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By R. W. Raymond

There is apparently no end to the doubts, inconsistencies and absurdities in which the courts of our mining States and Territories are involved in their attempts to apply to conditions of ever-increasing complexity the provisions of our anomalous mining law. In previous papers, I have called this statute " the law of the apex," because it based upon that vague, novel and mysterious condition the most important grant of title. But the apex is scarcely a more essential feature than the end-lines and the side-lines; for the rights which it may confer may be limited in various ways by these; so that we have, in many a case, the most ridiculous result that the United States, in return for the money of a citizen, conveys to him with much solemnity, under its broad seal, nobody knows what, bounded nobody can tell how. A decision recently made at Butte by Judge De Wolfe, of the United States District Court of Montana, in the case of King et al. vs. The Amy and Silversmith Mining Company, furnishes a fresh illustration of this criticism. The diagram on the following page, constructed without precise regard to courses and distances, simply to assist in the statement of the essential features of the case, will, 1 hope, make clear the principles . involved : The plaintiff occupies a location (the Nonconsolidated) adjoining on the north the defendant's location, a b c d (the Amy), and the disputed mining-ground lies, let us say, in depth under the point W, that is, on the dip of the vein, VD, but not under the surfacelocation, a b c d. The defendant has the prior title, and claims this ground under its extra-lateral right. It is admitted that the apex does not cross the end-line, a d, and does cross the side-line, a b. Whether it crosses, at the other end of the location, the end-line, b c

Jan 1, 1889

By John C. Sawyer

The mechanism of catastrophic oxidation of chromium and 446 stainless steel is examined. Data are presented to show that accelerated oxidation of these two materials, as caused by lead oxide, can occur in the absence of a liquid layer contrary to presently accepted theory. An alternate theory is proposed in which the rate of accelerated oxidation is a function of the rate at which lead oxide destroys the protective oxide formed on the base metal. An example of the application of the theory is given for the catastrophic oxidation of chromium in the presence of lead oxide. WHEN stainless iron-, nickel-, or cobalt-base alloys are heated in air to moderate temperatures in the presence of certain metallic oxides, oxidation will proceed at an accelerated rate. This phenomenon, often called "catastrophic oxidation", is most pronounced for the stainless steels. With these alloys the condition is so severe that large masses of oxide will form on the surface of the alloy in 1 hr or less at temperatures of 1200o to 1700oF. While a number of oxides are known to cause this effect, PbO, V2O5, and Moo3 are the most familiar, having been the subject of one or more investigations which have appeared in the literature.1-7 In presenting the results of these investigations, many of the authors have offered possible explanations to account for the more rapid rate of oxidation observed; however, the liquid layer theory as proposed by Rathenau and Meijering 2 has been the most commonly accepted mechanism. The liquid layer theory proposes that a low-melting oxide layer is formed on the surface of the alloy as the result of the interaction of the alloy oxide and the contaminating oxide. When the temperature of oxidation is above the melting point of the oxide on the surface, a liquid layer will form and oxidation will proceed at an accelerated rate. At temperatures below the melting point of the surface oxide, oxidation will proceed more slowly in the normal manner. It is argued that the rates of diffusion of oxygen and metal ions through the liquid layer are extremely rapid thereby accounting for the high rate of oxidation. Various experimental data have been presented to show that the temperature at which accelerated oxidation first becomes apparent coincides with the melting point of the eutectic oxide which would be present on the surface. Some exceptions have been observed, e.g., silver will oxidize in the presence of Moo3 at temperatures below the lowest melting eutectic; on the other hand, stainless steel will not be catastrophically oxidized at 1500oF in a molten bath of PbO and SiO2. In reviewing the various theories which have been used to explain catastrophic oxidation, Kubaschewski and Hopkins 8 favor the liquid layer theory, but note that, ".. .as experimental observations are not altogether in agreement with this theory (liquid layer theory), one should consider it a necessary but not a sufficient condition." In contemplating the liquid layer theory, it appears that sufficient evidence has not been presented to establish the theory beyond question. As a means of further clarification, a program of research was undertaken to determine in greater detail the mechanism of accelerated oxidation as caused by lead oxide. The first part of the program deals with a comparison of the oxidation of both AISI 446 stainless steel and chromium metal in the presence of lead oxide, vs the oxidation of these two materials in air alone. These comparisons are made at a number of different temperatures, most of which are below the melting point of the surface oxides. The second part of the program is concerned with a presentation of an alternate theory of accelerated oxidation exemplified by the system Cr-PbO-Air. PROCEDURE AND RESULTS Several experimental methods are commonly used to follow the progress of oxidation. One of these, the weight-gain method, was chosen for this work. This procedure requires that a specimen of the alloy be weighed, oxidized for a given period of time at an elevated temperature, and reweighed—the difference between the two weights being noted. The weight gain of the specimen represents the amount of oxygen acquired from the atmosphere to transform a portion of the specimen to oxide. In those cases where there is a tendency for the specimen or oxide to volatilize at the testing temperature, additional data must be collected so that a correction factor can be determined. This factor must be applied to the weight change in order to ascertain the actual amount of oxidation which has taken place. The specimens used for this work were 1 1/2 in.

