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By E. J. Harris

Mathematical solutions to complex mine ventilation problems are possible, but often the airway network is so complex that the mathematical solution becomes tedious and impractical. A fluid network analyzer, designed and built for analyzing mine ventilation problems has been in service at the Bureau of Mines' Pittsburgh station for approximately nine years. Using this analogue as a model, the mine ventilation network is simulated electrically by a combination of series and parallel circruits laid out to conform with actual mine airways. A tungsten filament lamp, referred to as a Fluistor, is used to simulate mine airway resistance. With the analogue ventilation model established, voltages of the proper amplitude to represent ventilating pressures are impressed across the circuit at points where mine fans and airshafts are located. Comparison of mathematical solutions of complex systems against analogue results showed a maximum variance of 3% for pressures and 2% for quantities. An electrical fluid network analyzer, designed and built especially for analyzing mine ventilation distribution problems, has been in service at the Bureau of Mines, Pittsburgh, for approximately nine years. It is a nonlinear, low voltage, fluid network analyzer of the type developed by the late Malcolm S. McIlroy, Professor of Electrical Engineering, Cornell University, who cooperated with G. E. McElroy, of the Bureau of Mines, in adapting the instrument to mine ventilation systems. Several modifications have been made since the original installation, but a considerable part of this paper is drawn from G. E. McElroy's original description of the analogue.' The analysis of water or gas distribution systems2,3 led to the development of this type of network analyzer. Several similar units are now employed by utility companies for this purpose; however, the Bureau of Mines unit is the only one designed specifically for mine airflow problems. Other airflow analogues employing a similar principle have been used at the Central Research Station of the Netherlands State Mines,4 in England,5 and in South Africa.6 Information on these devices indicated they were somewhat inflexible because commercial lamps with a sufficient range of resistance are difficult to obtain. Computers for mine ventilation analysis have been developed in Germany which instead of lamps use a variable resistance to adjust for turbulent flow laws. These units are expensive, but excellent results have been reported in their application. THE ANALYZER Theory of Application: As airflow generally follows the law of turbulent fluid flow, resistance to flow is nonlinear; consequently, the problem has been to find a nonlinear resistance element of suitable range that can be used for electrically simulated airflow. Tungsten filament lamps operated on alternating or direct current approximate the square-law resistance characteristics of mine airflow over a large range below maximum or rated voltage; that is, the voltage drop varies approximately as the square of the current. Consequently, the heart of the network analyzer is a nonlinear resistor known as a Fluistor, which is simply a custom-made low voltage, tungsten filament lamp that is available in a progressive series of relative resistance values ranging from 0.05 to 500 in nominal 5% steps. However, variations in manufacturing large groups result in differences of 1 to 3%, but series arrangements required for high-loss branches can be matched within about 1%. Utilizing a combination of Fluistors and load circuits, the mine ventilation system is duplicated electrically. Intake load circuits are connected from power intake to primary points of the circuit network; segments of unregulated flow along intakes and returns are represented by Fluistors, regulated splits and leakage paths are represented by load circuits and Fluistors of proper capacity; and mine exhausts are connected to ground from the last point of the network to complete the circuit. For the special purpose of representing booster fans or natural draft conditions, boosters or separate source circuits are provided that can be inserted between any two points of a network to increase voltage to the required value. Physical Layout: The analyzer consists of three 42

Jan 1, 1963

By H. P. Rue

The Bureau of Mines has recently collected two samples of crude oil from wells in the Greasewood Flat area of northeastern Colorado. Sample 31310 was taken from the Continental Oil Co.'s well Briggs No. 1 which care in or September 27, 1931, with a maximum production of 940 barrels per day. Sample 31311 was taken from tie Reiter-Foster Oil Co. Is well Ida Johnson No. 1 which came in on August 24, 1931 with a maximum production of approximately 1000 barrels per day.

Jan 1, 1932

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is 'uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b'e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970

By David Vergara Segura

Una empresa minera, en condiciones normales, maximiza su operación y minimiza sus pérdidas por tener operativos y equipos ligados a la producción. Por lo que es necesario la integración entre las áreas de la empresa, específicamente entre las de Mantenimiento y Logística. En este sentido, el presente texto señala la importancia del trabajo en equipo entre estas dos áreas, cuyo objetivo común es optimizar la gestión del activo que tiene un impacto significativo y directo en la producción. También se plantea bajo del esquema de una empresa minera ficticia, el desarrollo de estrategias conjuntas, y se define un modelo de gestión logístico, generador de ventaja competitiva, el cual está orientado a la optimización del uso del activo.

