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By D. K. Crampton, H. l. Burghoff, J. T. Stacy

The study of copper alloys of the age-hardening type has received considerable attention, and, among the alloys which the authors have, considered, those containing small amounts of nickel and phosphorus as essential constituents seem especially interesting. Such alloys have attractively great capacity for being hardened and also have relatively high electrical and thermal conductivity in the hardened state. In addition, it has been found that the increase in hardness and strength imparted by aging can be greatly augmented by cold-working, so that excellent combinations of conductivity and strength are obtainnble. In view of the possible importance of the alloys, it was considered desirable to investigate the solubility relationships in the copper-rich portion of the copper-nickel-phosphorus system. This paper present's some of the results obtained in this investigation to date and also gives propertics of typical alloys that appear to be of commercial interest,. Review of literature Copper-nickel System,.—The binary coppcr-nickcl system has long been known to consist of a series of simple solicl solutions, copper and nickel being miscible at all tempcrat'ures and concentrations. This was establisl~cd by Guertler arid Tammannl in 1907 and confirmed by Tafel2 in 1908. Copper-phosphorus System.—The copper phosporus system has been studied by numerous investigators, so that the copper-rich portion is now definitely known. As most recently determined by Lindlief," his system has a cutectic at 8.38 per ccnt P, cuteetic temperature being 714° C. Components of the cutectic are Cu3P and alpha solid solution. Solid solubility of phosphorus in copper, according to Mertz arid Mathewson decreases from a maximum of about 1.75 per cent at 714' C. to about 0.6 per cent at 300' C.

Jan 1, 1940

By D. K. Crampton, H. l. Burghoff, J. T. Stacy

The study of copper alloys of the age-hardening type has received considerable attention, and, among the alloys which the authors have, considered, those containing small amounts of nickel and phosphorus as essential constituents seem especially interesting. Such alloys have attractively great capacity for being hardened and also have relatively high electrical and thermal conductivity in the hardened state. In addition, it has been found that the increase in hardness and strength imparted by aging can be greatly augmented by cold-working, so that excellent combinations of conductivity and strength are obtainnble. In view of the possible importance of the alloys, it was considered desirable to investigate the solubility relationships in the copper-rich portion of the copper-nickel-phosphorus system. This paper present's some of the results obtained in this investigation to date and also gives propertics of typical alloys that appear to be of commercial interest,. Review of literature Copper-nickel System,.—The binary coppcr-nickcl system has long been known to consist of a series of simple solicl solutions, copper and nickel being miscible at all tempcrat'ures and concentrations. This was establisl~cd by Guertler arid Tammannl in 1907 and confirmed by Tafel2 in 1908. Copper-phosphorus System.—The copper phosporus system has been studied by numerous investigators, so that the copper-rich portion is now definitely known. As most recently determined by Lindlief," his system has a cutectic at 8.38 per ccnt P, cuteetic temperature being 714° C. Components of the cutectic are Cu3P and alpha solid solution. Solid solubility of phosphorus in copper, according to Mertz arid Mathewson decreases from a maximum of about 1.75 per cent at 714' C. to about 0.6 per cent at 300' C.

Jan 1, 1940

By Frank Van Horn

IT is customary to ascribe two general modes of occurrence to natural gas, namely shale. gas which, as the name indicates, is found in' shale, and reservoir gas, which occurs ill sandstone, conglomerate and dolomitic limestone. Both of these types are found in the Cleveland district. The shale gas has been produced on a small scale for a long period of years, probably dating back as far as 1883. Shale gas is a low-pressure gas, small in volume with variable pressure, and is limited to no definite horizon. It is generally independent of oil, may last for a long time, and is not dependent to any great extent on the structure of the rocks. There are many such wells in the district which range from 400 to 1,840 ft. in depth, although most have been completed at about 800 ft. This indicates that the wells pass through the Cleveland and Chagrin shales into the Huron or Portage shale of the Upper Devonian. During the last 2 years great interest has developed in a deeper-seated reservoir gas. What is commonly called reservoir gas is generally a high-pressure gas occurring in large volume at a definite horizon. Oil may, or may not, be associated with the gas, and in most regions in which reservoir gas is found, the geological structure is of great importance. This type of gas occurs in all large fields such as those of West Virginia which have been supplying Cleveland until the recent discovery of local gas at great depths in commercial amounts.

