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FRED TURRELL GREENE Fred Turrell Greene was born in Brooklyn, N. Y., Nov. 22, 1872. His father, William A. Greene, was born in Providence, R. I., and his mother, Angenora Semlear, was born in Brooklyn, N. Y. Fred's early school clays were spent in Boston, whence his father moved to Canada in 1882. Attending first the Collegiate Institute in Toronto, .then the High School at Berlin (now Kitchener), Ontario, where he graduated, Fred progressed to the Toronto University and the Michigan College of Mines, at Houghton, where lie graduated in 1897. He secured employment almost immediately at Butte with the engineering force of the Boston & Montana Consolidated Silver Mining Co., under Chas. S. Batterman. In 1899 he went to Rossland, B. C., where he spent more than a year as mining engineer and assistant superintendent of the War Eagle Consolidated Mining and Development Co. and the Center Star Mining Company Ltd. Returning to Butte in 1900, he acted as assistant geologist for the Anaconda Copper Mining Co. until 1906, when he filled a similar position in St. Paul with the Great Northern Railway for about two years. From 1908 until his tragic death on Christmas day, 1917, his headquarters were in Butte, where he enjoyed an excellent reputation -as consulting mining engineer, with a rapidly widening circle of clients. During the past four years he had been consulting engineer for the Elm Orlu and other mines controlled by Hon. W. A. Clark, and was in charge of underground developments and law-suit preparations for the celebrated apex case between the Elm Orlu and the Butte & Superior companies. At the time of his death he was in charge of similar work for the Utah Metals Co., in connection with their mines at Bingham, Utah. He was also for some years active in the Coeur d'Alenes, as consulting geologist for the Federal and other companies there, and was considered an authority on this as well as the Butte district. Mr. Greene was unmarried, and is survived by his parents, a younger brother, who is in the army, and one sister, Mrs. James A. Hatch, of New York. Some of the most important and valuable ideas regarding the nature and origin of copper ores have originated in Butte, since that district is not only one of the greatest examples of mineralization known in any land, but has gone through a long course of mining litigation, and was, one of the first to be studied intensively by geologists. In connection with the early investigations, as well as with the most recent in that camp, Mr. Greene played an important part. His conscientious devotion to his duties and his intelligent handling of the problems presented for solution sufficiently explain the esteem in which he was held by his employers and his professional associates.

Jan 5, 1918

By Herbert Hoover, Harlod Washburn

This paper is in the nature of a rough preliminary report on the progress that has been made in the application of the mass spectrometer to various problems arising in the petroleum industry. A few years ago the authors considered a number of the problems that were arising in the qualitative and quantitative measurement of small amounts of hydrocarbons. The methods available of making analyses by chemical techniques appeared to leave much room for improvement. Without going into the reasons at this point, attention was turned to the possibility of employing physical instead of chemical methods of accomplishing the desired results. A preliminary investigation disclosed that the mass spectrometer presented a possibility of solving many problems which could not easily be accomplished by other methods. Work was begun in developing the necessary apparatus and technique. A great deal of encouragement and many valuable suggestions were received from Dr. Robert A. Millikan, Dr. W. R. Smythe, and Dr. W. N. Lacey, of the California Institute of Technology, and from Dr. E. 0. Lawrence, who recently received the Nobel Prize, of the University of California. The authors particularly wish to acknowledge the very great willingness of these outstanding scientists to be helpful in solving many of the problems that were involved. So far as the authors are aware, this was the first application of the mass spectrometer to commercial work. The results were considerably better than had at first been anticipated. Briefly, it is possible to run a qualitative and quantitative analysis of an unknown mixture of hydrocarbon gases, with an accuracy of better than plus or minus 5 per cent of each of the various constituents. An exceedingly high degree of sensitivity has been obtained, and a relatively short time is required to complete an analysis. Furthermore, it is unnecessary to separate a mixture of gases into its various components in order to complete the analysis. The Mass Spectrometer The mass spectrometer should not be confused in any way with the optical 01 grating type of spectrograph now in general use. The operation of the mass spectrometer is entirely different in principle and bears practically no resemblance to the optical or grating instruments. The original conception and development of the mass spectrometer dates from and is generally credited to Aston, of Cambridge, England. An early accomplishment of his research, about 20 years ago, was the discovery that the inert gas neon was actually a mixture of two kinds of atoms, one of the atomic weight 20 and the other of atomic weight 22. These two components occurred mixed in such proportion as to yield the usual atomic weight of 20.2. The study was continued and most of the elements were shown to be mixtures of components whose atomic weights can, to in

