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By Douglas D. Donald

The New Jersey Zinc Co. successfully holed through a 2 1/2-mile haulage tunnel connecting its new Ivanhoe shaft with the Van Mater Shaft at Austinville, Va. This 8x 10-ft cross-section tunnel was driven from both ends and met at a point approximately a mile from one shaft and a mile and a half from the other. In order to make certain that the faces met accurately on line and grade it was necessary to refine conventional mine surveying practices. The mines that are serviced by these shafts are located in the southwestern part of Virginia approximately midway between Roanoke and Bristol at the west foot of the Blue Ridge. While the presence of lead-zinc sulfide ores has been known in this area for more than 200 years, it was in 1902 that New Jersey Zinc Co. acquired the Austinville property, which has been in constant operation since that time. About ten years ago the company undertook an extensive diamond drilling program at Ivanhoe several miles to the southwest. This program was successful in locating sufficient ore to justify the purchase of a number of the properties in this area and plans were made to develop the new orebodies. The discovery of this ore as well as substantial addi- tional reserves at Austinville resulted in a decision by the company to increase its daily milling capacity to 3000 tons, of which about 1000 tons would be supplied from the Ivanhoe mine. After careful consideration of all possible methods of transporting this volume of ore from Ivanhoe to the mill, it became evident that diesel locomotive haulage through a 2½-mile tunnel between the two mines would best suit prevailing conditions. Since the lowest operating level, known as the 1100 level, of each mine would be at approximately the same elevation, it was obvious that such a tunnel should be driven on this level. Not only would this tunnel facilitate feeding Ivanhoe ore into the underground crusher and skip loading installation at Austinville, but it would also open up a known orebody 5000 ft southwest of the Van Mater shaft. In addition it would provide a valuable diamond drilling base from which a large and a potentially favorable but untested block of ground might be explored. In order to hasten the completion of the tunnel, it was felt that it should be driven from both ends. ENGINEERING CONTROL PROCEDURES It was vital that the tunnel junction be made accurately on line and grade; thus it was felt that engineering control of an unusually high degree of reliability was required to prevent an accumulation

Jan 1, 1959

By L. Obert, D. E. Stephenson

The objectives of this investigation were to develop a laboratory procedure in which core discing could be produced under known (and variable) stress conditions, and to study the discing characteristics of several fypes of rock. Discing of rock cores refers to the formation of discs or wafers of relatively uniform thickness which fracture or rupture on surfaces approximately *Fracture is a type of failure in which there is a complete loss of cohesion and fresh surfaces are created. Rupture is a type of failure in which there Is only a partial loss of cohesion. normal to the axis to the core (see Fig. 1). Usually the surfaces of the discs are concave-convex with the concave side toward the collar of the hole. The surface of the fractured discs are like those created by a tension failure (or possibly a shear failure with virtually no normal compressive stress). This phenomenon has been observed by a number of investigators1-5 in the course of diamond drilling in underground mines, especially in areas suspected of being under high stress. The state of stress in the core required to produce discing is not exactly known. Tranter and craggs6 theoretically investigated the stress distribution in an infinite cylinder, subjected to hydrostatic pressure, minus p, from z = 0 to z = 8 and unloaded from z = 0 to z = 8, Fig. 2. The exact solution to this problem shows that a tensile stress develops in the loaded region near z = 0 with the greatest tensile stress on the axis of the cylinder. A tensile stress also developed on the surface of the cylinder at a point just outside of the loaded zone. Jaeger and Cook3 experimentally investigated the discing mechanism by biaxially loading cores in a pressure jacket sealed at the ends by O-rings. According to the Tranter and Craggs theory it would be expected that failure should occur at the pressure discontinuity at the O-rings. The experimental results showed that if the specimen was unjacketed it broke at random points within the pressurized zone and at a pressure somewhat greater than the tensile strength of the specimen, presumably due to the development of a

