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By M. S. Klima, P. T. Luckie

Interfacing new or improved unit operations SUBMODULES with the EXECUTIVE of a macro analysis simulator usually requires modification of the input data. For example, particle processing SUBMODULES that are sufficiently general in nature to provide useful predictions require input data for rather narrow size fractions. Such data is not always available for the EXECUTIVE and must therefore be generated by the SUBMODULE. A successful interface to allow incorporation of a new SUBMODULE for comminution and one for classification in a general stream state flowsheet simulator is presented. The general nature of the SUBMODULES, as well as the logic of expanding and contracting the required data input is discussed.

Jan 1, 1983

By H. D. Dahl, Roger C. Parsons

In order to improve roof stability, Continental Oil Co.'s research program, initiated in 1969, was directed toward defining the geological parameters that affect the severity of roof conditions in any particular area of the mine. In addition, the program was seeking to define why roof falls in the Humphrey No. 7 mine (and in northern West Virginia-southwestern Pennsylvania coal mining areas) are oriented so that they occur primarily in north-south rooms or entries. Conclusions and recommendations from this study of roof fall orientation are given.

Jan 1, 1973

By A. A. Dor

Out of nine new major iron ore concentrators put in operation during the last three years, or expected to be commissioned in 1968, seven incorporate primary grinding mills and have a total design capacity of 13,150,000 ltpy of pellets, while only two include conventional rod and ball mill grinding circuits for a total design capacity of about 6,100,000 ltpy (Table I). This evolution in the application of primary grinding to hard, fine grained magnetite ores represents an important development in the technology of mineral processing. It has been the outcome of comprehensive testwork in the laboratory and in pilot plants.

Jan 11, 1968

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Position open as assistant superintendent at a steel plant. Practical experience in the manufacture of crucible and open-hearth steel and heat treatment of steel and alloy steels required. This position offers an excellent future. No. 9. A company in Virginia desires a man with experience in Western mines to act as superintendent of its pyrite mine. No. 15. Position open as instructor at a University in Middle West to teach the mechanical side of mining, such as hoisting, haulage, drilling, and mine surveying. Salary, $1,500 to $1,800. No. 16. Experienced amalgamator wanted at a mill in Ivory Coast, Africa. An American speaking French preferred. No. 18.

Jan 5, 1914

By W. H. Moore, E. T. Powell

IN the early days of mining in the Anthracite field, only the thicker and better seams of coal were mined, because of the limited mining and coal-cleaning facilities, therefore many of the thinner and less productive seams were permitted to remain unmined. With improvements in mining methods, the introduction of modem preparation plants, and the increased market demand for small-size coal, the thinner and more laminated seams have now become assets. In many instances these seams overlie the mined-out beds of the thicker and better seams, from which all recoverable coal was removed by the conventional breast-and-pillar method of mining. Some collieries in certain sections of the Anthracite field are now relying on these thinner and laminated seams. For the purpose of illustration, a large area in the Hickory Swamp-Ridge Basin of the western middle coal field has been selected, where as early as 1898 the No. 4, or Little Buck Mountain, seam was mined and pillars removed. The No. 5, or Buck Mountain, seam lying on a comparatively light pitch and with intervening strata of but 55 ft. of rock was not mined until 1935. Farther east, in the same basin the Nos. 8 and 9 seams, which are two splits of the Mammoth seam, have been mined and robbed and the workings have been abandoned since 1896. The overlying No. 9 ¾ seam, or the upper split of the Mammoth, and the No. 9 ¾ or 4-ft. seam remained virgin, with only an interval of 50 ft. of rock separating them, and with 40 to 50 ft. of rock strata separating the No. 9 ½ seam from the completely mined area of the Nos. 8 and 9 seams. These seams lie on a pitch of 45° on the south side of the basin and on 75° on the north side of the basin. Mining has been carried on in the 9 ½ and 9 ¾ seams for 3 years on both dips of the basin, for a distance of 3500 ft. In some sections the overlying strata of the thicker seams previously mined have settled without any apparent breaks in the upper strata, as indications have shown in the top split of the Mammoth; while in other areas the roof and bottom of this top split of the Mammoth have settled unevenly, thereby causing the bottom and roof to break into blocks. In attempting to mine over a large area of the No. 5 or Buck Mountain seam, a similar settlement has been encountered; the roof of the seam has been broken and a considerable amount of timbering has been necessary in order to make the mining of the seam possible. The conventional breast-and-pillar method, using shaker conveyors, has been used in the No. 5 seam, and a slant-breast method in the mining of Nos. 9 ½ and 9 ¾ seams. MINING OF LIGHT-PITCH SEAMS The No. 4 seam was mined and robbed by the conventional breast-and-pillar system. In this area the seam pitched from 5° to 25° on the north dip, averaged 8 ft. in thickness and had a slate bottom and a

