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By K. G. Davis, P. Fryzuk

A study has been made of the effect of undercooling on the grain structure and solute distribution in small ingots of pure bismuth and of a 100 ppm Ag in bismuth alloy. Autoradiographic evidence shows that in undercooled melts a network of dendrites is formed throughout the melt immediately after nu-cleation. At large undercoolings the dendrites are very thin and closely spaced. The origin of the observed grain morphology can be explained on the basis of information about the mode of solidification revealed by the impurity substructure. WHILE a great number of studies of nucleation in undercooled molten metals have been made, comparatively little attention has been given to the mode of solidification from melts with large undercool- ings. Colligan and Bayles1 and Walker2 have measured the rate of advance of the solid-liquid interface in undercooled nickel melts, but the morphology of the solidifying material remained a matter of speculation. Fehling and Scheil3 have described the grain structure in ingots formed from undercooled melts of nickel, palladium, and copper, and a series of Ni-Cu and Ni-Pd alloys. At small undercoolings, equiaxed structures are observed, the grain diameter tending to increase as the temperature of nucleation is lowered. At greater undercoolings, a columnar structure is developed, while with still further undercooling there is a smaller grain size incorporating rather coarse subgrains. All-bright and Colligan4 examined the grain structure shown by ingots solidified from melts of nickel and of Ni-Ag alloy at an undercooling of 105°C, and concluded that considerable grain growth had taken place after solidification. The object of the present work is to correlate the mode of solidification from undercooled melts with both the grain structure and impurity segregation, using tracers to examine the latter.

Jan 1, 1965

By Arno C. Fieldner

METALLURGICAL coke and the by-products of the carbonization of coal continue in strong demand. Nearly 500 new by-product ovens were constructed in 1943. Output of by-product coke in the first ten months of the year was about 2 1/2 percent higher than in the corresponding period of 1942, but beehive production remained on approximately the same level as last year and constituted about 11 per cent of the total coke output.

Jan 1, 1944

By Joseph C. McCaskill

The writer assumes that this volume is not intended to serve as a source of statistics on international trade and that the reader is not interested in wading through a lot of statistical tables copied from the various reporting agencies. Generalizations therefore are made whenever possible and not always is the source of the information meticulously cited. The United Nations regularly publishes trade data on mineral commodities. E. J. Gealy, and C. L Kimbell, of the U S Bureau of Mines (USBM), work with these data and estimate that they cover approximately 78% of total mineral commodities traded. In addition the General Agreement on Tariffs and Trade (GATT) publishes analyses of certain trade data The most complete report of production and trade in minerals 1s probably the international volume of the U.S. Bureau of Mines Yearbook The latest available edition is for 1968, and some of the data in this edition cover only as late as 1967. Unless otherwise stated, the source of data used in the chapter is this Yearbook Other staff members of the Bureau were most helpful and cooperative They are not to be held responsible for conclusions or points of view to be found in the chapter. THE NATURE AND SCOPE OF INTERNATIONAL TRADE The two and a half decades since World War II have witnessed an unprecedented growth international commerce The end of the war found the world economy seriously crippled. Many countries had suffered severe war damage; international trade was disrupted and nations had to resort to exchange controls and bilateral trading arrangements. The postwar recovery, however, was remarkably rapid Within two decades, world Income more than doubled, and world trade which was less than $60 billion in 1948 exceeded $200 billion in 1968, 8 and reached $278 billion in 1970.18 The growing world trade contributed to world prosperity which in turn fostered growth of trade. This dramatic growth of international commerce was made possible by the progressive liberalization of trade and capital movements by the major trading nations of the world which began immediately after the War and has not yet completely lost its steam. The modern-day stimulus of the expanded trade movement was the enactment by the Congress of the United States in 1934, of the