Jan 1, 1941

By W. I. Garms, J. L. Stevens

Because of the many conflicting opinions regarding the functioning of the ball load and the characteristics of ball wear in ball-mill grinding, the following résumé of reports covering recent tests conducted at the Hayden plant of the Kennecott Copper Corporation is submitted with the view of pointing out certain salient features that should throw additional light on the subject. Mills Used Cylindrical drum mills with trunnion feed and discharge were used. The discharge trunnion was 13½ in. in diameter. Dimensions inside the lining were 6 ft. 6 in. in diameter and 9 ft. 6 in. long. The mills were Britannia-lined and nine lifter bars projected 2 in. from the lining. The mill speed was 162/3 r.p.m. Feed to the mill was 9 per cent on 10-mesh, 85 per cent on 100-mesh, 77 per cent solids. New balls measured 2 in. in diameter and the approximate weight of the ball load was 40,000 pounds. Initial Test During a test that was being conducted to determine the relative economic value of standard cast balls vs. forged steel balls in the local 'grinding operation, certain observations were made in regard to the functioning of the various ball sizes and the characteristics of ball wear, which warranted a supplementary test for the purpose of confirming such observations. For the initial test, the necessity for developing a graduated load of the new forged balls before the test could be started was realized, but the time required to obtain a graduated load and the functioning of the various ball sizes was not clear. No advantage could be seen for starting out with a full load of forged balls, as this initial load, at the least, would have to be completely ground out and replaced by daily additions of balls before the graduation could be complete and a normal static condition of ball sizes reached. For a considerable period prior to exhaustion of this initial charge there would be an unusual quantity of worn balls of a certain size, which would not be typical of a normal charge and could influence the characteristics and functioning of the entire load. Therefore, it was decided to start by daily addition of the forged balls to a mill that contained a normal operating load of cast balls. After 88 days of operation the mill was shut down for inspection. By that time the load consisted of a mass of forged balls functioning around a large core of the residual material of the former cast-ball load. This core of cast slugs, locally referred to as "the kidney," was well defined from the forged-ball load.

Jan 1, 1947

By W. I. Garms, J. L. Stevens

Because of the many conflicting opinions regarding the functioning of the ball load and the characteristics of ball wear in ball-mill grinding, the following résumé of reports covering recent tests conducted at the Hayden plant of the Kennecott Copper Corporation is submitted with the view of pointing out certain salient features that should throw additional light on the subject. Mills Used Cylindrical drum mills with trunnion feed and discharge were used. The discharge trunnion was 13½ in. in diameter. Dimensions inside the lining were 6 ft. 6 in. in diameter and 9 ft. 6 in. long. The mills were Britannia-lined and nine lifter bars projected 2 in. from the lining. The mill speed was 162/3 r.p.m. Feed to the mill was 9 per cent on 10-mesh, 85 per cent on 100-mesh, 77 per cent solids. New balls measured 2 in. in diameter and the approximate weight of the ball load was 40,000 pounds. Initial Test During a test that was being conducted to determine the relative economic value of standard cast balls vs. forged steel balls in the local 'grinding operation, certain observations were made in regard to the functioning of the various ball sizes and the characteristics of ball wear, which warranted a supplementary test for the purpose of confirming such observations. For the initial test, the necessity for developing a graduated load of the new forged balls before the test could be started was realized, but the time required to obtain a graduated load and the functioning of the various ball sizes was not clear. No advantage could be seen for starting out with a full load of forged balls, as this initial load, at the least, would have to be completely ground out and replaced by daily additions of balls before the graduation could be complete and a normal static condition of ball sizes reached. For a considerable period prior to exhaustion of this initial charge there would be an unusual quantity of worn balls of a certain size, which would not be typical of a normal charge and could influence the characteristics and functioning of the entire load. Therefore, it was decided to start by daily addition of the forged balls to a mill that contained a normal operating load of cast balls. After 88 days of operation the mill was shut down for inspection. By that time the load consisted of a mass of forged balls functioning around a large core of the residual material of the former cast-ball load. This core of cast slugs, locally referred to as "the kidney," was well defined from the forged-ball load.