Sep 12, 2005

By Jack D. Webber

The successful use of oil well packers requires, in part: an understanding of the pressures which exist at the packer in various applications and an understanding of the characteristics of the various types of packers. It is with these pressures, the resultant forces, and the characteristics of packers. that this paper is primarily concerned. An oil well packer may be defined as a mechanical device for blocking the passage of fluids in an annular space. In the more usual case, the annular space is that between the tubing or drill pipe in a well and the casing, and packers which block such an annular space are broadly referred to as casing packers. In the other case. the annular space is that between the tubing or drill pipe and the walls of an open hole, and packers for blocking this space are generally called formation packers. While the hydraulics involved are essentially the same for casing and formation packers. a greater variety of conditions are encountered in the use of casing packers and only casing packers will be discussed. After a packer has been set and a pressure seal effected between tubing and casing, the packer is comparable to a piston in a cylinder. Pressures acting upon a piston result in forces which will move the piston unless some means is provided to prevent such movement. In the same manner, pressures acting upon a packer will move the packer unless there is present a sufficiently great restraining force. PACKER CLASSIFICATIONS Packers may be classified according to the pressure conditions under which they are capable of blocking the annular space between tubing and casing. Fig. 1 shows schematically two types of packers in common use. These packers are capable of blocking the annular space against the passage of fluids under a differential pressure of significant magnitude only when the pressure in the annular space above the packing element is greater than the pressure below. It may be seen that in Fig. l-a. slips with teeth which bite into the casing and prevent downward movement are provided. In Fig. 1-h. an anchor prevents downward movement. In each case, there i-only the tubing to prevent upward movement when differential pressures act to move the packers upwardly. Packers which hold only a significant differential pressure acting downwardly have been in use since the early days of the oil industry and will hereafter be referred to as conventional type packers. In many packer applications operating conditions will 1.crult in differential pressures across the packer which will at times act to move the packer upwardly, and at other times, act to move the packer downwardly. For these applications, designs are available which will block the annular space and resist movement in either direction. Fig. 2-a shows schematically a packer of this type which is designed to be run into a well and set, and removed when desired by merely pulling the tubing. It will be noted that two sets of slips are provided-— one set above the packing element to prevent upward movement, and another set below the packing element to prevent downward movement. This packer is built around a mandrel which is essentially a part of the tubing. and which is free to move longitudinally within certain limits through the set packer. Fig. 2-b shows schematically a permanent type packer which is capable of holding pressures from either direction. Here again, two sets of slips are provided to prevenl movement of the packer. This packer is designed to become virtuallv a part of the casing when set and it is made of drillable material so that it may be drilled out when its removal is desired. The seal nipple shown effects a pressure seal between the tubing and the packer. This seal nipple is a part of the the tubing, and the nipple and tubing may be withdrawn from the well without disturbing the packer. It should be noted that these figures are not representative of all available packers which are designed to hold pressures from both above and below. Packers which resist movement in either direction will hereafter be referred to as universal type packers. There is a third type of packer in general use and this type is designed to block the passage of fluids when the pressure below the packing element ii greater than that above. This type is provided with slips which prevent upward movement of the packer and is somewhat similar to a conventional type packer run upside-down. Packers designed to hold pressure only from below are made in a variety of designs and are usually owned and operated by service companies.