Jan 1, 1965

Elected Died 1903 * ADAMS, CHARLES C. 1905 1884 *ADDY, MATTHEW 1896 1894 *ALLFN R B 1896 1874 *AMIOT, H 1892 1886 *AMSLER, CARL 1894 1895 *ÅNGSTROM, CARL 1901 1895 *ARMSTRONG, JOHN F 1898 1882 *ARNOLDS, HUGO 1886 1875 *ASHBURNER, CHARLES A 1889 1872 *ASIIBURNER, WILLIAM 1887 1883 *ATKINS, C M , JR 1885 1897 *AYERS, WILLIAM 1898 1885 *BABCOCK, GEO H 1893 1884 *BAILEY, EDWARD 1889 1880 *BAILEY, JACKSON 1887 1900 *BALLOU, FRANKLIN 1903 1886 *BARNES, F W 1892

Jan 1, 1910

By Paul H. Lu

Methods and results of measuring three basic parameters for ground stability control, ground pressure, strata movement, and geomechanical properties of mine rock are presented in this paper. It is found that these parameters can be measured in situ by simple and practical techniques with nonsophisticated and inexpensive instruments. Specifically, a drillhole dilation technique employing a cylindrical hydraulic borehole pressure cell (CPC) was used to determine the modulus of rigidity. Premining ground pressures were determined by pressure convergence tests with a combination of one CPC and two pre-encapsulated flat hydraulic borehole pressure cells (BPC) installed in a single drillhole. Abutment pressures and pillar loading were monitored with BPC's. Differential strata movements and bed separations were measured with self-recording 10-anchor-point extensometers. Roof-to-floor convergence was measured with self-recording convergence meters. Some applications of these in-situ-determined parameters to mine design and ground stability control are also discussed.

Jan 1, 1984

By M. N. Brodie, John Chapman

INTRODUCTION - DEFINITION & HISTORICAL PERSPECTIVE While this symposium is concerned with comminution which, by definition, relates to all stages of size reduction of an ore body to a form suitable for mineral separation, the electrical drive aspect of the grinding section will receive most attention in contrast to the crushing, screening and materials handling elements of the process. The reason for this is that today's large mills, thirty feet diameter and upwards, present mechanical and electrical problems which require a degree of sophistication in their solution not previously required. The ability to satisfy these demands, so far as electrical technology is concerned, largely results from the development of semi-conductor devices. These can now handle typical electrical distribution power levels within remarkably s m all volumes and with high efficiency when compared with the motor-generator sets, mercury arc rectifiers, rotating amplifiers, magnetic amplifiers and vacuum tubes which were commonly used to provide speed and torque controls as recently as the early nineteen-sixties. The hardware available to the electrical engineer has changed dramatically whereby even the simplest control system formerly using hard-wired relays is now superseded by the program m able logic controller with its computer-like memory containing the sequence of operation, in other words, the software. Reverting now to the mineral process itself, it is assumed that the ore body has been mined using explosives and is delivered to the concentrating plant in its 'run of mine' form. The problem becomes one of reducing the material to a size which will permit an acceptable recovery of the mineral with the most economical use of energy. The size of 'run of mine' material will range from about minus five feet for high tonnage open pit operations to minus two feet for the smaller underground mine. The final reduction in size may range from minus ten mesh to minus two hundred mesh (exceptionally as fine as minus six hundred mesh) depending upon the concentration method and dissemination of the mineral values within the ore. There is no single circuit that satisfies all applications, but the pattern of metallurgical equipment use shown in Table 1 appears discernable from current practice, in general terms.