Jan 1, 1947

By Harlod Washburn, Herbert Hoover

This paper is in the nature of a rough preliminary report on the progress that has been made in the application of the mass spectrometer to various problems arising in the petroleum industry. A few years ago the authors considered a number of the problems that were arising in the qualitative and quantitative measurement of small amounts of hydrocarbons. The methods available of making analyses by chemical techniques appeared to leave much room for improvement. Without going into the reasons at this point, attention was turned to the possibility of employing physical instead of chemical methods of accomplishing the desired results. A preliminary investigation disclosed that the mass spectrometer presented a possibility of solving many problems which could not easily be accomplished by other methods. Work was begun in developing the necessary apparatus and technique. A great deal of encouragement and many valuable suggestions were received from Dr. Robert A. Millikan, Dr. W. R. Smythe, and Dr. W. N. Lacey, of the California Institute of Technology, and from Dr. E. 0. Lawrence, who recently received the Nobel Prize, of the University of California. The authors particularly wish to acknowledge the very great willingness of these outstanding scientists to be helpful in solving many of the problems that were involved. So far as the authors are aware, this was the first application of the mass spectrometer to commercial work. The results were considerably better than had at first been anticipated. Briefly, it is possible to run a qualitative and quantitative analysis of an unknown mixture of hydrocarbon gases, with an accuracy of better than plus or minus 5 per cent of each of the various constituents. An exceedingly high degree of sensitivity has been obtained, and a relatively short time is required to complete an analysis. Furthermore, it is unnecessary to separate a mixture of gases into its various components in order to complete the analysis. The Mass Spectrometer The mass spectrometer should not be confused in any way with the optical 01 grating type of spectrograph now in general use. The operation of the mass spectrometer is entirely different in principle and bears practically no resemblance to the optical or grating instruments. The original conception and development of the mass spectrometer dates from and is generally credited to Aston, of Cambridge, England. An early accomplishment of his research, about 20 years ago, was the discovery that the inert gas neon was actually a mixture of two kinds of atoms, one of the atomic weight 20 and the other of atomic weight 22. These two components occurred mixed in such proportion as to yield the usual atomic weight of 20.2. The study was continued and most of the elements were shown to be mixtures of components whose atomic weights can, to in

Jan 1, 1941

Discussion of the papers of Dorsey A. Lyon and Samuel S. Arentz, p. 789; S. E. Bretherton, p. 802; H. A. Wentworth, p. 809; and Richard D. Drvine, p. 814. GeoRge W. RiteR, Salt Lake City, Utah.—We have every reason to believe that oil flotation will soon come into general use as a final guard against slime losses in concentrating mills, not only in the case of zinc ores, but also in the case of other semi-precious ores. It also promises much as a primary process for the concentration of minerals that are not adapted to gravity methods. Moreover, modifications of the process involving selective or preferential flotation are gradually becoming understood, and will make it possible to eliminate pyrite and other minerals occurring as undesirable impurities in zinc concentrates. And what perhaps is of equal importance, further modifications promise an effective method of separating zinc blende from ores that are chiefly valuable for copper, lead, and precious metals, thereby making an asset out of zinc which has heretofore been a liability. The tendency of certain pulverized minerals to float on water, especially after having been in contact with grease, has been known to mill-men for a long time, and was formerly something to be deplored and to be striven against. All at once, this tendency has become a saving grace; and now, like tardy converts to a new faith, we are zealous advocates of something we once despised. I was once employed at a mine in the Tintic mining district of Utah— the old Eureka Hill property—where ores that were too low in value to warrant being sent to copper or lead smelters were treated in a combination mill. The ores contained gold, silver, lead, copper, zinc, manganese, arsenic, etc., in varying quantities and in varying mineral forms, mingled in a quartz and calcite gangue. The material was stamped fine and then concentrated on Frue vanners so as to make a smelting concentrate, after which the tailings were thickened and treated in amalgamating pans for the recovery of non-concentratable precious metals. In the amalgamating pans, under the influence of heat and agitation, a dark greasy froth or scum sometimes formed on the surface of the ore mixture. This froth or scum was composed mainly of mineral sulphides, and its occurrence might have meant only casual losses in the previous concentration, except that the phenomenon was accompanied by faulty amalgamation of the precious metals and by excessive losses in the mill tailings. Grease and oil, present by accident, were the cause of the trouble. Whether the intense vibration in the mill, due to the pounding of the heavy stamps, had caused small particles of grease to be shaken loose

