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By Arnulf Muan, D. P. Masse

PHASE relations in the system CoO-SiO2 have been determined as a basis for further investigations of thermodynamic properties of olivine solid solutions involving Co2SiO4 as a component. Previous data on the system CoO-SiO2 are incomplete or uncertain. Biltz and Lemke1 determined the melting point of cobalt orthosilicate as 1345°C , but Asanti and Kohlmeyer2 have later found a considerably higher temperature, 1420°C. The latter authors also studied melting relations of one mixture on the CO side and two mixtures on the SiO2 side of the orthosilicate composition and sketched a tentative phase diagram for a limited composition range of the system. However, no phase identification was carried out, and the authors left unanswered the question of the possible existence of a stable meta-silicate phase. Greig3 showed that a 90 wt pct SiO2-10 wt pct Co mixture at 1725°C consists of two immiscible liquid phases. The quenching technique was used in the present investigation. Mixtures of high-purity cobalt oxide ("Fisher Certified") and dehydrated silicic acid ("Baker Analyzed") were equilibrated in air atmosphere. The samples were then quenched to room temperature and the phases present were identified by microscopic and X-ray examination. The samples were kept in small envelopes made from thin (0.0004 in.) platinum foil. Thermodynamic data which have become available recently for Pt-Co alloys4 were used to check that the losses of COO from the oxide samples by alloying of cobalt with platinum in the present investigation were too small to change significantly the compositions of the oxide material during the equilibration. A vertical tube furnace with an 80 pct Pt 20 pct Rh resistance winding was used in runs up to 1510°C. Temperatures in these runs were measured with a Pt vs 90 pct Pt 10 pct Rh thermocouple calibrated against the melting point of diopside (CaMgSi2O6, 1391.5?C). The given temperatures as measured by this technique are estimated to be accurate to *5°C. Quench runs at temperatures above 1650°C were made with a modified Roberts and Morey5 strip furnace, using strip resistors composed of a 60 pct Pt-40 pct Rh alloy. Temperatures were measured with an optical pyrometer which was calibrated against the liquidus temperature of a mixture composed of 10 wt pct CaO, 90 wt pct SiO2 (1707°C). The temperatures measured with this technique have an estimated accuracy of +15°C. The results are shown graphically in Fig. 1. Only one intermediate phase, the orthosilicate Co2SiO4 with olivine-type structure, is stable in addition to the end members cobalt oxide and silica. The melting point of the orthosilicate was found to be 1415" ± 5°C. The metastilicate CoSiO3 is not stable at the temperatures of the present investigation. The two eutectic points in the system CoO-SiO2 where COO plus olivine, and olivine plus silica, coexist with liquid were found to be 72 wt pct COO and 1407°C and 63 wt pct COO and 1381°C, respectively. The melting point of cobalt oxide in air was taken as 1745?C, based on the previous data of Aukrust and Muan.6 Within limits of error (+ 5?C), identical eutectic temperatures to those determined in air were found when two representative mixtures were equilibrated at 1 atm O2 pressure and in an atmosphere of 84 vol pct CO2, 16 vol pct H2. This suggests that changes in oxidation state of cobalt in the condensed phases are not significant as far as their effect on the phase relations are concerned. This inference was substantiated by failure to detect7 any "excess oxygen" (i.e., oxygen in excess of that contained in Co2SiO4) in a sample of orthosilicate composition equilibrated in air 10°C above the liquidus temperature and subsequently quenched to room temperature. This work was carried out as part of a research program sponsored by the U.S. Atomic Energy Commission under Contract No. AT(30-1)-2781.

Jan 1, 1965

By AIME AIME

THE STANDARD herewith submitted is the result of several years of research and consideration by the A.I.M.E. Technical Committee on Milling Methods. In the early work of this committee it was found necessary to undertake the development of a standard laboratory method for screen testing of ores. During the research stages the desirability of having this standard, when completed, approved as American Standard was brought out. In accordance with this idea, its initiation as a project of the American Standards Association (then the American Engineering Standards Committee) was approved by the latter body and the A.I.M.E. designated as sponsor. In 1929, the A.S.A., on recommendations of its advisory committee, the Mining Standardization Correlating Committee), authorized the A.I.M.E. to be sole sponsor for this project. The personnel of the Institute's Committee on Milling Methods was then increased to make it thoroughly representative of all diversified interests in the mining field. Two years ago the standard was circulated and has been given wide distribution. Early in 1932 the committee voted unanimously, with 38 affirmative votes, that the standard be recommended to the Board of Directors of the Institute for submission to the American Standards Association for approval as American Recommended Practice. This was accordingly done, at the Feb. 1.6, 1932, meeting of the directors, and the American Standards Association approved the standard on July 6; 1.932, designating it as ASA M5-1932.

