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By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By Blamey Stevens

The following paper aims to make a full explanation of the phenomena of rock jointing. It may be unnecessary to give any general description of what are termed joints in rocks, but Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given for introducing the following and other quotations into this paper : " Almost all rocks are traversed by vertical or highly inclined divisional planes termed joints. These have been regarded as due in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure and movement within the crust." 1 General Explanation.—In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of the porous material may be considered to be separately compressed by the water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from moving freely by other material around its boundariee. The mass of rock thus becomes broken up. This phenomenon is known as " shrinkage" jointing. The term " shrinkage " is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.—The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting. At the moment of the formation of joints this stress is equal to the cohesive compressive stress. This is more commonly known to engineers as the tensile breaking stress.

Jan 1, 1914

By R. M. Rose, K. A. Jones

Resistive measurements ulere made on superconducting niobium single crystals in transverse magnetic fields. Crystals were grouln in both high and ulfrahigh vacua, doped with stnall quantities of oxygen, and annealed in ultrahigh vacua at temperatures from 900' to 1350°C. Maxima in the fluxoid pinr~ir~g force were observedfor the [100] and [210] directions. The increase of the critical current density with dissoved oxygen was seen to saturate at relatively low concentration. This behavior, and the variation of J, and residual resistivity (as a function of oxygen content and annealing) of both clean and dirty gassy) crystals, is seen as a consequence of the formation of clusters with (210)~b habit planes and (200)ffo common boundaries. These suboxide clusters are apparenlly stable at high temperatures and very low oxygen concentrations. It is generally known that dissolved oxygen at concentrations well below the solubility limit sharply increases the critical current density of superconducting niobium.' Such a result would not be expected if Nb-0 solutions were random, not even as the result of segregation on the scale usually encountered in solid solutions. According to the Kim-Anderson theory of flux creep,' the critical transport current density is determined by the pinning force Fp associated with some feature of the microstructure. As the Lorentz force. a or (J X R), of the transport current in the magnetic field approaches Fp, flux creep and then flux flow occur. The pinning force is expected to be quite small if the heterogeneity involved is significantly smaller than tte range of coherency which for niobium is circa 250~.~ Although the strain field of an individual oxygen atom in the niobium lattice is relatively large, it does not seem plausible that individual atoms could be so effective as to account for the data. Also, ~ramer~ found that straining and strain aging specimens containing small amounts of oxygen on occasion decreased the residual resistivity. A possible explanation for the above behavior may be found in the work of van Ooijen and van der Goot,= who found that annealing changed J, for niobium foils containing oxygen, and they attributed the changes to ordering of the oxygen atoms. This phenomenon has been observed by other investigators using X-ray and PROCEDURE Cylindrical 4-in.-diam niobium single crystals with axial orientations [ill], [110], [112], and [oo~] were grown from pure niobium, see Table I for analysis, in an ion-pumped ultrahigh-vacuum system using the electron beam floating zone technique. Total pressure during growth was lo-'9 torr: the oxygen partial pressure was less than lo-" torr, as determined by a mass spectrometer. These crystals will be referred to as the "clean" crystals. Similar crystals were also grown in another system at a pressure of 5 X 10"6 torr. These crystals will be referred to as the "dirty" crystals. Specimens 14 in. long were cut from the as-grown crystals and one end was polished down to no. 600 carbide paper smoothness. A back-reflection Laue photograph was then taken in order to fix the crystallo-graphic directions transverse to the crystal. The critical current density J,, the current density necessary to produce a voltage drop of 1.0 pv between voltage leads placed a in. apart, was determined as a function of the magnitude and direction of the transverse magnetic field and of the oxygen concentration. The technique and experimental arrangement was essentially similar to that of Tedmon et al.' In the remainder of this paper, the azjmuthal angle $ for the field H is referenced to the [ I101 direction in all four crystals, and oxygen was added in small equal increments by anodization and annealing.7 The resistivity ratio, RR, of the resistance at room ternperature to that at 4.2"K (H =7.00 kG) was determined as well.

Jan 1, 1970

Robert Campbell Gemmell, assistant managing director of the Jackling allied porphyry mining properties in Utah, New Mexico, Arizona and Nevada, died suddenly on Oct. 25, of heart trouble, while traveling from Hurley, N. M., to Los Angeles. To shape justly even an outline of the brilliant career and uniquely charming personality of Mr; Gemmell is well-nigh impossible, and any effort so to do can but demonstrate the inadequacy of language to sound the depths of soul-stirring sentiments. To touch upon his more important work, and afford even a limited conception of his general worth and character, is all I can hope to do.