Jan 1, 1982

By H. T. Kennedy, S. G. Dardaganian, J. L. Clanton

This paper presents equilibrium ratios measured on oil and gas samples taken from the Kelly-Snyder field at the reservoir temperature of 128°F. From these data smoothed curves were constructed for the reservoir fluid up to the bubble-point, 1,874 psia. A material balance calculation, based on the use of equilibrium ratios instead of the usual solubility and shrinkage meayr~rements is made on the field and compared to the con\.entional method. DETERMINATION OF EQUILIBRIUM RATIOS The equilibrium ratios, or K values were obtained by recombining separator samples of oil and gas taken when the reservoir was above its bubble point, and thus represented the reservoir fluid before any change had occurred due to the evolution of gas. The well sampled had a gas-oil ratio of 617 cu ft of high pressure sepalator gas per barrel of separator oil. and a bottom-hole temperature of 128°F. Samples were brought to equilibrium by agitating for 24 hours in a thermostat, maintained at the proper temperature within 0.2ºF, mercury being added when necessary to maintain the pressure constant. Samples of oil and gas were then taken by constant pressure displacement, and analyzed by low temperature frac-tionation. Equilibrium ratios were determined at 128°F and 500, 800, 1,000 and 1,400 psig. At the latter pressure, there were indications that the gas samples were contaminated with small quantities of oil, and only data taken at the first three pressures were included in Fig. I. This figure has been extended to higher and lower pressures by the use of the Fluor charts for 3,000 psi convergence pressure, on which the experimental points fit well. MATERIAL BALANCE EQUATIONS The possible errors involved in conventional material balance equations have been analyzed by Muskat1. Where the errors occur in field measurements, or in obtaining effective averages from variables such as gas-oil ratio and pressure, they will evidently be involved in any attempt to estimate the content of the reservoir. On the other hand, substantial errors may be introduced in conventional material balance calculations by: (1) the neglect of the amount of oil dissolved in gas at high pressures and temperatures in the reservoir, but which condenses under separator conditions; (2) the assumption that the separation of oil and gas in the reservoir may be duplicated by a differential liberation in the

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in

By Irving Palmer

DURING the past 15 years in this country there have been few additions to the literature of lead smelting. After the consolidation of the principal smelting companies at the beginning of this period it became the policy of the larger company not to permit the publication of details in regard to many of its metallurgical processes. This led to similar action on the part of some of its competitors. The result, of course, was a decided decrease in the number of papers written upon the practical side of the subject. Even upon the theoretical side the contributions have been few. It would seem that the industry as a whole has suffered from this general unwillingness to exchange information. While it is true that a given company is entitled to the reward that may come from its own development of a new process, it is also true that a still greater reward might be the result of a free exchange of ideas with other plants. This principle has been recognized for a long time in other metallurgical industries, notably those engaged in the smelting of iron and the manufacture of steel. It is pleasing to note that the leading lead-smelting company has very recently decided to modify its policy of secrecy, and to permit the publication of papers covering some details of its metallurgical methods. The statement has been made that there has been but little progress in lead smelting during the period just referred to. This impression is due in part to the scarcity of papers written on the subject. There has been, it is true, some discussion of the new sintering processes, but with little reference to detail, and to the effect that blast roasting has had upon the industry as a whole. In spite of the prevailing belief, it may be said that lead smelting, in common with other metallurgical industries, has made steady and substantial progress. It is the purpose of the present paper to discuss briefly some features of the industry as it is now conducted, with special reference to the blast-furnace practice in the larger silver-lead smelting plants of the United States and Mexico.