Jan 1, 1932

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By W. H. Gauvin, N. J. Themelis

Jan 1, 1963

By ALBERT P. J. BORDEAUX

THIS paper briefly describes the general outline of cyaniding silver-ores in Mexico, with special reference to personal experiments made in the Temascaltepec district. The most important papers on the subject deal with cyaniding gold-silver-ores, the gold predominating in value, so that the treatment is nearly the same as for gold-ores, the losses of silver being considered of little importance. I describe here the treatment of silver-gold-ores containing very little gold, which is more general in Mexico than elsewhere. The cyanide treatment, which was so successfully applied to gold-ores, did not succeed immediately with silver-ores on account of their varying composition. Gold occurs in nature usually in the native state, while silver occurs generally in combination with sulphur (argentite), and various combinations of sulphur, antimony, and arsenic. In former times there was a complete difference in the treatment of gold-ores and silver-ores. Amalgamation, which was successful with gold-ores, was generally inadequate with silver-ores. The usual treatment in Mexico for silver was the patio process, the theory of which was satisfactorily explained only quite recently by Mr. Ortega and others. GENERAL OUTLINE OP THE CYANIDE TREATMENT. The general tendency of the present practice is to slime the silver-ore as much as possible, and in order to obtain a higher efficiency, with less loss of cyanide, and greater speed, the following lines are observed 1. Crushing by stamps with 30- or 40-mesh screens, then crushing by Huntington or Chilean mills, through 60- or 80-mesh screens. 2. Concentration upon vanners.

Jan 1, 1910

Geological and Natural History Survey of Minnesota, Minneapolis, Minn W. H Emmons, Director A list of publications will be sent upon application Orders for publications should be addressed to The University of Minnesota Press, Minneapolis, Minnesota The Geological Survey of Minnesota has a record of long and useful service Some of the papers published have been outstanding in their field A series of 24 Annual Reports, covering the years 1872 to 1895-98, inclusive, was issued, of which 16 are still available at a price. More important however, are the six volumes of Final Reports, in which is collected the material presented in the earlier Annual Reports. All the strictly geological papers are found in four of the volumes of the Final Reports. vol 1 (1872-1882), principally geology by counties, 2 (1882-1885), same as 1, 4 (1896-1898), same as 1, 5 (1898-1900), Structural and petrographic geology Prices for each volume, leather $3, cloth $2 50, excluding postage, unless other directions accompany the order, volumes of the Final Reports will be sent express collect. A series of Bulletins has been issued, of which a few are out of print. Considering only those available, and of greatest interest, they are: Bulletin 5, Natural gas in Minnesota, by N H Winchell (1889), 50 cents, 6, Iron ores in Minnesota, their geology, discovery, development, qualities and origin, by N H Winchell and H V.

Jan 1, 1933

By Kent W. Pilz

Wet dust suppression can be achieved by 1) confinement of the dust within the dust producing area with a curtain of moisture, 2) wetting of the dust by direct contact between the particles and droplets of moisture or 3) the formation of agglomerates too heavy to remain airborne, or too heavy to become airborne, by combining small dust particles with each other and with the droplets of liquid. From the standpoint of economy, availability and safety, water is the ideal fluid; however, it is not as effective for dust suppression as when small percentages of specially formulated dust control compounds are blended with it. Performance of dust control com pounds is related to surface active agents and surface activity. In all liquids there is an attractive force between molecules which varies inversely as the sixth power of the distance between molecules. Thus, in the liquid phase where molecules are crowded together, the intermolecular forces are powerful; whereas in the liquid-vapor phase where the molecules are relatively far apart, these forces diminish rapidly. In the body of a fluid there is an uneven distribution of forces resulting in an inward pull called surface tension. The force which keeps two surfaces apart or causes them to coalesce is termed interfacial tension. Fluids of high surface tension exhibit poor wetting, spreading and penetrating qualities. Water has the unusually high surface tension of 72.75 dynes per cm at 20°C.

Jan 7, 1972

By Robert W. Bartlett

A computer model for predicting the rate of oxidative leaching of copper from fragmented low grade sulfide ores is presented. The model involves the kinetics of the dissolution of chalcopyrite grains and solution diffusion of oxygen within rock pores. Adjustable curve fitting parameters are not used. The model was tested by comparing computed extraction curves with experimental results for a -11 inch ore obtained by block caving and leached at 90°C and 400 psi oxygen for one year at the Lawrence Livermore Laboratories.