Jan 1, 1941

Report of Secretary TO THE BOARD OF DIRECTORS OF AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen -I have the honor to present the following report for the calendar year 1920 The activities which-seem to call for special com¬ment are THE NEW FORM OF MAGAZINE MINING AND METALLURGY appeared every month during the calendar year and has been developed until it contains some ten departments It has brought forth more commendatory letters than have been received at headquarters on any other subject throughout the year Less than a dozen letters unfavorable to the change have been received, and the indications are that the magazine has met a want deeply felt, especially by members distant from headquarters The technical papers printed by the Institute are published in abstract in the magazine and opportunity is given to members who desire them to receive full copies of any or all papers published The Bound Volumes, as usual, contain all the papers in full and discussions thereof FINANCES The greatly increased cost of paper and printing has put a tremendous burden on the Institute's finances, since the dues of $12 per year are only 20 per cent greater than the members paid when the Institute was founded forty-nine years ago This has resulted in a temporary deficit, similar to that encountered by many of our sister engineering societies The fact that our Institute has lower dues and gives more in the way of publications to its members than any other of\the national engineering societies has rendered the situation more difficult for us MEETINGS The Annual Meeting in New York, the Field Meeting in the Lake Superior District, the meeting of the Petroleum and Gas members at St Lours, and of the Institute of Metals Division in Columbus, Ohio, have all been described in full in the magazine

Jan 1, 1923

INTO their great Pacific Northwest counting house went the members of the Industrial Minerals Division recently, to count their blessings amidst the scenic grandeur and mineral wealth of the State of Washington. From their vantage point in Seattle, those who attended the IMD's fourth Pacific Northwest meeting turned their sights to the South and Southeast, scanned Montana, Idaho, Oregon and Utah, and predicted a very healthy economic future for their region. The praises of Idaho's booming phosphate industry were sung by Earl W. Murphy, secretary of that State's Chamber of Commerce. He said the establishment of Fort Hall, on the banks of the Snake River near Pocatello, first turned the eyes of the world toward what is now the center of the greatest known deposits of phosphate rock-the section adjacent to the common corners of Idaho, Wyoming and Utah. With the founding of Fort Hall, Mr. Murphy said, historians will also rank the construction of the first electric furnaces for the production of elemental phosphorous as equally significant in the commercial history of the West. Those furnaces were installed only last year by the Westvaco Chemical Div. of the Food Machinery & Chemical Corp. at Pocatello, at a cost of $8 million.