Jan 7, 1914

By H. B. Charmbury, D. R. Mitchell

Everyone in the coal industry from top management to the preparation engineer is vitally interterested in recovering as much salable coal as possible from the run-of-mine product. Coal losses from a preparation plant occur in the solid refuse material being discharged from the plant and in the bleed-off slurry from the water circuit. The refuse is generally hauled from the plant in solid form by trucks, conveyors, or aerial trams to the refuse or culm banks or it may be crushed and transported by hydraulic methods to refuse ponds or dams. The loss of coal in refuse material and the extent of this problem has been covered in another paver.' The loss of salable coal in the plant bleed-off slurry is one of the water circuit problems in coal preparation plants. Slurries originate at various places in the processing circuits and are usually disposed of by transportation to waste ponds known as slurry ponds. Even though the combustible material discharged as slurry and refuse from the plant is labeled a loss, the loss must only be considered temporary. There is a tendency at the present time to examine refuse and slurry losses and to reprocess these materials to recover valuable coal. Slurries from eight bituminous coal preparation plants in central and western Pennsylvania have been sampled and examined to determine the amount of recoverable coal in each. Examinations of the samples were made to determine the tons per hour of solids and the gallons per minute of water in the slurry; the size, ash, and sulfur analyses of the solids; and the sink-float characteristics of the larger solids. The extreme fines (—325 mesh material) from one of the samples has been examined further to determine the micron size fractions as well as the ash and sulfur content of the micron sizes. Collection of the Samples: Field trips were made to each of the plants where samples were obtained and discussions held with the preparation engineer prior to sampling. The flowsheet of the plant operation was studied and a time-period selected to obtain a representative sample. At least 20 1-gal samples of total plant bleed-off suspensions were collected at each plant in increments over designated periods belived to be typical of the plant flow Three of the samples were obtained from plants in the Pittsburgh area. Each plant supplied information on the capacity, operating time, type of cleaning equipment used, water and material balances, and auxiliary equipment. From the time required to collect given amounts of slurry and from the amount of solids in the slurry, total solids discharges from the plant were calculated and compared with the plant flow. Ash and sulfur analyses of the total solids were also checked, at some plants, with company figures. In all cases where checks could be made there was reasonable agreement between company figures and those reported here. Analysis of the Slurries: Representative fractions of properly agitated samples were examined in the laboratory to determine the specific gravities of the slurries. The solids and water were separated by filtration to check the weight of each so that the percent of solids in the pulp could be determined. From the resulting data, presented in Table I, it may be seen that the percent solids in the slurries ranges from 2.8 to 39.0 and the amount of solids from 2.61 to 45.61 tph. Size Analysis of Solids: Representative fractions of the slurries were permitted to settle and the clear water was removed by siphoning. The solids were then wet-screened at 28, 35, 48, 65, 100, 150, 200 and 325 mesh. Results of the size analyses are presented in Table 11. These results indicate the extreme variation of sizes and in most cases the degree of fineness of the solids. The amount of —325 mesh ranges from 22.5 to 84.5 pct and the amount of+200 mesh from 8.3 to 69.1 pct.

Jan 1, 1961

By H. E. Hawkes, D. A. Barr

Time variations in the copper content of the sediments of streams draining mineralized areas were studied in two areas of contrasting climatic environment, one in northern and one in southern British Columbia. In each area, samples were collected and observations made of rainfall, stream discharge and air and water temperature at intervals throughout the summer season. Samples were analyzed for total and cold-extractable copper. Results showed a weak inverse relation between cold-extractable copper and discharge in two out of the three test sites in the southern area, and a decrease in ratio of COld-extractable to total copper over the duration of the test period at a highly anomalous site in the northern area. In suspended rock flour resulting from glacial erosion of mineralized rock in the northern area, virtually all the copper was found to be soluble in cold, dilute hydrochloric acid. None of the variations observed is sufficient to cause serious problems in geochemical sediment surveys. Systematic collection and trace analysis of stream sediments has seen wide application in recent years as a method of primary prospecting in primitive areas. Common practice is to collect fine-grained samples of sediment either from the active channel or from the flood plain near the channel. Samples are dried, sieved and the -80-mesh fraction analyzed after breakdown of the sample by a relatively strong attack, such as by fusion or by treatment with hot perchloric acid. Drying, sieving and rigorous chemical attack requires established facilities, either in a well equipped central laboratory or in base camp. Thus analysis for total metal involves a substantial delay from the time the samples are collected until the analytical data can be reported. An alternative system uses a cold aqueous extrac-tant in place of the hot acid or flux.4 Advantages of the cold-extraction techniques are that kits can be prepared for use directly at the sample site and that, in some problems, the patterns in cold-extractable metal, usually abbreviated cxMe, are more useful as ore guides than the patterns in total metal.' In the course of operational geochemical sediment surveys, a problem that has come up repeatedly is failure to reproduce anomalous values or patterns by resampling the same areas. The mystery of the vanishing anomaly has led to speculation as to whether there is a significant variation in the metal content of sediment samples with the weather or with the time of year. Review of the published literature shows that a number of experiments have been carried out on time variations in the metal content of stream water.1,2,5,7-9 The only published report on time variations in stream sediments that has come to the authors' attention, however, is by Govett,3 working in Northern Rhodesia.