Jan 1, 1923

Robert Campbell Gemmell, assistant managing director of the Jackling allied porphyry mining properties in Utah, New Mexico, Arizona and Nevada, died suddenly on Oct. 25, of heart trouble, while traveling from Hurley, N. M., to Los Angeles. To shape justly even an outline of the brilliant career and uniquely charming personality of Mr; Gemmell is well-nigh impossible, and any effort so to do can but demonstrate the inadequacy of language to sound the depths of soul-stirring sentiments. To touch upon his more important work, and afford even a limited conception of his general worth and character, is all I can hope to do.

Jan 1, 1923

By Robert A. Cook

Among the new devices for cheapening the cost of material entering into the manufacture of iron is the mechanical drawing of coke, by which the coke from bee-hive ovens is extracted with a minimum of manual labor. About twenty years ago, an ordinary plate-conveyer was put in use at the plant of bee-hive coke-ovens owned by the firm of Bell Bros. & Co., near Middlesboro, England. This conveyer ran close along the front of the ovens, and carried the coke to the cars. The ovens were drawn by hand, and a very great saving in cost was secured, as one man could draw and clean out twice as many ovens after the conveyer was put in use—he having no forking to do, and the coke being carried away as fast as it was drawn to the mouth of the oven. The next step was further to eliminate hand-labor as far as possible; and Mr. Thomas Smith of the Thorncliffe Iron Works, near Sheffield, patented in 1891 the machine for drawing coke which I here describe. This machine, the outcome of several years of experimenting, has now been in successful use since 1891, and there are between twenty and thirty of them in operation at present, and others building. The machine, as may be seen from Figs. 1 and 2, consists of a wedge-shaped shovel of proper width and thickness, connected with a steel rack of sufficient length to reach the back of the oven. The rack is supported by rolls, and guided by a device operated by a hand-wheel, which directs the shovel in the oven. The rack is driven by a pinion on a vertical shaft carrying a bevel-gear on the upper end. This bevel-gear is driven by another on the engine-shaft. The engine is single-cylinder, with reversible gear; and engine and machine are mounted on a truck, which is propelled

Jan 1, 1897

EVERY intelligent and practical investigator of minerals says that copper ore is found in various regions of the world and that among others Italy is very rich in it. But very little is mined there, perhaps because of a cowardly Italian avarice which has the power to make us lazy and indolent in carrying out those lofty and fine designs which should reasonably make us proceed swiftly, or perhaps because we are not prone to attempt extraordinary profit but only undertake those enterprises in which we are certain of a return on our investment. The reason for this might also be found in the meager possibility of success, which, since these things are not easily attempted because they are enormous undertakings of doubtful outcome, cools the spirit of men and in place of enthusiasm introduces the fear of loss, the fear of having to sacrifice not only time but also the work and money invested; then they think of the difficulty [II] of discovery, of the impossibility of full ownership, and of the necessity of excavating the mineral marrow from the hardest bones of the mountains with the brawn and efforts of men. To this is added the fear common to many that in attempting such things they may be called fools by certain ignorant and dissolute persons, and it seems better to them to be praised for becoming rich through usury and by many other infamous and illicit methods than to lay themselves open to the danger of censure from such as these. But there are those who deserve still greater censure, particularly princes and all rich and powerful persons, and theirs is an even more useless error than that of those who refrain for the above reasons. If the occasion and means present themselves for both attempting and continuing such a profitable and laudable affair as mining ores and if they hesitate solely because of cowardice or because they give ear to the bayings of ignorant hounds, or if because of their own willfulness they wish to remain prisoners of a detestable and ugly avarice, then this is their own loss.

Jan 1, 1942

By AIME AIME

THOUGH born in England-on Nov. 23, 1372 William Wraith was brought to this country at the age of ten. Eight years later he entered the University of Illinois, transferring to the Michigan College of Mines where he got his E.M. in 1894. For the next three years he was a mine surveyor for the fuel department of the Santa Fe Railroad. Then he got into the copper-mining industry, which has occupied his attention for the last forty years. First he was engineer, at Butte, for the Boston & Montana company, and then helped to build the Washoe smelter at Anaconda, of which he was assistant superintendent from 1906 to 1913. The Anaconda company then sent him to Salt Lake City as manager of its subsidiary.

