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By T. N. Dixon, J. E. Briggs

A study was made of numerical techniques for solving the large sets of simultaneous equations that arise in the mathematical mode ling of oil reservoir behavior. It was found that noniterative techniques, such as the Alternating Direction Implicit (ADI) method, as well as some other finite difference approximations, produce oscillatory or unsmooth results for large time steps. Estimates of time step sizes sufficient to avoid such behavior are given. A comparison was made of the Point Successive Over-Relaxation (PSOR), Two-Line Cyclic Chebyshev Semi-Iterative SOR (2LCC), and iterative ADI methods, with respect to speed of solution of a test problem. It was found that, when applicable, iterative ADI is fastest for problems involving many points, while 2LCC is preferable for smaller problems. INTRODUCTION With the advent of high speed, large memory, digital computers, there has been an increasing emphasis on the development of improved methods for simulating and predicting reservoir performance. Two-dimensional, three-phase reservoir models with various combinations of PVT effects, as well as gravity and capillary forces, are common throughout the industry. Such models are also available through consulting firms, to anyone desiring to use them. Three-dimensional models will probably be practical in only a few years. We conducted a study of some of the numerical methods used for solving the large sets of simultaneous equations that arise in such models. A typical set of equations for a reservoir model is shown below:

Jan 1, 1969

By A. B. Parsons

LAST YEAR (1934) saw the completion of a ten-year program of reconstruction and modernization of the world's largest lead- smelting plant, that of the ' Broken Hill Associated Smelters Proprietary, at Port Pirie, South Australia, which has a capacity for smelting and refining 220,000 (short) tons of lead per year. It deals with the entire output of lead concentrates from the famous Broken Hill district in Australia, being owned .jointly by the three leading companies: North Broken Hill, Broken Hill South, and the Zinc Corporation. These companies, together with the Sulphide Corporation, are credited with a production of 198,000 tons of lead in 1934. When one says regarding any metallurgical plant that modernization is "completed" he should add "for the moment." Development in the art of metallurgy and in the equipment used never ceases; that which seems close to the last word today is likely to be obsolete in a few years even in a process so well standardized as smelting and refining lead. However, the reconstruction at Port Pirie has altered the procedure materially. More im-

Jan 1, 1935

By Albert Hill Fay

IN giving a sketch of the geology and mining of the tin-deposits of Cape Prince of Wales, a short description of the geographic and climatic conditions may be of special interest on account of this being a part of the world of which very little is known, even by the reading public. As shown in Fig. 1, the location of the Cape is lat. N. 65° 35' and long. W. 168°. It is bounded on the north by the Arctic ocean ; on the west by Bering strait and on the south by Bering sea. It is the western-most point of the mainland of North America, and to the west, across the strait, one can see East Cape, Siberia, which consists of a rugged, steep coast of granite cliffs. The climatic conditions are of interest because of the part they have had in the surface geology, and also because they affect mining from an economic standpoint. In connection with the climate and geography, it does not seem out of place here to quote a few lines from the prologue of The Wandering Jew, written by Eugene Sue, under the caption '1 The Land's End of Two Worlds."

