesis that the solid-air interface after the liquid has just receded is different from the same interface when no liquid has previously covered it.1,4 Adsorption of constituents of the air or liquid might play a role here. In this discussion the difference between advancing and receding contact angle will be neglected and plane surfaces where Eq. 1 describes the situation will be considered. But there is still a fundamental obstacle to the application of Young's equation. The surface tension of the liquid (rla) can easily be determined, but the two surface tensions of the solid (rsa and ySL) cannot be measured directly. Eq. 1, however, is not without value. By contact angle measurements it is possible to establish how ysl — ysl varies with the addition of solutes to the liquid phase. Also, Eq. 1 affords a convenient starting point for calculating net forces and energy changes involved in the process of bubble-particle attachment.1,2 . If for the moment surface tension of the liquid (yLa) is considered a constant, an increase in ysa — ysL, will tend to decrease the contact angle. A decrease in ySA — ysl, corresponds to an increase of the contact angle. In cases where ySA — ySL > yLa the contact angle is zero; it will only reach finite values when ysa — ysa has been decreased below YLA. Thus on the basis of Young's equation and contact angle measurements alone, it can be learned how flotation reagents affect the difference Ysa — ysl, but no conclusions can be drawn as to the effects of reagents on the individual surface tensions ysa, and ysL, not even as to signs or directions of the surface tension changes resulting from reagent additions. A quantitative relationship between the surface tension or interfacial tension and the adsorption occurring at a surface or an interface is given by the Gibbs equation, which for constant temperature and pressure reads dy = — 2 T, du, [2] where dy is the infinitesimal change in surface tension accompanying a change in chemical potential

Jan 1, 1955

By G. W. Thomas

A mathematical tnodel of forward combustion in an oil reservoir is treated in this paper. The model describes a radial system having a vertical section of essentially infinite thickness, all of which is permeable to gas flow. Combustion, however, is presumed initiated over a limited thickness of the total vertical section. In the interval supporting cotnbustion, the mechanisms of radial conduction, convection and heat generation are taken into account. Above and below the burning interval, heat transport in the radial direction is by cottduction and convection. Vertical heat losses from the ignited interval are accounted for by conduction alone. A general solution is presented for the temperature distribution caused by radial movement of the combustion front. The results show that no feedback of heat occurs into the ignited interval when convection and conduction are acting in the bounding media. Peak temperatures are also 5 to 10 per cent higher than in the case where heat transport in the bounding media is by conduction alone. We arbitrarily define vertical coverage to be that fraction of the total ignited interval which is at 600F above atnbient, or greater, at any given time. The radial distance at which the vertical coverage becomes zero is the propagation range of the combustion front. It was found that an increase in vertical coverage results when the oxygen concentration, fuel concentration or gas-injection rate is increased. Moreover, the combustion front can be propagated 10 to 15 per cent further than in the case where only conduction is acting above and below the ignited interval. INTRODUCTION In the theoretical treatment of forward combustion in a radial system, one of the problems encountered is the determination of the transient temperature distributions caused by an expanding cylindrical heat source. Bailey and Larkin' and Ramey' simultaneously presented analytical solutions to the problem assuming heat transport by conduction alone. In a subsequent publication, Bailey and Larkin3 included the effects of both conduction and convection while treating linear and radial models. In this latter work, however, vertical heat losses were largely neglected. Selig and Couch' dealt with a radial model in which both conduction and convection were acting. Only a limiting case involving vertical heat losses was considered, however. Namely, temperatures on the boundary of the bed of interest were set equal to zero. Solutions thus obtained were representative of a system having a maximum vertical heat flux. Chu5 recently treated a more general case in which a permeable bed was considered bounded by impermeable media. Conduction and convection took place within the bed, and only conduction outside of the bed. The effects of vertical heat losses were included in his study. Solutions were obtained by numerical techniques. This paper is an extension of the theoretical work of other authors pertaining to forward combustion in a radial system. In particular, a mathematical model of the process is treated in which heat generation occurs over a small vertical interval of a larger permeable section. In the interval supporting heat generation, and above and below this interval, the mechanisms of radial conduction and convection are also presumed acting. Heat losses from the ignited interval are accounted for by vertical conduction. An analytical solution for the temperature distribution caused by radial movement of the burning front is presented. The effects of certain process variables are indicated and comparisons with Chu's results are made. THEORY To render the mechanism of forward combustion tractable to mathematical treatment, we idealize the problem to the extent of assuming continuous reservoir media possessing homogeneous and isotropic properties. The following additional assumptions are implicit in this analysis. 1. The thermal parameters, i.e., heat capacities, thermal conductivities and thermal diffusivities are invariant with temperature and pressure. Moreover, the bounding media possess the same thermal properties as the bed of interest. 2. The temperatures of the porous media and its contained fluids at any point and at any time are equal. 3. The reaction rate between the oxidant gas and the fuel is infinite. This assumption implies that the incoming oxygen concentration instantaneously goes to zero within an infinitesimal distance, i.e., the width of the combustion zone is negligible. 4. The rate of gas injection is constant and corresponds to the average rate throughout the lifetime of the project. 5. The fuel concentration is constant throughout the volume of rock swept out by the burning zone. 6. There is complete burnoff of fuel. This assumption demands that the rate of propagation of the burning front equals the rate of fuel burnoff. In a radial system, with a