Jan 7, 1950

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,' based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry' has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962

By Marvin Lee

Kansas continued holding, for its seventh year, the fourth position in the list of oil-producing states. The crude-oil production, according to purchaser's reports to the State Corporation Commission, was 40,008,940 bbl.; as assembled by the Oil and Gas Journal, 41,305,768, and by the U. S. Bureau of Mines, 41,942,000 barrels. Increase of production from 1932 was largely due to greater stability of the industry, and increased return of demand for Kansas oil, caused by the addition of Federal assistance in national production regulation which reduced illegal production, of some areas out of Kansas, that had been destructively competing with Kansas crude or its refined products, at less than cost of production. Prices continued to advance from the lowest level of 25c per barrel during part of May and June, until by the end of September 36" gravity crude had reached $1 per barrel and continued at this price the remainder of the year. Price stability, for a period greater than in previous years, has brought renewed confidence to those producing oil and has led to renewed interest and increased purchases of Kansas leases. Drilling was confined chiefly to the number of wells necessary to protect from offset and other drainage in the field and to meet the requirements of expiring lease contract deeper areas in Mid-Continent, are an added inducement to exploration. The renewal of interest in the search for new fields in Kansas is already apparent and 1934 will probably see more wildcatting than for several years. This is due both to the expiration of leases on large blocks and to actual demand of the industry for new fields. Exploration for favorable areas is being actively conducted by the various methods of surface, subsurface and core drilling and geophysical work. Much of western Kansas cannot be mapped by surface study and geophysical exploration has been of considerable assistance and has led to a large use of the seismograph. Several companies are conducting seismograph surveys and leasing on findings already secured. Development under the more favorable conditions of 1933 can be readily seen by the comparison of the following reports for the last weeks of December in the respective years.

Jan 1, 1934

By A. Rosen, P. Wynblatt, J. E. Dorn

The temperature, strain rate, and structure dependence of the flow stress in a poly crystalline Fe-2 pct Mn alloy was investigated between 77" and 370°K. It was possible to identify the low-temperature data from 77° to 160°K with Dorn and Rajnak's theory of the Peierls mechanism of plastic deformation. Above 160°K one or more thermally activated mechanisms must he operative; however, these were not identified in this investigation. The mechanistic basis for the rapid decrease in the flow stress of bcc metals with an increase in temperature over the low-temperature range is yet being debated. Various dislocation mechanisms have been suggested in the past but the agreement between the various proposed theories and the experimental results have not been definitive. In the present paper, the authors will demonstrate that the plastic behavior of polycrystalline iron containing 2 wt pct Mn plus interstitials agrees excellently with predictions based on the Peierls mechanism from 77" to 160°K whereas from 160" to about 370°K other as yet unidentified thermally activated mechanisms take over. Undoubtedly, the overlap of these mechanisms with the Peierls mechanism contributed to the difficulties of rationalizing the low-temperature behavior of iron and its alloys. I) EXPERIMENTAL TECHNIQUES AND RESULTS Although extensive data are now available on the effect of temperature and strain rate on the flow stress of various bcc metals and alloys, it was, nevertheless, deemed necessary for the objectives of the present study to obtain highly accurate data of the type most pertinent for checking the theories on a series of well-documented work-hardened states. Iron containing 2 wt pct Mn was used in this investigation in order to obtain a lower ductile to brittle transition temperature than that for iron.' The additional elements present were 0.004 pct C, 0.05 pct 0, 0.004 pct S, 0.003 pct P, 0.006 pct N, and 0.001 pct Si. The as-received 3/8 by 3/4 in. bars were cold-rolled to 0.100-in. thickness, recrystallized under argon for 30 min at 1073"~, further cold-rolled to 0.063-in. thickness, and finally recrystallized under argon for 30 min at 1000°K. This treatment gave a stable reproducible equiaxed grain structure having an average grain diameter of about 90 p. Prior to the final recrystallization treatment, the sheet was machined into tensile specimens 1/4 in. wide having a 1.625-in.-long gage section. All specimens were tested in controlled-temperature baths on an Instron Testing Machine. For convenience in the theoretical analyses the data will be given in terms of the shear stress for flow, 7, the shear strain rate, f, and the shear strain, y. A series of three standard strain-hardened states were obtained by prestraining specimens at 300°K and at a shear strain rate of 7.68 x lo-' per sec to three stress levels of 6.89 X l08, 10.3 X lo8, and 14.5 x 10' dynes per sq cm, respectively. Immediately following this prestrain the temperature bath was changed and each specimen was pulled in tension at either f = 7.68 X lo-' or f = 3.06 X 10"3 per sec. In terms of the accuracy that was achieved, the values obtained did not deviate more than *0.1 X 10' dynes per sq cm and * 1°K from the reported values of stress and temperature and not more than *5 pct in the reported values of the strain rate. The tensile stresses were converted to shear stresses using a factor of 1/2. The shear stress for the initiation of flow at the test temperature was determined by taking a y = 6.16 x 10'3 offset. from the modulus line at which point good accuracy could be achieved in determining y and the associated flow stress 7, with only a negligible increase in the pre-