Sep 1, 1907

By R. J. Arsenault

The yield drop that occurs in tantalum, Cu-AZ. and Ag-Al was investigated as a function of strain rate and at several temperatures. From the strain-rate dependence of the yield drop an activation volume was calculated and found to agree with that obtained from differential strain-mte tests. The temperature dependence of the yield drop can he explained in terms of the parameter temperature divided by activation volume. The yield drop is attributed to the rapid multiplication of dislocations during their motion. THE yield-point or yield-drop (upper yield stress minus the lower yield stress) phenomenon has been the subject of numerous investigations1-9 in both bcc and fcc metals. Also, there is no dearth of theoretical explanations10-20 to account for the yield-point phenomenon. The present explanations can be divided into two categories: the concept of dislocation locking and subsequent unlocking and the concept of multiplication of dislocations due to their motion. The Vottrell10,11mechanism of locking and unlocking, as applied to bcc metals, is the best known of the three proposed locking mechanisms. The two additional mechanisms, short-range order (SRO)7,16,17 and Suzuki-type locking,14,15 have been employed to account for the existence of yield points in fcc metals. The experimental evidence supporting the locking of dislocations, especially in bcc metals, is well-established. The dependence of the yield point on interstitial concentrations,' the kinetics of strain aging,2 and the observations by electron-transmission microscopy18 are some of these experimental results. The number of experimental observations supporting dislocation locking in fcc metals is not as extensive as in bcc metals. The unlocking of dislocations, which actually is supposed to account for the yield drop, is by no means well-established by experimental results for either bcc or fcc metals. The similar temperature dependence6 of the yielding and plastic flow is one of the experimental factors that cannot be explained in terms of the unlocking of dislocations. The mechanism based on the rapid multiplication of dislocations has been proposed by several investigators. 18-20 Johnston and Gilman19 have proposed a detailed model of yielding, which was later employed by Hahn21 to predict quantitatively the yield drop in iron. This mechanism was discussed in a previous paper22 and several limitations were pointed out. In the same paper it was shown that an activation volume could be obtained from the strain-rate dependence of the yield drop and that a correlation existed between the activation volumes obtained from the yield-drop tests and from differen-

Jan 1, 1964

By J. C. Bradley

THE relation of annealing temperature to conductivity of copper wire has been determined. Conductivity hard was 98.26 per cent. After a 10-min. heating at 200°C. it was 98.69. By annealing 10 min. at 300° C. a large increase, to 100.93, occurred. Maximum conductivity, 101.15, was attained after a 500° C. anneal; thereafter it decreased to 100.53 after a 950° C. anneal. If copper is gassed the decrease is much more than this. Materials and Methods The work was done on high grade electrolytic copper, 99.942 per cent. copper plus silver, silver 0.0008 per cent. It was hot-rolled to >/4 in., then cold drawn to 0.080 in. The wire was cut into 25 5-ft. lengths and numbered 1 to 25 as cut. Four samples were tested hard. The others were wound into 5-in. diameter coils. For the 100° C. heating a coil was put into water, the water brought to boiling, and the wire kept at this temperature for 10 min. For the higher temperatures the coils were placed in envelopes of sheet copper, a little water added, and the envelopes sealed by folding over the edges twice, and hammering them together. This kept the air out very well. The envelope and wire 'were brought to the desired temperature; this was maintained for 10 min., then the whole was water-quenched.

Jan 1, 1927

By E. A. Gulbransen, K. F. Andrew

Thermodynamic information on the solubility of hydrogen in exothermic metals is limited. Thus, the overall solubility decreased as the temperature rose, which suggests the heat of solution of hydrogen in the metal is negative; yet the terminal solubility in the metal phase increased, which suggests an endothermic reaction. A thermodynamic analysis, therefore, was made of the several equilibria involved when hydrogen dissolved in the metal. Equations were derived expressing the solubility, terminal solubility, and decomposition pressures of hydrogen in terms of the heat, entropy, and free energy of solution of hydrogen in the given phase. The relations between the thermodynamic functions for the a-zirconium and 8-hydride phase were developed. The thermodynamic quantities were determined experimentally by the measurement of the decomposition pressures over a broad composition and temperature range. Two new methods of analyzing the experimental data were developed for determination of the terminal solubility. STUDIES', ' of the impact strength of zirconium at room temperature indicated that small quantities of hydrogen, of the order of 10 parts per million, embrittles the metal. Micrographic' and X-ray diffraction' studies showed this embrittlement to result from the precipitation of a second phase upon slow cooling. These studies suggested that the terminal solubility of hydrogen in the metal phase increased with increase of temperature. This behavior appeared to contradict the effect of temperature on exothermic hydrogen occluders such as zirconium. For these metals, the solubility of hydrogen should decrease with increase of temperature. Before these facts could be understood, a thorough analysis of the several equilibria was essential. It was the purpose of this paper to consider the several equilibria involved when hydrogen was reacted with zirconium from both the theoretical and experimental points of view. Since the overall solubility of hydrogen in the metal has been considered by a number of workers, it was proposed to study the composition range 0 to 6 atomic pct H in detail. Literature Schwartz and Mallett' determined the terminal solubilities of hydrogen in the metallic phase from diffusion studies. They extrapolated concentration-penetration curves to the boundary between the solid solution phase and the hydride phase at the surface. Their results showed values of 2.6 atomic pct at 400°C and 5.2 atomic pct at 500°C. Extrapolations of the data to room temperature suggested very low values for the terminal solubilities. This study confirmed the hydrogen embrittlement results and indicated that the terminal solubilities increased as the temperature was raised. The solution of hydrogen in zirconium over the complete concentration range was studied by Hall, Martin, and Rees3 and by others. The results showed that hydrogen was absorbed up to a maximum composition of 66 atomic pct or ZrH This composition represented the t-hydride phase. The maximum amount of hydrogen absorbed increased with pressure and decreased with temperature. Due to this temperature behavior, zirconium was classed as an exothermic occluder." In 1930 Hägg studied the crystal structures of the Zr-H alloys over a broad composition range. Four hydride phases were found. However, the range of homogeneity of the several phases was not studied. Gulbransen and Andrew" recently studied the phase diagram of this system by X-ray diffraction methods and by a thermodynamic method based on decomposition pressure measurements. The results showed that only two hydride phases existed for low temperatures, the 6 and the .-phases of Hagg.' Both phases had broad regions of homogeneity. The lower limit of the two-phase region of a and d-phases suggested a terminal solubility of 4 atomic pct at 500°C. This value was in agreement with the results of Schwartz and Mallett.' To avoid hydrogen embrittlement at low temperatures, it was necessary to heat the metal in high vacuum at elevated temperatures. To choose the conditions of temperature and high vacuum, it was