Jan 1, 1963

By J. E. Warren, J. H. Hartsock

Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, helve motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through. a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitcitions implied by the assumptions that were made, the following general conclusions were drawn. 1. For a radius of drainage at least four times us large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated. 2. The productivity of the hydraulically fractured system, relative to that of the unfructured well, can be determined from the apparent skin effect and can be used to establish design objectives. 3. In the evaluation of a fracture job, it is not Possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary. lNTRODUCTION Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years, it is only in the last few years that improvements in fracture design1-6 and fracturing technique' have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following. I. For a particular well in a given formation, what are the optimum design specifications for the fracture treatment? 2. Have the design objectives been achieved by the fracture treatment? The significance of these questions has been recoguized, and some attempts to obtain answers have been made. Howard, et al,8 endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy9 utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen10 to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al,11 attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner.12 These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should be sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments. Because this study is exploratory in nature, its scope

By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy's law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy's law,

By T. M. Daulton, Chester F. Lee

The Atlin Mining District is in the northwest corner of the Province of British Columbia. Ruby Creek, where the operation to be described is situated, is 17 miles east of the town of Atlin and about 18 miles south of the south line of Yukon Territory (Fig. 1). Gold was discovered in the district in January, 1898, and the production to date from placer mines has been $4,518,000, according to the reports of the Minister of Mines for the province. Geology The essential points in the regional geology are given in the following paragraphs. Long erosion produced a plane-like surface slightly above sea level with a few peaks and ridges.' A gradual uplift followed and erosion increased, the streams cut deeper, the cuts so made being afterward increased by glaciation. The ice straightened and planed the slopes of the main valleys and widened and lowered their floors, in some cases flooring the valleys with silt, sand, gravel, and clay. As the glaciers rapidly retreated, lakes were formed. As to the origin of the gold, J. C. Gwillim says? "The Surprise granite has been carried northward toward Gladys Lake and Teslin, and the granite of the great plateau on the Taku trail was found in blocks on the opposite range across Hurricane River 10 miles north of its original position. Otherwise there is little evidence of far removed material, the boulders of the lake shore and creek beds being of local appearance. This appears to strengthen the opinion that the placer gold had its origin within the drainage basins where it is now found." In the gold-bearing creeks of the Atlin district there are two "runs"

Jan 1, 1917

By Jr. F. M. Perkins.

Capillary forces play a controlling role in water-drive displacement processes both in laboratory experiments and in actual reservoirs, but their quantitative importance may be quite different in the two cases. Because of the importance of conducting laboratory experiments which are representative of field conditions, it is necessary to understand exactly the role of capillary forces in the displacement process. Though a number of experimental investigations related to this subject are contained in the literature, there appears to be a lack of information pertaining to unsteady-state experiments in water-wet media. This experimental study was conducted to obtain additional laboratory data to clarify further the role of capillary forces in both the macroscopic and microscopic flow of oil and water in porous materials. THEORETICAL CONSlDERATlONS The capillary pressure is defined as the difference in pressure between a continuous oil phase and a continuous water phase in a porous material.' The magnitude of this pressure difference depends on the interfacial curvature and the interfacial tension. The interfacial curvature is determined by the geometry of the pore spaces, the wettability of the rock surfaces, and the quantity of cach phase present. Capillary forces are involved in a water-drive displacement process in that they exert a controlling influence on the microscopic fluid distribution which in turn is reflected in the saturation or macroscopic flow behavior. Microscopic Fluid Distribution Because of the microscopic nature of the displacement of oil by water, it is necessary to consider the flow and the fluid distribution in individual pores. On this microscopic scale the capillary Forces, which act over a distance of one or two sand grain diameters, control the distribution of oil and water under static equilibrium conditions. When an external force is applied to the fluids, such as in a water-injection experiment, the applied forces tend to distort the oil-water interfaces. However, in most fine-grained, water-wet sands, the applied pressure difference across one or two grain diameters is usually several orders of magnitude less than the capillary pressure difference. These con-siderations lead to the theory' that even during flow the capillary forces continue to control the microscopic distribution of oil and water within the pores of a porous material for all practical reservoir and laboratory flow rates. This concept of capillary forces controlling the microscopic distribution of fluids has been substantially verified by other investigators3-7 who have found a lack of dependence of relative permeability and residual oil saturation on rate of fluid injection. Macroscopic Distribution The microscopic influence of capillary forces cannot be observed easily and only the effect on the macroscopic or average saturation can be detected. The saturation, of course, is really the point of interest. During a water flood, large differences in saturation at the flood front cause large capillary pressure gradients. This, in turn, causes water to advance ahead of the flood front thereby reducing the capillary pressure gradient in this region. The result is that in homogeneous porous media capillary pressure gradients tend to cause a diffuse displacement front. At low rates in laboratory columns, the front may extend over the entire column length. When the advancing water first reaches the outflow face of a core, the water, which is the wetting phase, cannot be produced because the pressure in the water just inside the core is lower than the pressure in the oil-filled space around the outflow face. This difference in pressure is equal to the capillary pressure for the water saturation existing at the outflow face. Water, therefore, accumulates at the outflow end of the core which causes a reduction in the capillary pressure. Because the capillary pressure does not vanish except at the residual oil saturation,7,8,9 water will not be produced until the residual oil saturation exists at the outflow face. This entire effect,"' which is called the "boundary effect", results in a region of relatively high water saturation near the outflow face. At low rates of injection in a short column, this region of high water saturation may extend over a considerable portion of the column. The influence of capillary forces on the macroscopic flow of oil and water have been described by Leverett.10 For unidirectional, viscous flow in the absence of gravity segregation, the expression in dimensionless form for the fraction of water in the flowing stream, f, is