Jan 1, 1938

By Albert S. Trube

The purpose of this paper is to clarify the definition of compressibility and to present a uniform basis upon which instantaneous compressibilities of liquids and gases can be compared. The equations gaverning the instantaneous compressibilities of imperfect gases are derived and the concept of pseudo-reduced compressibility is introduced. Part of the data presented by Brown, Katz et a1 on compressibility factors for natural gases has been rearranged. A graph of pseudo-reduced compressibility vs pseudo-reduced pressure for various pseudo-reduced temperatures is presented. The need for additional work in relating the compressibilities of liquids and gases is discussed. This information should be of value to reservoir engineers in making non-steady state performance calculations in gas reservoirs. It should be of further use irz pointing the direction for additional research in the nature of liquid and gas compressibilities. INTRODUCTION With the increasing use of steady and non-steady state well and reservoir data, there is a corresponding increase in the importance of the various factors entering into such calculations. Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of the reservoir fluids well in advance of the more accurate laboratory data. One such factor is the isothermal coefficient of expansion of the media which are transmitting and attenuating the non-steady state pressure waves. The average isothermal coefficient of expansion, or "compressibility" is a complex function controlled by the physical properties of the formation and the fluids contained therein. The isothermal expansion coefficients for reservoir gases are usually quite variable, in many cases being highly-pressure sensitive. The coefficients for reservoir liquids tend to be pressure sensitive, but not nearly so much as reservoir gases. The coefficients for solids, usually expressed in terms of a "modulus of elasticity" are relatively insensitive to pressure variations within their elastic limits. For this reason, and also because many previous applications have been limited to rel- atively small pressure ranges, there has been a tendency to ignore the variable nature of isothermal expansion coefficients and treat them as constants. Also, the term "compressibility" by which these coefficients are generally designated is commonly confused with a similar term, z, used to define the deviation of an imperfect natural gas from the perfect gas laws. A clear distinction should be made at the outset between the term "compressibility", which is an isothermal coefficient of expansion of a substance, and the term "compressibility factor", z, which refers to the deviation of a gas from the perfect gas laws. Although the scope of this paper is limited to the compressibility of single phase natural gases, it is definitely related to the problem of accurately estimating the compressibilities of single phase hydrocarbon reservoir liquids, which will form the basis of a future presentation. BASIC PRINCIPLES The coefficient of isothermal compressibility of a substance, c, is usually determined from pressure-volume or pressure-length -measurements depending upon whether the substance is single phase gas, liquid, or solid. A convenient method for making such estimates for a finite change in pressure and volume at constant temperature is to use the well known equation V1-V2/V1 (p2 - p1) .....(1) Eq. 1 is negative because the volume of a confined substance decreases as the pressure is increased. In this case V1 > V2 and p2 > p1. This equation is useful in approximating the compressibilities of single phase gases and liquids undergoing small pressure changes. It is evident, however, that this equation is almost identical with the determination of Young's modulus of elasticity for solids. If the assumption is made that change in length is directly proportional to change in volume, as would very nearly be the case for a steel rod in tension within its elastic limit, then E5=-L1 (p2 - p1)/L1 - L2 .......(2) in which E. is the isothermal expansion coefficient, or Young's modulus of elasticity, for a solid. And further, for this special case L1 (p2 - p1)/L1 - L2 .......(3)

Jan 1, 1958

By Douglas Bunting

In the anthracite fields of Pennsylvania, mine fires occur with more or less regularity and their existence is an ever-present hazard in coal mining. In all probability 90 per cent. of the mine fires can be ascribed directly or indirectly to the ordinary miner's open lamp. Other causes may be smoking, electrical installations, gas explosions, gas feeders, and the communication of fire to the outcrops from ash dumps, culm banks, timber and brush fires. Fires in pump rooms, engine rooms, and barns have been largely eliminated as a result of the Act of Assembly, approved June 15, 1911, which provides that all inside buildings, including engine rooms, pump rooms, barns, etc., shall be constructed of incombustible materials. Smoking of pipes, cigars, and cigarettes should be prohibited in the mines and too much care cannot be exercised in preventing fires by enforcing all rules designed for that purpose. Mine fires that involve underground fighting are invariably dangerous, and all fires, irrespective of the method pursued in extinguishing them, involve property loss and expense. Each fire generally presents a more or less original problem, dependent on the particular conditions. Generally mine fires may be divided into two classes: Those occurring in inaccessible workings and those occurring in accessible workings. The methods pursued in extinguishing or controlling mine fires are as follows: (I) direct attack, (2) smothering by sealing, (3) flushing with silt or other solids, (4) flooding with water, (5) cutting off, (6) surrounding with incombustible materials, (7) digging out by stripping from the surface. Most fires arc extinguished in their incipiency by direct attack and failure to extinguish by this method is due to late discovery, lack of water, and facilities for fighting, or improper procedure in the initial attack. Should the method first pursued be unsuccessful, careful consideration should be given in determining next the method to be adopted; then the work should be carried on as rapidly as possible and under the supervision of the most competent persons. Materials and supplies should be furnished without delay and in sufficient quantities for the work to be accomplished.