Jan 1, 1965

By G. J. Heuer, J. N. Dew, G. C. Clark

The effect on well behavior of partial permeability barriers, changes in producing rates and well spacings have been calculated through use of a radial, unsteady-state, two-phase-flow mathematical model. This model allows for variations in permeabilities and porosities with distance from the wellbore. The numerical methods necessary to solve the problem require use of a highspeed digital computer, in this case an IBM 704. In each instance, pressure and saturation gradients, gas-oil ratios and recoveries around a well producing by solution-gas drive have been calculated as a function of time and distance from the wellbore. Comparisons are made to show the effect of changes in producing rate and of varying permeability near the wellbore and out in the formation on the production and pressure history of the well. The effect of different well spacings on producing rate and ultimate recovery is considered. Although the mathematical description of the reservoir is simplified in comparison to an actual reservoir, the results do give some insight into the difficult problem of spacing and proration in a heterogeneous solution-gas-drive reservoir. Results show that for the cases considered spacing has little effect on ultimate recovery and that permeability barriers removed from the well decrease producing rate for a period of time but have only a small effect on ultimate production. INTRODUCTION The effect of spacing and producing rate on the production characteristics and ultimate recovery of a well producing by the solution-gas-drive mechanism have been topics of interest to the oil industry for many years and the subject of many hearings before state regulatory bodies. The problem is very complicated because of the difficulty of simulating in the laboratory a reservoir producing by the solution-gas-drive mechanism under anything like normal field conditions. This paper gives the initial results of a study aimed at determining the effect of these factors on production from reservoirs simulated by a mathematical model. Two-phase, unsteady-state equations are used to calculate pressures, saturations, and rates of oil and gas flow as a function of time and distance from the wellbore. The model is radial, and reservoir properties may be varied with distance from the wellbore. A decrease in permeability at a given distance results in a low-permeability ring concentric with the wellbore through which all the fluids from more distant portions of the reservoir must flow. The current mathematical model allows for variation of permeability, porosity and saturations as a function of distance from the well. Any desired drainage radius for the well may be selected. Drainage radii of 745 and 1,053 ft, which correspond to 40- and 80-acre spacing, were chosen for the calculations which follow. A large amount of the input data has been held constant. No investigation was made into the effect of changes in fluid properties and relative permeability characteristics on oil and gas production behavior. Fluid properties and relative permeabilities are essentially those of the White Mesa portion of the Greater Aneth area in southeastern Utah. A recently concluded hearing before the Utah Oil and Gas Conservation Commission to determine spacing for the field aroused interest in the possible effect of permeability constrictions located some distance from the well on production and recovery. This interest stimulated the present study. In this paper, no attempt has been made to simulate any field production characteristics exactly. Only the solution-gas-drive mechanism has been investigated, and production by liquid expansion has not been considered. This investigation is exploratory in nature but does give some insight into the problems of spacing and proration in a solution-gas-drive field having permeability variations. THE MATHEMATICAL MODEL The mathematical model is similar to that proposed by West, Garvin and Sheldon.' Approximately the same techniques have been used in arriving at a solution. The equations are nonlinear, partial differential equations which have been known for some time. The particular equations used for this study neglect the effects of capillary pressure and gravitational forces. The advent of modern digital computing equipment has made their solution practical. Basically, the method solves for pressure, saturations, and oil and gas flow rates as a function of distance and time. In our model, distance to the