Jan 1, 1973

By RAY J. CORFIELD

IN a previous paper, "Electric Shovel Operation at Utah Copper Mine," which was read before the Western Division of the American Mining Congress, the problem of electrifying a fleet of steam shovels was described. This paper deals with the electrification of the haulage system which, when completed, will make the mining operation completely electric, with the exception of drilling operations which will continue to be performed by air. The general layout of the haulage system involves the use of heavy curves in addition to heavy grades of between 4 and 5 per cent. In a mining operation of this kind no trackage can be called permanent; this complicates the overhead construction somewhat and makes it necessary to design special forms of trolley construction, some of which will be described in detail below.

Jan 1, 1929

By Daniel Martin

THE dendritic pattern of steels shown by deep etching is used exten-sively as a guide in the inspection and control of the great majority of steels used in ordnance construction and for many applications in indus-try. The value of macroexamination lies in the fact that it enables a qualified observer to make deductions concerning the general quality of relatively large pieces of metal. Not the least of these general character-istics is the nature and extent of the dendritic segregation in the steel, either in the cast condition or after mechanical or thermal treatments. PREVIOUS WORK Detailed methods for macroetching were outlined by Yatsevitch1 and have been standardized by the American Society for Testing Materials. A comprehensive study of the occurrence, origin, and the chemical and crystalline nature of the dendritic structure was given by Keshian.2 The marked persistence of dendritic segregation in nickel steels is fully recognized and has been discussed by Sauveur and Reed' and by others. Very little, however, has been written on the effect of the various elements on the macrostructure of steels, and the purpose of this report is to submit evidence concerning the influence of chromium, nickel and molybdenum on the macrostructure of some 4 by 4-in. ingots cast and treated under closely controlled conditions.

Jan 1, 1939

By George Simkovich

It was hypothesized that solid-state point defects should alter the flotation properties of solids. Tests conducted on pure AgCl and AgCl doped with CdC12 show that atomic point defects exhibit an important role in the floatability of AgC1. Tests conducted on PbS doped with Ag2s or Bi2S3, also show that the defect structures resulting from these dope additions, i.e., a combination of electronic and atomic point defects, contribute significantly to the flotation of PbS. IT has been established that flotation occurs only when a finite contact angle exists between a solid and a gaseous bubble.' This angle, measured through the liquid phase, is expressed by the equation where the are inter facial free energies and the subscripts S, G, and L represent solid, gas, and liquid phases, respectively. As is seen in Eq. [I] three interface free energies, sG, sl, and GL, enter into the contact angle equation. Therefore, any variation in these energies which sufficiently varies the contact angle will, in turn, vary flotation processes. Changes made in any of the phases concerned, i.e., gas, liquid, or solid phase, are reflected through the changes occurring in two of the surface energy terms. Thus, a change in the liquid composition would be noted in sL and GL, and it is this phase, the liquid, which is most frequently altered in flotation studies., Changes in the solid phase must be reflected through the changes occurring in the sG and sL terms. In particular, it is hypothesized that changes in the surface concentrations of point defects in the solid-phase will alter the sG and sL terms which, in turn, will be reflected by flotation results. As an illustration of this hypothesis one may consider the defect structure and the flotation of AgC1. The bulk defect structure of AgCl is essentially one involving equal number of cation vacancies and interstitial cations.3 Upon adding CdC1, to AgC1, a greater number of silver ion vacancies are created in the bulk of the crystal.4 On the surface of the crystal the smaller binding forces and the free space accomodations may also allow for the creation of "surface interstitial anions", which will be designated as ad-anions. Thus, the point defect structure of the surface of AgCl doped with CdCl, will consist of cation vacancies and/or adanions. If the molecular forces responsible for the surface energies, ?SG and ?sL, are significantly altered by the presence of these surface point defects, then differences in flotation results will be noted as the concentration of these defects is varied. The defects present in AgCl are predominantly atomic in nature. In the case of PbS both electronic and atomic defects are present.5 This compound conducts electrically by either electrons or electron holes depending upon whether excess lead or excess sulfur is present. Upon disolving BiS3 in stoichio-metric PbS, one increases the concentration of cation vacancies and the number of electron carriers in the bulk of the crystal.5" At the surface, the possibility of ad-anions must also be considered. Conversely, upon dissolving AgS in stoichiometric PbS one increases the concentration of interstitial cations and the number of electronhole carriers in the bulk of the crystal.5,6' At the surface the interstitial cations will be designated as ad-cations. Thus, the point defect structure of the surface of a PbS crystal doped with Bi2S3 will consist of a number of cation vacancies and/or ad-anions and an excess of electrons. Conversely the point defects on the surface of a PbS crystal doped with Ag2S will consist of a number of ad-cations and an excess of electron holes. Again, as in the case of AgC1, should the molecular forces responsible for the magnitude of the interface free energies, ?sG and ?sL, be significantly altered by the presence of these surface defects then significant differences in flotation results will be noted as the concentration of these defects is varied. EXPERIMENTAL To test this hypothesis flotation tests were conducted on pure and doped AgCl and on PbS doped with either Bi2S3 or Ag2S. Preparation of the AgCl samples was performed as follows: AgCl and weighed amounts of CdC1, were melted in a porcelain crucible. The melt was then forced through a capillary tube and the particles emitted solidified in air as they fell about 1.5 meters. Spherical particles, -0.50 + 0.25 mm, were separated from the remaining solidified material