Jan 1, 1922

By S. G. Cupschalk, F. A. Dahlman, J. J. Wert

Studies have been undertaken to determine the indicidual effects of particle size, degree of long-range ovder, antiphase domain size, and root mean square stran on the microhardness and yield strength of ordered alloys. Dnta have been analyzed for Cu3Pt initzally ordered to a value of 0.82 and after deformations of 1 and 6 pct. It was observed that deformation fleatly reduced the degree of long-range order. Furtherrnore, wztkin this range of relatively small deforntntlons, the average particle size changed very little while the antiphase domain size was greatly reduced. Smultaneosly, the mcrohardness changed by a factor of two durzng the deforrtation process. PREVIOUS studies have reported some of the effects of cold work on the broadening of X-ray diffraction peaks. These investigations were performed on powder and wire samples representing both ordered and disordered states; i.e., the specimens were initially studied in a severly cold-worked condition. By comparing the difference in line shape between the annealed and cold-worked peaks, fundamental information was obtained concerning particle size, strain distribution in different crystallographic directions, degree of long-range order, and change in antiphase domain size. Considerable theoretical work has been done concerning the analysis of diffraction data obtained from cold-worked metals. Stokes' expressed the change in diffraction profiles in terms of Fourier coefficients. Much of the work in this area has been summarized by warren2 in an extensive review article concerning the analysis of plastic deformation by X-ray diffraction. Cohen and Bever3 applied these techniques in studying the effects of cold work on alloy systems exhibiting long-range order. They utilized the Fourier coefficients of fundamental peaks in conjunction with those of the superlattice peaks to determine the change in antiphase domain size. Little work of this nature has been reported for ordered systems that have undergone small degrees of plastic deformation. The purpose of this investiga-tion was to determine the effects of small deformations in such a material with respect to particle size, strain distribution in various crystallographic directions, antiphase domain size, degree of long-range order, and hardness. EXPERIMENTAL PROCEDURE CusPt was used for the initial investigation since the order-disorder transformation takes place with- out a change in crystal structure. The transformation is readily detectable via X-ray diffraction techniques due to the large difference in the scattering factors of copper and platinum. Additionally, the alloy is relatively low melting (approximately 1300°C) and is easily deformable in both the ordered and disordered states. 1) Specimen Preparation and Cold Working. A 100-g, 12-in. diam., cylindrical specimen of Cu3Pt was prepared by melting and casting 99.99 pct pure Cu and Pt i.n vacuo. Prior to any mechanical working, the material was homogenized in a vacuum for 60 hr at 100O0C, and surface defects were removed by machining to a depth of approximately 116 of an in. The material was then cold-rolled, with an intermediate anneal, into a strip approximately 12 in. wide by 14 in. thick. Straightening and flattening removed another 0.025 in. from the thickness. After a recrystallization treatment at 750°C for 30 min, the specimen was slow-cooled from 55OoC, at the rate of 6°C per hr, down to 150°C to induce superlattice formation. This treatment yielded an ASTM grain size of 7 and a degree of long-range order equal to 0.83 0.06. After obtaining X-ray and Knoop hardness data, the sample was cold-rolled approximately 0.75 pct in one pass through a hand-operated jewelers' mill. X-ray and hardness data were again obtained and the specimen was reduced an additional 5.41 pct in a single pass through the mill. 2) X-Ray Measurements. The specimen was examined in the ordered condition and after the two degrees of cold working previously mentioned using a General Electric XRD-5 unit equipped with a spectrometer and scintillation counter. Using Mo-Ka radiation with a zirconium filter, six orders of the 100 reflection were obtained. It was anticipated that point counting would be necessary for an accurate determination of the low-intensity peaks and tails: however, it was demonstrated that, by using a scanning speed of 0.2 deg per min and the appropriate time constant, the recorded data were sufficiently accurate. Thus, for ease of experimental procedure, all peaks were recorded on chart paper. Specimen position in the holder was considered to be insignificant after making a series of measurements of the same peak area in different positions with respect to the beam. Since peak overlapping did occur at high values of 20, it was necessary to separate the peaks graphically prior to analyzing the data in order to minimize this source of error. The peak tails were also carefully drawn to obtain the best possible data. Fourier coefficients of the line profiles were calculated on an IBM 7072 computer, and graphical meth-ods2j3 were employed in analyzing the results. For this type of calculation, in which the line profile is represented by intensities taken at set intervals, the intervals selected must be sufficiently small to give an accurate representation of the line profile. It was decided that for 20 = 0.02 deg the line profiles were