Jan 1, 1917

By Pol Duwez, Ellis P. Frink, Paul Pietrokowsky

Ti-Au alloys in the composition interval 0 to 66 213 atomic pct Au have been studied over a temperature range from 400° to 1500°C. A partial phase diagram has been established from micrographic and macroscopic observations. All intermediate phases, Ti3Au, TiAu, and TiAu., exhibit open melting maxima. It has been observed that small additions of gold lower the allotropic transformation temperature of titanium. The P solid solution decomposes eutectoidally to a solid solution plus Ti3Au. The solubility of gold in a solid solution decreases with temperature. THERE have been several papers in the literature pertaining to the alloy system Ti-Au. However, a comprehensive study of this interesting constitu- tion diagram has not been conducted. Previous investigations have been concerned with the crystal structure of intermediate phases or partial phase diagrams. This paper represents a partial constitution diagram, Ti-TiAu,, the first portion of an investigation of the entire binary system. Laves and Wallbaum' reported the intermediate phase Ti,Au to be isomorphous with CuAu, L12 type. In a more recent paper, Duwez and Jordan' have concluded that TiAu has an atomic arrangement which is related to Cr,Si. The intermediate phase

Jan 1, 1957

By B. Ladanyi

The problem of rock behavior under concentrated loadings has been the subject of a number of studies in the past and has been receiving increasing attention by rock mechanics investigators in recent years. Its application covers various fields, but main interest in its solution has arisen in connection with the problems of drilling, bearing capacity, and rock testing. These widely different purposes and fields of interest probably have been one of the reasons why, in spite of the large amount of published experimental data and several theoretical studies, there are still many points which need further clarification. Another reason for this situation undoubtedly is due to the fact that the rock behavior in indentation is complicated by a great number of influencing factors. Experimental evidence shows that, depending on the rock type (mechanical properties, porosity), environment (ambient effective pressure, pore fluid, temperature), and the type of loading (indenter shape, initial embedment, load level, loading rate), the rock response to indentation may vary within very large limits. The widely different rock behavior has made it impossible up to now to treat the problem with a consistent single mathematical theory, but has required instead a series of simplified models covering only certain most important events in the failure sequence. As far as the theory of rock indentation is concerned, this chapter does not add much new information. Its main purpose is, however, to state the indentation problem in a general manner and to indicate which points need to be studied in more detail before its definite solution is attempted. Also, since excellent reviews of the state-of-art of rock indentation in drilling have recently been given,1-4 this will not be repeated here, and only references pertinent to the points of the problem under study will be quoted. The theoretical part of this study attempts to give a quantitative evalu-

Jan 1, 1972

By N. Nemeth, L. L. Sirois

The role of the filter medium in continuous-vacuum filtration and the special circumstances which influence the resistance to flow through the porous cake and filter cloth are discussed. Due to negative pressure differential, gas bubbles evolve in the slurry, constrict passages in the filter cake and medium, and further restrict flow through the tortuous channels. Filtration is a liquid-solid separation process taking place at a porous medium under a pressure differential. The liquid passes through the medium; the solids are retained on the medium as a partially dewatered cake. Filtration is far from a simple process and has been described in terms ranging from "complex" to "subtle." Because of the many variables involved, no unified filtration theory has been developed, and the filtration process is still considered very much an art. In industrial filter design, basic relationships, whether derived for idealized conditions or developed empirically, are usually adapted to suit local conditions. In the mining industry where continuous-vacuum filtration is the main dewatering process, the physical state of the concentrates and the relatively low pressure differentials permit the assumption that the cakes are noncompressible, an assumption which leads to the use of theoretically sound rate equations. Notwithstanding this simplification, there are other problems, unique in the application of vacuum to dewatering, and until now completely ignored, which demand special attention. The basics of filtration involve the capture of solids on, while permitting the flow of liquid through, a porous layer of cake and cloth. Flow is determined by the structure of the solids which make up the cake and the particles permanently attached to the cloth. The problem of this structure, essentially one of solid geometry, has been considered insoluble by Hatscheckl as early as 1907 and by Freshwater as recently as 1967. Since cake structure is determined by the slurry parameters, that problem is far too large for inclusion in this study. For theoretical considerations, uniform buildup of the filter cake must be assumed; and for efficient practical operation, the resistance of the medium must be kept constant over long periods. The latter can be achieved by careful selection of the filter cloth, since the greatest part of the total filtration resistance will develop at the cake-cloth contact. This paper discusses the role of the filter medium in continuous vacuum filtration and the special circumstances which influence the resistance to flow through the porous cake and the filter cloth.

