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By P. W. Bridgman

DURING the war, the Navy undertook the construction, under my direction, of an experimental gun embodying features designed to lessen the cost and time of production. These experiments were initiated after representations as to their, desirability had been offered by myself, by the Naval Consulting Board, and by the National Research Council. The first drawings were made in June, 1917, and the experiment was completed in November, 1918. For the sake of clearness it will pay to recapitulate briefly the fundamental idea of gun construction. It is well known that if a hollow cylinder is subjected to internal fluid pressure, the maximum stress occurs in the inside layers, the outer parts carrying much less than their due share of the stress. This inequality of stress is more pronounced the thicker the walls of the cylinder. If such a cylinder is pushed to the elastic limit, failure in elasticity will take place long before the outer layers have reached the limit of their capacity. Economical use of the material would demand, however, that all parts of the cylinder reach the limits of their capacity simultaneously. This may be brought about, at least in cylinders of not too great thickness, by producing in. the inner layers an initial compression, and in the outer layers an initial tension. The effect of internal pressure is at, first to relieve the compression of the inside layers, while increasing the tension of the outside layers. If the initial stresses are properly distributed, all parts of the cylinder will reach their elastic limits simultaneously, thus giving a cylinder of maximum strength for its weight. In gun construction as hitherto practiced, this initial distribution of stress is produced either by winding the inner tube with wire, a common English practice, or by shrinking hoops over the inner tube, which has been the standard American practice. Either process is long and expensive, particularly with the larger guns, 12- or 14-in., which require

Jan 2, 1920

WASHINGTON, D. C. HERBERT C. HOOVER, Chairman H: FOSTER BAIN, Vice-chairman DAVID WHITE, Vice-chairman HARVEY S. MUDD, Secretary-Treasurer, Room 2114, Dept. of Interior Bldg. J. F. CALLBREATH HENNEN JENNINGS E. W. PARKER T. T. READ An inspiring meeting of the Washington, D. C., Section was held at the Cafeteria of the Interior Building on Friday evening, Dec. 6, 1918. One-hundred and thirty-five members and guests attended, and Vice-chairman H. Foster Bain presided. The Committee on Nominations reported: for Chairman, Herbert Hoover; for Vice-chairmen, Frederick G. Cottrell, and F. L. Ransome;

Jan 1, 1919

By S Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- [ ] fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

By Frances H. Clark

DEVELOPMENTS in powder metallurgy have been disappointing in 1943. If any new part has gone into large-scale production, knowledge of it has been restricted by considerations of national security. Nor have any outstanding papers appeared to advance the theory of the subject during this period.

Jan 1, 1944

By S.G. Bankoff

Ince1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (—200 mesh) and 50 C.C. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which precumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1943

By S. G. Bankoff

Ince1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (—200 mesh) and 50 C.C. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which precumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1943

By Edwin H. Olson, Morton Smutz, Charles J. Baroch

IN 1949 an orebody containing some 10 billion lb of recoverable rare earth metals was discovered in the Mountain Pass district of San Bernardino County, California.1 The following year Molybdenum Corp. of America purchased a number of claims at the deposit and a mill on the property which had been constructed to process the district's gold ores. Average composition of ore from the San Bernardino deposit is less than 0.1 pct ThO2, 25 to 35 pet calcite, 10 pet rare earth oxides, 15 to 20 pet silica, and 30 to 40 pet barite.2 Rare earth content of the ore analyzes 50.7 pet CeO2, 4.2 pet Pr6O11, 11.7 pet Nd2O3, 1.3 pet Sm2O3, and 34.3 pet La2O3, and others.2