Jan 1, 1976

Roof Bolts An expansion shell and plug Westinghouse roof bolting assembly made for use with threaded steel rods and large flat washers or steel channel employs a plug larger in diameter than those for trolley wire service. The notched plug helps prevent shell and plug from turning. The unit is shipped complete. Circle No. 1 Fan The Jeffrey Mfg. Co. Aerodyne Midget fan is a self contained blower or exhauster for auxiliary ventilation through tubing. Operating rating with 5 hp motor is 6.5 in. maximum static pressure, and 6200 cfm free delivery volume. Weight is 340 to 475 lb and it may be furnished in open or permissible form. Circle No. 2 Heavy-Density Initial installation in the Mesabi Range country of the Wilmot-Daniels heavy-density concentrating system was a 175 ton per hour plant at the [ ] Skubic Bros. Virginia, Minn., operation. This Wilmot Engineering Co. unit has a separatory vessel providing unidirectional medium flow and as the only moving part uses a standard drag-line conveyor for lifting sink out of the bath. Circle No. 3 Portable pH Meter A low priced battery-operated portable pH meter of utmost simplicity announced by the Photovolt Corp. uses only 3 ordinary radio batteries which give over 2000 hours of service. Accuracy of 0.03 pH is claimed by the manufacturer for the model 125, and AC power line supply is available. Circle No. 4

Jan 1, 1952

By J. E. Tobey

UNDER war conditions coal immediately assumes a position of highest importance for coal must carry the basic load for industry. The upward trend in production continued through 1941. Bituminous coal production alone about equaled the total output of bituminous and anthracite in 1940. The figures for 1941 approximated 500,000,000 tons for bituminous, and 54,000,000 tons for anthracite, and production of by-product and beehive coke exceeded that of the previous year. The coal industry, under the National Bituminous Coal Act, is going through a period of readjustment, and is beginning to stabilize itself under the statute. The Federal Mine Inspection Nill became law during the year.

Jan 1, 1942

By CHRIS A. HARTNAGEL

For the second consecutive year, the production of crude petroleum in New York has fallen below the 5,000,000-bbl. Mark that had prevailed previously since 1937. In 1945, the output totaled 4,658,000 bbl., a decrease of slightly more, than one per cent from the 1944 production. This total represents 2 per cent of the stripper-well production of the United States, which in turn is I 3 per cent of the total annual yield of the nation's petroleum.

Jan 1, 1946

By Warren B. Weeks

The year 1940 saw an increase of 20 per cent in oil production over the previous year—compared with a 16 per cent increase the previous year. In all, 25,790,380 bbl. were produced, an increase of 4,414,150 bbl, over 1939 and the largest production figure for south Arkansas since 1928. The older settled production continued to decline. Magnolia accounted for most of the increase, with aid from the other recent deep fields. During the year, 169 wells were drilled, 79 fewer than in the previous year. Of 131 wells drilled in proven fields, 18 were dry. Three of the 38 wildcats were pool openers. The drilling depth record was increased from 9028 to 9550 feet. Trend of Prospecting For the first time since 1936, the search for oil in the deep Smackover limestone slackened perceptibly; g dry wildcats ended in Smackover, 2 in. the underlying Eagle Mills; 7 penetrated Paleozoic beds, while 9 ended in Hosston, 2 in Glen Rose, 2 in Paluxy and 4 in Gulf. Geology The wells listed in Table 2 either resulted in the discovery of new oil pools or, because of their depth or location, afforded impor-tant stratigraphic or structural informa-tion. Fig. I is a general columnar and stratigraphic section showing the relation-ship of the strata within the Comanche series. The nomenclature shown was ac-cepted by the Shreveport Geological Society. It was subsequently published by Imlay,l who indicated probable correlations with other areas and presented evidence for the possible Jurassic age of the under-lying Cotton Valley and Smackover formations. New Fields Pouke.—On June 10, 1940, the Louark Producing Co. completed its No. I Sturgis, sec. I, T. 17 S., R. 27 W., in central Miller County, producing between 3583 and 3607 ft. in the upper part of the Paluxy forma-tion. The well flowed I00 bbl. of 3r.4' gravity oil per day through Ns-in. tubing choke. This discovery resulted from seismograph work. Six other wells were drilled in the area, none of which found production in the original sand. One of these wells is producing from a sand 50 ft. deeper in the section. The others were abandoned. No further development is in prospect. Production is from lenticular sands of the upper Paluxy; 45,556 bbl. had been pro-duced by the end of 1940. There is structural closure against a fault to the northwest. McKanzie.—The Atlantic Refining Com-pany's No. I Bodcaw Lumber Co., sec. 29, T. 17 S., R. 23 W., eastern central La-fayette County, was completed June 8, 1940, as the eighth and farthest west of the Smackover (Reynolds o6lite) limestone pools. The well flowed 10 bbl. an hour of 58.6' gravity distillate through an 1 1/64 Ma-in. tubing choke, with a gas-oil ratio of 8400:I.