Jan 1, 1915

By J. N. Hobstetter

It is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spoutaneous difiusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow. Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Beckerl in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r, beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration. The increase in free energy per mole accompanying the formation of a nucleus which is just stable, AF., is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. The Nature of the Nucleus It is necessary ti have rather detailed knowledge of the nature of a nucleus if AF, is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown

Jan 1, 1949

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By R. C. Buehl, J. P. Riott, E. P. Shoub

PILOT-PLANT tests have demonstrated that it is possible to produce low-sulphur sponge iron (0.03 to 0.05 per cent sulphur) as a continuous process in an internally fired rotary kiln from iron ore or mill scale; a solid carbonaceous reducing agent; and dolomite to control the sulphur content. The proportion of dolomite employed is small, so that it does not add materially to the cost of the sponge iron. The entire operation is carried out at temperatures well below the melting point of iron, so that the product is discharged in granular form. Compared with other methods for the production of sponge iron, the rotary-kiln method has the advantage of simplicity and low cost of equipment and; in addition, requires little labor for the operation of the process. The pilot-plant equipment used for this work was sufficiently large to demonstrate that the production of low-sulphur sponge iron in rotary kilns is feasible and that the costs are not excessive for applications in which sponge iron has distinct advantages over competing materials. This report constitutes a part of a program by the Bureau of Mines under a special Congressional appropriation for studying gaseous and solid fuel reduction of iron ores. Numerous articles on various phases of these investigations have appeared in Bureau of Mines publications or technical journals. Other articles are being prepared and will be published in the near future. The present program, which is under the supervision of Dr. R. S. Dean, Assistant Director of the Bureau of Mines, was initiated in .1942. However, a considerable portion of the work was a continuation of previous research performed by the Bureau. Previous investigators1-4 utilizing the rotary kiln for the production of sponge iron did not develop a suitable method for controlling the sulphur content. A review of the literature shows that the sulphur content in the product usually exceeded 0.2 -per cent unless reducing agents with very low sulphur contents were employed. This high sulphur value made the product generally undesirable for use as melting stock in electric or open-hearth furnaces. The production of sponge iron in an internally fired rotary kiln has been described in detail in Bureau of Mines Bulletin 2702; consequently, this article will be confined mostly to new features of the process-that is, means for controlling the sulphur content of the sponge iron. Suitable raw materials include iron ores or mill scale; coal or coke for reducing them, and sized dolomite (-20+100-mesh) as the sulphur-controlling agent. A mixture of the raw materials in granular form is fed into the elevated end of the kiln, which is fired axially from the lower or discharge end. In the reducing zone, which is approximately one third the length of the kiln measured from the dis-