By A. M. Gaudin

IN flotation lime is used to depress pyrite. For this purpose it is preferred to caustic soda. The low cost of lime and the widespread availability largely account for this preference. However, there is some evidence1 that pyrite is more readily depressed by calcium than by sodium ions at the same pH. To measure the difference in adsorption of calcium and sodium, which is thought to lie at the basis of the differences in depressing action, radionuclides of

Jan 2, 1953

By Claudia Gasparrini

Silver occurs in nature in major, minor and variable amounts in a very large variety of minerals and in several mineral species in the same ore. Because these minerals may respond differently to the same flotation or leaching agents, detailed studies to establish the correct silver mineralogy become essential for optimum recoveries in those situations where the silver is treated as a primary product. On the other hand, fine grain sizes, which often affect gold recoveries, are not generally as critical in silver metallurgy, due to the lower market price which allows for more of the element to remain In the tailings before incurring in economical losses.

Jan 1, 1984

By N. A. Ziegler

A CERTAIN amount of interest has been indicated recently in the resistance to oxidation at high temperatures of iron-aluminum alloys (rich in iron). Hautman1 published a paper in. which some interesting results are given. According to his paper, only alloys containing at least 8 per cent aluminum indicate a marked improvement in their resistance to oxidation. At about this aluminum content, however, alloys become brittle, which considerably reduces their commercial value. About two years ago the author, performed a series of experiments, the results of which are presented here. A series of iron-aluminum-carbon alloys was prepared by melting electrolytic iron, aluminum and high-carbon iron alloy in an induction vacuum furnace.2 The list of these alloys is given in Table 1. Each alloy was forged in the ordinary way to

Jan 1, 1932

By Y. Takahashi, I. Iwasaki, S. Tanabe

Supported by the vigorous capital investment of the heavy and chemical industries and by the ever-increasing demand for durable consumer goods in the past decade, Japan has now emerged as the world's third largest steel producer, surpassed only by the United States and the Soviet Union. In 1968, the crude steel production is expected to exceed 50 million tons; the per capita steel consumption at that time will reach 886 lb, approaching the level of Western Europe. Characteristics of the Japanese steel industry is the high dependence of raw materials on overseas sources. Before World War II the industry relied on North China and Manchuria for coking coal, and on middle China, Hainan Island, the Philippines and the Malayan Peninsula for iron ores. After the war, the major sources of iron ores were shifted to the Philippines and the Malayan Peninsula, supplemented by shipments from the United States, Canada, India and Goa. The United States, in addition, became the primary source of coking coal.

Jan 1, 1967

By Arthur L. Bishop

INTRODUCTION Purpose The in-situ leach method for uranium extraction is a relatively new and innovative method of uranium mining. In 1975, the first commercial in-situ facility began operation in south Texas. Since that time numerous other operations have been initiated as either pilot or commercial ventures. Considerable literature has been published that deals primarily with generalities of the process or environmental concerns. Several federal agencies have published documents which do not reflect the true operating or environmental nature of the in-situ leach method of uranium extraction. From an environmental standpoint, this is also evident in the promulgation of rules and regulations. Hence, the purpose of this paper is to present experience with an environmental concern--non- production zone excursions--such that the industry and the regulatory agencies will gain greater insight devoid of preconceived ideas and misconceptions. General Process Description In south Texas, in-situ leach mining is utilized to extract uranium from permeable sandstone ore deposits 61 to 213 meters (200 to 700 feet) below the surface. Uranium is present as an insoluble uranium oxide. In the in-situ or solution mining technique, anoxidizing lixiviant is injected into the formation through injection wells. The solution reacts with the insol uble carbonate complex. This soluble uranium complex is produced at recovery wells, each containing a submersible pump. During production there is a constant sweeping of lixiviant through the formation from the injection wells to the recovery wells. Injection and recovery wells can be arranged in any of a number of geometric patterns dependent upon ore body configuration, aquifer permeability, and operator preference. Submersible pumps in the recovery wells pump the uranium rich pregnant solution to the initial processing facility. Monitor wells surrcsund the pattern area and are screened in appropriate stratigraphic horizons (production and non-production zones) to detect any lixiviant migration that may occur (Fig. 1).

