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Jan 1, 1880

By A. A. Archer

Marine mining is here defined as the commercial recovery of minerals other than oil and natural gas from the surface of, or below, the seabed by operations connected only indirectly with the land. The number of operations falling within this definition and the number of countries involved are remarkably limited in view of the widespread interest shown in marine mining prospects during the last few years. Marine mining is still restricted to continental shelves, where the only superficial minerals currently being mined are sand and gravel, calcium carbonate in different forms, and tin and iron sands.

Jan 12, 1973

By Henry E. Colton

NeaR the town of Christiansburg, Va., occurs a singular feature in topographical as well as geological structure, which may be said to have an important bearing on a large area to the southwest. The great water-shed ridge, which divides the waters flowing into the St. Lawrence from those flowing into the Atlantic ocean, coming southwestward, forms all of what was the boundary of Maine as agreed upon by the treaty of 1783, and a part of the present boundary, all of the northern New Hampshire boundary, and entering Vermont, continues south of Lake George. Passing irregularly through New York, it enters Pennsylvania, and there bifurcating, sends one prong to the west as a divide between the waters of the lakes and the Ohio, while the other becomes the steady, regular ridge which gave it the name of Alleghany, and thus passes on southwestward through Virginia. At no point has it ever been the geological divide. Its course, commencing in the Archean rocks, has passed through nearly every series of formation, and comes into Virginia in the Carboniferous strata. The geological divide—the line between the fossiliferous and the non-fossiliferous rocks—lies, in Canada, to the west of it, but from New York south into Virginia is far to the east. Reference to Dr. Hitchcock'k map will show this. But at the locality noted these positions are changed; the water-divide becomes the eastern chain, and the geological divide is the western, returning, it may be said, to the positions occupied in the region where they originated. These relations are shown on the large map accompanying the present paper. For several miles, the track of the Norfolk and Western Railroad

Jan 1, 1888

By C. C. Mattax, J. E. Bobek, M. O. Denekas

ABSTRACT investigations in recent years have shown that rock wettability can exert a profound influence on the displacement of oil by water from oil producing reservoirs. Core analyses frequently show oil recoveries from preferentially water-wet rock to be significantly greater than those from preferentially oil-wet rock. Thus, an accurate prediction of water-drive or waterflood oil recovery is dependent on the evaluation of reservoir rock wettability. Laboratory and field studies have been undertaken to examine and develop methods which may be used to measure rock wettahililiy, to investigate factors which may alter the wettability of reservoir rock, and to determine the wettability of specific reservoirs. It has been found that measurement of the rate and volume of spontaneous imbibition of the wet-ting phase by a rock is a reliable and reproducible test for semi-quantitarive determination of preferential rock wettability. Laboratory tests have shown that the wettability of reservoir rock may depend on both the crude oil composition and the rock type. Field and laboratory tests have indicated that coring flulids and core handling techniques can cause significant changes in the wettability of rock surfaces. However, a few fluids, brine in particular, appear not to affect core wettability and may be used when coring to determine reservoir wettability. Core handling and packing procedures have been developed which preserve core wettability during storage and laboratory testing. The wetfability characteristics of six reservoirs have been evaluated by wettabilify tests performed in the field on fresh cores cut with brine or special water-base muds. The tests indicated that all six reservoirs are water wet; however, the de-gree differed from one reservoir to another. INTRODUCTION Although surface properties of reservoir rock and interfacial characteristics of rock, crude oil, and water systems have been discussed for many years, the full significance of these properties to the production of oil is still in the process of evaluation. It is known, however, that one surface characteristic—preferential wettability of the reservoir rock—-is of paramount importance when the reservoir is being produced by water-flood or water-drive mechanisms. The importance of rock wettability has been pointed out by several authors'.',%* who have found that pref- erentially water-wet cores flood more efficiently than oil-wet cores; that is, more oil is recovered from water-wet cores in the early flooding stages than from oil-wet cores. Other authors'," indicate that waterflood oil recovery from cores of intermediate wettability may be greater than that from either strongly water-wet or strongly oil-wet cores. These recent investigations emphasize that the true wettability of a reservoir must be known before the performance of waterflood or water-drive reservoirs can be accurately evaluated. When reservoir wettability is to be determined by core analysis, precautions must be taken to maintain the original wettability which can be altered readily during coring5 nd testing.' In the coring operation the core may be partially or completely penetrated by the drilling fluid which, if it contains surface active materials, may drastically change the wettability of the core. Also, improper core handling during stcrage and testing may change its wettability because of evaporation of fluids or exposure to oxygen or surface active contaminants. One purpose of this paper is to discuss methods for obtaining, preserving, and testing cores without altering their original wettability. In addition, the results of wettability tests on fresh and preserved cores from six reservoirs are presented where special precautions were taken to obtain samples without altering their wettability during the coring operation.