By G. R. Speich

The precipitation of the Feab and Fe,Ti Laves phases (MgZn, type, C14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been studied in the temperature range 500" to 800°C using hardness measurements, light and electron microscopy, and X-ray and electron diffraction. The Fe-Nb alloys contained 0.96, 1.67, and 3.80 pct Nb and the Fe-Ti alloys 3.5, 5.8, and 8.8 pct Ti. In both systems only the equilibrium Laves phase is formed, with nucleation occurring at grain boundaries, at dislocations, and in the matrix. No cellular precipitation or transition phases were observed. The precipitation of the Laves phase in a fine dispersion leads to significant hardening in both systems. The hardness of the aged alloys is proportional to the reciprocal of the square root of the interparticle spacing. The maximum solid solubility of titanium in a! iron is 9.0 pct Ti at 1280°C. THE precipitation of the FezNb and FezTi Laves phases (MgZn2 type, C 14) from Fe-Nb and Fe-Ti solid solutions, respectively, has been investigated as part of a continuing study of the mechanisms of precipitation from ferritic binary iron-base alloys. The iron-rich portions of the Fe-Nb and Fe-Ti phase diagrams are shown in Fig. l(a) and l(b). The Fe-Nb diagram is essentially that given by ansen' with the more recent work of Hume-Rothery and Gibson2 added. Goldschmidt3 indicates that the FezNb Laves phase has a solubility extending from 32 to 55 wt pct Nb. The Fe-Ti diagram is also essentially that reported by Hansen.l The recent results of Nishimura and kamei, Murakami, Kimura, and Nishimura,' indicate that the FezTi Laves phase has a solubility extending from 22.5 to 30.5 wt pct Ti. The L/6 + FezTi eutectic temperature of 1298°C indicated by Kornilov and oriskina' has been adopted. The addition of niobium or titanium to iron lowers the 6 — y transformation temperature and raises the y — a! transformation temperature. This results in a closed y field in the Fe-Ti system, but the lower solubility of niobium in a! (6) iron results in a eutec-toid, 6 — y + FezNb, at 1200°C, and a peritectoid, y + FezNb —-a, at 989°C in the Fe-Nb system. The maximum solubility of niobium is reported to be 4.5 wt pct in 6 iron,' 1.0 wt pct in y iron,7 and 1.8 wt pct in a iron.' Some results from the present work indicate that the maximum solubility in a! iron is actually less than 0.96 wt pct Nb. The maximum solubility of titanium in a! (6) iron is somewhat uncertain since the early work of To faute and Butting-haus indicated a value of 6.0 wt pct while later work of Kornilov and Boriskina6 yielded a value of 14.0 wt pct. The present work indicates that the maximum solubility is actually 9.0 wt pct. In both systems the phase in equilibrium with the iron-base solid solutions is a Laves phase (Mg znztype, C14), FezNb or FezTi. Both of these Laves phases have a wide range of Solubility. The precipitation-hardening behavior of Fe-Nb or Fe-Ti alloys has not been studied extensively. Genders and Harrison' reported that binary Fe-Nb alloys hardened upon aging. Peter and Fisher7 studied the mechanical properties of Fe-Nb and Fe-Ti alloys quenched from different phase fields.