Jan 1, 1941

By Warren B. Weeks

The year 1940 saw an increase of 20 per cent in oil production over the previous year—compared with a 16 per cent increase the previous year. In all, 25,790,380 bbl. were produced, an increase of 4,414,150 bbl, over 1939 and the largest production figure for south Arkansas since 1928. The older settled production continued to decline. Magnolia accounted for most of the increase, with aid from the other recent deep fields. During the year, 169 wells were drilled, 79 fewer than in the previous year. Of 131 wells drilled in proven fields, 18 were dry. Three of the 38 wildcats were pool openers. The drilling depth record was increased from 9028 to 9550 feet. Trend of Prospecting For the first time since 1936, the search for oil in the deep Smackover limestone slackened perceptibly; g dry wildcats ended in Smackover, 2 in. the underlying Eagle Mills; 7 penetrated Paleozoic beds, while 9 ended in Hosston, 2 in Glen Rose, 2 in Paluxy and 4 in Gulf. Geology The wells listed in Table 2 either resulted in the discovery of new oil pools or, because of their depth or location, afforded impor-tant stratigraphic or structural informa-tion. Fig. I is a general columnar and stratigraphic section showing the relation-ship of the strata within the Comanche series. The nomenclature shown was ac-cepted by the Shreveport Geological Society. It was subsequently published by Imlay,l who indicated probable correlations with other areas and presented evidence for the possible Jurassic age of the under-lying Cotton Valley and Smackover formations. New Fields Pouke.—On June 10, 1940, the Louark Producing Co. completed its No. I Sturgis, sec. I, T. 17 S., R. 27 W., in central Miller County, producing between 3583 and 3607 ft. in the upper part of the Paluxy forma-tion. The well flowed I00 bbl. of 3r.4' gravity oil per day through Ns-in. tubing choke. This discovery resulted from seismograph work. Six other wells were drilled in the area, none of which found production in the original sand. One of these wells is producing from a sand 50 ft. deeper in the section. The others were abandoned. No further development is in prospect. Production is from lenticular sands of the upper Paluxy; 45,556 bbl. had been pro-duced by the end of 1940. There is structural closure against a fault to the northwest. McKanzie.—The Atlantic Refining Com-pany's No. I Bodcaw Lumber Co., sec. 29, T. 17 S., R. 23 W., eastern central La-fayette County, was completed June 8, 1940, as the eighth and farthest west of the Smackover (Reynolds o6lite) limestone pools. The well flowed 10 bbl. an hour of 58.6' gravity distillate through an 1 1/64 Ma-in. tubing choke, with a gas-oil ratio of 8400:I.