Jan 1, 1949

By Jack D. Webber

The successful use of oil well packers requires, in part: an understanding of the pressures which exist at the packer in various applications and an understanding of the characteristics of the various types of packers. It is with these pressures, the resultant forces, and the characteristics of packers. that this paper is primarily concerned. An oil well packer may be defined as a mechanical device for blocking the passage of fluids in an annular space. In the more usual case, the annular space is that between the tubing or drill pipe in a well and the casing, and packers which block such an annular space are broadly referred to as casing packers. In the other case. the annular space is that between the tubing or drill pipe and the walls of an open hole, and packers for blocking this space are generally called formation packers. While the hydraulics involved are essentially the same for casing and formation packers. a greater variety of conditions are encountered in the use of casing packers and only casing packers will be discussed. After a packer has been set and a pressure seal effected between tubing and casing, the packer is comparable to a piston in a cylinder. Pressures acting upon a piston result in forces which will move the piston unless some means is provided to prevent such movement. In the same manner, pressures acting upon a packer will move the packer unless there is present a sufficiently great restraining force. PACKER CLASSIFICATIONS Packers may be classified according to the pressure conditions under which they are capable of blocking the annular space between tubing and casing. Fig. 1 shows schematically two types of packers in common use. These packers are capable of blocking the annular space against the passage of fluids under a differential pressure of significant magnitude only when the pressure in the annular space above the packing element is greater than the pressure below. It may be seen that in Fig. l-a. slips with teeth which bite into the casing and prevent downward movement are provided. In Fig. 1-h. an anchor prevents downward movement. In each case, there i-only the tubing to prevent upward movement when differential pressures act to move the packers upwardly. Packers which hold only a significant differential pressure acting downwardly have been in use since the early days of the oil industry and will hereafter be referred to as conventional type packers. In many packer applications operating conditions will 1.crult in differential pressures across the packer which will at times act to move the packer upwardly, and at other times, act to move the packer downwardly. For these applications, designs are available which will block the annular space and resist movement in either direction. Fig. 2-a shows schematically a packer of this type which is designed to be run into a well and set, and removed when desired by merely pulling the tubing. It will be noted that two sets of slips are provided-— one set above the packing element to prevent upward movement, and another set below the packing element to prevent downward movement. This packer is built around a mandrel which is essentially a part of the tubing. and which is free to move longitudinally within certain limits through the set packer. Fig. 2-b shows schematically a permanent type packer which is capable of holding pressures from either direction. Here again, two sets of slips are provided to prevenl movement of the packer. This packer is designed to become virtuallv a part of the casing when set and it is made of drillable material so that it may be drilled out when its removal is desired. The seal nipple shown effects a pressure seal between the tubing and the packer. This seal nipple is a part of the the tubing, and the nipple and tubing may be withdrawn from the well without disturbing the packer. It should be noted that these figures are not representative of all available packers which are designed to hold pressures from both above and below. Packers which resist movement in either direction will hereafter be referred to as universal type packers. There is a third type of packer in general use and this type is designed to block the passage of fluids when the pressure below the packing element ii greater than that above. This type is provided with slips which prevent upward movement of the packer and is somewhat similar to a conventional type packer run upside-down. Packers designed to hold pressure only from below are made in a variety of designs and are usually owned and operated by service companies.

Jan 1, 1949

By J. D. Hunt, D. T. J. Hurle

A uariety of eutectic structures are formed in faceted/nonfaceted eutectics. The various structures are explained in terms of the absence or presence of small facets in the liquid groove. Regular structures are produced when, for purely geometric reasons facels cannot form. The presence of a facet in the liquid groove leads to the formation of an irregular or a cell-like complex regular structure, due to the relative immobility of the groove. A classification of eutectics was proposed by Hunt and jackson, based on the presence or absence of facets on the primary phases (the absence of facets may be predicted from the dimensionless entropy of melting2). Eutectics were divided into three groups: 1) eutectics in which both phases grow in a nonfaceted manner; 2) eutectics in which one phase grows faceted, the other nonfaceted; 3) eutectics in which both phases grow faceted. It was suggested that regular1 rodlike or lamellar structures1 should be formed in the first group, that irregular or complex regular structures1 should be formed in the' second, and that irregular structures1 should be formed in the third. Recently it has been shown that the structural classification is incomplete. Regular rodlike structures (InSb-NiSb eutectic3), or broken lamellar structure (Bi-Zn eutectic, Fig. 8), are formed in alloys of the second group when the faceted phase has a large volume fraction. Hunt and jackson' argued that regular structures could form in faceted/nonfaceted systems, but that such structures would be unstable in the presence of microfacets on the lamella of the faceting phase, because the growth rate at a point on such a facet would depend on the kinetic undercooling at the point of nu-cleation on the facet, and not on the local kinetic undercooling. In these circumstances it would not be possible to consistently balance the compositional and kinetic undercooling over a lamellar structure and thus obtain a stable isothermal interface. In this paper we discuss in detail the origin of the various structures formed in faceted/nonfaceted systems, pointing out that the most important factor promoting the formation of a regular structure is the absence of a facet in the liquid groove. 1) FACET FORMATION IN SINGLE-PHASE MATERIALS Facets form when there is an energy barrier for the addition of a new solid layer on an existing solid. When a barrier is present,2 growth proceeds by the lateral movement of steps across a crystallographic plane. The rate-controlling stage of the process occurs when the step is first formed. Hulme and Mullin6 have shown that faceting in single-phase materials can only occur when both interface curvatures are convex with respect to the solid and when the surface is tangential to the facet plane. When even one of the curvatures is concave a facet does not form because new layers of solid from adjacent regions can always feed the facet plane, Fig. 1. Growth under these conditions is then as easy as elsewhere. Similar considerations will apply to eutectic growth; consequently the shape of the faceted phase is extremely important. 2) LAMELLAR SPACING CHANGES IN EUTECTICS Jackson and Hunt7 have shown that the interface undercooling AT of a growing lamellar interface (neglecting kinetic undercooling) is related to the lamellar spacing, A, and growth velocity, v, by an expression of the form: where m, Ql, and nL are constants of the system given in Ref. 7. Eq. [I] is plotted for fixed v in Fig. 2. Jackson and Hunt postulate that a regular eutectic grows near, but to the right of the minimum in the AT vs A curve. They argue that the spacing cannot be to the left of the minimum because the interface is then unstable to fluctuations in A. It cannot grow too far to the right, because when the spacing becomes too wide an isothermal interface can no longer be maintained over the large-volume-fraction phase.7 It is argued that during any change in growth rate the lamellar spacing remains in the permitted range by the movement of lamellar faults. When the spacing is too wide, the fault, shown in Fig. 3, moves to the left; when the spacing is too narrow it moves to the right. The faults, however, have to be formed. heir formation has been shown to occur when local regions deviate considerably from the spacing defined by the lamellar When the spacing is locally too narrow (it passes to the left of the minimum, Fig. 2), pinching off of the narrow phase occurs. When the spacing is locally too wide, the interface on the large volume-fraction phase can no longer be maintained as an iso-