Jan 1, 1962

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By M. R. Geer, H. F. Yancey

THE performance of coal-washing equipment, that is, the effectiveness with which coal and impurity are separated, is a subject of undisputed interest to all concerned with the preparation of coal. Through the years much has been written in both American and European literature on the performance of coal-washing equipment and its interpretation, but until recently no effort has been made to consolidate this wealth of information into a single, comprehensive treatment of the subject. A splendid effort in this direction was made at the First International Conference on Coal Preparation held in Paris in June 1950 in which representatives from virtually every coal-producing country participated. Although the scope of the conference covered the entire field of coal preparation, many of the sixty-odd papers and a great deal of the discussion dealt with the subject of evaluating washery performance. Prominence was given this subject by the Centre d'Etudes et Re-cherches, des Charbonnages de France, which sponsored the conference. This research organization, generally referred to as Cerchar, was formed in 1948 following the nationalization of the French coal industry. Since that date it has conducted an intensive study of coal preparation. Perhaps because of a fresh viewpoint, Cerchar realized immediately that complete information on the performance of French washeries and a thorough understanding of the mechanism of gravity separation were the fundamental prerequisites in a program to improve preparation practice. For this reason Cerchar concentrated on obtaining performance data and on a comprehensive study of methods of evaluating such information. Some idea of the magnitude of this work will be appreciated from the fact that 175 performance tests were made in 44 plants. The work performed by Cerchar emphasized a condition that is recognized by many of those concerned with coal preparation, namely that the lack of uniformity in presenting data on washery performance, the diversity of methods used in evaluating such information, and the frequent confusion of the terms related to performance have been prime factors militating against the progress from art to science. Thus, Cerchar feels that standardization of the methods employed for evaluating washery performance, not only in France but in the entire world, is essential to progress, and the prime objective of the Paris conference was to seek international standardization of the evaluation methods advocated by Cerchar. At the conclusion of the conference the question of standardization was referred to the International Standards Organization. A careful study of the dozen papers on the subject of evaluating washery performance presented at the conference reveals that none of the methods is new; most of them date back over a decade. Nevertheless, the intensive scrutiny of these methods brought about by the conference unquestionably has resulted in a valuable exchange of ideas and a clarification of thought that could scarcely be achieved in any other way. The object of the present report is to make available to the American coal industry the ideas developed at the conference which seem most important from an American viewpoint and to provide a critical analysis of some of the evaluation methods advocated by Cerchar. The various methods of evaluating washery performance are illustrated partly with data that have been published in American literature, and some new data have been obtained as the result of experimental work undertaken since the conference to provide information on certain controversial points. An English translation of the proceedings of the conference, including the discussion as well as the papers, will be available,' and previous to the conference Coal Age2 published a very brief description of some of the principal evaluation methods used by Cerchar. Americans will appreciate as well as do the French the desirability of standardizing both the termi-

Jan 1, 1952

By F. E. Bash

CONSTANTAN is an alloy of copper and nickel that is extensively used, under a number of trade names, as a resistance wire with a low temperature coefficient of resistance, and one of the elements of base-metal thermocouples, iron usually being the other thermoelement, although for low-temperature work copper is also used. Before the war, constantan was imported, in common with many other technical necessities. Since it required considerable time to receive the constantan after it was ordered, fairly large stocks were kept on hand; but after the beginning of the war no more was imported acid the stocks of foreign material were exhausted about the same time that the steel and munition manufacturers began to need great quantities of it for thermocouples for the heat treatment of steel. To meet this demand, the International Nickel Co. began manufacturing constantan that met all the requirements of the users of resistance wire but did not give the same electromotive force against iron as the German material and consequently could not be used with instruments calibrated for a definite e.m.f.-temperature relation. It so happened that all the constantan made had an e.m.f. lower than that necessary to meet the specifications of the Leeds & Northrup Co. for whom this investigation was carried out. If some had been higher and some lower, good wire could have been obtained by a, process of selection, but as it was no wire at all could be procured. To remedy this situation, a thorough investigation was started with the close cooperation of the International Nickel Co. and the Electrical Alloys Co. The specifications to which the constantan had to conform were that it should give an e.m.f. of 47.40 millivolts. against pure iron at 1500° F. (816° C.) with the cold-junction temperature at 0° F., or a proportional e.m.f. at temperatures near 1500° F. The method of checking a wire was as follows: It was first welded to a piece of iron wire; Armco iron was found to be satisfactory but iron with greater than 0.1 per cent. carbon would give a lower e.m.f. against the same piece of constantan than pure

Jan 9, 1919