Jan 1, 1941

By Jim F. Lemons

INTRODUCTION A nickel doesn't buy much anymore. That's even true in the cost of recovering nickel -- the commodity. A 5[C] per pound (11 [c] per kilogram) increase in the nickel price won't cover a 10-percent increase in fuel costs for processing laterite ores, nor will it cover a 10- percent increase in wages for recovering nickel from a sulphide ore. It won't even cover a 5- percent increase in the capital cost necessary to mine and process ocean nodules. The basis for this statement and a quantitative analysis of the variations in costs to recover nickel from different types of nickel ores will be discussed in this paper. During the early part of the 1970's, the interest in nickel and its potential development was shifting from Canada to the Pacific Basin area. Canadian growth rate was slowing and each additional increase in nickel capacity was very expensive (Argall, G.O., 1970). Laterite ores were attractive to developers since they were easy to mine at a low labor cost, and technologies were being developed that would allow the recovery of nickel in marketable forms (Mohide, T.P., Warden, C.L., Mason, J.D., 1977). During the last decade, new laterite production was achieved in the Philippines and Botswana, and a significant increase in production from Indonesia and New Caledonia occurred. However, recent reports on nickel identify numerous problems plaguing the industry, i.e., high energy costs that are forcing shutdowns (INCO, 1980), (Mohide, T.P., Warden, C.L., Mason, J.D., 1977), high Canadian sulphide mining labor costs (Anon., 1976), and rapid inflation of nickel capital costs (Anon., 1981b). No definitive study has been made to determine how sensitive the total cost of production is to rising energy, labor, or capital costs, or to identify to what extent increased byproduct revenues could be used to offset these production costs. The purpose of this paper is to quantify the effects of increases in energy, labor, capital costs, and by-product credits on the future cost of production from nickel reserves and/or resources. METHODOLOGY OF ANALYSIS In order to evaluate the sensitivity of nickel production costs to changes in energy, labor, and capital costs, and in byproduct revenues, an analysis was made of existing and proposed nickel operations, their costs, and their sensitivity to change. The data for these analyses were obtained from numerous sources including international govern¬ment and university publications, professional journals, company reports, private communications, U.S. Bureau of Mines contracts, and estimates by Bureau of Mines personnel. These data were collected, in part, as an ongoing effort of the U.S. Bureau of Mines Minerals Availability System (MAS) to systematically measure and classify identified mineral resources according to their respective extraction technologies, economics, and commercial availability. The MAS Program is currently evaluating the present and potential availability of nickel to the United States in relation to mining, beneficiation, smelting, refining, leaching, transportation, infrastructure, environment, land use, labor, productivity, technology efficiencies, operating capacities, deposit life, and political factors. As a summary of this data, the following briefly describes nickel ore types as each relates to energy, labor, capital, and byproducts. Sulphide Operations Nickel is currently available from sulphide deposits. Roughly 55 percent of the current world nickel production in market economy countries is from sulphide ores, although only about 20 percent of the known land-based nickel reserves and/or resources are sulphides (INCO, 1981). In 1979, the Western World sulphide reserves were estimated at about 9.2 million metric tons of nickel (Little, A.D., 1979). Sulphide ores are typically mined underground, thus resulting in high mining costs; however, these ores can often be upgraded by flotation prior to final nickel recovery and require about one-third of the energy required to recover nickel from laterites (Anon., 1981c). In addition, nickel in sulphide ores may be associated with economically recoverable byproducts, which include copper, cobalt, gold, silver, and other precious metals. Laterite Operations Forty-five percent of current nickel production is from laterite deposits. Laterite deposits account for 80 percent of the known land-based nickel reserves and/or resources (INCO, 1981). In 1979, the Western World laterite reserves were estimated at over 35 million metric tons of nickel (Little, A.D., 1979). Nickeliferrous laterites are residual soils formed by weathering, typically under tropical or near tropical conditions. They can be easily mined by open-cut methods, but generally cannot be beneficiated; thus, recovery of nickel must entail processing of the total mined ore. Usually, these ores have high moisture content (20 to 30 percent by weight) that result in additional fuel costs to dry the ore. Nickel silicates, garnierites, are, processed by pyrometallurgical methods; limonite nickel oxides are normally leached. Byproduct cobalt is not recovered from most ferronickel operations, and is only recovered to a limited extent from many leach operations.

Jan 1, 1982

By JESSE L. MAURY

ONE OF the most hopeful features of the current depression is the discussion which it has en- gendered of ways and means to counteract similar recurrences in the future. 1t is widely recognized that fruitful attack will be directed toward the steady employment of labor, through which the purchasing power of this preponderant class in society will be maintained. S. A, Lewisohn's article' has presented the major factors to be considered; the physical suffering and mental torture endured by those who are deprived of income through no fault of their own, the direct economic losses' sustained in the degradation of 'great, numbers of our population and the disintegration of efficient working forces, and the prime responsibility of owners and managers.

Jan 1, 1931

By William B Price, Ralph W. Bailey

Arsenic, antimony and phosphorus are now used in the brass industry as standard inhibitors in preventing dezincification in condenser tubes. This subject has been thoroughly covered by Barry,l who de- scribed the testing procedure by total immersion of suitable specimens in a I per cent cupric chloride solution at definite temperatures. Effects of dezincification were then determined by loss in tensile strength and elongation of the test specimens after definite periods of immersion. In the crystallography of the chemical elements as tabulated by William Hume-Rothery,2 phosphorus (metallic), arsenic, antimony and bismuth are placed in group V-B and the type of crystal lattice for arsenic, antimony and bismuth is given as rhombohedral. The Metals Handbook3 lists them as 'rhobomhedral hexagonal," with the additional notation that for arsenic this is the ordinary form at 20°C.; other modifications known or probable at other temperatures. In view of these statements and of the fact that phosphorus, arsenic and antimony are effective in increasing the resistance to dezincification, it was natural to assume that bismuth would act in the same manner. A series of tests was therefore carried out employing the methods described by Barry. Much to our surprise, bismuth did not inhibit dezincification, but rather seemed to accelerate it. Tensile-test speci-