Jan 1, 1969

By J. D. Mote, J. E. Dorn

This investigation was undertaken to study the effects of piledup arrays of dislocations on inducing slip, twinning, and fracturing in magnesium bicrystals. A series of variously oriented bicrystals of magnesium having a vertical grain boundary were prepared and tested in tension. It was found that piled-up arrays of dislocations at the grain boundary could, under appropriate conditions, induce slip, twinning- and cracking. The results that were obtained substantiate, at least qualitatively, the general dislocation mechanism for transmission of strain across grain boundaries and the Petch-Stroh concept of fracturing. WHEREAS single crystals of magnesium generally exhibit extensive deformation, coarse-grained poly-crystalline magnesium at subatmospheric temperatures fractures after a few percent elongation.' Although a small amount of ductility is obtained, several features of this fracturing are characteristic of typical brittle behavior. Over a rather broad temperature range the fracture stress is insensitive to the test temperature and the fracture stress increases linearly with the reciprocal of the square root of the mean grain diameter. The course of fracturing is predominantly intergranular, but small fragments of adjacent grains frequently adhere to the fractured surface.2 The brittle behavior of polycrystalline magnesium is attributable to the limited number of facile deformation mechanisms it exhibits at low temperatures. For a general deformation of a randomly oriented polycrystalline aggregate, each grain must exhibit at least five independent mechanisms of deformation to permit accommodation of the imposed deformation from grain to grain.= Although minor amounts of prismatic slip occur in corners of grains where stress concentrations are known to be high, glide in polycrystalline magnesium at low temperatures takes place almost exclusively by basal slip.' The common type of twinning, which takes place on the (1012) pyramidal planes, can under the most favorable orientations, lead to a. strain of only 6.9 pet; the contribution of twinning to the tensile strain would indeed be much less than this in a randomly oriented polycrystalline aggregate of magnesium. Since the three mechanisms of basal slip are coplanar, they are equivalent to only two independent mechanisms, a number insufficient for a general deformation. Consequently, once the permissible twinning has taken place in conjunction with basal slip, no further plastic deformation is possible because of interference to slip at the boundaries of dissimilarly oriented grains. At this stage brittle fracturing takes place due to high stress concentrations at the juncture of slip bands with the grain boundaries; the predominance of intergranular fracturing in magnesium, in preference to transcrystalline fracturing which is prevalent in zinc, has not yet been rationalized. A more atomistic description of the plastic behavior and fracture characteristics of magnesium follows from the analyses made by stroh4 on the stresses induced by piledup arrays of dislocations. Slip first takes place by dislocation motion in the most favorably oriented grains. As the dislocations approach the boundary of a dissimilarly oriented adjacent grain they begin to form an array of dislocations with its attendant stress field. Piledup arrays of screw and edge dislocations introduce high localized shear stresses at the spur of the array; piledup arrays of edge dislocations also induce high tensile stresses localized in the vicinity of the grain boundary. Whereas the shear stresses can induce slip to take place, the tensile stresses, if sufficiently high, can cause fracturing. The localized shear stress will be relieved if sufficient numbers of mechanisms of deformation become operative in the original and the adjacent grain to permit accommodation of the dislocations in the grain boundary. In this event a ductile behavior will be obtained. But if the number of deformation mechanisms is insufficient for complete migration of dislocation arrays into the grain boundary, the tensile stresses due to the edge components of piledup dislocation arrays will continue to increase with increasing applied stress until fracturing takes place. Whereas face-centered-cubic metals have a sufficient number of mechanisms of slip for accommodation of dislocations in their grain boundaries to exhibit ductile behavior, hexagonal-close-packed metals, in general, do not. Consequently, hexagonal-close-packed metals are usually brittle except when conditions such as alloying or temperature permit facile slip by a number of mechanisms. The arguments presented above suggest that the mechanical behavior of magnesium depends on whether or not dislocation arrays in adjacent grains can enter the grain boundary. When such accommodation is possible, ductile behavior is expected; but when such accommodation is impossible, fracturing will ensue. To further test the validity of these arguments it was considered advisable to study the