Jan 1, 1956

By Charles W. Perry

The options of enhanced oil recovery, coal syncrude, and shale syncrude are compared by approximately equivalent economics. The physical constraints for the major enhanced oil recovery processes are described, followed by new estimates of cost. The range for all three options in terms of light syncrude equivalent are $22 to $40 per barrel in 1980 dollars.

Jan 1, 1982

By R. S. Archibald, L. S. Chabot

The Blueberry mine is about 10 miles west of Ishpeming, Marquette County, Michigan. The property consists of about 2000 acres in sees. 3, 4 and 5, T. 47, N.R. 28W. and secs. 32, 33 and 34, T. 48, N.R. 28W., and, excepting one intervening 80-acre tract, contains the iron formation for a length of about 21/4 miles. The property is traversed by State Highway M-28 and is served by three railways, the Chicago & Northwestern, the Duluth, South Shore & Atlantic, and the Lake Superior & Ishpeming. The Northwestern transports the ore to a dock at Escanaba; the other railways, to Marquette. Ore for Chicago goes via Escanaba and that for Lower Lake ports, as Detroit, Cleveland, and Buffalo, via Marquette. History The presence of iron formation in this property has been known for many years, and mining operations on a small scale have been carried on intermittently. The Dexter mine, on the SE.1/4 of the NW.1/4 of sec. 3, was worked from 1883 to 1897 and 118,000 tons of ore was mined. From 1907 to 1915 extensive exploration was carried on over the whole of sec. 3, including 79 diamond-drill holes with a total footage of 26,000 ft. The Chase mine, on the NE.1/4 of the NE.1/4 of sec. 3, was developed from this exploration work, but after about 200,000 tons had been mined the property was abandoned. From 1908 to 1910 exploration was carried on by another company on sec. 4, 47-28, including four drill holes with a total footage of about 5000 ft. Much of the drilling on sec. 3 and of the exploration work on sec. 4 are within the present developed area of the Blueberry mine. A general campaign of diamond-drill exploration was undertaken in 1924, and within a year a considerable amount of ore was developed. The Ford Motor Co. then took an option on the property and carried on check drilling and diamond-drill work until the spring of 1926, when enough ore had been developed to warrant the sinking of a shaft