By E. W. Greene, J. B. Duke

This paper deals with the application of froth flotation techniques to the beneficiation of kaolin clay and phosphate slimes, two very fine particle sized materials. The kaolin problem involves the removal of a small amount of a contaminating mineral (anatase), while the phosphate problem involves the concentration and recovery of a much larger percentage of apatite. Due to these differences, and also different response to flotation, the two problems are discussed in separate parts of the article. An idea of what is meant by "Ultrafine Minerals Or Slimes" as used in the title can be had by an examination of Fig. 1. Particle size distributions are presented for a crude kaolin clay, a coarse fraction and a fine fraction. The crude kaolin as mined was blunged with water, degritted through a 325-mesh Tyler screen, and dispersed with sodium silicate. The dispersed crude was then centrifuged in the laboratory into the coarse and fine fractions shown in the figure. The distribution curves were obtained by the well known sedimentation technique of Casa-grande1 using a long arm centrifuge to obtain equiva- lent spherical diameters down to 0.2 p on the finer fraction. Fig. 1 shows the coarse fraction kaolin to be 50% finer than 3 p, while the crude kaolin is 509 f'lner than 1.4 p, and the fine fraction 50% finer than 0.46~. For comparison 53 p on the horizontal scale would represent Stokesian diameters which would just pass a 325-mesh Tyler screen, taking into consideration the Andreasen sieve correction factor of 1.22 times the screen opening. 2 Another helpful comparison is the surface areas, which in square meters per gram, are 0.044 for 53 p particles, 0.77 for 3p, 1.65 for 1.4 p and 5.0 for 0.46 p particles. Fig. 2 is an electron micrograph of a similar fine fraction kaolin showing the hexagonal plate-like particle shapes.

Jan 1, 1962

By R. J. Wasilewski

THERMAL expansion of rhenium data have been reported by Agte et al.,&apos; and Medoff and cadoff,&apos; respectively, while the linear expansion coefficient was determined by Sims et Al.3 Denoting expansion coefficients parallel and at right angle to c axis by all and Al respectively, their weighted mean should be equal to dilatometric linear coefficient of a random polycrystalline specimen. The values reported for these coefficients are tabulated below: Since these values are in poor agreement, and because of anomalous expansion behavior observed in titanium 4 and chromium, a rede termination of the axial expansion was carried out. A Unicam 19-cm-diam high-temperature camera was used, with unfiltered CuK radiation. Camera calibration was carried out using at Pt wire standarde at temperatures up to 1100oC, the variation between indicated and true temperature being within the experimental error (estimated at <3oC) above 750o C. Rhenium Johnson Matthey spectrographic standard) was vacuum annealed at 1000 oC prior to X-ray diffraction experiments. Lattice parameters were obtained by least-squares solution using the reflec- tions (1232), (1015), (2024), and (3030) for all the patterns, and the additional reflection (2133) for higher temperature (400°C and above) patterns. The relative expansion data obtained are shown in Fig. 1, lengths of the vertical bars indicating the spread in the parameter values obtained by using various combinations of three spacings from the four or five measured. The data calculated from the equation of Ref. 2 are included for comparison purposes. Several specimens were used to obtain the above data, neither of them showing a significant parameter change after completion of the high temperature runs. Some parameter data and the corresponding expansion coefficients between 25 oC and the measurement temperature are tabulated below. The comparison of the present data with those previously reported shows reasonable agreement with the results of Medoff and cadoff2 within the temperature range covered by them (up to 1000 oC). The a values are appreciably higher throughout most of the investigated temperature range. The basal expansion is—in agreement with their findings—appreciably higher than that in the direction of hexagonal axis. The expansion coefficient, al, however, decreases rather more slowly with temperature than previously reported. The expansion along the c axis up to nearly 1000°C appears in excellent agreement. However, at higher temperatures there is a marked deviation towards higher expansion, reproducible between different specimens. Furthermore, there seems to be some irregularity in the variation of all with temperature, the apparent local minimum and maximum values at 510o and 1024o C, Table II, being well outside the experimental error limits. It must be stressed that the apparent discontinuity in the c parameter expansion is still insufficient to account for the expansion value reported by Agte et al.&apos; since a total expansion of close to 2 pct would