Jan 1, 1980

By S. J. Green, R. D. Perkins

Little data exists on the high strain rate behavior of geologic materials. Uniaxial stress tests by Kumar1 and by Serdengecti and Boozer2 present some results to strain rates in the range 10 to 103 per sec. The two references cited are the only ones the authors found for high strain rates. Techniques for experiments at high strain rates are not well developed and, in general, leave questions with respect to interpretation of data when the material behaves in a brittle manner. The most reliable data at very high strain rates (104 to 106 per sec) are found in some recent flat-plate work3-5 where experimenters have impacted one plate into another, thereby creating a uniaxial strain loading. The standard uniaxial stress-strain curves cannot be obtained directly from these tests; however, yield (or fracture) may be studied by measuring the "elastic" wave magnitude. These data then may be compared to uniaxial stress data by resorting to some preassumed yield/fracture criteria. Even with the most liberal interpretation of existing data, little can be said of the effects of high strain rate on stiffness, yield/fracture, and post-fracture behavior of geologic materials. It is the purpose of this work to begin to add to the understanding. The data presented here are intended to provide material information for use in calculating the response of geologic materials to high rate deformations. These data can be applied directly to determine parameters such as the elastic modulus and Poisson ratio as a function of stress. Furthermore, these data can be used to derive an understanding of yield/fracture and the effect of rate on the yield/fracture surface. The work presented is a first step, and is

Jan 1, 1972

By T. S. Hutchinson, C. E. Kemp

The bottom water drive analysis presented by Muskat has been extended to include fields with wider well spacings. Curves are presented from which volumetric sweepout, water-oil ratio, and rate relations may be calculated. The effects of non-unity ratios on sweepout eficiency and productivity decline have been studied by an approximate method. Also, the effect of gravity on volumetric sweepout has been approximated for a particurlar geometry. INTRODUCTION The purpose of this paper is to report work done in applying the analysis of bottom water drive reservoirs given by Muskat1 to a larger class of reservoirs, to extend this analysis to include the effects of gravity and non-unity mobility ratios in an approximate manner, and to investigate the rate of decline of productive capacity. The bottom water drive type reservoir is one where the oil is underlain by a water zone of sufficient thickness that water movement is essentially vertical. This system is defined in more detail in the appendix and a one well element is shown diagrammatically in Fig. 1. Muskat obtained solutions to the equations describing the volumetric displacement efficiency of idealized bottom water drive systems by assuming that gravity effects due to differences in density betwecn oil and water were negligible and that the mobilities of oil and water were the same. If either of these assumptions is not made, the complexity of the system makes an analytical solution well nigh impossible at the present stage of mathematical development. Coles and Stade' developed an approximation to consider these factors. The authors have refined approximations, starting with the same basic assumption, which should give a somewhat quantitative picture of bottom water drive performance when mobilities are not equal and the effects of gravity are not negligible. The results of these approximate calculations can then be used to obtain the decline in well productivity as the field is depleted.

Jan 1, 1957

By Frank H. Skelding

Still the world's largest producer, consumer and importer/exporter of minerals, the United States has, in recent years, become more and more aware of the many diverse forces that increasingly affect its ability to maintain free access to and trade in minerals, both domestically and abroad. The nation's growing dependence upon foreign sources of minerals in the face of mounting competition is causing many changes, not only in the mineral industries, but in national attitudes and policies as well. This paper examines the position of the United States in the world mineral economy relative to the significant trends that have and are developing. It attempts to define and evaluate the major present and future impact of these trends and to anticipate the probable effects upon the U.S. and its mineral economy.

Jan 1, 1976

Jan 1, 1969