Jan 1, 1967

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957

By R. E. Morgan, D. L. Douglass

The determination of phase relationships and solid-solubility limits can be performed by quantitative metallography in addition to the usual X-ray and metallographic techniques. For example, Beck and smith1 redetermined the ß/ß + ?, ß + ?/?, a/a + ß and a + ß/ß boundaries in the Cu-Zn system by measuring the volume fraction of second phase of several alloys and extrapolating the volume fraction-composition curves to 0 and 100 pct. A modification of this technique is suggested for certain alloy systems, in which it is not necessary to use several alloy compositions but merely one. A single two-phase alloy may be used to determine terminal solubilities in the following manner. The method consists of equilibrating samples of the alloy in a two-phase region adjacent to the desired solid solution, at three or more temperatures, quenching, measuring the volume fraction of second phase present, and applying an analytical treatment to calculate the unknown solid solution. However, two restrictions are inherent in this technique. They are: 1) only certain types of alloy systems are amenable to it, and 2) the general features of the system must be known. The first drawback to the new technique, i.e., that only certain types of systems may be studied, necessitates that the composition at one end of the tieline must either be constant with temperature or well established as a function of temperature. Either a pure metal or some intermetallic compounds fulfill the former. If it is assumed that the volume per gram-atom of a dilute solution is unchanged by the addition of element B to element A, the composition of the solid solution in equilibrium with the second phase may be determined by a material balance and is given by where X, = volume fraction of B in a solid solution Xc = volume fraction of B in compound c X = volume fraction of B in alloy f = volume fraction of second phase The composition by weight may then be determined by the use of tables in the Metals Handbook2 when the density ratio of the solid solution constituents is known. A possible alternative treatment involving the use of the lever rule is less precise than the above tech- nique. This may be used when the density of the solid solution is either known or may be calculated from X-ray data for several compositions. The following analysis is then made. The ratio of compound to solid solution (by weight) may be expressed as follows: x0 - x wc = xr-x = x0 - x r2i Xc -X where Wc = weight of compound w = weight of solid solution x, - alloy composition, weight percent x = unknown composition Xe = compound composition but where V, = volume of compound VA = volume of solid solution pc = density of compound p, = density of solid solution fc = volume fraction of compound fB = volume fraction of solid solution and fs = l -fc then If pc and xc are known, and f, is measured, then pB is the only unknown on the right side of Eq. [4]. The known densities of the solid solution can be plotted for various compositions and can then be expressed mathematically as a function of composition. The use of an expression of pB = f(x)reduces the equation to one unknown—the desired solubility. In the event that the densities are unknown, they may be calculated for various compositions from Vegard&apos;s law. The calculated values are then plotted and expressed analytically. The most accurate results are obtained for Eq. [4] when fc<< 1, i.c., when (x, -x,) - 0, &/l-f, - m; but as fc/l -fc - 0, (xl-x,)- (x, - x), and x - x,,. However, the accuracy with which fc can be measured decreases as f, decreases.3 Alloys for investigation must be selected by a compromise, which is based upon an error analysis of Eq. [4] and knowledge of the accuracy of volume fraction measurements. An examination of phase diagrams in the literature showed many which were amenable to the technique described here. The zirconium-copper system was selected in order to determine the solubility of copper in beta zirconium. Pieces of an alloy which was arc-melted three times were wrapped in tantalum foil and sealed under an argon atmosphere in Vycor tubes. The sealed samples were equilibrated at temperatures from 850" to 960°C for 3 weeks and quenched to room temperature by smashing the capsule in water. Several planes of polish were examined, and