Jan 1, 1962

By Charles W. Merrill

IF we follow the threads of the mining problems, upon which I have touched, we find them all leading to one great fundamental desideratum. The people of this State, of this Nation, and of this world must be brought to a better understanding of the basic nature of our industry-must be made more mineral-minded. It is my belief &apos;that there is not a man present among this earnest gathering of those interested in the mining industry, who has not a deep-seated and heartfelt desire that the existing unprecedented welfare and prosperity of the whole mass of American people be maintained not merely through our own generation but through the generations of our children and their children. In the decades to come there can be no question of the keenness of the foreign competition which we are doomed to meet, and in this great international contest that Nation which has the best balanced program of development and that broadness of vision in its governmental direction, which recognizes the necessity of a sympathetic attitude toward the upbuilding of such a broad pro- gram will be the Nation which will maintain and pre- serve that welfare of all of its people.

Jan 1, 1929

By Bjorn N. P. Paulsson

A number of granitic rock specimens have been studied from the Stripa mine site in connection with a large-scale geomechanics research program. The purpose of the program was to evaluate and develop field and laboratory techniques for rock mass characterization and to determine design parameters for storage of nuclear waste. In this paper a minicomputer-based technique for studying dynamic rock properties in the laboratory is described, together with results from the tests. The specimens were tested under different uniaxial and saturation conditions. Specimens from a field-heated rock mass were also tested to determine if temperatures typical of those encountered with nuclear waste would introduce additional fracturing. Both Vp and Vs increased with stress for both saturated and dry specimens. Both Vp and Vs were higher for saturated specimens at all stress levels compared with the dry. The velocities increased linearly or near linearly with saturation. The test results on the previously heated samples indicate that attenuation is more sensitive to thermally-induced microfracturing than velocities. Analysis of the attenuation values with stress show that rock heated to 200°C is damaged, and that the damage is in form of low-aspect ratio fractures.

Jan 1, 1984

By George W. Hezzelwood

THE Balatoc mine, one of the Haussermann group,[t] is on the Island of Luzon, the largest of the Philippine group, about 260 km. north of Manila, and 12 km. from the city of Baguio. The Baguio district is the most important gold-mining area of the Philippines, with 14 producing mines in 1939, milling 2,3;8,894 tons of ore, yielding [P]40,881,048, approximately 55 per cent of the total Philippine production of [P]74,131,216. PRODUCTION HISTORY The Balatoc mine began production in January 1929 with a 150-ton cyanide mill. Increases in mill capacity have taken place as follows: March, 1932, to 350 tons June, 1933, to 470 tons December, 1933, to 515 tons July, 1934, to 700 tons December, 1934, to 1000 tons May, 1935, to 1200 tons October, 1938, to 1300 tons April, 1939, to 2000 tons January, 1941, to 2150 tons Production during the period of expansion has steadily increased in total value in spite of the fact that grade of ore milled has dropped-from $31.06 in 1929 to $5.78 in 1940. Annual reports give production as shown in Table 1, the average values being based on gold at the old price of $20.67 per ounce. [ ] GEOLOGY The ore occurs in quartz-calcite veins that vary in width from narrow stringers to mineralized zones 40 to 50 ft. wide. Wall rocks consist largely of diorites, with some andesite, and a fragmental breccia called locally the "Balatoc plug." Texture of the ore varies widely in the different veins-from a soft, highly altered, gouge material filled with quartz fragments through a soft, unaltered quartz-calcite to a hard, massive quartz ore. Three major vein systems have been extensively developed, and smaller amounts of work have been done on several others. These veins strike east-west to N. 60°, dipping south from 50° to 90°, and are essentially tension breaks between a series of faults or shears striking N. 30°E. to N. 50°E. and dipping southeast from 50°to 90°. The shear veins and tension veins probably formed more or less simultaneously,