Jan 1, 1958

By W. E. Crawford

The Fresnillo Company's mill at Fresnillo, State of Zacatecas, Mexico, treats oxide ores from the Fresnillo mine, dump ores and underground ores from the Plateros district, company leases and custom ores from the Zacatecas district, custom ores from other districts and tailings from old dumps at Fresnillo. The normal capacity of the mill is approximately 2600 dry short tons per 24 hours (a ton of 2000 lb.). The final product of the mill is a precipitate containing gold and silver, which is smelted and shipped as doré bullion to the refinery of the Compania Minera de Penoles, S.A., at Monterrey, State of Nuevo Leon, Mexico. The geology of the district was described in 1923, by T. C. Baker,' from whose paper the following data have been taken: The mineralization of the district was effected in the Tertiary period, following the intrusions and preceding the appearance of the flows. The area within which productive veins have been found is 1 mile long by 1/2 mile wide. The important units of each of the four general fracture systems meet in the central portion of Proano hill, which is an outcrop of graywacke, and where the rock was also intensely fractured by subsidiary movements, resulting in a shattered zone 1200 ft. long by 400 ft. wide. The mineralization was more intense in the immediate vicinity of the principal channels through which the solutions rose. The valuable metals are silver and gold, the ratio by weight of the former to the latter being 1000 to 1.5. Argentite is the predominant silver mineral, and is associated with pyrite and manganese mineral. The sulfides are primary throughout. A slight secondary action is represented by small quantities of native silver and silver halides, principally cerargyrite, which are found in the upper part of the mine. Oxidation has penetrated with great thoroughness to the lowest horizon so far exposed, this being 420 ft. below the present ground-water level. The shattered mass within the central portion of the hill and near the surface was sufficiently mineralized to produce a large stockwork

Jan 1, 1935

By W. B. Phillips

The earliest mention of the sulphur deposits in what is now Culberson County, Texas, seems to be contained in " Explorations and Surveys for a Railroad Route from the Mississippi River to the Pacific Ocean, United States War Department, 1853-54." Captain John Pope (he was not commissioned Captain until 1856) had charge of one of the divisions of the Survey. In his report on the geology of the route, William P. Blake noted the analysis of a greenish earthy powder from the bed of Delaware Creek, at the springs, which contained 18.28 per cent. of free sulphur. The report states: "From the chemical examination of the waters of the spring, by Dr. Booth, it appears that chloride of sodium is the principal solid ingredient, but considerable quantities of sulphide of sodium are present. ***** The waters from the springs examined by Dr. Booth were alkaline, but it is possible that some of the springs are acid; and in this case the precipitation of sulphur would ensue on the mixture of the acid waters with those charged with alkaline sulphurets and the origin of the deposits of sulphur would be thus explained." This is the first reference to the existence of sulphur in that region, the first mention of the character of the water found there and the first suggestion as to the origin of the deposits. The possibility of the existence of acid waters was confirmed by E. M. Skeats, nearly 50 years later.' In this publication, Skeats says that the water from the sulphur deposits in Section 11, Block 114, Township 6, contains 79.08 grains of free sillphuric acid per gallon. This locality is about 13 miles (21 km.) south . of Delaware Creek and about 35 miles (56 km.) east of the Delaware Springs. The next published reference to the existence of sulphur in Trans-Pecos. Texas is in the Pirst Annual Report of the Geological Survey of Texas, 1889, page 226, where W. H. von Streeruwitz mentions that sulphur is found in that region, but gives no further information. In the