Jan 1, 1960

By J. S. Levine, M. Prats

A homogeneous and uniform cylindrical reservoir containing oil and gas is fractured vertically on completion and is produced at a constant bottom-hole pressure. The fracture has an infinite flow capacity, is of limited lateral extent and is bounded above and below by the impermeable strata defining the vertical extent of the reservoir. Results show that such a fractured reservoir can be represented by a reservoir of circular symmetry having very nearly the same production history. The well radius of this circular reservoir is about 1/4 the fracture length and is essentially the same as that obtained previously for a single fluid of constant compressibility. At the same value of cumulative oil production, gas-oil ratios of fractured reservoirs producing at constant terzinal pressure are larger than those of reservoirs having no fractures. This leads to more inefficient use of the reservoir energy in fractured wells and results in lower reservoir pressures for the same cumulative oil production. The reduction in operating life due to fracturing a reservoir is not as great as that for a slightly compressible fluid. This diflerence can be accounted for by the lower reservoir pressure in the fractured reservoir and its adverse effect on the average mobility and compressibility of the oil. As anticipated, the reduction in operating life increases czs the reservoir permeability decreases. The type of results presented in this report can be used to determine the economic attractiveness of fracture treatments per se, to setect the initial spacing to be used in developing a field, and to compare the relative merits of fracturing available wells and infill drilling. INTRODUCTION The effect of vertical fractures on a reservoir producing either an incompressible or a compressible liquid has already been discussed in the 1iterature.l,2 Those results indicate that the production history of such a reservoir is essentially the same as that of a circular reservoir having an effective well radius of approximately one-fourth the fracture length. The present work reports on the effect of a vertical fracture on a reservoir producing two compressible fluids —oil and gas—by solution gas drive. Because of the empirical nature of the PVT and relative permeability data used to obtain the performance of such reservoirs, results can only be obtained numerically and with the aid of high-speed computers. Since reservoirs lose their radial symmetry when fractured vertically, pressure and saturation can no longer be given only in terms of distance from the well. Two coordinates (such as x and y) must now be used to describe the pressure and saturation within the reservoir, and, since we are dealing with compressible fluids, time is also a variable. Thus the solution of a vertically fractured reservoir requires finding two unknowns (pressure and saturation) in two space variables (say x and y) and in time (t). Since no means are readily and generally available for solving such problems at the present time, we have used the results of previous work1,2 to approximate the effect of a vertical fracture on a reservoir producing both oil and gas by depletion. The purpose of the present wmk, then, is to investigate the possibility of using available numerical techniques (limited at the moment to one space variable) to study the two-space-variable flow behavior resulting from a vertical fracture. Results obtained in the course of this investigation are also reported and discussed. Input and output data of the numerical methods used are given in practical units: BOPD, feet, psi, cp, and md. Results are discussed fist in terms of specific reservoir and crude properties and geometries. Later, dimensionless parameters are introduced in order to extend results to different values of some of the reservoir and fracture properties. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable, circular, cylindrical outer boundary of radius r,. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below&apos; the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. 1 indicates the general three-dimensional geometry of the fractured reservoir. Gravity effects and the effects of differential depletion resulting from variations in hydrostatic head (pressure) will be neglected. Thus, the flow behavior in the fractured reservoir is described by the

By MAGNE MORTENSON

IN laboratory work and industrial tests it is important to set forth the results of research, clearly. This is generally achieved by means of some form of diagram or graphical illustration. The most common form for such graphs of flotation research is a simple chart with two curves for percentage and recovery of the concentrate. This may be quite useful, especially for minerals which may be floated: by means of one reagent in variable and another in constant amounts. If both reagents are used in variable quantities the process may be illustrated by means of several diagrams, .keeping one reagent constant in each series of tests. A more useful form of diagram for a. system with two variable - components (reagents) may be established by drawing a chart with the weights of the two reagents as .abscissas and ordinates. Every test is marked down -in the diagram with an indication of the extraction and concentration gained. In this diagram there are drawn lines for equi-extraction and equi-concentration of the mineral that is floated out in the - concentrate. The contour of these lines gives a relatively clear impression of the conditions for flotation by means of .the chemicals used. The best conditions are of course found in diagrams where the &apos;areas for maximum extraction and high conntration are coincident