Jan 1, 1971

By George E. Aiken

Modern high speed bucket wheel excavators (BWEs) can dig materials which power shovels can't handle without blasting. Yet these machines are not used in any large, open pit ore mines in the United States. American mining has been slow to use the wheel's special capabilities of high production volume at low cost, due perhaps to a traditional familiarity with shovels and draglines and/or the lack of data of BWE operation, design and cost. Of course, shovels and draglines can not be replaced by BWEs in all cases, but under suitable conditions bucket wheels can out-perform other conventional excavators and simultaneously permit significant operating savings. The latter aspect will become increasingly important to American mining men because as more low to medium grade orebodies are found in regions of thick overburden, better and cheaper ways of uncovering them must be developed. Typical of such areas are the thick alluvial fans of the Southwest and the glacial drift areas in northern regions. Much of this material would handle well with a wheel excavator without blasting, although ripping might be necessary in some cases.

Jan 1, 1966

Jan 1, 1950

By W. D. Douglas, M. J. Hampshire, G. J. C. Young

This paper describes the replacement of a conventional filtration, clarification, and zinc precipitation plant by a carbon-in-pulp (CIP) electrowinning plant, with the objective of improving the recovery of gold from cyanide leached, acid plant calcines. The discussion covers early laboratory studies to the design and erection of the full-scale plant. Particular emphasis is placed on the problems encountered with commissioning and the strategies employed to solve them.

Jan 1, 1985

By Louis Jordan

THIS paper presents in an abbreviated form the chief points of interest in an investigation of the tarnish-resistant qualities of silver alloys, an investigation which has been carried out as a joint research by the Bureau of Mines and the Bureau of Standards and will later be reported in detail in an official publication from these bureaus. In 1923 a Commission of Gold and Silver Inquiry was created by a Resolution of the U. S. Senate to study the causes of the depressed condi¬tion of the gold and silver industry. In cooperation with this commission the Bureau of Mines made a preliminary survey to determine in what ways, if any, it might be possible to increase the uses of silver. One of the possibilities indicated by this survey was the development of silver alloys which should be non-tarnishing, or at least less-tarnishing, than the usual sterling silver (copper-silver). The preparation of a rather wide variety of silver alloys and the determination of their behavior under accelerated tarnish tests in the laboratory was therefore undertaken by the bureaus, of Mines and Standards as a joint investigation. PREVIOUS WORK ON TARNISH RESISTING SILVERS At about the time this work was undertaken interest in tarnish-resisting silvers was rather keen due to announcements from England that there had been developed a new silver alloy, "Silanca," which was resistant to tarnish. It was even frequently described in the popular press as "non-tarnishing." A few samples and several analyses of "Silanca" which were available indicated that it was an alloy of sterling fineness, that is, it contained about 93 per cent. of silver, with approximately 4.5 per cent. of antimony and either cadmium or zinc, or both, to make the remaining 2.5 per cent.

Jan 1, 1927

Mounting pressures to increase efficiency and yield, conserve energy, or minimize pollution have all taken their toll on the minerals industry. As management and technical personnel take a harder look at their operations for ways to shave cents off operating costs or to squeeze a bit more productivity out of existing equipment, instrumentation often comes up as the most effective answer. When Amax Lead installed an automatic grind control system in its Buick mill, ore throughput increased by 3 to 5%. Mill operators calculate that the initial investment is returned to them several times annually.