Jan 1, 1937

By George A. Laird

I. INTRODUCTION. THIS old and once famous district played, through its enormous production of silver and gold, an important part in the history of the State of San Luis Potosi. According to a pamphlet prepared under the direction of the Governor of the State, Sr. Don Blas Escontria, and presented to the visiting members of the Institute during the Mexican meeting of 1901, this district is situated 20 km. east of the city of San Luis Potosi, in a range of mountains of moderate height, extending 135 km. N. and S., and 16 km. E. and W.; and the mineralized area hitherto developed is about 600,000 sq. m. The history of the district,. as given by the record dated 1778, and formerly kept in the San Francisco convent, says that it was discovered in 1575 by Sr. Don Pedro Irarte, and adds that the city of San Luis Rey de Francisco del Potosi received its name (in allusion to the famous Potosi mines in Bolivia) by reason of the remarkable productiveness of its gold- and silver-mines in the first period of their exploration, during which they paid to the Crown, as " quintos " (the fifth part of the product), $97,000,000, as appears from the accounts of the royal treasury. The amount of the quientos paid during the " bonanza period " of 80 years was $72,000,000. The larger sum first mentioned probably represents a longer series of years. But either will suffice to indicate the great wealth of the mines. In 1663, the decadence of the industry began with the caving¬ in of several mines, concerning which the record of 1778, al¬ready cited, says, in substance, that on Good Friday one of the owners in the enterprise, in view of the unfavorable prospect of a lawsuit in which he was engaged, set fire to the timbers supporting the underground galleries and workings of the San

Jan 1, 1905

Jan 1, 1880

By D. C. DERINGER

METALLURGISTS and mill operators appreciate, in a general way, .the economic or commercial relationship between recovery and grade of product but few have correlated in detail fluctuating metal prices with the metallurgy. They know that many factors such as metal price, dedusiions for returning charge, transportation, percentage of metal in head ore, etc.; all affect the commercial relationship between recovery and grade of product. In practically every mill some one at some ' time has calculated the amount of recovery that can be sacrificed for each percentage increase in grade of concentrate and from this calculated ratio the commercial or ., economic tail has been established. Such a ratio finally becomes a well-entrenched rule by which the progress of the metallurgy is judged.. When once established, these-, ratios are but seldom corrected to changes of metal prices for each possible grade of concentrate that may be produced. The calculation is tedious when often repeated. Other methods have been suggested and used to correlate the commercial with the metallurgical phase. A factor .derived ,by multiplying the grade of concentrate by recovery is often used, but is of little importance because it does not possess a single commercial quantity. The percentage monetary recovery calculated by dividing the gross value of the ore into the net smelter return gives a good economic index and, is to be commended, but it is difficult to correlate exactly and quickly the work of each day on a commercial basis.

Jan 1, 1931

By Henry S. Rawdon

Any laboratory corrosion test, as judged from the practical point of view, is valuable only to the extent that it foretells what will, in all probability, occur in service. Such a test is most properly to be considered as a "pilot test," that is, a test which indicates the direction along which action may be expected to occur rather than as a truly quantitative test which would be expected to tell just how and to what extent the action would proceed. It is generally recognized that laboratory corrosion tests should be chosen with particular reference to the character of service expected for any particular type of metal, so far as it can be foreseen. Even when this requirement has been fulfilled, however, the question whether the actual service behavior of the material is in accordance and general agreement with predictions based upon such laboratory tests is always a pertinent one. The information available in the technical literature bearing on the correlation between the service behavior of metals from the corrosion standpoint, and the results obtained with the same metals in laboratory corrosion tests is very meager, indeed. The results which have been obtained in weather-exposure tests of sheet duralumin which form the body of this discussion are presented here for their bearing on this particular phase of the problem of the corrosion resistance of duralumin. Although the exposure tests described have not been completed, in the sense that all of the tests, in the series initially laid down, have been accomplished, still the general trend shown by the results is so clear that a number of definite conclusions at this stage (subject, of course, to possible modification in the light of later results) are believed to be warranted. The tests reported upon here form one phase of the much broader study of this subject which has been under way for several years in which the National Advisory Committee for Aeronautics, the Bureau of Aeronautics of the Navy Department, the Army Air Corps and the Bureau of Standards have cooperated. Without the very helpful cooperation of the manufacturers in furnishing the