Jan 1, 1931

By R. Wachtell

IN order to study better the phenomena at work in various phases of diffusion of the Fe/Si system when compounded and alloyed by powder metallurgy methods, several attacks have been planned. Electrical, hardness and other measurements have been discussed e1sewhere.l,2 The metallographic phenomena will be considered here. Concerning the metallography of the ferrosilicon alloys, some initial discussion is in order. As this laboratory discovered to its chagrin, there are many traps that lie in wait for even the experienced metal-lographer when he deals with alloys of high silicon content. Chief of these is probably the anomalous behavior of these materials under conventional etching techniques. We have before us, for instance, Corson&apos;s paper" of 1928, wherein is mentioned and illustrated (probably for the first time) the peculiar "barley shell" structure sometimes found in these alloys. Again in 19412 he same author reports the structure in 5-14 pct silicon irons. Houghton and Becker mention its presence&apos; but make only tentative effort to explain it. In 1943, Hurst and Riley6 discussed the "barley shell" and declared it to be a false structure, resulting from the peculiar and characteristic film-forming propensities of the alloy. At about the same time, Wrazej7 proved correct the contentions of Hurst and Riley, establishing pretty well the mechanisms of formation and identifying the constituents involved. Hurst and Riley6 a1so describe in their paper (1943) a "cracked film" structure, also a pseudo-morph, the precise nature of which they do not suggest. Careful examination of such a film reveals that it not only cracks but begins to curl away from the surface of the metal and peel, much in the manner of flaking paint. The careful microscopist will be able to focus on the topmost edge of the flake, and, by optical sectioning, follow it down to the metal surface. We have been able, by oblique illumination of such specimens, to observe the raised segment of the film, the shadow that it casts, and the mating segment on the metal into which it fits. As late as 1946, Hurst and Riley8 found occasion to correct misinterpretation of this "cracked film" structure in a work by others on a 12 pct Si/Fe alloy. The "barley shell" and "cracked film" pseudo-morphs are not the only ones encountered in studies of these materials. A third pseudomorph, which may, however, have some structural significance is a fine striation of the surface. Closely spaced and parallel striae extend entirely across single grains. Each grain shows a different direction for the striae, and different closeness of the spacing. The regularity of this structure, and the fact that the striae do not cross from one grain to another, suggest that the structure is a film cracking controlled in some way by the crystal plane orientation of the surface being etched. In general it is wise for the metallographer dealing with these alloys to cultivate a feeling of uncertainty not only of the more complex questions of interpretation, but also of the basic question of whether that which he sees is indeed a true representation of the structure. We have taken, as a first test of the validity of a structure, its reproducibility "in situ" after repolishing and re-etching of the samples. Thus we knew the "barley shell" to be false (fig. 1) even before encountering the definitive works on the subject. The Metallography of Silicon Diffusion in Laminate Bars: As a first step in the study of the metallography of the diffusion process, we have pressed a series of laminate bars. These bars, or "sandwiches" as we have termed them, were pressed with covering layers of iron powder, and a "filler" of the Fe/Si master alloy under study. Bar dimensions were approximately %, x 3 x 1/4 in. The total

Jan 1, 1951

By E. G. Woodruff

Few authors of treatises and papers on engineering subjects hare given adequate attention to topographic maps. The statement applies especially to mining engineering in all branches. Even those who have discussed such maps have treated the subject only in a general way. Therefore it is proposed to outline in this paper a few of the uncommon yet important relationships which topographic maps and their by-product, structure-contour maps, have to modern methods of mining investigation and development when the facts depicted on such maps are properly interpreted. Topography, as suggested by the etymology of the word, means a detailed description of particular places. Written descriptions have been found less effective than the pictorial representations, therefore attempts have been made in various ways to picture the surface features of places. Lines and shading have been used, hachures drawn, and, finally, the contour topographic map. To a large extent this style of map is the result of the demands of engineers. It is designed to meet their needs far more than those of the man untrained in engineering. In fact,. the average man obtains a better idea of the topography of an area from the hachure system than from contour maps. Since the maps have been made chiefly for the use of the engineer, they ought to meet his demands on the one hand, and, on the other, should be used by him to the fullest extent. Such maps, when properly made, accurately portray a portion of the earth&apos;s surface and should present the topography better than a personal examination of the area without a map could present it, because the person making such examination views only a limited portion of the surface at a time, and estimates distances only roughly with his eye. Let the engineer consider carefully the fact that in many instances the topographic map is superior to a personal examination of the surface features of a property because the map is based on careful instrumental measurements, whereas the eye gives imperfect data because it can be used merely for the estimation and

Jan 1, 1914

By Howard Scott

Manganese being perhaps the least expensive of the metallic alloying elements that can be advantageously added to iron in considerable quantities, the basic characteristics of its alloys with iron are properly receiving much attention at present. In the course of a dilatometric investigation of this system several years ago, the writer observed certain transformation phenomena not found in other iron-base alloys. The interpretation of those effects was not evident from the information then available, but recent X-ray studies clear up at least one anomaly and permit a more satisfactory description of the results than would have been possible otherwise. Aside from the new phenomena observed, the effect of manganese on the Arg transformation is of timely interest because of its bearing on the critical compositions of austenitic alloys, the applications of which are now being greatly extended. It is known that the properties of these alloys are unstable unless the As transformation occurs at a tem-pcrature considerably below atmospheric and that manganese is very effective in depressing the temperature of this transformation. The writer aims to establish a simple general relation which expresses the location of Ar3, quantitatively in terms of the content of the common alloying elements used in steel. A step in that direction is taken here. Early dilatometric investigations1 indicated that only one transformation other than the eutectoid A1 occurs in the high-iron alloys of the iron-manganese system. Dejean represents the Arg point as falling to 0" C. with a manganese content of 11 per cent and carbon content of between 0.30 and 0.40 per cent. Esser and Oberhoffer," sing alloys low in carbon (under 0.03 per cent), arrived by extrapolation at 14 per cent for the manganese content at which As is depressed to 0" C. Not until both low carbon contents and alloys having a manganese content