Jan 3, 1959

By Arnulf Muan

PHASE relations in three isothermal sections (l000°, 1100°, 1200°C) of the system Ag-Fe-Pd have been determined as part of a program to develop improved crucible materials for containing low-melting iron silicates at low oxygen potentials. The following experimental method was used: Two- to 3- g samples of each of forty different alloys within the system Ag-Fe-Pd were made up from metals of 99.9 pct purity. The mixed metal powders were contained in a 1-cc crucible of dense recrystal-lized alumina and heated in a protective atmosphere (90 vol pct A, 10 vol pct H2), first to complete melting for approximately 30 min and subsequently at the desired equilibration temperature (1000°, 1100°, or 1200°C) for approximately 24 hr. The samples were then quenched rapidly to room temperature and examined metallographically as well as by X-ray techniques. Unit cell dimensions were compared with standards obtained by study of one-phase alloys of known compositions. The results are summarized in diagrams (a), (b), and (c) shown in Fig. 1. Heavy solid curves outline areas comprising compositions of mixtures consisting of the phases labeled for each area. Mixtures in which liquid is the only condensed phase present are confined to very narrow areas adjacent to the Ag-Pd join at high silver contents. An enlarged, distorted picture of the phase relations prevailing in these areas is shown in the upper-left circular insert. Particular attention is directed toward the misci-bility gap which occupies major parts of the composi-

Jan 1, 1962

By M. V. Nevitt

THE Cr,O-type, or P-tungsten, structure having the space group (Oh2— Pm,n) is one of the most widely occurring structures found among the intermediate phases involving transition metals. Including the phases reported here for the first time, the total number of these A,B phases now known is 39. Greenfield and Beck' have correlated the lattice parameters of these phases with the Goldschmidt radius of the close-packed chains of A atoms. Laves' discussed the apparent size of the A and B atoms in this structure. Gel1er" proposed a scheme for reproducing the lattice constants of the phases by the use of a list of effective C.N. 12 radii for the component elements. Reported here is a survey of the A,B combinations which appeared favorable for the stability of the Cr,O-type phase but which, at the time the investigation was begun, either had not been reported upon or had conflicting reports as to the existence of the structure. Seventy systems were investigated, and 8 Cr,,O-type structures were found. Six of these also were reported by other investigators in the interval between the start of this investigation and its completion. This survey yielded information as to the influence of the relative sizes of the A and B atoms on the stability of the phase and, for the various families of Cr,O-type phases, the effects of the sizes of the A and B atoms on the lattice constant. Likewise, a somewhat clearer picture of the connection between the position of the A and B elements in the Periodic Table and their Cr,O-type phase-forming tendencies has become apparent. Experimental Procedure Alloys were prepared in the form of arc-melted 3-gram buttons in all cases where the vapor pressure of neither component was high enough to cause

Jan 1, 1959

[Abrahamson, Guy C., (5'43) 1st Lt., A.C., 0-880861, Base Weather Sta., Fairfeld-Suisun AAB, Suisun, Calif. Adam, Howard Wilbur, (S'46) 45 Eaton Ave., Woburn, Mass. Aguilar, Ruperto G., (S'43) Texas College of Mines, El Paso, Texas. Ainge, Ronald Farra, (S'43) Otago University, Dunedin, New Zealand. Albala, Américo, (S'44) Casilla 4106, Santiago, Chile. Albrecht, Theodore J„ (S'42) Pfc., Co. F, Syme Hall, Rm. 1, SCU 3421, ASTP, N. C. State College, Raleigh, N. C. Aldridge, E. E., Jr., (S'39) Box 58, Eagle Pass, Texas. Alfred, Robert M., (S'40) 25 South St., Brighton, Mass. Allan, Douglas H. W., (S'40) 460 Main St., E., Hamilton. Ont.. Canada.]

Jan 1, 1946

By S. G. Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments [c] through g are more insoluble than lead carbonate, therefore should prevent the formation of lead carbonate on the galena surface. In experiment [i] the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments [j] through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