Jan 1, 1942

By Paul A. Beck, M. N. Parthasarathi

The vecrystallization texture. formed by selective growth of random nuclei in an 80 pct volled 99.997 pct A1 crystal of initial orientation mear (123) (41.21 was found to consist of components related to the single-component rolling texture by 40 deg. rota-tiows around [111]axes. The relative-volume fractiovz of the various recrystallization-texture componezts may be accouzted for 012 the basis of the Lou) mobility of twist boundaries, if it is assumed that the mobility of the tilt boundaries also varies with their orientation. Similar results with a, aluminum-alloy cystal of the (110) [112] orientation, containing iron, silicon, and zinc, show that these solute contents do not impair the effectivezess of the oriented growth mechanism of re cry s-tallization- texture formation. In a previous investigation1,2 it was found that a sharp recrystallization texture is formed as a result of the oriented growth of random artificial nuclei in an aluminum crystal rolled to 80 pct RA, on the (110) plane in the [ 112] direction. Four recrystallization-texture components were found to occur, with orientations corresponding to 40-deg rotations around [111 1 axes of the deformation texture. Reorientations of this type were already found in earlier work,3,4 where the presence of random nuclei could be reasonably assumed, but was not rigorously documented. The same orientation relationship was found also by Lucke and Liebmann, who actually measured the orientation dependence of boundary-migration rates in the recrystallization of A1 crystals slightly deformed in tension.5,6 The occurrence in the recrystallization texture of only four of the eight crystallographically equivalent orientations of the type referred to above remained unexplained,1,2 although it was clearly not a result of the absence of suitable nuclei. Recently Burgers7 suggested that this effect may be due to the aniso-tropy of boundary mobility observed2&apos;6; it was found that the recrystallized grains of the 40-deg [111]-rotated type grow much faster in directions perpendicular to the [ 111] they have in common with the matrix than parallel to this direction, i.e., the tilt boundaries have much higher mobility than the twist boundaries. The four orientations corresponding to

Jan 1, 1962

By Walter Miller

ALTHOUGH confident of its ability to meet any demands which may be made, the petroleum refining industry is not complacent about the situation and realizes that the quantities of petroleum products to be furnished are so enormous and so far beyond what was previously estimated that the full co-operative effort of the industry must be exerted. Establishment by the President in May of the Office of Petroleum Coordinator for Defense with Secretary of the Interior Ickes at its head, plus the formation of the Petroleum Industry Council for Defense, in November, provide the channels for united endeavor within the industry and the means for gearing that endeavor within the industry and the means for gearing that endeavor in full harmony with the nation?s needs. Great strides have been made and a rapid understanding of the situation and the magnitude of the task is being attained by all concerned.

Jan 1, 1942

By C Gunther

Ore deposits are commonly divided into two classes, syngenetic and epigenetic, according to whether the ore was deposited together with the enclosing rock or was introduced after its deposition or solidification. Epigenetic deposits, which are by far the more important class, owe their formation to the channels that permitted the ingress of their metals, and both classes are subject to great modification by post-mineral changes in the containing rocks. A discussion of the structural features of rocks, therefore, necessarily precedes any consideration of ore deposits or processes of ore deposition. The arrangement of sediments in parallel and approximately horizontal layers is called stratification, and is an original prop¬erty of sedimentary rocks. Successive strata of the same sedimentary bed commonly differ from each other in some minor characteristic, such as texture or color, which results in a bedded or stratified appearance. The subjection of a rock to pressure develops within it parallel planes of weakness, called cleavage planes, along which the rock breaks into relatively regular slabs or blocks; the direc¬tion of these cleavage planes, which bear no relation to stratifica¬tion, is determined by the direction of the pressure that produced them. Where there are more than one set of cleavage planes, one of them is likely to be more prominent than the others. In sedimentary rocks, the cleavage may coincide with the stratifica¬tion but more commonly cuts across it. Van Hise has defined cleavage as the "capacity present in some rocks to break in some directions more easily than in others." Cleavage, therefore, does not imply the existence of subdivisions, but rather the tendency to subdivide along certain planes.