Jan 1, 1961

By D. L. Feucht, R. L. Longini

The semiconductor heterojunction is considered in terms of simple models which may lead to an understanding of move complex heterojunctions. Metallurgical and electrical properties of hetero-junctions aye discussed including the interface structure, energy -band diagram, and carrier transbovt across the interface. It is found that in a heterojunction all mechanisms such as injection, tunneling, and junction recombination found in simple junctions play modified voles. INTERFACES between materials (grain boundaries, the electrical junction between two differently doped materials in a single crystal, the oxide-metal interface, or metal-metal junctions) are of considerable importance in many situations. These various interfaces all have one very fundamental thing in common. Quantum mechanically speaking, the wave functions of the electrons in one material may penetrate the other material but, in general, only to the extent of angstroms. From an electrical point of view the conduction mechanism changes as a current passes through such junctions. In some cases the change is tremendous, in others almost negligible. The interface, then, is the locus of a change of conduction mechanisms. Some of these, particularly in semiconductors, are well-understood. The ordinary p-n junction in a single crystal can be the locus of an injection mechanism or a tunneling process, depending on conditions. The mechanisms are probably best understood in semiconductors because of the possible simplified view of particlelike conduction. The bands are either nearly filled or nearly empty and band overlap is seldom involved. The same fundamentals are probably important in other situations too but they are very difficult to look at naively. Although the simple look at the semiconductor case only gives us a relatively rough picture which must then be refined, the other systems, which involve a more complex situation, immediately are in many ways too difficult. There are too many initial choices of complex systems and therefore it is not possible to be even reasonably certain of any one model. Because of the relative simplicity of semiconductors, their good and controllable structure, and because of the ability to make many measurements on them not normally available to either metals or insulators! they are probably the best understood materials. It is therefore desirable to use them as a tool to further the understanding of interfaces in general. Semiconductor-heterojunction concepts were first proposed by kroemer1 in 1957. This was followed several years later by reports on the fabrication and experimental characteristics of heterojunction structures by Anderson2 and Diedrich and jotten.3 I) THE HETEROJUNCTION STRUCTURE To get down to hardware, when we refer to a semiconductor heterojunction we imply that there exists an intimate contact between different semiconductor materials. We could put two pieces of material together, complete with oxide layers, we could remove the oxides, or we could even melt the interface and hopefully get wetting and a good "bond" on solidifying. In fact we could by some means grow a crystal of one material using the other as a seed. Essentially we are interested only in the last two because they are the simplest to look at analytically. The degree of perfection of fit varies greatly and is reflected somewhat in the arc welder's joint strength. The lattice match of the two materials, their orientation, and so forth. is obviously necessary for a good bond but so is the continuity of any polar bonds which are involved such as in the III-V semiconductors. The mechanical misfit between two similar lattices can be described in terms of edge dislocations. The edge-type dislocations must be very close together for the usual misfit and there must be dislocations for each of several different Burger's vectors in order to produce a lattice match. The .'dangling bonds'' resulting will be involved in producing interface charge. Order of magnitude estimates of the charge density extrapolated from low densities of dislocations in homogeneous materials give 5 x 1013 cm-2 Ge-Si and 1 X 1012 cm-2 Ge-GaAs electronic charges. Edge dislocations also act as very active recombination centers between holes and electrons. One lattice "matching" difficulty usually exists even if two structures have essentially the same lattice constants as they will have different coefficients of therma1 expansion. Thus, on cooling from the usually high temperature of fabrication to room temperature, dislocations are produced, a good fit not existing at both temperatures. In brittle materials this shrinkage may even result in cracking. For the Ge-Si interface the mismatch is about 2 x 10 -6 per degree whereas it is less than 10"7 per degree between germanium and GaAs. The exact effect of the misfit is dependent on the thickness of the materials involved. For a very