Jan 1, 1929

By Henry S. Rawdon

Any laboratory corrosion test, as judged from the practical point of view, is valuable only to the extent that it foretells what will, in all probability, occur in service. Such a test is most properly to be considered as a "pilot test," that is, a test which indicates the direction along which action may be expected to occur rather than as a truly quantitative test which would be expected to tell just how and to what extent the action would proceed. It is generally recognized that laboratory corrosion tests should be chosen with particular reference to the character of service expected for any particular type of metal, so far as it can be foreseen. Even when this requirement has been fulfilled, however, the question whether the actual service behavior of the material is in accordance and general agreement with predictions based upon such laboratory tests is always a pertinent one. The information available in the technical literature bearing on the correlation between the service behavior of metals from the corrosion standpoint, and the results obtained with the same metals in laboratory corrosion tests is very meager, indeed. The results which have been obtained in weather-exposure tests of sheet duralumin which form the body of this discussion are presented here for their bearing on this particular phase of the problem of the corrosion resistance of duralumin. Although the exposure tests described have not been completed, in the sense that all of the tests, in the series initially laid down, have been accomplished, still the general trend shown by the results is so clear that a number of definite conclusions at this stage (subject, of course, to possible modification in the light of later results) are believed to be warranted. The tests reported upon here form one phase of the much broader study of this subject which has been under way for several years in which the National Advisory Committee for Aeronautics, the Bureau of Aeronautics of the Navy Department, the Army Air Corps and the Bureau of Standards have cooperated. Without the very helpful cooperation of the manufacturers in furnishing the

Jan 1, 1929

By S. J. Hruska

Rate expressions for the formation of two-and three-dimensional nuclei on foreign substrates are developed, taking into account previously neglected contributions to the standard Gibbs free energy of formation of critical nuclei. The temperature dependence of critical super saturation data predicted using these expressions is in accord with data for cadmium on copper and sodium on CsCl. EXPERIMENTAL data on the heterogeneous nuclea-tion of metal crystals from the vapor phase1&apos;2 exhibit the temperature dependence predicted by a nucleation rate equation derived by Pound et al.3 In their treatment, the critical nuclei are visualized according to the Volmer4 model as cap-shaped (three-dimensional). Accordingly, it seems desirable to compare these data with a nucleation rate equation which is derived on the assumption of disk-shaped (two dimensional) nuclei. Further, Lothe and Pound5 have recently shown that the standard Gibbs free energy of formation of these critical nuclei contains a contribution which has heretofore been neglected. Thus it is necessary to re-examine these nucleation data using a rate equation which contains this contribution. The van&apos;t Hoff isotherm relates n(i), the concentration of nuclei of critical size i (i = number of atoms), to nil), the concentration of adsorbed single atoms: where standard Gibbs free energy of formation of critical nuclei given by is temperature insensitive and is the bulk free energy change/volume of transformed material], T = substrate temperature and k = Boltzmann&apos;s constant. Previously,3 was determined by considering only the contributions of bulk and surface free energies in transforming i atoms from the population nil) to a cluster of i atoms. It has been shown5 that this procedure does not take into account the free energy contribution arising from the multiplicity of sites, q, where the clusters can be situated. If this contribution, -kT In q/n(l),is added to iG3 [Note that this increases n(i) by a factor q/n(l).] Since the above does not affect the remaining terms in the rate expression of Pound et al., the details are referred to their paper. The resulting nucleation rate is If the experimental AGV and T values at some common value of are employed, a plot of vs T(ln C3/l + In p&apos;) should yield a straight line of slope k/B<p and intercept . The corresponding plots for / = 1 nucleus per sq cm sec and C3 = 1018 are shown in Figs. 1 and 2 for cadmium on copper1 and sodium on CsCl2 and the values of obtained therefrom are entered in Table I. It is apparent that the data yield reasonable straight lines with about the same scatter as found using the equation of Pound et al. When the configuration of minimum free energy for a nucleus is a circular monatomic layer, the standard free energy of formation is

Jan 1, 1963

By R. A. Young

Zinc metal production in the operating plants in the United States during 1948 was approximately equal to that of the year 1947, although new developments during the year assure higher output in 1949, if economic conditions are favorable. In the Western plants, the man-power shortage was almost completely overcome and new capacity has been or is in the process of being added to three plants; thus by December of 1948 daily zinc metal production had risen to the highest point since May of 1944 despite strikes in one large primary smelter and in one secondary plant.