By H. Hubert

THE first attempts at direct utilization of blast-furnace gas in engines were made in 1895. For a considerable time the gas had been burnt in Cowper stoves for heating the blast for the furnace, and under the boilers which supplied steam to the blowing-engines, and others serving the furnaces. It was natural, therefore, that the idea of directly employing it in gas-engines should have occurred simultaneously to several engineers, notably to Lürmann and to Lencauchez, who had pointed out the blast-furnace as a powerful -gas-producer. Nevertheless, nowhere had any attempt been made to apply it to this purpose up to the end of 1894, when Thwaite proposed it to Mr. James Riley, of the Glasgow Iron & Steel Company. About the same time investigations were being made in Belgium and in Germany, independently of Thwaite's experiments, which were not generally known on the Continent. The industrial world, which up to that time had hardly favored the idea, had thus been gradually prepared to receive it. The gas-engine, long restricted to small sizes and dependent upon the use of an expensive fuel obtainable only in large centers, now began to make headway. At the Paris Exhibition of 1889 two engines of 100 h.p. were shown and excited much interest among engineers. One had four cylinders, and was made at the celebrated works of the Deutz Company, and the other was a single-cylinder engine, exhibited by two French designers, Messrs. Delamare-Deboutteville and Malandin. In the meanwhile the design of gas-producers had made important progress, completely freeing the new engine from its

Nov 1, 1906

By Samuel B. Christy

At the last meeting of the Institute, several contributions were made to the subject of miners' aid funds. Such matters will always form important factors in the administration of large industrial enterprises. From the frequently remote and isolated position of mining properties, it is a subject that often forces itself upon the attention of the mining engineer. Local conditions are usually so variable that no single method can be found equally well adapted to all localities. At the same time, a study of different types is often suggestive and valuable, and it is with this in view that these notes are presented. The Miners' Fund of New Almaden is a remarkably successful example of what may be done for miners by a wise and at the same time firm management, by simply directing their own efforts and without incurring any great expense to the stockholders,—a practical consideration not without importance in most cases. The quicksilver mines of New Almaden are situated at a distance

Jan 1, 1885

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman's paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author's comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman's paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author's comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By John J. Stokes

Literature on the electrolysis of aluminum from cryolite melts and on the structure of these .melts is surveyed critically. Data on density, freezing point, and other properties are reviewed. Theories of the electrolysis are examined in the light of these data. Two theories are presented which account equally well for the observations. In the early days, the process was thought of as a simple one. The actual mechanisms must be tremendously more complex. This paper is devoted to a rather narrow part of the whole subject, namely, what ions are present in the bath, and by what mechanism the current is carried. Using cryoscopic data, Rolin has determined the following composition for molten cryolite. Na2,AlF 3Na + 3F + AlF [1] He postulates the following equation for the ioniza-tion of alumina at low concentrations Al2O3 Al + AlO2 +O. [2] At concentrations above 0.025M he supposes the ionization of alumina to proceed as follows Al2O3 AlO + AlO2. [3] Rolin's mechanism of electrolysis for the more concentrated solution in Eq. 3 is as follows. The AlO' ion migrates to the cathode. where it is dis- charged, giving metallic aluminum and 0' ions which migrate to the anode. The AlO2- ion migrates to the anode, where it is discharged, giving Al ions and oxygen which reacts with carbon to form CO2 In the case of the extremely dilute solution in Eq. 2 the Al ion migrates to the cathode and the AlO2-and 0 migrate to the anode as before. Another possible mechanism for the electrolysis follows. Ionization of Cryolite Na3AlF4 = 2Na + 2F + NaAlF, Na + AlF-AlF+Na + F [4] Addition of Alumina 2Na2AlF+ 2AL2O4 6Na + 3A12O3F4 [5a] Al2O2F 2AlOF2 [5b] Cathode Process AlF, + 3e+ 4F + Al. [6] Anode Process AlOF2 + 2F AlF1 + 1/20, + 2e or A12O2F + 4F-2A1F; + 0, + 4e. [7] Although both Rolin's and the present mechanism of the Hall process may be qualitatively satisfactory, present data are not adequate for quantitative tests of the theories.

Jan 1, 1959

By Bauer. Larry G.