Jan 1, 1932

By Lane, K. S.

The problem of stability of slopes in reservoirs is one of real interest in civil engineering. The problem is whether the valley walls will remain stable or whether they are likely to slide as conditions are changed by storage of water in the reservoir. If major slides are indicated, as on the walls of relatively steep canyons, one must estimate whether they will be so located and of sufficient size as to interfere with operation of the reservoir-as by blocking the outlets, or by displacing sufficient water to over-top the dam in a huge wave. Some cases involve problems in soil mechanics for slides in earth or weaker rock; other locations need the assistance of rock mechanics for slides in harder rock. While this is not a new problem, attention has recently been focused on its importance by the hugh landslide into the Vaiont reservoir in 1963, which claimed the lives of over 2000 people and forced abandonment of the dam and powerhouse.

Jan 1, 1969

By J. E. Forciea, O. E. Palasvirta, L. G. Hendrickson

All pilot and commercial plants working with Mesabi Range taconite employ wet magnetic separation. Progress is being made with a dry magnetic process,9-11 but this has not yet been applied to taconite except in the laboratory and pilot plants. Flowsheets in all five plants are similar, including multiple stages of grinding, each followed by magnetic separation, which rejects a finished tailing. The flowsheet in Fig. 1 is used in the preliminary and commercial plants of the Erie and Reserve mining companies and in Unit C of Oliver&apos;s Pilotac plant. At Erie the desliming operation is omitted. In the Reserve plants two ball mills are used with each rod mill. Pilotac uses flowsheet 2 in Unit A-B and has also tested flowsheet 3. Principal differences in the three flowsheets are the number of grinding stages and the type of roughing. The terms open- circuit roughing and closed-circuit roughing are best defined by the diagrams.

Jan 12, 1958

By A. A. Berk

LAGGING technology and the slow spread of information have been the chief obstacles to widespread participation in minimizing the industrial pollution load. These obstacles can be conquered by fact finding and applied research. There are three aspects to the problem of water-borne mineral waste: to minimize the amount being thrown away, to select a predisposal treatment, and to use the products or dispose of them. It is often possible to minimize the waste by making very minor changes in the process that produces it. For example, a manufacturer of automobile bumpers greatly reduced the dragout &apos;from a plating bath by modifying the design and position of two boltholes.&apos; A plater of automobile hubcaps installed a drainage bar and decreased the loss of chrome-plating solution to the rinse water by about 80 pct.&apos; The mill at a western mine found it possible to discard 60 to 70 pct of an ore with minimum treatment," so that the processing effort could be concentrated on a high-graded slime, with significant reduction in costs and improvement in recovery. The possibilities for waste reduction through process changes are limited only by the imagination. A recent patent points out the advantages of using No. 1 fuel oil instead of water in wet-process cement making;& the fuel oil presumably has better properties than water for this purpose and is said to be almost com&apos;pletely recovered or utilized, so that there is no waterborne waste. Recycling to reduce wastes and improve process economy is very well illustrated in vanadium and uranium recoveries from relatively low grade ore. Ores containing 6 pct calcium carbonate were found to give poor vanadium recovery by the salt-roasting process because the vanadium was converted to water-insoluble calcium vanadate. Following the salt-roasting process, sulfuric acid was used to leach the uranium. Enough calcium sulfate was formed

Jan 1, 1958

By Herbert Clark Hoover, Lou Henry Hoover

DIFFERENT methods of parting gold from silver, and, on the other hand, silver from gold, were discussed in the last book; also the separation of copper from the latter and further, of lead from gold as well as from silver ; and, lastly, the methods for refining the two precious metals. Now I will speak of the methods by which silver must be separated from copper, and likewise from iron.1 The officina, or the building necessary for the purposes and use of those who separate silver from copper, is constructed in this manner. First, four long walls are built, of which the first, which is parallel with the bank of a stream, and the second, are both two hundred and sixty-four feet long. The second, however, stops at one hundred and fifty-one feet, and after, as it were, a break for a length of twenty-four feet, it continues again until it is of a length equal to the first wall. The third wall is one hundred and twenty feet long, starting at a point opposite the sixty-seventh foot of the other walls, and reaching to their one hundred and eighty-sixth foot.