Jan 1, 1942

By Ralph W. Bailey, William B. Price

Arsenic, antimony and phosphorus are now used in the brass industry as standard inhibitors in preventing dezincification in condenser tubes. This subject has been thoroughly covered by Barry,l who de- scribed the testing procedure by total immersion of suitable specimens in a I per cent cupric chloride solution at definite temperatures. Effects of dezincification were then determined by loss in tensile strength and elongation of the test specimens after definite periods of immersion. In the crystallography of the chemical elements as tabulated by William Hume-Rothery,2 phosphorus (metallic), arsenic, antimony and bismuth are placed in group V-B and the type of crystal lattice for arsenic, antimony and bismuth is given as rhombohedral. The Metals Handbook3 lists them as 'rhobomhedral hexagonal," with the additional notation that for arsenic this is the ordinary form at 20°C.; other modifications known or probable at other temperatures. In view of these statements and of the fact that phosphorus, arsenic and antimony are effective in increasing the resistance to dezincification, it was natural to assume that bismuth would act in the same manner. A series of tests was therefore carried out employing the methods described by Barry. Much to our surprise, bismuth did not inhibit dezincification, but rather seemed to accelerate it. Tensile-test speci-

Jan 1, 1942

By Louis E. Reber

Jan 1, 1922

By Elbert Rowland

THE widespread interest in the alloys of beryllium with copper is due principally to the fact that certain compositions show very favorable precipitation-hardening characteristics and are, in fact, the strongest nonferrous alloys known at the present time. Investigations have been conducted by Masing and Dahl and others on the physical characteristics of ternary beryllium alloys, in an attempt to produce precipitation-hardening effects with a smaller amount of beryllium than that required in the binary copper-beryllium alloys (2.0 to 2.5 per cent Be). The results of these investigations show that ternary alloys of beryllium with Cu-Sn, Cu-Al and Cu-Zn, among others, exhibit promising improvements in physical properties after precipitation-hardening treatment and, while the increases in properties obtained are not as high as those realized from the binary copper-beryllium alloys, excellent properties are obtained with beryllium contents averaging about one-half the amount required in the binary alloys. This paper presents the results of an investigation of the equilibrium relations of certain alloys containing copper, tin and beryllium. The alpha-phase boundary of the ternary system is given for alloys containing from 0 to 1 per cent beryllium. The equilibrium conditions beyond the alpha-phase boundary are presented for alloys containing up to 32 per cent tin and 1 per cent beryllium. The data were collected by means of

Jan 1, 1935

By R. W. Smith, R. W. M. Lai

Although several recent papers have shown that equilibrium contact angle in dodecylamine solution-quartz systems can often be directly correlated with flotation behavior, it appears that under conditions of relatively high amine strength and pH such a correlation can't be made. Under these conditions, when there are precipitated amine dipoles present, it appears that a dynamic contact angle formed immediately after introduction of fresh gas bubbles into the system is also of importance. The dynamic angle decreases in magnitude as a function of time. Apparently the decrease is the result of changes in interfacial tensions (liquid-gas and solid-gas) as a function of time. Dynamic angles of the type described can't be observed in trimethyldodecylammonium chloride solution-quartz systems. Several recent papers1-3 have shown quite conclusively that contact angle data can often be correlated directly with flotation behavior in cationic surfactant solution-quartz systems. At the same time, Iwasaki, Cooke, and Colombo4 have shown data for a dodecylammonium chloride solution-goethite system where, in the vicinity of pH 12 and a collector concentration of 10" M, 100% flotation occurs when equilibrium contact angle appears to be zero. A clue to this discrepancy can be found in the work by smith2 who reported the occurrence of dynamic, time dependent, contact angles in a quartz-dodecyl-amine solution system at relatively high pH values and at surfactant concentrations greater than or equal to 10-4 M. It was found that under these conditions, if a fresh bubble was brought into contact with a properly conditioned and polished quartz surface, a large angle was obtained. The large angle, however, instantly started to diminish in magnitude, sometimes to a smaller stable angle and sometimes to its complete disappearance. Also, if the bubble was preconditioned for some minutes (or sometimes even seconds) in the same amine solution, the smaller or sometimes zero stable angle was obtained when the bubble was brought in contact with the quartz surface. One is immediately led to the thought that perhaps it is these dynamic angles when they exist, not stable angles, that are of primary importance in flotation. The present investigation attempts to further study the relationship between contact angle and flotation