Jan 1, 1965

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

By J. H. Swisher, E. O. Fuchs

Rate equations were derived to describe the kinetics of internal oxidation of cylinders and spheres. The derived equations for cylinders were checked experimentally by means of sub scale thickness and electrical conductivity measurements on Cu-Cr alloy wires. The properties of the internally oxidized samples were examined with conductivity applications in mind. It was possible to produce uniform dispersions of Cr2O3 in copper with an initial chromium content as high as 3 wt pct. While electrical conductivities only a few pct less than that of OFHC copper were obtained, the Cr2Os particle size and spacing were too large for effective dispersion hardening. T.HE process of internal oxidation has been used widely in basic studies of the permeability of gases in metals. In a review article, Rapp1 has discussed the principles of internal oxidation in considerable detail. From a technological standpoint, internal oxidation is often considered undesirable, since it is a means by which inclusions can be introduced into an otherwise clean material. Another important aspect of internal oxidation is its use as a means of dispersion hardening a material. Broutman and Krock2 discuss this and other methods for making dispersion hardened alloys. The only internally oxidized material known to the authors which is commercially available is a Cu-BeO alloy.3'4 This alloy is made from Cu-Be alloy powder, using a so-called Rhines pack. It has a tensile strength of 80,000 psi and retains its strength at relatively high temperatures. The objectives of the present study were to derive rate equations for the internal oxidation of cylinders and spheres, to check the derived equations for cylinders experimentally, and to examine the structure and properties of internally oxidized Cu-Cr alloys. The Cu-Cr system was chosen for this study because uniform dispersions are obtainable at high alloy contents, which is a desirable characteristic in dispersion hardened materials. RATE EQUATIONS FOR VARIOUS GEOMETRIES A number of authors5--9 have derived equations to describe internal oxidation kinetics. These derivations differ somewhat in mathematical assumptions and approximations, and all except one of the derivations deal exclusively with the internal oxidation of plates. The exception is a brief treatment of cylindrical and spherical geometries given by Meijering and Druy-vesteyn9 as a part of a comprehensive paper on the general subject of internal oxidation. These authors did not obtain rate data to check their derivations, although they did show that the hardness profile across an internally oxidized sample is directly related to the rate of interface movement. For cylindrical and spherical geometries, a quasi-steady-state approximation is needed to circumvent mathematical complications in obtaining a solution to the basic differential equations. In using this approximation, we consider the concentration gradient of dissolved oxygen in the internally oxidized zone or sub-scale to be the same as the gradient which would be present if there were no movement of the subscale interface. The steady-state approximation introduces an error of about 1 pct in computing the rate of internal oxidation of an Fe-1.0 pct Mn alloy plate, if the present method is compared to the more exact method of Wagner.7'10 The details of the derivations of the rate equations for cylinders and spheres are given in the Appendix, and only the results of these derivations are given below. The final equations obtained by Meijering and Druyvesteyn9 can be shown to be equivalent to our Eqs. [1] and [2], although the two approaches are somewhat different. Cylindrical Geometry. [2] where r1 is the outer radius of the cylinder or sphere, cm, r2 is the radius of the unreacted core, cm, see Fig. l(a), D is the diffusion coefficient of oxygen in copper, cm2 per sec, %O is the concentration of dissolved oxygen at the surface of the specimen, wt pct, %Cr is the initial chromium concentration in the alloy, wt pct, and t is the reaction time, sec. Plate Geometry. The analogous rate equation for a plate has been derived previously for internal oxidation of Fe-Al alloys.8'11 For Cu-Cr alloys, we may write the same equation as follows: [3] where r1 is the half-thickness of the plate, cm, and r2 is the distance from the mid-plane to the subscale intherate is An analysis of Eqs. [1], [2], and [3] shows that for a plate the rate is completely parabolic. The initial