Jan 1, 1946

By E. P. Shoub, J. P. Riott, R. C. Buehl

Pilot-plant tests have demonstrated that it is possible to produce low-sulphur sponge iron (0.03 to 0.0; per cent sulphur) as a continuous process in an internally fired rotary kiln from iron ore or mill scale; a solid carbonaceous reducing agent; and dolomite to control the sulphur content. The proportion of dolomite employed is small, so that it does not add materially to the cost of the sponge iron. The entire operation is carried out at temperatures well below the melting point of iron, so that the product is discharged in granular form. Compared with other methods for the production of sponge iron, the rotary-kiln method has the advantage of simplicity and low cost of equipment and, in addition, requires little labor for the operation of the process. The pilot-plant equipment used for this work was sufficiently large to demonstrate that the production of low-sulphur sponge iron in rotary kilns is feasible and that the costs are not excessive for applications in which sponge iron has distinct advantages over competing materials. This report constitutes a part of a program by the Bureau of Mines under a special Congressional appropriation for studying gaseous and solid fuel reduction of iron ores. Numerous articles on various phases of these investigations have appeared in Bureau of Mines publications or technical journals. Other articles are being prepared and will be published in the near future. The present program, which is under the supervision of Dr. R. S. Dean, Assistant Director of the Bureau of Mines, was initiated in 1942. However, a considerable portion of the work was a continuation of previous research performed by the Bureau. Previous investigators1-4 utilizing the rotary kiln for the production of sponge iron did not develop a suitable method for controlling the sulphur content. A review of the literature shows that the sulphur content in the product usually exceeded 0.1 per cent unless reducing agents with very low sulphur contents were employed. This high sulphur value made the product generally undesirable for use as melting stock in electric or open-hearth furnaces. The production of sponge iron in an internally fired rotary kiln has been described in detail in Bureau of Mines Bullelin 2702; consequently, this article will be confined mostly to new features of the process—that is, means for controlling the sulphur content of the sponge iron. Suitable raw materials include iron ores or mill scale; coal or coke for reducing them, and sized dolomite ( — poi-100-mesh) as the sulphur-controlling agent. A mixture of the raw materials in granular form is fed into the elevated end of the kiln, which is fired axially from the lower or discharge end. In the reducing zone, which is approximately one third the length of the kiln measured from the dis-

Jan 1, 1948

By R. C. Buehl, J. P. Riott, E. P. Shoub

Pilot-plant tests have demonstrated that it is possible to produce low-sulphur sponge iron (0.03 to 0.0; per cent sulphur) as a continuous process in an internally fired rotary kiln from iron ore or mill scale; a solid carbonaceous reducing agent; and dolomite to control the sulphur content. The proportion of dolomite employed is small, so that it does not add materially to the cost of the sponge iron. The entire operation is carried out at temperatures well below the melting point of iron, so that the product is discharged in granular form. Compared with other methods for the production of sponge iron, the rotary-kiln method has the advantage of simplicity and low cost of equipment and, in addition, requires little labor for the operation of the process. The pilot-plant equipment used for this work was sufficiently large to demonstrate that the production of low-sulphur sponge iron in rotary kilns is feasible and that the costs are not excessive for applications in which sponge iron has distinct advantages over competing materials. This report constitutes a part of a program by the Bureau of Mines under a special Congressional appropriation for studying gaseous and solid fuel reduction of iron ores. Numerous articles on various phases of these investigations have appeared in Bureau of Mines publications or technical journals. Other articles are being prepared and will be published in the near future. The present program, which is under the supervision of Dr. R. S. Dean, Assistant Director of the Bureau of Mines, was initiated in 1942. However, a considerable portion of the work was a continuation of previous research performed by the Bureau. Previous investigators1-4 utilizing the rotary kiln for the production of sponge iron did not develop a suitable method for controlling the sulphur content. A review of the literature shows that the sulphur content in the product usually exceeded 0.1 per cent unless reducing agents with very low sulphur contents were employed. This high sulphur value made the product generally undesirable for use as melting stock in electric or open-hearth furnaces. The production of sponge iron in an internally fired rotary kiln has been described in detail in Bureau of Mines Bullelin 2702; consequently, this article will be confined mostly to new features of the process—that is, means for controlling the sulphur content of the sponge iron. Suitable raw materials include iron ores or mill scale; coal or coke for reducing them, and sized dolomite ( — poi-100-mesh) as the sulphur-controlling agent. A mixture of the raw materials in granular form is fed into the elevated end of the kiln, which is fired axially from the lower or discharge end. In the reducing zone, which is approximately one third the length of the kiln measured from the dis-

Jan 1, 1948

By John N. Hobstetter

IT is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spontaneous diffusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow,' Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Becker1 in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r. beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration, The increase in free energy per mole accompanying the formation of a nucleus which is just stable, ?fe, is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. THE NATURE OF THE NUCLEUS It is necessary to have rather detailed knowledge of the nature of a nucleus if ?Fe is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown3