The vast coal reserves in the Wyoming, Montana, North and South Dakota region are sufficient to supply the total energy needs of the United States for several hundred years. Not only is there an abundance of this sub-bituminous and lignite coal available, but it is easily obtainable by strip-mining . The overburden varies from several feet to several hundred feet. This western coal has yet another asset, namely, a low sulfur content. Whereas eastern and midwestern coal has a sulfur content of 2.5%, the upper Great Plains coal contains sulfur in the 0.5% range. The importance of the sulfur content of the coal is a direct result of federal government emission standards for sulfur dioxide (SO2). Hand (1) points out that "sub-bituminous coals and lignites have a propensity for retaining this sulfur in the ash under certain conditions which is not evident in higher rank coals." This would tend to reduce further the SO2 concentration in the combustion gases of boilers. Western coal is no panacea, however, in that it is far removed from most population and industrial centers. Furthermore, the moisture content of the coal varies from 20 to 40%. This moisture is almost exclusively inherent, that is, it is chemically and physically bound to the organic matter of the coal. It is believed that the water forms a part of the coal structure perhaps as water of hydration of organic salts or organic acids, perhaps by hydrogen bonding, or perhaps by simple adsorption (2). The primary market for this coal is the electric power industry. Lesser markets will be as coke for the steel industry and possible as a raw material for coal gasification and coal liquefaction plants.

Jan 1, 1983

By PALMER H. TYLER

WHEN the Mid-Continent Section of the A. I. M. E. met at the roof garden dining room of the Tulsa Club on Monday evening, May 13, most of the members present came prepared with a credulity-stretching yarn of some sort or other, gathered from actual experience. Perhaps it was not realized at the time that such anecdotes would eventually burst into print, but while the excellent dinner was appeasing the inner man the word was passed around that informality and spontaneity of expression would characterize the meeting, with the result that the shackles of convention were eventually cast aside and the meeting waxed better and better until the hour grew ,late, and the chairman, L. G. E. Bignell, originator of the idea, brought to a close what was agreed to be a profitable and entertaining evening. The ball was started rolling by Paul Ruedemann of the program committee, who offered the following:

Jan 1, 1929

By Tormod Forland

FROM equilibrium measurements on the system NaF-Na 3A l Fo-A 1 2 O 3-Na CO 3-CO 2 with high contents of NaF, Forland, Storegraven, and Urnesl concluded that complexes are formed containing two oxygen, three aluminum, and a less defined number of fluorine per complex. The same number of oxygen atoms per complex was also found by cryoscopic measurements for mixtures high in NaALF 6. In a recent paper by Stokes: some other complex ions, Al2O2F42- and AlOF2-, have been suggested. Here an additional argument in favor of the complex ALO2F. suggested by Forland, Storegraven, and Urnes will be given. When fused Na3AlF6 containing some A12O3, is cooled slowly, the solid phase will consist of the two components as separate phases. The melting point and the heat of fusion of Al2O3 are so high that this component will form the stable solid phase even though in the liquid state the complex may have a high stability. If, however, the fused mixture is quenched, the decomposition of the oxygen-containing complex and the formation of solid Al2O3 does not proceed fast enough, and a solid solution of A12O3 in Na3AlF6 is obtained. Zintel and Morawietz3 obtained cryolite containing 10 pct AL2O3 in this way. The density and the lattice parameters of the A12O3 containing cryolite were also measured, and from this it was concluded that the Al2O3 enters the cryolite lattice as Al3AlO0 groups replacing Na3AlF6 groups. However, the experimental data could as well be explained by assuming that one Na+ ion and two of its neighboring F- ions are replaced by one Al3+ ion and two O2- ions. This may be pictured schematically as: F F F F F F F Al F Na F Al F ,-Na+ + Al8+ F Al 0 A1 0 A1 F F F F —2 F- + 2O2- F F F solid cryolite cryolite-alumina solid solution This means that the complex in the solid solution, derived from X-ray and density measurements, is the same as that which Forland, Storegraven, and Urnes derived from equilibrium measurements in the liquid state. References IT. Forland, H. Storegraven, and S. Urnes: Ztsch. fur anorgan-ische und allgemeine Chemie, 1955, vol. 279, p. 205. 2J. J. Stokes: AIME Trans. To be pubhshed. s E. Zintel and W. Morawietz: Ztsch. pubhshed.fur anorganische und allgemeine Chemie, 1939, vol. 240, p. 145.

Jan 1, 1958

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967