Jan 1, 1931

By K. H. Ribe

Water often enters an oil reservoir during completion or workover operations on a well and forms a partial "water block" to oil production. A mathematical study of radial two-phase flow, neglecting capillary effects, has been employed to study the formation of such a water block and subsequent re-moval by production from the well. The effects of reduced oil permeability about the well on the well productivity were studied. The fluid saturation distributions about the well during formation and removal of the water block have also been computed. Several relative permeability relations and viscosity ratios were employed. If water has invaded the formation, its influence through relative permeability effects alone can cause the following. 1. Oil productivity will be depressed for extended periods after production is resumed and will build up only gradually as the water is removed. 2. Oil injected for treatment of water blocking will delay rather than promote restoration of full well productivity by enlarging the region invaded by water. Thus, unless the specific action of chemicals contained in the oil is needed, oil injection appears undesirable. INTRODUCTION During oilwell workover operations, water may enter the oil-bearing formation from the wellbore. When production is resumed, oil must flow through the region invaded by this water. The presence of this region can cause both well productivity and oil production rate to be low and oil to be produced with high water-oil ratio for some time after production is initiated. This situation is sometimes described as a water block. The introduction of water into the formation may result in other actions which also lead to reduction in well productivity and which are also usually included in the connotation of the broad term, water block. Often considered, for example, are the possibilities of clay swelling by contact with fresh water and the formation of emulsions with the formation oil. If it is suspected that such specific actions have taken place, remedial treatments are undertaken which usually involve the injection of chemicals in oil. Since the introduction of water, even in the absence of specific interactions with the formation or oil, will cause a temporary water block (which might be misinterpreted as evidence of a more severe situation), it is of importance to evaluate the magnitude and duration of this blocking which results purely from the reduction in relative permeability to oil in the vicinity of the wellbore. It is also of interest to evaluate the effect of oil injection on the productivity of a well blocked by water in this manner. Inasmuch as this unfavorable condition may persist for some time, it may lead to premature condemnation of a workover or premature abandonment of a potentially productive pay zone. A quantitative evaluation of the influence of water entry on the oil productivity through changes in relative permeability was made by solving a radial form of the Buckley-Leverett equation. The distribution of water saturation around the wellbore during the entry of water was calculated and was followed by a similar calculation of the saturation distribution during the period of resuming production. At any stage in the removal of the invading water, knowledge of the distribution of its saturation permitted calculating the attendant loss in oil productivity. The influence of the shape of the relative permeability relationships was also evaluated by carrying out the calculations for two hypothetical cases. Further, the effect of the oil-water viscosity ratio was examined by repeating the calculations, for several ratios of unity and greater, with the same relative permeabilities. Fi-nally, results are presented to show how the length of time a well must be swabbed to resume production depends on the length of time it has been subjected to invasion by water. STATEMENT OF THEORY Differential Equations Water is assumed to enter a producing formation which is initially at the connate-water saturation and contains no gas. The water and oil are treated as in-

By E. G. Woodruff

(Butte Meeting, August, 1913.) FEW authors of treatises and papers on engineering subjects have . given adequate attention to topographic maps.. The statement applies especially to mining engineering in all branches. Even those who have discussed such maps have treated the subject only in a general way. Therefore it is proposed to outline in this paper a few of the uncommon, yet important relationships which topographic maps and their by-product, structure-contour maps, have to modern methods of mining investigation and development when the facts depicted on such maps are properly interpreted. Topography, as suggested by the etymology of the word, menus a detailed description of particular places. Written descriptions have been found less effective than the pictorial representations, therefore attempts have been made in various ways to picture the surface features of places. Lines and shading have been used, hachures drawn, and, finally, the contour topographic map. To a large extent this style of snap is the result of the demands of engineers. It is designed to meet their needs far more than those of the man untrained in engineering. In fact, the average man obtains a better idea of the topography of an area from the hachure system than from contour maps. . Since the maps. have been made chiefly for the use of the engineer, they ought to meet his demands on the one hand, and, on the other, should be used by him to the fullest extent. Such maps, when properly made, accurately portray a portion of the earth&apos;s surface and should present the topography better than a personal examination of the area without a map could present it, because the person making such examination views only a limited portion of the surface at a time, and estimates distances only roughly with his eye. Let the engineer consider carefully the fact that in many instances the topographic map is superior to a personal examination of the surface features of a property because the map is based on careful instrumental measurements, whereas the eye gives imperfect data because it can be used merely for the estimation and

Jan 6, 1913