Jan 2, 1978

By Dr. O’Neil Thomas J., Donald W. Gentry

"There is nothing so disastrous as a rational investment policy in an irrational world. " John Maynard Keynes INTRODUCTION The principles of time value of money concepts were discussed and illustrated in Chapter 3. The importance of time value of money and the role it plays in the discipline of engineering economy have been well established. Chapter 9 further illustrates that project evaluation criteria that fail to consider this aspect are seriously deficient in providing appropriate capital budgeting decisions. Obviously future project receipts and expenditures must be discounted to permit valid comparisons with current cash flows. Although the concept of discounting is widely accepted, the selection of the appropriate discount rate has been the source of considerable debate and much disagreement. This chapter, then, provides an overview of the theoretical and practical considerations for determining or calculating the appropriate rate for discounting, the corporate cost of capital. Note specifically that the assumption of constant business risk among the various investment alternatives is maintained throughout this chapter. THE INTUITIVE APPROACH The fact that interest exists suggests that all money has a cost associated with its use. The cost of this money may be the result of either explicit or implicit charges or some combination of the two. Any time an individual or a firm consumes less than the total earnings generated in a given time period that individual or corporation has either consciously or unconsciously decided to "invest" these excess funds in some type of activity. For instance, the individual or corporation may decide to invest the excess funds in tangible property, place the funds in a money market account, or simply keep these funds in cash. In any case, these funds have been invested in some type of activity which promises the investor some return on the invested capital. Remembering that the firm's primary objective should be the maximization of shareholder wealth, then intuitively it seems reasonable to suggest that the firm should not invest in any project where the anticipated return does not exceed the cost of funds (capital) committed to the project. Indeed, if the firm always invests in projects having returns in excess of the cost of capital committed to them, then the wealth of the firm (as measured by the price of common stock) should be in-

Jan 1, 1984

By T. Sterry Hunt

THE geognostical relations of the metals and their ores present many problems of great interest, alike for the geologist, the chemist, and the mining engineer. The association with certain rock-formations of characteristic mineral species may help to guide the geologist in the identification of geological horizons, and throw light on the chemical activities which have been especially manifested in certain periods; while it is clear that such relations, if established, must be of great utility to the miner, and especially to the explorer of new regions. In inquiries of this kind, however, it is only by careful observations over wide areas, and by the collocation of a great number of facts, that anything like a safe basis for induction can be attained. The effects of hasty and imperfect generalizations in this field have already in many instances been felt to the prejudice of scientific progress. I come before you to-night, therefore, not to lay down any laws or general principles, but to call your attention to certain facts, many of them doubtless known to you, which have forced themselves on my attention, with regard to the associations of various metallic ores and other useful minerals with different series of stratified rocks, and to ask you to aid the progress of this branch of geognostical inquiry. Your observations in the various regions to which you may be called by your professional duties will enable you to determine how far these associations are mere coincidences, and how far they are chemical and geological constants. The associations here to be noticed concern only those mineral species which occur, either distributed through the strata in such a manner as to show that they are contemporaneous deposits, or occupy rifts or gash-veins in these strata, and may be supposed to have been

Jan 1, 1873

By T. Sterry Hunt

THE geognostical relations of the metals and their ores present many problems of great interest, alike for the geologist, the chemist, and the mining engineer. The association with certain rock-formations of characteristic mineral species may help to guide the geologist in the identification of geological horizons, and throw light on the chemical activities which have been especially manifested in certain periods; while it is clear that such relations, if established, must be of great utility to the miner, and especially to the explorer of new regions. In inquiries of this kind, however, it is only by careful observations over wide areas, and by the collocation of a great number of facts, that anything like a safe basis for induction can be attained. The effects of hasty and imperfect generalizations in this field have already in many instances been felt to the prejudice of scientific progress. I come before you to-night, therefore, not to lay down any laws or general principles, but to call your attention to certain facts, many of them doubtless known to you, which have forced themselves on my attention, with regard to the associations of various metallic ores and other useful minerals with different series of stratified rocks, and to ask you to aid the progress of this branch of geognostical inquiry. Your observations in the various regions to which you may be called by your professional duties will enable you to determine how far these associations are mere coincidences, and how far they are chemical and geological constants. The associations here to be noticed concern only those mineral species which occur, either distributed through the strata in such a manner as to show that they are contemporaneous deposits, or occupy rifts or gash-veins in these strata, and may be supposed to have been

By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,'.' who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy's law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy's law, as extended to two-phase flow including the effect of capillary pressure,' is as follows:

By Arcy A., D&apos Shock

This paper delineates the scope of the developments which have taken place in expanding the utilization of the soluble salt provinces. The location, geology, extractive technology, as well as the growth of uses are reviewed. An expanding recent growth has been in the use of solution cavities for storing hydrocarbons. The development of the technology to obtain and operate these storage cavities as well as the development of the methodology for solution mining of the soluble salts are discussed.