Jan 1, 1963

By E. M. Wise

THE practice of dentistry, particularly the construction of artificial dentures and "bridges," involves a unique and difficult application of the precious-metal alloys. Appliances used in the mouth are continuously exposed to corrosive agencies which can hardly be described as mild, and must remain free from tarnish and be substantially immune to corrosion. Limitations with respect to space and weight demand high physical properties, while complexity of form requires ease of working. The high corrosion resistance required necessitates the use of alloys of high precious metal content. The usual expedient of resorting to mechanical working to produce the requisite strength and stiffness cannot be utilized because of the frequency of annealing and soldering operations. To meet these difficult conditions manufacturers of dental goods were early led, unknowingly perhaps, to the production of precipitation-hardening or temperable alloys. The excellent properties of iridium-platinum may have suggested the addition of platinum metals to the conventional gold-silver-copper alloys to produce greater strength and hardness. It was found that such quarternary alloys retained their high physical properties after passing through the usual soldering process; i, e., heating to 7500 to 8000 C. and cooling naturally in the air. Later it was discovered that they could be softened and rendered more ductile by heating to the same temperature and quenching, in water. These early examples of precipitation hardening, for years the common knowledge, of dental practitioners and laboratory technicians, escaped the attention of the scientific world and discovery of the transformation which was responsible for this hardening was discovered by the Russian investigators of the system Au-Cu, Kurnakow, Schemtschushny and Zasedatelev,(1) § although the optimum conditions for securing good properties in aged alloys were not given attention.

Jan 1, 1932

By John Fritz

MEMBERS of the American engineering societies who were in London and Paris during the last days of. June and early July were present at many interesting gatherings. The official delegates of the Founder societies were the specially honored guests of the foreign engineering societies, but other American engineers took part in the meetings. The members of the delegation were: Arthur S. Dwight, Charles F. Rand, William Kelly, representing A. I. M. E.; Ambrose Swasey (general chairman of deputation), Ira N. Hollis, Jesse M. Smith, representing A. S. M. E.; F. B. Jewett, A. E. Kennelly, G. O. Squier, representing A. I. E. E.; Charles T. Main, Robert A. Cummings, John R. Freeman, D. C. Henny, representing A. S. C. E.

Jan 1, 1921

The following paragraph of appreciation of the Engineering Societies Employment Bureau is from the letter of a young engineer who found the Bureau of service. "I wish to sincerely thank you for the services rendered. They are of immense value to anyone located as I am, in a small town without the opportunities for keeping in touch with openings in manufacturing lines."

Jan 12, 1919

Henry D. Hibbard, New York City (communication to the Secretary): The title of Mr. Sargent's paper is somewhat misleading, since the paper itself relates chiefly to various kinds of annealing and their effects, and in very small part only to heat-treatment proper. This term has a well-defined meaning in steel metallurgf, and always includes a rate of cooling faster than the material treated would have in the open air. In bringing about this accelerated rate of cooling, some medium other than air at rest is brought into contact with the heated steel. Usually a liquid (almost always either oil or water) is employed ; but for certain steels a blast of air, and for others an easily fusible or soft metal, such as led (either solid or melted), may be used. Heat-treatment usually includes also subsequent moderate heating, followed, it may be, with another accelerated cooling.