Jan 1, 1918

By C. L. Dake

Iron is much more soluble in the ferrous than in the ferric form. Where, as in the case of the ferrous silicates and. the sulphides, the iron is already in the ferrous form, it may go at once into solution and be removed, upon the breaking down of the parent rock. If in the ferric form, it must first be reduced; usually by the decay of organic matter, the demand of the decaying carbonaceous matter for oxygen being so great that the latter is abstracted from the ferric compounds and the iron is thereby reduced and rendered soluble. The iron may go into solution as the sulphate, or in the presence of excess CO2 as ferrous carbonate. It is probably soluble as salts of the organic acids.' Recent work indicates that these are important in the formation of bog ores.2 There is considerable variety of opinion concerning the behavior of these organic compounds.3 The secretions about the roots of plants and trees also cause the solution and removal of iron and a consequent bleaching of the soil,4 While the matter is not yet well understood, we can probably say definitely that the so-called organic acids are a group of colloids which possess slightly acid properties, and the salts of which are partly soluble and partly insoluble.5 Their iron salts readily change from the ferrous to the ferric form, and their solubility is greatly modified by the presence of ammonia.

Jan 1, 1916

By H. G. Doll

A new electrical logging method is described which measures the resistivity of small volumes of material near and behind the wall of the bore holes. The very small electrode systems used are supported in the face of the flexible insulator pad of appropriate dimension maintained in contact with the wall. The measurements are recorded simultaneously with two different electrode spacings. This method provides a very detailed record of the formations and particularly of the permeable beds traversed by the bore holes. The application of MicroLog to the location of permeable zones within compact formaltions, such as limestone, and to the determination of the amount of sand existing in sequences of thin shale and sand streaks is discussed. The possibility of quantitative determination, providing a step toward the evaluation of formation porosity and mud cake thickness, is also examined. Field examples illustrate the essential features of the method. INTRODUCTION In conventional electrical logging, the spontaneous potential (SP) log is used to delineate the permeable beds, and the resistivity logs are used primarily to provide indications concerning the fluid content of the beds. When the formations are much more resistive than the mud, as happens, for example, in limestone fields, the SP currents are short-circuited by the more conductive mud column, with the result that the SP log is quite rounded. In that case, the SP log generally gives the approximate location of the permeable formations but it cannot be used for an accurate determination of the boundaries of each permeable bed.' Solutions for the problem of obtaining a better determination of the permeable beds in limestone fields were developed from two angles. One approach consisted in improvements to the logging of the SP, as given by Selective SP logging and Static SP logging. These new methods, which have been described in an earlier paper,' give good results when the mud is not too salty, but they are still in a somewhat experimental stage, mostly because the development efforts have lately been concentrated on another approach to the problem, i.e., the MicroLog.

Jan 1, 1950

By John F. Elliott, John R. Rawling

The rate of reduction of silica to silicon by carbon at 1550° to 1700°C in iron blast-furnace type slag-metal systems has been investigated. In the tower portion of the temperature range oxygen transport in the metal boundary layer at the slag-tal interface is probably rate limiting. A second step, which apparently involves a chemical process in the slag at the slag-metal interface, appears to be rate limiting when the oxygen-transport limitation is avoided. Above 1650°C rate control of the reduction by carbon probably is mixed between the two steps. INVESTIGATIONS1.2 into the equilibrium distribution of silicon between graphite-saturated slags and metals typical of iron blast-furnace practice show that, under the experimental conditions specified, the reduction of silica to silicon is relatively slow compared with the rates of other slag-metal reactions under similar conditions. For this reason, the reduction of silica in blast-furnace slag-metal systems was considered to be an interesting subject for further study. Investigations of the kinetics of the reaction3-5 suggest that several possible steps may be rate controlling, and that the rate-controlling step depends not only on the physical state of the systems but also on the configuration of the apparatus. The main objects of the investigation reported here were to sug- gest plausible reaction paths for the reduction of silica under the experimental conditions chosen and to determine the step or steps which control the rate of reduction of silica. EXPERIMENTAL Two types of experiments involving the reduction of silica from the slag were carried out. In the first, the only reducing agent present was carbon (graphite), for which the over-all reaction is (SiO2) +2C(gr) —Si + 2Co(g) [l] The second type was a graphite-saturated ferro-silicon-iron concentration cell. In it silica in the slag could be reduced either by carbon according to Eq. [I], or by a reaction of electrochemical nature in which silicon was oxidized at the ferrosilicon-slag interface and silica was reduced at the slag-iron interface without the formation of CO. The two types of experiment are described below. Reduction of Silica with Carbon as the Only Available Reducing Agent. The reduction of silica was accomplished by allowing a liquid lime-alumina-silica slag and graphite-saturated iron to react in an induction-heated graphite crucible. The crucible was 2.25 in. diameter and 5 in. deep; it was fitted with a graphite stirrer which penetrated through the slag and into the metal, Fig. 1. The slag and metal charges weighed 350 g each. Pure carbon monoxide at a pressure of 1 atm was maintained above the melt by passing the purified gas through the crucible at a rate of 0.5 liter per min. The gas did not stir either the slag or metal. Temperature measurements were made by sighting an optical pyrometer down the hollow stirrer rod into a 1/4-in. hole drilled in the stirrer blade. The crucible temperature was maintained within *15"C of the required value by manual control of the power supply to the