Jan 1, 1963

By George C. Coupland

Ecstall Mining Limited, a wholly owned subsidiary of Texas Gulf Sulphur Company, is the owner and operator of the Kidd Creek Mine including the concentrator complex located near Timmins, Ontario. Canada, approximately 450 miles north of Toronto. The mine, concentrator and Timmins form a triangular arrangement with a 17-mile rail link connecting the mine and concentrator and both of these facilities 18 and 14 miles respectively by road from Timmins. A core drilling program in the spring of 1964 established the presence of a large massive sulphide orebody which was to become the Kidd Creek Mine. Texas Gulf Sulphur had been conducting an intensive search for base metal in various parts of Northern Ontario and Quebec since 1957. Of several thousand anomalies detected in airborne electromagnetic surveys, several hundred warranted ground inspection, but only one of more than sixty drilled became a commercial orebody, the Kidd Creek Mine. The geophysical exploration work has been well covered in a paper written and presented by Van Donohoo, presently a Vice-President of T.G.S., at the American Mining Congress in San Francisco in October 1969. GEOLOGY The orebody lies within a series of overturned rhyolitic flows and pyroelastics with a major peridotite intrusive to the east. The hangingwall and footwall are composed chiefly of intermediate volcanics, andesite and dacite. The southern end of the orebody appears to terminate abruptly against greywacke while the north end is bifurcated and the structure obscured.

Jan 1, 1970

By Enrique Touceda

FOR a number of years prior to the world war, the firm of Geo. H. Thacher & Co., of Albany, N. Y., was engaged in the manufacture of marine and other gray-iron castings. At -the outbreak of the war the firm decided to specialize in the manufacture f propeller wheels. It attacked the problem, therefore, from a foundry point of view, seeking to produce a casting that would be so accurate that no subsequent machining would be required on the blades, also from the point of view of the ship builder. There were two general methods f manufacture, the shortcomings of which have been freely acknowledged. In the sweep method, the nowel, or bottom half-mold, for each blade is swept up by a spindle beam and pitch race, while the top half-mold for each blade is built up individually. In the pattern method one individual blade, with the hub or hub portion, is mounted on a spindle and the individual -blade mold formed, the pattern is then rotated on the spindle to the position- for the next blade, etc. In rare cases wheels were made from a solid pattern. Owing to the cost of the pattern, its failure in many instances to be correctly made, and (when made of wood) its early and sure distortion the disadvantage of this practice is obvious, while metal patterns in most instances were prohibitive in cost. In these methods both green-sand and loam molding was practiced. The casting produced by either method can be considered only as a blank from which the propeller must be machined. The back surface f each blade must be chipped too the templet and through this procedure chipped to such accuracy, as will be required for a static balance. Inasmuch as the' work done by the machine tool is confined to the driving face of the blades, not only is perfection most difficult, but corrosion will be greater because of the removal of the dense skin f the casting and the local strains set up by the pneumatic tool in chipping. To produce a finished 9-ft. propeller for a Navy destroyer required from 8 to 21 days f foundry work and about the same length of, time for the machining. Through the use f the Thacher process, only as many hours are required, besides it is possible to produce a finished casting in perfect conformity, with any particular propeller-wheel design,

Jan 4, 1921

By C. Dinis da Gama

Because of the growing importance of back analysis for the interpretation of rock slope failures, particularly in open pit mines, it is suggested a methodologic sequence of activities for dealing with those problems. The principal mathematical tools for the interpretation of the most common mechanisms of slope failures are reviewed, including methods of stress and strain analysis, which seem to be more powerful for parametrization studies, and for developing more realistic explanations of slope behaviour, such as the measurement of displacements. An application of those methods is described, using slope failures detected in a Brazilian uranium mine (Cercado), thus providing reliable shearing strength parameters for the rock mass discontinuites, which were used in the final pit design. The concept of using backanalysis results to supply input data for pit design was implemented by means of the excavation of an experimental trench within mine limits, where specific instruments were installed, and several slope failures were monitored and backanalysed, in order to yield information about sliding mechanisms in the future open pit.