Jan 1, 1967

By O. W. Shimer, D. C. Helms, C. E. Brown

The early history and progress of anthracite stripping, from the first known operation at Summit Hill in 1821 through 1917, was covered in 1917 in a paper by J. B. Warriner,1 then chief engineer, now president of the Lehigh Navigation Coal Co., and stripping methods between 1917 and 1931 were the subject of a paper in 1931 by H. H. Otto,2 of the Hudson Coal Company. The present paper is confined to methods used today on pitching beds in the western middle and southern anthracite fields. The anthracite industry, not unlike other large industries, had been affected for more than a decade by the adverse economic conditions of the country. High development and operating costs and the competition of other fuels caused some collieries to be closed temporarily, while others were permanently abandoned. In order to obtain a larger tonnage at a lower development cost, a larger stripping program was put into effect by many companies. In 1932, stripping operations accounted for 3½ million tons, or 7 per cent of the total anthracite production of the year, and in the next 10 years this increased until more than double that amount, or over 14 per cent of the total production, was from stripping operations. These figures represent the total production of the entire anthracite region; unfortunately, the figures have not been separated from the different fields. There are some operations in the southern and middle western fields where the tonnage obtained from stripping amounts to more than 30 per cent of the total colliery production. Stripping operations on pitching beds present difficult problems. Owing to the various geological formations, a different situation is encountered in nearly every stripping pit; and because of the proximity of an overlying bed, it is very often necessary to load the entire overburden into trucks and haul it out of the pit to the dump area, although back filling and casting is done whenever possible. Beds in the areas described in this paper pitch from 20" to 90° and some are on the invert in many sharp folds and faults. Planning The more successful strippings have had adequate engineering analysis. Some work is being done without much preliminary planning, but many strippings would have failed completely if close supervision by the engineering department had not been maintained. Locations of stripping areas are determined as follows: I. By constructing cross sections over the areas and drilling sufficient diamond-drill or well drill holes to study the strata and to determine the location, thickness and pitch of the beds.

Jan 1, 1946

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By G. W. Tracy, R. D. Carter

Numerical calculations were made to determine the behavior of reservoirs with high-pressure drawdown and wide well spacing where the initial productivity is low and the wells are completed by hydraulic fracturing. The two-phase flow equations were solved for the flow into a single well. This well was assumed to be producing from a reservoir with hydraulically created horizontal fractures (four different systems with fractures were studied). For comparison purposes, additional two-phase flow calculations were made assuming a reservoir with uniform rock properties. The two-phase flow results were also compared with the conventional calculation methods, which do not include the effect of saturation gradients resulting from a simultaneous flow of oil and gas which are normal to this type reservoir. It was found that the conventional methods predict (1) a high and too optimistic value of ultimate recovery, (2) a high producing rate and a high reservoir pressure at a given oil recovery and (3) a low trend of gas-oil ratio with oil recovery. Included in the two-phase flow calculations were provisions to control the oil production rate by an allowable rate and, also, by a gas-oil ratio penalty rule. For the systems with hydraulic fractures, the producing rate was controlled by the gas-oil ratio penalty rule for most of the life. This is in contrast to the system with uniform rock properties which went "on decline" almost immediately. An unexpected characteristic of the systems which included fractures was the early rise in producing gas-oil ratio from 730 cu ft/bbl to approximately 1,200 cu ft/bbl, followed by a "leveling off" before the normally expected gas-oil ratio rise began. Additional features which are a result of hydraulic fracturing are (I) greater ultimate recovery, (2) higher average producing rates and (3) a lower average reservoir pressure at a given oil recovery. INTRODUCTION Some oil fields discovered during the past few years are producing from certain volumetric ally controlled reservoirs (often referred to as solution or internal gas- drive reservoirs) which are characterized by high-pressure drawdown at the wells. Since the available pressure drawdown at a well is limited by the static reservoir pressure and the producing rate is controlled by the available drawdown, wells completed in this type of reservoir usually produce at a rate less than the allowable from the time of completion. Because of this, this type of reservoir is referred to as a low productivity reservoir. Economic considerations require the use of wide well spacing and well stimulation by hydraulic fracturing to make commercial wells in this type of reservoir. Performance predictions for volumetrically controlled reservoirs have been made using a combination of two standard equations. 1. The "Schilthuis" or "Muskat" type material balance equation is used to relate the average reservoir pressure and the cumulative oil recovery. 2. The results from the material balance equation and the productivity factor as described by Pirson' are used to relate the cumulative recovery with producing rate and time. The material balance equation assumed uniform pressure and liquid saturation conditions throughout a reservoir. The steady-state radial flow formula allows for a pressure gradient toward a well but assumes uniform liquid saturation. These calculation methods are adequate for application to reservoirs wherein the drawdown at the well to realize satisfactory producing rates is small compared to the total pressure. In low productivity, volumetrically controlled reservoirs, the pressure drawdown at the well is large cornpared to the total pressure. Although a precise number cannot be given for the magnitude of a large pressure drawdown, values in excess of 1,000 psi would definitely be included. For practical considerations, this usually occurs when the formation flow capacity is less than about 100 md-ft. However, this limit of formation flow capacity will vary with the well producing rate. The low pressure in the neighborhood of the well which results from a high drawdown causes evolution of large volumes of gas. This causes the gas saturation to be higher near the well than at a greater distance—-hence, a non-uniform gas saturation. Also, the relationship between the relative permeability to oil (K/K) and gas saturation is nonlinear but decreases approximately in an exponential way with increases in gas saturation. Because of this, the following chain reaction is established.