Jan 1, 1965

By O. F. Walker, W. C. Hahn, V. A. Johnson, J. D. Wood

The diffusion coefficients of zinc in single-crystal zinc and carbon in single-crystal and poly crystalline nickel were measured by means of radioactive tracer techniques both with and without the application of ultrasonic vibrations under conditions such that the temperature of the sample was closely controlled. The results of this investigation indicate no enhancement of diffusion in any of the samples. It is suggested that previously reported enhancement may have been due either solely to temperature increases caused by ultrasonic vibrations or in combination with changes in the boundary conditions. A number of observations have been reported in the literature in which it has been implied or inferred that the application of ultrasonics enhances diffusion (see, for example, Refs. 1-5). The present study was undertaken in an attempt to observe this effect under carefully controlled conditions, particularly with regard to measurement and control of the temperature of the sample. Two different types of systems were studied; these were the self-diffusion of zinc and the diffusion of carbon in nickel. EXPERIMENTAL For diffusion with ultrasonic energy applied, the samples were included as part of a resonant ultrasonic system operating at 58.5 kcps. The ultrasonic generators used were rated at 100 and 250 w and could be tuned over a frequency from 10 to 100 kc. A PZT (lead titanate/lead zirconate) ceramic transducer provided the driving vibration. This system requires no metallurgical joining of the specimen to the acoustical transmission line since the ultrasonic driver and the follow-up section clamp the specimen in position by means of a constant pressure of 50 lb developed by an air cylinder. The ultrasonic driver and follow-up section, both made of titanium, were 4 in. in length from clamping point to the end in contact with the specimen. Using the relationship given by Mason,6 A = V/f, the resonant wavelength, A, in titanium is calculated to be 3.3 in. at a frequency, f, of 58.5 kc, taking the velocity of sound in titanium, V, as 1.95 X 105 in. per sec. The 4-in. driver and follow-up section, therefore, are each 4.0/3.3 =1.21 times the resonant wavelength. Clamping pressure must be applied at stress nodes of the transmission line in order to preserve resonance. Therefore, a specimen length of 0.58 times the wavelength in the specimen was required to place the clamping pressure application points at stress nodes exactly three wavelengths apart. A stress antinode was contained in the center 3 in. of the specimen. A small PZT ceramic disc attached to the follow-up section provided an output voltage proportional to the intensity of the standing wave. This output voltage was monitored on an oscilloscope and the ultrasonic system was tuned to resonance by varying the frequency until the output signal was a maximum amplitude. The amplitude of the output signal was maintained constant throughout the diffusion anneal. A split cylindrical stainless-steel chamber, which was purged with argon prior to and during the runs, was placed around the specimen. The chamber in turn was surrounded by a movable furnace whose temperature could be controlled to 7C. Heat exchangers were used to cool the driver, follow-up section, and ultrasonic transducer. Great care was taken to obtain the true specimen temperature in all cases. Several different methods were tried; the most successful was that in which the thermocouple was held in contact with the midlength of the specimen by means of an asbestos insulating pad and wire straps. In the case of zinc, single-crystal specimens of 99.999 pct purity were used. The samples were 0.25 by 0.25 in. square and of the proper length for resonance, that is 1.1 in. long with the c axis parallel to the long dimension of the specimen for the case of diffusion perpendicular to the c axis and ultrasonic motion parallel to the c axis, and 1.9 in. long with the c axis perpendicular to the long dimension of the specimen for the case of diffusion parallel to the c axis and ultrasonic motion perpendicular to the c axis. In each case, one of the rectangular faces was electroplated with a thin film of zinc containing Zn The constant pressure used to clamp the specimen in place in the ultrasonic system caused some deformation in some of the samples. For these samples the deformation was concentrated in either end of the specimen; thus, for all samples (both zinc and nickel) the center in. was cut from the specimen after the diffusion anneal to be used for sectioning and counting. The nickel single-crystal samples, of 99.999 pct purity, were used in the form of rods 0.25 by 0.187 by 2.07 in. long with the (100) direction parallel to the rod axis. The polycrystalline nickel samples of 99.97 pct purity had an average grain diameter of 0.007 in. and were used in the form of rods 0.25 by 0.125 by 1.87 in. long. The direction of ultrasonic motion was parallel to (100) direction (bar axis) for the single-cqstal samples and parallel to the bar axis for the polycrystalline specimens. A thin film of c14 suspended in methanol was applied to the diffusing face of the specimen. Two specimens were butted together lengthwise for each diffusion anneal to minimize oxidation. After diffusion, a precision lapping device similar to the one described by Goldstein7 and a radiation detector were used to obtain a plot of specific activity vs penetration distance for each specimen. (A scintil-