Jan 1, 1948

By J. M. Markowitz

The movement of hydrogen in two-phase Zircaloy-2 under the influence of a thermal gradient was studied in specimens of cylindrical geometry. A gross displacement of hydrogen toward the cooler regions of the specimen was observed with consequent copious precipitation of 6-ztrconium (ZrH) there. The kinetics of the diffusion are analyzed and discussed. X HE temperature-gradient redistribution of hydrogen in a-Zircaloy-2 has been treated both theoretically and experimentally Hydrogen moves toward the cold side of the temperature gradient until a steady state has been established; tendency for further hydrogen movement because of temperature differences is nullified by the tendency to move in the reverse direction because of the concentration gradient. The steady state condition is described by the equation in which iV is the concentration of hydrogen at a point in the specimen corresponding to absolute temperature T, R is the gas constant,k is a constant of integration, and Q is a parameter called the heat of transport, characteristic Of the particular system. The value of Q has been determined for hydrogen in Zircaloy-2 by several investigators, using Eq. [11. There is considerable variation in the results, the cause of which has not been resolved; reported values lie in the range 3 to 6 kcal per mole. The physical situation for two-phase thermal migration is much more complex. The -phase boundary for the solubility of hydrogen in Zircaloy-2 ranges from a concentration of 25 ppm at 200°C to a maximum of about 600 ppm at 550°C.4a Thus, if the concentration of hydrogen in Zircaloy-2 is sufficiently great (>600 ppm), the specimen will be entirely two-phase, consisting of a matrix of a-Zircaloy-2 surrounding particles of zirconium hydride. At time zero, with a temperature gradient imposed, the relative amounts of hydride and a-phase in each infinite-simally thin isothermal section of the specimen can be determined from the phase diagram by the lever rule. Moreover, the concentration of hydrogen in the matrix phase varies from point to point, following the a solubility line. Over most of this temperature range (<450°C) 6 phase, Fig. 3, has a constant concentration.5 The diffusion rate toward the cold side should be governed by 1) the slope of the a solubility line and 2) the temperature gradient, The extra complication of two-phase thermal diffusion lies in the fact that migration of hydrogen would leave the a-phase concentration gradient unaffected, since it is fixed at any temperature only by the solubility; gross concentration changes would reflect only the relative amounts of matrix and hydride, which could vary continuously at every point. Migration of hydrogen out of a region would lead to dissolution of hydride, and

Jan 1, 1962

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By Eric Kula, Åke Josefsson

L. J. Dijkstra and R. Sladek, (Ontario Research Foundation, Toronto, and Institute for the Study of Metals, Chicago, respectively)—This interesting paper confirms some results obtained some years ago in collaboration with Fast: namely the broadening of the nitrogen peak by the presence of small amounts of manganese. Later on a more extensive study of this effect was made at the Institute for the Study of Metals at Chicago. As the work has not yet been submitted for publication we wish to mention here briefly some of the results. The effect of about 0.5 atomic pct manganese, chromium, molybdenum, or vanadium on the nitrogen-peak in iron was examined. The broadening found previously in the case of manganese was even found to be more pronounced for chromium. In the case of molybdenum and vanadium a double peak was observed which seemed to justify the idea that in all cases mainly two relaxation times were involved: namely, the normal relaxation time as found in pure iron and a second relaxation time related to the existence of abnormal interstitial lattice sites introduced by the foreign metallic element. The analysis showed that for the normal nitrogen-peak as a reference at 22°C the abnormal peak was found at about 32°, 47°, 75°, and 87°C in the case of manganese, chromium, molybdenum, and vanadium, respestively. In the manganese alloy the free energy difference for a nitrogen-atom at an abnormal and a normal lattice site was estimated at 2800 cal per mol. This means that for temperatures above 100°C the solid solubility and overall diffusion rate of nitrogen is not much affected by additions of 0.5 pct Mn. We believe that the difference in rate of precipitation of nitrogen in pure iron and the manganese alloy is mainly a question of the number of potential nuclei available in the different steels. In studying the effect of these alloying elements on precipitation of nitrogen, a distinction must be made between the para reaction and ortho reaction, using terminology introduced by Hultgren.7 The ortho reaction in which the alloying metallic element participates in the diffusion under formation of nitrides occurs at high temperatures such as 600°C. The para reaction in which the alloying metallic element does not diffuse and in which the nitride inherits its alloy content from the matrix occurs at lower temperatures. To prevent the ortho reaction the alloys have to be quenched rapidly from the phase. It is not surprising that the authors find that the height of the peak indicates a lower nitrogen content than chemical analysis. In the first place the peak is not a single relaxation peak and secondly, the steels were not quenched from the phase after the nitrogen was introduced at 580 °C.