By Will B. Jamison

Man's material advance from one level of civilization to the next has involved the development of new, more useful tools and the utilization of energy greater than he alone could produce. These two essentials for material progress have developed at an ever increasing rate in the last century. While the first really successful use of mechanical energy derived from burning fuel was in James Watt's steam engine which pumped water from coal mines in Cornwall about 1770, there was still very little use of mechanical energy in mining by 1900 except for pumping and hoisting. Compressed air, having some of the characteristics of steam and which operated engines not unlike steam engines or steam hammers, powered the first attempts to mine coal with energy greater than human muscle could provide. When direct current-powered traction cars replaced horse-drawn transportation cars on city streets, it was natural that direct current locomotives should begin to replace animal and human power in mine haulage. Slowly, trolley and battery locomotives were developed and introduced. With d-c systems being established for haulage, it was natural that improved cutting machines should be developed and powered by d-c motors. Thus began the years of

Jan 5, 1960

By C. A. Zapffe

BOTH the foundryman and the theoretical metallurgist are now generally agreed that the anomalous "rising" or "bleeding" of certain ferrous castings of killed metal is primarily attributable to hydrogen. How and why the phenomenon occurs, however, have not been made clear. The following discussion is intended to harmonize foundry experience with metallurgical theory so that the foundryman may possibly improve his ability to prognosticate whether a certain casting may bleed or not. BLEEDING, RISING, AND PIPING The "rising" to be discussed here is not to be confused with the action in rimming ingots as a result of the carbon-oxygen reaction, although a conclusion will be drawn that may apply to the art of controlling the rimming action. Only killed metal is considered, which includes both steels and irons. In Fig. I, three killed, chill-cast ingots are shown: a porous ingot whose evolution of gas during late stages of solidification has ejected metal through the top; an ingot in which moderate gas evolution during solidification has lifted the mushy central metal, i.e., it has "risen"; and, third, a sound ingot with good piping characteristics. The first type is referred to as "bleeding," and generally infers that a solid skin had first formed through which the liquid metal later erupted. There is no fundamental distinction between bleeding and rising in reference to killed metal.* POROSITY Hydrogen appears as a cause of bleeding because the gas evolution simultaneously leaves a porosity of a type traceable to hydrogen. Twenty years ago, Melmoth1 noted that killed steel that rose unexpectedly in the mold, if returned while liquid to the furnace and heated further under a reducing lime slag, would again rise in the mold; but that if the ingot were allowed to solidify and was then remelted no rising occurred. A critical quantity of the responsible gas is therefore removed by the rising action. Melmoth associated rising with high silicon (0.7 to 0.9 per cent) and concluded that silicon increased gas absorption. Because silicon is a strong deoxidizer, oxygen must, therefore, be eliminated from consideration of the three common gases in steel-oxygen, nitrogen, and hydrogen. Butterworth2 later decided that pinhole porosity was caused by gases dissolved in the metal and that hydrogen was obtained from steam in the mold. Allen's classical work on copper castings,3 soon followed by

Jan 1, 1942