Jan 1, 1949

By Evan Evans

WITH the expiration on April 30, 1941, of the agreement between the anthracite operators and the United Mine Workers of America, a new agreement was entered into, providing for a general wage increase of 7 1/2 per cent effective May 1, to be brought to a total of 10 per cent on Oct. 1. Contract rates were increased from the rates established under the agreement of September 1923, and hourly rates were raised above the agreement of May 1936 as modified from the eight-to seven-hour day in May 1937. The new rates are to be in force for the duration of the agreement, ending April 30, 1943.

Jan 1, 1942

By Merlin H. Aylesworth

THE subject assigned to me is peculiarly appropriate to the anniversary of the birth of Abraham Lincoln. If we applied to our present problems the ideals and methods of the Great Emancipator, the future of American institutions would be so definitely assured that there would be little need to discuss the matter. The only inquiries would relate to the pace of progress, not to the possibility of progress. As a nation we have grown more and more to revere the memory of Lincoln, to honor his character, to extol his teachings and to eulogize his concepts of democracy. We rec-

Jan 1, 1940

Aamot, Olav Crone, (M&apos;29) Chem. Engr., Elektrokemisk, Raadhusgt. 23, Oslo, Norway. Abadilla, Quirico A., (M&apos;3S) Min. Engr., Dir., Bu¬ reau of Mines. Manila, P. I. Abbott, Agatin Townsend, (J&apos;40) Jr. Engr., Phelps Dodge Corp., Morenci Branch, Morenci. Ariz. Abbott, Clarence E., (M&apos;04) Civil Engr., V.P., Ten¬nessee Coal Iron & R.R.. Co., 1542 Brown -Marx Bldg.. Birmingham, Ala. Abel, Raymond L., (M&apos;28) Chem. Engr., Command¬ing, Officer, Pittsburgh Chem. Warfare Procurement Dist., American Bank Bldg., Pittsburgh. Pa. Abel, Walter D., (M&apos;32) Alin. Engr.. Div. of Cor¬porations, State of Calif., 403 California State Bldg., Los Angeles, Calif. Abele, Louis T., (M&apos;31) 423 3rd Ave., Decatur, Ga. Abell, Leo M., (M&apos;31) Mill Supt. & Met., Emperor Gold Min. Co., Led., Vatnkoula, Fiji Islands. Abernathy, G. E., (M&apos;38) Geol., Kansas State Geol. Survey, Pittsburg, Bans. Abernathy, Jack H., (M&apos;40) Peer. Engr., c/o Superior Oil Corp., National Bank of Tulsa Bldg., Tulsa, Okla. Aborn, Robert H., (M&apos;10) Asst. Met., Research Lab., U. S. Steel Corp., Lincoln Highway, Kearny, N. J. Abraham, A. W., (M&apos;39) Peer. Engr., Richfield Oil Corp., 555 S. Flower St., Los Angeles, Calif. Abramowitz, William L., (J&apos;40) Chem., Industrial Inventions, Inc., 103 Foster Se., Peabody, Mass.

Jan 1, 1942

By Bieniawski, Z. T.

The importance of understanding the phenomena associated with rock fracture has long been fully appreciated in rock mechanics. This is clearly apparent from the special attention paid to rock fracture in the comprehensive papers published within the past four years. These papers present a picture of how the knowledge of brittle fracture of rock was gradually enriched and also show that what was often taken for granted three or four years ago is no longer considered as valid today.

Jan 1, 1972

By Joseph N. Morrison

A comprehensive solution is offered to the problem of dust emissions at belt conveyor transfer points. Details of enclosure design are discussed and a straightforward procedure for calculating required dust control exhaust volume is presented. Many design variables are taken into account which heretofore have been commonly ignored or inadequately considered. These include belt widths, belt speeds. enclosure openings, material flow rate, material bulk densities, material lump sizes, height of material fall, material temperature, and ambient air temperature. All of these questions are handled by means of a "fill-in-the-blanks" type of calculation form, permitting quick, reliable solutions by relative "non-experts."

Jan 1, 1972