Jan 1, 1969

By A. Aly Selim

A computer model was developed to calculate the fragmentation cost for in situ leaching operations as a function of the blast design and deposit parameters. The model is based on blasting an ore zone only or an ore zone plus overburden by either a coyote blast or a vertical blasthole system. The model calculates the blast design parameters and the fragmentation cost based either on a user input powder factor value or on a powder factor calculated by the model as a function of the overburden height and the ore zone thickness. Examples of blast design parameters calculated by the model are the number and spacing of blastholes for a vertical blasthole system and the number and spacing of crosscuts for a coyote system. The model also calculates the total amount of explosives, the detonating cord length, and the number of primers. The cost of blasthole drilling can be calculated by the model based either on purchasing and operating a drill or on a user input value of the contracted cost of drilling. Application of the model to an example ore deposit showed that the vertical blasthole systems were more economical than the coyote system when there was no overburden and the deposit had an average ore thickness less than 45 meters. With no overburden and ore thickness greater than 45 meters, the vertical blasthole system was either more or less expensive than the coyote system depending on the number of levels used in the coyote system. With overburden, the coyote system was less expensive than the vertical blasthole system for blasting either the ore only or the ore plus the overburden. A coyote blast will usually produce larger particle sizes than a vertical blasthole system. Larger particle sizes can result in lower copper recoveries so that a less expensive coyote blast may not improve the overall economics of an in situ leaching operation. Blasting the ore zone only was generally less expensive than blasting the ore plus the overburden by either blasting system. Also, for the example considered, the coyote system costs were less sensitive to changes in overburden thickness and powder factor while the vertical blasthole system costs were less sensitive to changes in ore thickness.

Jan 1, 1977

By M. E. Lombardi

The cost of maintaining the production of an operating oil company is one of the most important, as well as one of the most difficult to estimate, of the various items which go to make up the total cost of producing oil. In the opinion of many operators the cost of drilling and developing new wells, whose, production takes the place of the loss in production through decreased yield of the old wells, is considered an operating expense, for the reason that the total income-producing power of the property is not increased. The cost of these new wells may be added directly to production expense, or it may be charged to capital account, and this account depreciated to the same extent. In either case, after an oil company is on a satisfactory income-producing basis, the money for drilling new wells to maintain production must be taken from the income of the company. Three factors determine the cost of maintaining production: First, the rate of decline in yield of the wells; second, the cost of drilling and equipping new wells in terms of their production; third, the decrease in initial production of new wells as the property is drilled and gas pressure taken off the sands, etc. In order to check theoretical figures for the cost of maintaining production the writer, with the assistance of Reed Bush and Fred Tough, has compiled the following figures. It is necessary first of all to choose a' period of time during which production for the field or territory studied remains fairly constant. The longer the period of time over which this condition prevails, the better. It is also necessary to eliminate or allow for any extraneous condition which may have affected the production returns, such as the shutting down of a large number of wells, the bringing in of a well of exceptionally large yield, the opening up of virgin territory where the flush yield is greater than will be had from new wells in after years, etc. All these conditions are exemplified most simply in the case of the Coalinga field, and perhaps these figures are more truly prophetic than the two other cases given. In applying these figures to the future it is well to assume that the average yield of new wells will constantly de-

Jan 1, 1916

By J. L. Gillson

The big mass of anorthosite in the Lake Sanford district and the bodies of titaniferous magnetite that occur in a small area near the south margin of the mass have been described repeatedly, and the puzzling problems of the genesis of the rocks and ores have stimulated the deductive reasoning of geologists for a hundred years. Some of these men have taken a leading part in describing the anorthosite rock and forming hypotheses concerning its origin; some have contributed most to the study of the ore deposits; and some have made classical Studies introducing a basic approach to the problems of the anorthosite rock and genesis of the titaniferous magnetites. Much of the writing on the problems of rock and ore genesis has been based on physical-chemical reasoning rather than on field and microscope observations of the rocks and ores. Most of these geologists conclude that the anorthosite was formed by true magmatic crystallization, involving previous settling or squeezing out of ferromagnesian minerals from the parent magma. The associated gabbro is a separate segregation or later intrusion, and the lighter colored and finer grained facies of the anorthosite is either a chilled border zone of the anorthosite or the result of granulation by crushing of the coarse, dark blue rock of the main mass. This blue rock, called the Marcy type, is named after the highest peak in the range. The finer grained and lighter colored rock is called the Whiteface, after another mountain appropriately named for a cliff colored by this facies of the anorthosite.