Jan 1, 1950

By Molly Gleiser

The standard free energies of formation of some gaseous metal oxides together with those of their condensed oxides have been plotted against temperature. The heats of formation of the gaseozcs oxides are tabulated. An explanation is given of the use of the data to predict the importance of the gaseous metal oxides at high tenzperatures. RECENT mass spectrometric work1 has resulted in the detection of several hitherto unknown gaseous oxides and the measurement of their free energies of formation. Of especial interest is the fact that several of the refractories in common use either as crucibles or furnace tubes, and metals used in Knudsen cells and in furnace windings, have been found to have one or more stable gaseous oxides. In view of the present emphasis on high-temperature techniques, the development of vacuum metallurgy.z heating by electron bombardment and plasma jets, and the resultant shift to ever higher temperatures, it is no longer possible to plan experiments without taking into consideration the significance of the presence of these gases in the system, the reactions they undergo. and their contribution to the vapor pressure. A good example of what went wrong in earlier work, when the existence of these gaseous molecules was not yet known, is presented by the work of Hoch, Nakata, and Johnston. Hoch and coworkers attempted to measure the vapor pressure of solid ZrO2 by letting the vapor in equilibrium with zir-conia effuse from a tantalum Knudsen cell. The free energies of formation of solid zirconia and tantala are such that a short calculation showed that the reaction

Jan 1, 1962

By T. S. Spicer

The relationship of coal characteristics to the principal types of firing equipment has been known to the coal combustion engineer, but is not as familiar a subject for purchasing agents, salesmen, consumers, and executives of coal-producing and consuming companies. This general survey of characteristics determined by standard laboratory tests, of major types of combustion techniques, and of the relationships between the two is directed toward the latter audience. It will also serve as a review for those actively engaged in the combustion of coal. Although the relationship of coal characteristics to the principal types of firing equipment is well known to the experienced coal combustion engineer, apparently there is need for a summary article on this subject. The author has received numerous requests for such a paper from purchasing agents, coal salesmen, coal customers and executives of coal-producing and consuming companies. Consequently, the scope of this paper will be directed to this audience, with the hope that it may serve also as a review to others actively engaged in the combustion of coal. The magnitude of this subject is so great that only a brief general treatise is possible. The author realizes that because there are so many special cases and exceptions to the generalities which follow, he is in jeopardy of contradicting himself. It is the hope, however, that the many references cited will prove valuable to those who wish to study the details excluded by necessity, due to space and time limitations. Hence, the characteristics of coals as determined by standard laboratory tests will be discussed; the major types of combustion techniques reviewed; and then the characteristics and firing will be related. CHARACTERISTICS OF UNITED STATES COALS The coals of the United States range from lignite to anthracite and each has its own general characteristics. The extensive coal fields of the U. S. are shown in Fig. 1 and the estimated reserve according to rank for each state is illustrated in Fig. 2. Coals may be classified according to rank as shown by Table I from the ASTM Standards on Coal and Coke, D-338-38.1 The basis of this classification is ac- cording to fixed carbon and heating value (Btu per pound) calculated to a mineral-matter-free basis. The high-rank coals are classified according to fixed carbon on the dry basis; and the low-rank coals according to Btu on the moist basis. Agglomerating and slacking (weathering) indices are used to differentiate between certain adjacent groups. While rank is not itself a characteristic it does signify certain characteristics that accompany a class of fuel. Anthracite, for example, immediately implies a hard, free-burning, smokeless coal of low volatile matter, usually having an ash of high fusibility. Coals may also be classified according to grade as described by ASTM Designation D-398-37.1 This quality classification is determined by size, calorific value, ash, ash-softening temperature, and sulfur. This type of classification is not used as extensively by the industry as the rank classification. Fig. 3 shows the heat value of different ranks compared to proximate analyses. Coals may also be classified by sizes, as shown in Tables IIA and IIB, and sizes can be on both top and bottom limits. If this is done, then the coal is called double screened; otherwise, either top or bottom sizes can be specified as a limit. Bituminous coal sizing varies from field to field and depends upon the market demand. The common sizes and their main uses are outlined in Table IIA. Anthracite is usually available in many sizes at the colliery, and Table IIB summarizes standard sizes and names. Although rank, grade, and size designations help identify and describe a coal in question, there still remain other characteristics such as indicated by moisture, free swelling index, grindability tests, etc. A bituminous coal information chart Table III) suggested for use in studying the available coals in a region, lists origin and chemical and physical characteristics. Even this more comprehensive list does not completely spell out all the characteristics of a heterogenous material like coal. For example,