Jan 1, 1985

By Henry Mulryan

Diatoms are microscopic aquatic plants of the order Bacillariaceae. They are unicellular plants with skelctons made up of amorphous opaline silica. The skeletons show highly ornate, complicated geometrical designs. Diatoms live in water virtually everywhere. They are found in clean sea water, brackish water, and fresh-water lakes and ponds. When conditions are right, diatoms propagate by subdivision in huge numbers. Alkalinity, temperature, and the presence of high concentrations of silica in the water largely control diatom life. When the diatoms die the skeletons drop to the bottom of their habitat to form oozes of varying thicknesses. Diatomites Diatomite, or diatomaceous earth, is composed essentially of the siliceous remains of the diatoms, although other organic skeletons are also present, especially in sea-water deposits where radiolaria, sponges and silico-flagellates are common. Impurities are generally carbonaceous material, fine-grained silt, volcanic ash and dust, and occasional coarse grains of sand. Diatomites are marine, brackish, or fresh-water, depending upon types of diatoms and their method of deposition. Diatoms More than 8000 species of diatoms have been named and classified. Some are definitely classified as to their habitat; some are so well recognized as to their living conditions that they can be stated to be diagnostic types, and when encountered in a deposit determine the origin of the deposit. Some of the commoner types of diatoms found in the freshwater diatomites on the Pacific Coast are: Cymbella lanceolata Agardh Fragilaria virescens Ralfs Encyonema prostratum Ralfs Diatoma vulgare Dory Surirella biseriata Brebison Eunotia major Ehrenberg Amphipleura pellucida Kützing Stictodiscus niagarac Ehrenberg Gomphonema geminatum Lynberg Melosira granulata Ehrenberg Epithemia turgida Kützing

Jan 1, 1942

By Henry Mulryan

Diatoms are microscopic aquatic plants of the order Bacillariaceae. They are unicellular plants with skelctons made up of amorphous opaline silica. The skeletons show highly ornate, complicated geometrical designs. Diatoms live in water virtually everywhere. They are found in clean sea water, brackish water, and fresh-water lakes and ponds. When conditions are right, diatoms propagate by subdivision in huge numbers. Alkalinity, temperature, and the presence of high concentrations of silica in the water largely control diatom life. When the diatoms die the skeletons drop to the bottom of their habitat to form oozes of varying thicknesses. Diatomites Diatomite, or diatomaceous earth, is composed essentially of the siliceous remains of the diatoms, although other organic skeletons are also present, especially in sea-water deposits where radiolaria, sponges and silico-flagellates are common. Impurities are generally carbonaceous material, fine-grained silt, volcanic ash and dust, and occasional coarse grains of sand. Diatomites are marine, brackish, or fresh-water, depending upon types of diatoms and their method of deposition. Diatoms More than 8000 species of diatoms have been named and classified. Some are definitely classified as to their habitat; some are so well recognized as to their living conditions that they can be stated to be diagnostic types, and when encountered in a deposit determine the origin of the deposit. Some of the commoner types of diatoms found in the freshwater diatomites on the Pacific Coast are: Cymbella lanceolata Agardh Fragilaria virescens Ralfs Encyonema prostratum Ralfs Diatoma vulgare Dory Surirella biseriata Brebison Eunotia major Ehrenberg Amphipleura pellucida Kützing Stictodiscus niagarac Ehrenberg Gomphonema geminatum Lynberg Melosira granulata Ehrenberg Epithemia turgida Kützing