Jan 1, 1902

By Evan Just

Attempting to analyze a 25-year forecast after less than a third of the time has elapsed may seem premature. The President's Materials Policy Com- mission's report necessarily painted with a broad brush and made no claim for pinpoint accuracy in its predictions. More importantly for present purposes, it made no attempt to predict the detailed courses of production and consumption during the period forecasted. Several statistical highs and lows may very well lie between now and 1957, so comparing recent figures with points taken from the report on a straight-line basis would be illogical. Moreover, the report assumed that the general trend of consumption-domestic and foreign-would be upward. Contrarily, domestic figures were lower in 1957 than in 1950. Therefore, to project curves from 1950 through 1957 leads to conclusions that are probably false. Many in the industry would feel more uncertain about forecasting 1975 domestic conditions now than they would have been in 1950, even though nearly a third of the 25 years has elapsed. In making comparisons, several statistical problems are encountered. The Paley report figures for 1950 were estimated in several cases and corrected figures vary as much as 10 pct. For example, the report placed 1950 lead consumption at 800,000 tons, whereas actual consumption was 885,000 tons. Obviously, in comparing more recent figures with the report's projections, adjustments must be made for positions taken in error from the start. Over the long pull, such discrepancies will probably be insignificant, but they must be noted in comparing short-term changes.

Jan 10, 1959

By James Aston

Three years ago the writer presented a paper on the trend of development in the wrought iron industry,' wherein was described a process in the development of which he has been a factor, which at that time had passed through several years of progressive experimental development but which had not then been put upon a commercial scale of operation. The present paper deals with two years of observation and experience in the commercial operation of a plant by the A. M. Byers Co. at Warren, Ohio. It will not enter into the controversial field of the relative merit of wrought iron and steel in various classes of service, nor will it elaborate upon the characteristic services or fields of utility to which wrought iron is particularly adapted. It is sufficient to state that the wrought iron industry is upon a substantial basis and that the material finds service in pipe, where its advantages are in superior corrosion, fatigue, welding and threading qualities; in bar iron for staybolts, engine bolts, and rivets, demanding maximum service against corrosion and fatigue; in plates for corrosion service; and in chains, because of welding and shock-resisting characteristics. In short, ability to withstand the stresses of shock and vibration, or the ravages of corrosion, to hold protective coatings, and to give maximum efficiency in welding, are its features of relative superiority. If these features were not well recognized, the wrought iron industry would have shrunk to insignificance in the face of high costs and acknowledged limitations in manufacture. To charge that this industry is built upon a structure of assumption, psychology, and improperly weighed evidence is an impeachment of the integrity or belittling of the powers of observation of users through many centuries of service experiences. In a history which extends to prehistoric time, and which is linked up with the earliest records of ferrous products, the dominant method of manufacture, as we have known it for little over a century, occupies a very small niche in the span of years that mark production and use of wrought iron. Puddling, the outstanding manufacturing method of

Jan 1, 1929

By JOHN MARKLE

JOHN MARBLE, mining engineer, coal operator, philanthropist, member of the Institute since 1879, vice-president in 1903-04, has been paid the well deserved tribute of Honorary Membership. The presentation of the diploma was made at a luncheon in New York on Feb. 13, the citation reading: "In recognition of his work as an engineer and administrator of mines and his services to mining engineering education." Within the last month Lafayette University dedicated the new John Markle Mining Engineering Building, the gift of the eminent alumnus for whom it is named. In addition, Mr. Markle has contributed a maintenance fund for the carrying out of far-reaching plans for improving the mining courses to be given at the Institution. One of his theories is that quality rather than quantity of engineering graduates is the need of the profession. John Markle was born in Hazleton, Pa., in 1858. He received his degree of M. E. at Lafayette in 1880, and married Mary Estelle Robinson in New York City in 1884. Since 1880 he has been associated continuously with the firm of G. B. Markle & Co., and its successor companies. He has also been an official of numerous other important companies, although he is now retired from active business life.

Jan 1, 1930

By Milnor Roberts

WAR struck the mineral industry of Washington with cross currents that produced a peculiar result. The State's production of coal, industrial minerals, and metals for 1941, valued at $28,507,282, was increased in 1942 under war pressure to approximately $35.000,000. Meanwhile a tremendous demand had arisen for men to construct airfields and many other large projects for the Army and Navy in Washington and Alaska, and Government plants for the mineral industry costing $140,000,000 or more, as well as a call for employees in the U. S. Navy Yard at Bremerton, the sixty shipyards, the four Boeing airplane factories with many auxiliary shops, and hundreds of other plants turning out war materials. In spite of an influx of nearly 300,000 people, causing an increase of 17.1 percent in the population since 1940, according to the Census Bureau, the State clearly is still engaged in an unusual amount of war production in proportion to its population. A large proportion of the workers have been drawn from the mineral industry to the war plants, whether through motives of patriotism, high wages, or, in the Boeing plants at least, the glamour of the operation

Jan 1, 1944

By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958