Jan 1, 1970

By Jerry L. Straalsund, D. Bruce Masson

A dew-point technique was used to determine the thermodynamic activity of zinc at 430°C in a series of e phase Ag-Zn alloys. The composition of the alloys ranged from 72 to 88 at. pct Zn. This range included the composition at which Massalski and King3 found a reversal in the composition variation of the crystallo-graphic c/a ratio, which they attributed to an overlap of the Fermi surface across the (002) faces of the Brillouin zone. The data is presented in a graph in which RT In yz,, where yz, is the activity coefficient of zinc, is shown as a function of atomic percent zinc. This curve has an unmistakable change in slope at the same composition that Massalski and King observed the beginning of the reversal in the c/a ratio. This change in slope of the thermodynamic data is also attributed to a Brillouin zone overlap. Equations are presented to demonstrate that the thermodynamic activity can be related to the density of states of the conduction electrons, and that the observed phenomena are consistent with this model. It is also demonstrated that the contribution of the density of states can be related to the excess stability, a phenomenological parameter recently shown by Darkeen" to be significant in the interpretation of thermodynamic data of metallic phases. The data seem to indicate that zone overlap has caused a spinodal point, and the resulting misci-bility gap, in the phase diagram. THE problem of developing an adequate thermodynamic model of solid solutions has proven to be difficult, and is still only partially solved. The main approach has been to develop a statistical model, such as that of an ideal solution, regular solution, and so forth, to which can be attached corrections for electronic, vibrational, magnetic, ordering, or other contributions. Such corrective terms are usually derived on an ad hoc basis, and it is difficult to predict in advance what their relative importance will be. This problem has been discussed in general terms by Oriani and Alcock,' who have reviewed several thermodynamic models and a few empirical correlations. The measurements described in the present paper were made to demonstrate in a special case the importance of one such corrective term, the contribu- tion of the energy of the conduction electrons of an alloy. It was our premise that the contribution of the energy of the conduction electrons to the thermodynamic activity of the alloy components could be detected; further, that such an effect would be observed at alloy compositions where other phenomena, also ascribed to the energy and density of states of the conduction electrons, are observed. The idea of the importance of the conduction electrons is hardly new. Hume-Rothery and his adherents have developed the well-known theory of alloy phases in which the sequence of phase fields in binary equilibrium diagrams, especially those involving the noble metals with the IIB, IIIB, and IVB subgroups, can be correlated by replacing the composition variable with the ratio of conduction electrons to atoms, e/a. Jones and others have developed a physical explanation for this correlation, in which they consider the solubility limits of phase fields to be restricted by an intersection between the Fermi surface and a Brillouin zone. The general features of the model are also quite well-known—presumably zone intersection causes the density of states to decrease at critical alloy compositions. The attendant increase in energy of conduction electrons in the original crystal structure allows an alternate structure to become more stable as the concentration of polyvalent solute is increased. In spite of the wide acceptance of these ideas on phase stability, there is only indirect* evidence, such as the variations in lattice parameter recorded extensively by Massalskizy3 and others, that Brillouin zone interactions occur. There are few experimental measurements, other than the correlations of the phase sequence, that substantiate the premise that the energy of conduction electrons affects the solubility limits of alloy phases. Much thermodynamic data of alloys has been found to be consistent with the theory; yet there is a lack of detailed data at compositions where zone intersection and overlap are thought to occur. One would expect that the energy of the conduction electrons would make a measurable contribution to the thermodynamic properties of alloys at compositions near zone intersection and overlap if the theory of Hume-Rothery and Jones is correct. This conclusion cannot be avoided, because the phase boundaries are determined by the requirement that the chemical potential of the components be equal in both phases at equilibrium. An electronic effect large enough to alter the stability of a phase should also affect the thermodynamic activity by a measurable amount.

Jan 1, 1969

By E. P. Whittemore

Experience with the ASC multipoint gas lift system was obtained in Colonia zone of the West Montalvo field near Oxnard, Calif. The wells in this pool produce from depths varying from 10,500 to 12,000 ft. Oil gravity is generally 14 to 15' API with a few extremes of 12 and 20" API. Some salt water is produced which causes some very viscous emulsions. Viscosities at 150F (which is the approximate wellhead temperature) vary from 5,000 to 100,000 SSU. Most of the production is by gas lift, although a few wells are produced by rod and hydraulic pump. About half of the gas-lift wells are on continuous flow and the remainder are on intermittent lift using large, ported, pilot-operated valves for single-point transfer of gas from casing to tubing. Gas-liquid ratios vary from about 6 to 10 Mcf/bbl of gross fluid lifted. Wells are produced to a 450-psi trap system. The following remarks will be confined to intermittent lift only, since this is the type of lift which has been achieved with the ASC valve system. The maximum gross fluid which has been produced by single-point intermittent lift is about 350 B/D in 3-in. tubing and 200 B/D in 21/2-in. tubing with gas-liquid ratios of approximately 7 to 9 Mcf/bbl. Some design changes could reduce this ratio. The ASC multipoint system has provided production as high as 480 BOPD in 21/2-in. tubing with gas-liquid ratios just under 4 Mcf/bbl. To be able to apply the multipoint system, it is recommended that a detailed explanation be obtained concerning transition-point pressure and stabilizer setting—what its significance is to the string design, how it may work for or against the operation of the well, how it is related to tubing sensitivity and how it affects the unloading operation. The unloading operation may only be of academic interest in a technical paper, but to the production foreman, unloading and setting the valves in operation is a very real problem and should be understood in detail. One item touched lightly in the paper was the unloading valve. This valve controls the maximum pressure at which the well can be operated. When lifting heavy viscous fluids, it is most important to set this valve for the maximum possible realistic operating pressure at the surface. If the well lifts easily, it is simple to set the ASC valves at a lower operating pressure and the unloading valve will remain closed; but if the well happens to be heavier to lift than anticipated, it may be desirable to operate on the unloading valve itself and use all the energy obtainable at the bottom of the hole. In the Colonia pool very heavy wet-gas gradients are experienced due to the viscosity of the liquid and the dense mist which is left behind a slug of fluid. There are many combination strings of 3- and 21/2-in. tubing. This aggravates the wet-gas gradient problem and provides wet-gas gradients of about 50 to 70 psi/1,000. An advantage which multipoint lift has provided is increased slug efficiency through better maintenance of pressure under the slug and decreased fall back as the slug passes up the tubing. By using multipoint injection, wet-gas gradients have been reduced to about 30 psi/1,000. This has reduced bottom-hole operating pressure and given a production increase. The ASC valve is not a simple device. It's operation is difficult to understand, and it must be understood to be used efficiently in gas-lift design. Operating problems are difficult to diagnose—whether they be caused by the fluid lifted, valve malfunction, lift gas rate, or operating pressure. Calculations and reasoning are required to find out what is causing the problem. Inherent in the ASC valve is the inability to create large pressure differentials across a slug. Large differentials may be required to overcome the inertia of very viscous fluid as it is being accelerated in the bottom of the hole. This is tied back to the design of the unloading valve and is one reason for the importance of setting the unloading valve for the highest possible operating pressure. ~u; to the narrow spread the ASC valves provide, it is impossible to cycle slower than about 24 cycles/day on choke control. If small production of 150 BOPD and less is expected, a surface time-cycle controller will be required if the most economical operation is to be achieved. To achieve a satisfactory operation, the operator must keep a record of any changes made in the operating pressure of the ASC valves. Anything which may cause changes in casing pressure in excess of the stabilizer setting will change the valve operating pressure, and if this is not noted from daily inspection of the well casing-tubing pressure recorder charts, the operator will lose control of the well. Significant results can be achieved using ASC valves; however, considerable knowledge is required to design with them, and attention to detail is required for satisfactory field operation.