Jan 1, 1942

By T. H. Ramsey, Richard Shield

A process has been developed for fabricating thin-film resistors that are compatible with integrated circuits. Films are produced by evaporation of single refractory metals using an electron beam heating source. Resistor paths are then made using standard photoresist etching techniques. A low-temperature coefficient of resistance is obtained by control of nucleation during deposition of the film. One application of the process has been the development of a discrete resistor used for current setting in linear integrated circuits. Multiple thin-film resistors were formed on oxidized silicon substrates using molybdenum metal as a source. An evaporated protective layer of SiO2 over the resistor prevents resistance changes which might occur during subsequent high-temperature processing. Properties of a typical resistor are as follows: R = 15.7 ohm per sq, tolerance surface dimensions = 0.028 by 0.028 in., stable after 4000 hr at 0. 75 w without heat sink. THIN-FILM resistors have been investigated for many years with a large selection of usable resistors resulting from a wide variety of materials. Many of the processes necessitate a high degree of complexity but in nearly all cases the conclusions have been that the materials used in each case were acceptable provided the deposition process was reproducible and could be controlled sufficiently to give the required tolerances. It is our opinion that simplicity is still the key to thin-film resistor fabrication. In this regard, the single metal is obviously the simplest process to control, provided all the necessary properties can be obtained. The idea is not original in this laboratory by any means. Others have taken this approach.' It has been demonstrated that a fairly wide range of resistivities can be obtained by careful control of deposition parameters for any given metal, and by selection of several single metals a very broad range of stable resistors can be obtained. The transition from one metal to the next is made when a film becomes too thin for adequate process control or long-term stability. A great deal of emphasis is once again being placed on the thin-film resistor. Although they have been thoroughly studied in the past, new applications have been found that require the properties obtainable only from thin-film resistors. Integrated circuits, in general, are advancing toward higher speeds and radiation environments which require replacement of the present diffused resistors. Linear circuits in particular are requiring high-power, high-precision resistors for the more advanced applications. The particular requirements of some linear circuits are such that a discrete resistor is required. The resistor described in this paper was developed as a 15.7-ohm precision discrete resistor for use in a current regulating circuit requiring a +2 pct end of life overall tolerance, a dissipation of 750 mw, and the ability to operate over a fairly broad temperature range (i.e., a low temperature coefficient of resistance, TCR). State-of-the-art integrated circuit and silicon processing technology lends itself well to the fabrication of thin-film resistors. Not only is the resistor thin film well-suited to integration on individual circuits, but the oxidized silicon surface provides one of

Jan 1, 1969

By W. A. Bruce

This paper covers the theory and present state of development of an apparatus for the nonmathematical analysis of complex problems of reservoir and well behavior. At the present stage of development of this apparatus, it is capable of solving the water-drive problem of any reservoir performance for which a mathematical solution has been presented in the literature, either on the basis of steady or unsteady-state flow analysis. The theory is presented for the extension of the scope of this analyzer along the lines of the present development. The resulting apparatus should be able to solve reservoir-performance problems previously thought too difficult for practical solution by mathematical means. As an illustration of its operation and present scope, the analysis of a reservoir problem and synthesis of expected performance is presented. Introduction In this method† of analyzing problems of petroleum-reservoir and well behavior, the porous continuum of the reservoir is assumed to be divided into small blocks, or units. Each block is assumed to be small enough so that for a material balance on the fluids in the block an average pressure for the block can be used. In analyzing reservoir behavior from this point of view by mathematical means, a set of simultaneous difference equations would be obtained (two for each block), which must be solved or combined into a partial differential equation. In the method to be described here, instead of solving these sets of equations analytically, electrical units are constructed, which will behave in respect to the flow of electricity exactly as the reservoir units behave under various conditions of fluid flow. The electrical units are then wired together in the same way that the reservoir units are connected naturally by virtue of their geometrical locations and shapes. Fluid-Flow Equations Consider a block in a reservoir. Assume that reservoir fluid (or fluids) is flowing in at one face and out at the opposite face, and that the block is small enough so that at all points the stream lines are within one degree of perpendicular to the face. Furthermore, assume that the pressure, pi, at the upstream face (Fig, I) is not more than one per cent greater than P2 the pressure at the downstream face. A material balance will show that the mass of fluid flowing out less the mass of fluid flowing in will equal the change in density times the fluid volume. This is expressed in the equation:

Jan 1, 1943