Mar 1, 1956

By J. H. Scaff, H. C. Theuerer

Germanium may be reversibly converted from n to p type by heat treatment. Data for the conversion and the associated changes in resistreatment.tivity are given and the results are interpreted in terms of changes in the donor-acceptor balance. MEANS for controlling the electrical properties of germanium in a predictable manner are of interest because of the increasing utilization of this element as the semiconducting material in electrical devices. Since both the mechanism and the magnitude of the electrical conductivity depend upon the kind and quantity of impurities present, the conductivity usually is adjusted by first carefully purifying the germanium, and then, by standard alloying procedures, adding the elements desired. The elements usually added are from the third or fifth periodic groups depending upon whether p- or n-type germanium is desired. However, in the development of germanium rectifiers during the war, it was found that it was possible also to modify reversibly the conductivity of germanium and even to produce conversion from n to p type by heat treatment.1,5 Since then a detailed study of this effect has been made. The data are presented in this paper and an explanation is offered for the effects observed. Preparation and Experimental Procedure The method used in preparing the germanium ingots for this investigation has been previously described.' The method consists essentially of (1) reduction of GeO2* and (2) preparation of a 50-g ingot from the reduced material. Graphite containers are used in both steps. In the first step the GeO2 is reduced in hydrogen at 650 °C to form a sponge germanium which, to assure complete reduction and to obtain massive materials, is fused subsequently in the reduction furnace by gradually raising the temperature to 1000°C. The button of germanium thus obtained corresponds to a yield of 99.8 pct. The final ingot is prepared by fusion of the germanium button in a helium atmosphere. A cylindrical crucible in a vertical silica tube furnace is employed and the crucible is heated by an external induction coil. The ingot is solidified from the bottom upward by raising the induction coil at a constant rate with power to the coil kept at a fixed value. In such ingots, segregation is normal and most of the impurities are concentrated in the last region of the ingot to freeze. It follows then that the major portion of the ingot is purer than it would have been if freezing had occurred in a random fashion. Moreover the orderly advance of the freezing surface during solidification establishes in the ingot a succession of surfaces of constant composition, if it is assumed that the liquid is homogeneous and that diffusion in the solid is negligible. Therefore, some information on the distribution of impurities in the ingot may be acquired by determining the shape of the solid-liquid interface at different stages of solidification. This is of importance because the concentration of impurities will be seen to affect the response of germanium to heat treatment. Such information is difficult to acquire by direct means, for the impurities responsible for the electrical properties of germanium prepared in this way are present

Jan 1, 1952

By Stuart E. Buckley, C. R. Hocott

The viscosity of the oil in the reservoir is one of the properties that influence its movement through the sand to producing wells. Measurements of viscosity, therefore, are pertinent to problems associated with well behavior and with the estimation of recoveries, and afford an indirect means for partial evaluation of various methods of controlling reservoir behavior. The effect of dissolved gases on the viscosity of crude oil has been determined,ls2 but no data have been published on the viscosity of representative samples of reservoir oils. This paper describes a simple instrument that has been used to determine the viscosities of a number of subsurface oil samples at the temperatures and pressures existing in the reservoirs, and presents the results of the determinations for typical fields. Construction oF the Apparatus The principal requirements of any instrument used for the examination of subsurface samples are that it be strong and simple both in design and in method of operation. Accuracy beyond that of the degree of reproducibility of subsurface Sam-~les from various wells in a reservoir or exceeding that of the common measure-merits of reservoir temperatures and Pressures is not required. Because of the expense of procuring subsurface samples, it is necessary also that the instrument operate on a relatively small fraction of a sample, leaving the remainder for other tests, and that there be few or no failures of the equipment to cause undue delay or loss of a sample. After preliminary experiments with a falling bullet, the results of which were not satisfactory, a simple viscosimeter was built of the rolling ball type first proposed by Flowers3 and later used by several investiga-tor. 5.8 The apparatus consists essentially of a removable, accurately bored cylindrical barrel of 1/4-in. nominal internal diameter, 8 in. long, in which a closely fitting steel ball rolls through the oil with the barrel inclined at a definite angle. The ball makes contact at one end of the barrel with ail insulated electrode, closing an electrical circuit, which actuates a buzzer. The meas-urements consist essentially in determining the time required for the ball to travel the length of the barrel. The details of the construction are shown in Fig. I. The barrel in which the ball rolls was made from a section of 25-caliber blank rifle barrel, specially bored to an exact uniform diameter and polished. The barrel slides snugly into a hole bored in a solid stainless-steel cylinder, an upper external shoulder of the barrel compressing a small spring, and is held in place by a hollow nut. The spring prevents the barrel from seating against the bottom of the bored hole in the cylinder, while narrow external longitudinal slots in the barrel permit fluid to flow around it and through the bottom. The upper part of the recess in the steel cylinder is enlarged to form a tapered chamber, which acts as a reservoir for the oil and affords space for agitation to ensure