Jan 1, 1965

By Jose P. T. Agapito

Several underground coal mines currently operating in the Beckley District of West Virginia are experiencing serious roof and floor problems. A significant portion of the estimated two billion tons of coal resources may be lost as a result of these ground control problems. Preliminary studies by the Bureau of Mines indicated that these problems are due in part to a high horizontal stress field. During this contract study, a field program was conducted to quantify the horizontal in situ stress. A total of 14 overcoring sites (using the Bureau of Mines strain-relief overcoring technique) in five mines were drilled producing 53 data sets. Analysis of the data was done to provide in situ horizontal stresses for each of the five mine, and for the district as a whole. Stress data indicate horizontal stresses far in excess of that predicted by theory and in some cases, up to six times the estimated vertical stress. In addition to the field testing, a detailed computer modeling study was conducted using finite element and boundary integral (displacement discontinuity) methods. Verification of in situ stresses was obtained by the models and analysis of various development geometries, mining methods and remedial techniques were conducted. Recommendations for reducing ground control problems and future studies are presented.

Jan 1, 1980

Visit to the Modderfontein factory of A. E. & C. I. Ltd 23rd November, 1972 A full programme was arranged to suit both the mining and metallurgical sections of the Institute. After refreshments were taken and visitors welcomed by the factory management we were split into two groups, viz metallurgical and mining. Book review Stress-relief Heat Treatment of Vanadium Steels by Or G. O. Joy and Or A. M. Sage (21 pp, 77 references).

By James L. Wilcox, Douglass P. Bacon

As the U.S. Environmental Protection Agency (USEPA) and state regulators increase the stringency and enforcement of regulations concerning emissions produced by open-air detonation of energetic materials, research must provide the means of obtaining emissions data. The BangBox emissions testing program established the technical foundations for emissions characterization which have been accepted by the USEPA and other regulatory agencies; the technical issues remaining are nettlesome and require new approaches in test procedures.

Jan 1, 1996

A theory is presented providing a concise mathematical description of the performance of a percussive rockdrill in terms of its principal mechanical dimensions. The theory defines the relationships between the values of thrust required to produce optimum rates of penetration at different throttle air pressures in terms of the piston areas and derives an equation for the prediction of these rates. An analysis of drillsteel life and bit wear is also made.

By H. M. Friede

A study was made of the smelting process in two experimental furnaces patterned on Iron Age furnaces excavated at Melville Koppies Nature Reserve, Johannesburg. In a number of smelting experiments, the influences of air supply, temperature, time of operation, fuel consumption, and other operational factors were investigated. Metallurgical and metallographic aspects of the furnace operation and smelting products are discussed, and the experiments are compared with similar research work conducted in Europe and Africa.

Jan 1, 1984

By Adrian J. Moore, Alan B. Richards, Rob Evans

Air and ground vibration from blasting is influenced by the delay pattern that is used. Wavefronts from blastholes fired in a blasting pattern can combine in certain circumstances to give increased blast vibration levels. A simple computer model has been developed which shows the combined effect of wavefronts from a multi-hole blast and identifies if wavefront reinforcement occurs, and permits delay patterns to be designed which will avoid or reduce wavefront reinforcement.

Jan 1, 1994

HAVING shown you before how moulds of statues and also those of guns are constructed, I wish to tell you at present how, if you wish to cast them in bronze, you are further to prepare and arrange these moulds so that they may receive the melted mass of the metals in a friendly manner and without disturbance. I know that you understand that a real and intense heat has been intro-

Jan 1, 1942