Jan 1, 1953

By W. Rosotoker

Using an expression for the free energy of a homogeneous phase as a function of composition, a relationship is derived which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. Comparisons between observed and calculated phase boundaries in the systems Fe-Ni, Fe-Mn, Fe-W, Ti-Mo, and Ti-Cb are presented. IT is the purpose of this paper to illustrate how the general free energy equations for two phases in equilibrium may be used to derive an expression which interrelates the phase boundaries extending from the allotropic transformation of the solvent metal. The free energy per gram atom of a disordered solid solution may, for many purposes, be represented by the equation:&apos; F = ½NZ [C-V,, + (1-C) VbB + 2C (l-C)V] + K(T) +RT[C-lnC+ (l-C)ln(l-C) ] [1] where N is Avogadro&apos;s number; Z, the coordination number; C, the concentration of the solute element in atomic percent; the subscripts refer to concentrations at phase mixture boundaries; VAA, VBB, and V,, are the bond energies between like and unlike adjacent atoms, respectively, at the interatomic spacing characteristic of the phase. The bond energies are usually assumed to be independent of small changes in the lattice parameter occasioned by solute additions and variations in temperature; V = VAB ---------------—— ; K(T) is the sum of the heat con- tent and heat entropy; R, the molar gas constant; and T, the temperature in degrees Kelvin. The free energy of a homogeneous phase is there- fore the sum of an internal energy, a specific heat, and a configurational entropy term, respectively. The compositions of two phases in equilibrium at a given temperature are governed by the minimum total free energy principle. Graphically, this is represented by the points of tangency of the tangent common to the free energy vs. concentration curves of the two phases. Analytically, this may be expressed as: ( df) = (df) [2] dc dc Expanding both sides using eq 1, the following equation is obtained after convenient readjustment of the terms: RT In[(ca)(1-c)]-½N (Vaa-Vbb)(Za-Zb) +NV [Za(l-2Ca)-Z,(l-2C,)] [3] The following assumptions have been made at this point: 1—The specific heats of the two phases are independent of composition variations within the range under consideration. Accordingly, the K(T) terms disappear on differentiation. 2— (Vaa)o = (VAA); (VBB). = (VBB); Va = V, Theyjustification for these assumptions can lie only in the successful application of the resultant equation. It may be noted that Zener2 has used assumption 1 in the calculation of the boundaries limiting the (a+j3) phase mixture in the Cu-Zn system.

Jan 1, 1952

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10&apos; per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By Paul F. Fulton, Robert K. Estes