Jan 1, 1941

By C. R. Hocott, Stuart E. Buckley

The viscosity of the oil in the reservoir is one of the properties that influence its movement through the sand to producing wells. Measurements of viscosity, therefore, are pertinent to problems associated with well behavior and with the estimation of recoveries, and afford an indirect means for partial evaluation of various methods of controlling reservoir behavior. The effect of dissolved gases on the viscosity of crude oil has been determined,ls2 but no data have been published on the viscosity of representative samples of reservoir oils. This paper describes a simple instrument that has been used to determine the viscosities of a number of subsurface oil samples at the temperatures and pressures existing in the reservoirs, and presents the results of the determinations for typical fields. Construction oF the Apparatus The principal requirements of any instrument used for the examination of subsurface samples are that it be strong and simple both in design and in method of operation. Accuracy beyond that of the degree of reproducibility of subsurface Sam-~les from various wells in a reservoir or exceeding that of the common measure-merits of reservoir temperatures and Pressures is not required. Because of the expense of procuring subsurface samples, it is necessary also that the instrument operate on a relatively small fraction of a sample, leaving the remainder for other tests, and that there be few or no failures of the equipment to cause undue delay or loss of a sample. After preliminary experiments with a falling bullet, the results of which were not satisfactory, a simple viscosimeter was built of the rolling ball type first proposed by Flowers3 and later used by several investiga-tor. 5.8 The apparatus consists essentially of a removable, accurately bored cylindrical barrel of 1/4-in. nominal internal diameter, 8 in. long, in which a closely fitting steel ball rolls through the oil with the barrel inclined at a definite angle. The ball makes contact at one end of the barrel with ail insulated electrode, closing an electrical circuit, which actuates a buzzer. The meas-urements consist essentially in determining the time required for the ball to travel the length of the barrel. The details of the construction are shown in Fig. I. The barrel in which the ball rolls was made from a section of 25-caliber blank rifle barrel, specially bored to an exact uniform diameter and polished. The barrel slides snugly into a hole bored in a solid stainless-steel cylinder, an upper external shoulder of the barrel compressing a small spring, and is held in place by a hollow nut. The spring prevents the barrel from seating against the bottom of the bored hole in the cylinder, while narrow external longitudinal slots in the barrel permit fluid to flow around it and through the bottom. The upper part of the recess in the steel cylinder is enlarged to form a tapered chamber, which acts as a reservoir for the oil and affords space for agitation to ensure

Jan 1, 1941

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By R. A. Bowen

The Montreal mine, operated by the Montreal Mining Co., is four miles west of Ironwood, Mich., in Iron County, Wisconsin. It is the westernmost producing property on the Gogebic Iron Range of the Lake Superior district. Its production is 4000 tons of hematite per day from an average depth of 2300 ft. This tonnage is hoisted through a five-compartment vertical shaft. Several mining methods are in use but in the larger orebodies the method is sublevel caving. ORE Occurrence and Chaeacteristics The main orebodies of the Montreal mine lie in eastward-pitching troughs formed by the intersections of intrusive dikes with impervious members of the iron formation. The formation has an average width of 425 ft., strikes east and west and dips north at approximately 62. The dikes dip south at 45° and bear north 20' from the strike of the formation, making the intersections with various members pitch east at 16°. The dikes are not continuous across the formation but are interrupted by a longitudinal bedding fault, which has a throw of 380 ft. vertically and 885 ft. horizontally. North of the fault zone the formation is called "hanging," south it is called "footwall" formation. The faulting has created two ore-bearing horizons; viz., at the intersection of banging dikes with the slate members and the foot dikes with the quartzite footwall. In each formation the main ore-bearing member consists of wavy beds of hard chert interlaid with hematite. In the most productive part of the mine, where the sublevel caving method is employed, a hanging-formation dike lies in juxtaposition with a footwall dike and the iron formation carries ore in certain sections from the quartzite footwall to the hanging dike. Here a horizontal section of the orebody may be 300 to 400 ft. wide for a length of 150 ft. or more and tail out lengthwise in both the foot and hanging formations. The footwall ore section is much longer than the hanging wall because of the orebody's greater height above the "pitching dike."

Jan 1, 1940