Jan 1, 1961

By Richard Thomas Newcomb

Chapters 5a, 5b, and 6 discuss the long- run supply of minerals and the characteristics of reserve search and production peculiar to extractive industries. It is now necessary to complete the picture by examining supply and demand in commodity markets to show how mineral prices are determined and how both price and production trends might be predicted over long periods of time. These practical interests can be served best by reviewing first some of the characteristics of the short-run static market models familiar to all readers of elementary economic texts, and then extending the theory to models of a more dynamic nature. It is important at the outset to note that economic theory provides a wide variety of economic models based on varying assumptions concerning the behavior of economic agents, the properties of the goods, the time period considered, and so on. Each variety of model offers certain analytical advantages and suffers certain shortcomings. The art of the applied economist or practioner lies in knowing enough both about the technology and practice of his problem and about theory to select the appropriate models for his analysis. In our approach it will be useful first to consider the role of markets for minerals and mineral products in relation to the efficient determination of what and how goods are produced in the whole economy, i.e., a general system of markets, before getting down to the task of analyzing supply and demand conditions in specific markets. The former study is called general equilibrium analysis, while the latter is called partial. By equilibrium is meant a state of the sys- tem under study in which supply equals demand in each market, and the prices which equilibrate the quantities offered and asked are called equilibrium prices. The tendency of prices to return toward equilibrium values if temporarily displaced, or to converge to new equilibrium values if important new conditions for supply or for demand are placed, defines "stable" equilibrium systems. The short-run describes a period in which adjustments to fixed capital are not made, although variable factors such as labor or materials can be adjusted. The long-run envisions a period in which fixed capital and other such constraints can be adjusted. Thus, it may take a sharp increase in price to bring out additional supply of a factor in the short-run with existing plant, while new capacity might permit additional quantities in the long-run without an increase in supply price.

Jan 1, 1976

By B. K. Larkin

Solutions to the diffusion equation for a line source located anywhere in a region bounded by a circular discontinuity are presented. Such solutions follow automatically from the Green&apos;s function presented by Jaeger.4 Petroleum industry applications of this problem would include transient compressible fluid flow in porous media bounded by a discontinuity. Since several recent papers have treated the subject in less general form, it would appear that many workers in this area of the petroleum industry are not aware of Jaeger&apos;s work. STATEMENT OF THE PROBLEM In several trearments1,2,3 of the transient flow of compressible fluids in porous media it was convenient to consider a region to be bounded by a circular discontinuity. In such a region (Fig. I), the properties in Region 1, r < a, are constant but different from the properties in Region 2, r > a. Hurst, l using the Laplace transform, obtained solutions for a line source located in the center of such a porous medium. The purpose of this work is to point out that a much earlier paper by Jaeger4 presents the solution for a line source located anywhere inside the discontinuity. The assumption is made that a line source may be used to approximate a well. In the following material it is convenient to use the terms source and well as being equivalent; however, the reader should remember the distinction in applications. SOLUTIONS Jaeger presented the Green&apos;s function for a line source, or well, in the composite region shown in Fig. 1. In the most general form, the solution for a system of j wells in Region 1, each producing at a time varying rate, qi (t), is