INTRODUCTION Relative permeabilities are factual data necessary to any prediction of reservoir production behavior. One important problem in determining relative permeabilities of porous media to gas is the effect of gas slippage on these determinations. Since certain aspects of the slippage phenomenon still remain unknown, this study is particularly concerned with that problem. The validity of the theory of gas slippage as it is applied to the flow of gas through porous media has been well established. 1,2,3 Therefore, in determining the permeabilities of porous media to gas by ordinary laboratory procedure, i.e., at atmospheric pressure, the slippage correction should be considered. Rose3 performed experiments on gas relative permeabilities which indicated that the effect of gas slippage on the measured effective gas permeabilities at various liquid saturations decreased with an increase in liquid saturation. Following Rose, it was substantiated experimentally&apos; that the effective gas permeabilities at the various liquid saturations extrapolated to infinite mean pressure were the same as the non-wetting liquid permeabilities at the same saturations. This same paper also presented data which showed that the magnitude of the slippage between those values of gas effective permeability determined at atmospheric pressure and those found by extrapolation to infinite mean pressure decreased with an increase in liquid saturation. However, these experiments were not performed at liquid saturations above 30 per cent. Therefore, the purpose of this experimental work was to determine the effect of gas slippage on permeability measurements at liquid saturations in excesh of 30 per cent. APPARATUS Five core samples were used In this work: two synthetic Alundum samples (A-1, and A-2). a Nichols Buff sandstone sample (NB-13), and two samples from producing formations, a Soso sandstone (S-1), and a vugu-lar dolomitic limestone (R-7). The core samples ranged in permeability from 32 to 663 md. These cores were chosen because they represented a fairly wide range of permeabilities and probably a considerable difference in pore size and pore size distribution. Fig. 1 is a schematic diagram of the apparatus which consists of an air dehydration filter A, two Moore null-matic sub-pressure regulators B and C, the differential oil manometer D, the core holder E, the flowmeter F, the soap reservoir G, and a mercury manometer H measuring the downstream pressure. The interesting features of the apparatus are the two Moore vacuum-pressure regulators. The regulators permit the rapid establishment and easy control during flow at sub-atmospheric pressures of both the differential and downstream pressures, and prevent the surging action of the vacuum pump from disturbing the system during flow. Provided there are no leaks in the system, these regulators will maintain without measurable change selected downstream and differential pressure. Specifically, regulator B controls the downstream pressure and regulator C controls the differential pressure. In opera-

Jan 1, 1957

Discussion of the paper of H! M. CHANCE, presented at the Pittsburgh meeting, October, 1914, and printed in Bulletin No. 91, July, 1914, pp. 1461 to 1466. R. V. Norris, Wilkes-Barre, Pa.-In his resume of coal-taxation methods Mr. Chance has apparently confined his investigation to bituminous coal, so a summary of the anthracite situation as to coal assessment should be of interest. The anthracite region of Pennsylvania in its 484 square miles of measures lies in the counties of Wayne, Lackawanna, Luzerne, Carbon, Schuylkill, Northumberland, and Dauphin, and in each of these different methods of assessment have been adopted. The assessments for taxation in Pennsylvania are made under Acts of the Legislatures of 1841 and 1842, under which the assessors are re¬quired to "assess rate and value every subject of taxation according to the actual value thereof, and at such rates and prices as the same would bring at a bona fide sale after due notice." Under this general law coal land has been assessed as such, but up to about 25 years ago the coal was assessed at rates so low as to be unimportant, though the rates in each township and municipality, even in the same county, showed no agreement or ascertainable basis. In the late &apos;80s, the need for greater revenue drew attention to the possibilities of collecting much larger taxes from the coal lands and, spurred by public demand, the assessing authorities in some counties undertook a reassessment of coal. The method pursued was to demand from each owner a statement of the area and average remaining thickness of coal on his lands. On this return, made in some cases under oath, an assessment based on foot-acreage was levied, with a resulting great increase in valuation, but the valuation per foot-acre was low and no serious objection was made. This assessment with occasional increases of rate remained in force until 1907, when, in the triennial assessment of that year, a complete revision of the valuation was again attempted, engineers were employed by the counties to check the accuracy of the returns from the owners, and, based on the foot-acreage thus obtained, an enormous increase, to $65 per foot-acre, was made in the valuation. This assessment was resisted in the courts by appeals resulting in very extensive litigation, and a final determination of the validity of the 1907 and all subsequent assessments has not yet been obtained. In the first appeals tried the rate calculated on a foot-acre valuation was reduced by the Luzerne County court to about $45, while the. Lackawanna County courts reduced a larger rate to $67. The county authorities were, how-

Jan 4, 1915

By M. Muskat, H. H. Evinger

A METHOD has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-pressure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. INTRODUCTION The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical properties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.1 Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of 0 to 100 bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* [ ] where k is the sand permeability, h its thickness, µ the liquid viscosity, [Ap] the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius [ro ]and [r ] is the well radius. This gives the productivity factor: [ ] which will have a numerical value for a liquid of I centipoise viscosity of 0.9316 or

Jan 1, 1941