Jan 1, 1983

By Zdzislaw Specht

THIS paper discusses elementary laws pertaining to seismic reflection methods and presents a general and simple criterion for determining the direction of dipping of a reflection horizon from observational data of distance and time. The important development of practical geophysics and the successful results obtained in America, Germany, and other countries, caused introduction of geophysical methods of prospecting in Poland. Of all methods, seismic prospecting has proved most successful in the area of the Carpathian foreland, where new oil reserves are to be expected. Because of the great depth of the sedimentary column in that area, rang-ing sometimes over 2000 meters, it was obvious that only the seismic reflection method could give reliable information regarding the structural features of these strata at such a depth. During the experimental surveys it appeared that the complicated geological conditions of that area do not always allow prediction of the depth and the angle of dipping of reflecting horizons, and for that reason information about the inclination of a given horizon has great importance in the determination of subsurface structure. Therefore the problem arises of obtaining from seismic reflection data reliable information as to the direction of dipping of reflecting strata, without any previous knowledge of the average velocity and depth of geologic horizons under consideration.

Jan 1, 1940

By G. R. St. Pierre, A. J. Wilhelem

In connection with the reduction of hematite or magnetite to metallic iron, it appeared desirable to study the rate of reduction of each oxide to the next lower oxide under conditions which excluded all other condensed phases. For this purpose, pellets of Fe,O,, Fe,O,, and oFeOo were prepared. A gas train for the preparation of Ar-Hz-H20 mixtures was employed to establish a continuous flow of a controlled atmosphere over a pellet suspended on a balance. In this manner the following individual reduction steps could be studied: For example, pellets of hematite were reduced solely to magnetite by adjusting the gas atmosphere such that it was oxidizing to wustite. In other words, the reaction was complete when the hematite pellet had been totally converted to magnetite. The pellets were prepared from Baker Chemical ferric oxide. The ferric oxide powder was moistened and handrolled. Air sintering at 950°C produced Fe,0, pellets with a density of 3.65 g per cm3. The pellets ranged in size from 0.6 to 1.2 cm diam. The magnetite and

Jan 1, 1962

By Charles R. Fettke

In connection with the gathering of data for a report on the geology of the Humacao district of southeastern Porto Rico during the summer of 1916, under the auspices of the Scientific Survey of Porto Rico and the Virgin Islands, conducted by the New York Academy of Sciences, the writer had an opportunity to make a brief examination of the magnetite deposits of the eastern portion of the island. Inasmuch as these deposits have attracted some attention as possible future sources of iron ore, and as there is only scanty reference made to them in literature,' a short description based on this reconnaissance survey was deemed to be worthy of record. The magnetite deposits of eastern Porto Rico occur in association with a belt of limestone, trending approximately S 53° E, which begins 11/2 miles east of Juncos and can be traced for about 6 miles toward the coast. Four outcrops of magnetite were observed, which are designated as Nos. 1, 2, 3, and 4, respectively, on the map shown in Fig. 1. Others are probably present, but escaped notice on account of the thick mantle

Jan 1, 1924

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By K. C. Ko, D. A. Pifer

The theory of probability with respect to the failure of structures is discussed. It is shown that the probability of safety, probability of failure, and factor of safety are directly related to each other and that as standard deviation approaches zero, the probability curves approach a unit step function which can be interpreted as the conventional factor of safety. The factor of safety is numerically the ratio of the load to the strength of the material at a particular point or plane in an engineering structure. Mathematically, it can be illustrated as a unit step function undefined at the point where the factor of safety is one (Fig. 1). The uncertainty of variation of soil and rock strengths require factors of safety much higher than those used in other engineering structures. The factors of safety used are generally determined from past experiences with similar structures. However, the factors thus determined do not have any theoretical meaning or do not indicate any relationship to actual safety.' It seems, therefore, logical to develop a system with a sound theoretical basis to obtain a more suitable factor of safety for structures. An application of elementary theory of probability indicates that it is possible to relate this number to theoretical and practical engineering facts.

Jan 1, 1971