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By R. P. McLaughlin

EXACT information as to performance of the gas lift from the mechanical engineering standpoint is hard to obtain. Several hundred wells are now producing in California fields by means of the gas lift, and a survey of results shows that the gas lift has increased production at these wells by approximately 60 percent. Similar or even larger figures describe results in Mid-Continent fields. Such an increase in output of oil is so satisfactory, to the average oil producer, that it may not encourage investigation looking to more efficient operation. The cost of lifting oil by compressed gas varies from 3 c. to 15 c. per bbl. of oil, depending upon the efficiency of the gas lift. A difference of 10 c. or 12 c. per bbl. of oil is immediately noticed by an oil operator and the cost in production is as real to him as is the price of his product. Therefore, the efficiency of gas-lift process deserves more consideration than it has been given in some quarters. It has been found that there is a wide variation between different operators and at different wells in the amount of gas used per barrel of oil lifted. Some of the most efficient operations show oil being lifted with only slightly over 400 cu. ft. of gas per bbl. of oil.1 On the other hand, wells are being flowed and using as high as 3000 cu. ft. per bbl. of oil. The cost of compressing gas to 300 or 400 lb. varies from 3 c. to 5 c. per 1000 cu. ft. of free gas. This figure has been obtained from a number of sources and as a matter of fact is the basis of actual business transactions involving gas compression. The cost of lifting oil with compressed gas is thus determined.

Jan 12, 1926

By H. C. Kenny

The annealing or softening temperature of cold-worked copper is appreciably increased by almost unbelievably small amounts of silver. As indicated by some data in this paper, the softening temperature of high-conductivity, tough-pitch copper may be increased from 200" to 350" C. by the addition of only 15 oz. per ton (0.052 per cent) of that element. Because it has this higher annealing temperature as compared with the silver-free metal, silver-bearing copper finds considerable use in industry. For example, when hard-rolled copper is used in operations that involve soldering or tinning, silver-bearing copper insures against loss of strength, whereas silver-free copper becomes "dead soft." Yet—though several investigators, beginning with Caesar and Gernerl in 1916, have shown that small amounts of silver do definitely raise the softening temperature of copper—data are lacking on the problem: What is the specific influence of different amounts of silver on this temperature? It was to help in filling this gap in the knowledge of what might be termed "alloy coppers" that the data given herein were obtained. The softening of cold-worked copper depends, of course, on a number of factors, of which the composition of the material is only one. Other highly important factors are the degree to which the material is cold-worked and the time it is held at the annealing temperature. The method of cold working and the grain size of the metal produced are also significant. All these variables were taken into account in the investigation reported here, and the influence of silver on the electrical conductivity and on the working was also considered. The coppers used in the softening tests were Lake coppers melted and cast by the Calumet and Hecla Consolidated Copper Co. The ires were fabricated by the Roebling Wire Co. and the sheets were rolled at the Battelle Memorial Institute. Partial analyses of some of the coppers are listed in Table 1, with their electrical conductivities.

Jan 1, 1934

By S. Stopek, E. D. Hinkley, R. H. Rediker

Epitaxial heterojunctions have been prepared by melting the lower -melting-point semiconductor of the interface between two dijferent semiconductors. when the temperature is reduced, the melted material recrystallizes, having alloyed into the higher -melting-point semiconditctor. The electrical and elcctro-optical properties of such single-crystal heterojunctions between GaAs and Gash and between p-type InAs and n-type Gash are the subject of this paper. The forward current varies as exp (AV), where A is substantially independent of temperatuve. For Gds-Gash heterojunctions at temperatures above, 370°K, if the current-voltage relationship were to he expressed as exp (qV/nkT), then n would he less than unity. The injection luminescence associated with forward current is, for the most part, characteristic. of the lower bandgap semicondutctor. These results can he explained by carrier injection into the lower bandgap semiconductor by tunneling through a barrier at the interface. The photovoltaic effect measured for incident photons having energies in the range between the bandgaps of the two semiconductors is much smaller than that produced by higher-energy photon The smallness of this between -the-gap photovoltaic response can he explained by the low probability for penetration of the barrier by the carriers produced in the smaller -bandgap semiconductor. THE technique of interface alloying has been used to produce single-crystal junctions between dissimilar semiconductors.' Oriented wafers are placed on a carbon heater strip, Fig. 1. so that semiconductor S1, which has the lower melting point, is supported by semiconductor S2. Electrical current passed through the heater strip produces a temperature gradient such that S2 is at a higher temperature than S1. As the temperature is raised the lower face of S1 begins to melt. Before the entire wafer can melt, however, the heater-strip current is turned off and, as illustrated in Fig. l. the melted portion recrystallizes, having alloyed into S2. Junctions have been fabricated by the above procedure between GaAs and germanium, between GaAs and GaSb, and between InAs and GaSb. Mroczkowski, Lavine. and Gatos have described the metallurgical and chemical aspects of the GaAs-Ge junction.2 The transition from GaAs to germanium is not monotonic and a portion of the recrystallized region consists of the GaAs-Ge eutectic. Since gallium is an acceptor and arsenic is a donor in germanium, since germanium dopes GaAs, and since the electrical properties of the GaAs-Ge eutectic have not been investigated, any interpretation of the electrical characteristics in terms of simple heterojunction theory would be incorrect. That the rectification of GaAs-Ge heterojunctions is not a property of the impurity doping of the GaAs or the germanium, but is most probably due to the impurity distribution in the recrystallized region, is clear from the fact that forward conduction occurred for all the GaAs-Ge interface-alloy junctions (whether they be n-n,n-p. p-n. or p-p) when the germanium was biased positively. The electrical characteristics of these GaAs-Ge heterojunctions will not be discussed further in this paper. Electron-beam microprobe analysis of GaAs-GaSb heterojunctions showed that the transition from arsenic to antimony atoms was without structure. and that the transition occurred within a 2 to 3 region.' In this paper we will describe the electrical properties of the GaAs-GaSb heterojunctions as well as electrical and electro-optical properties of the InAs-GaSb heterojunctions. A band model for the junction will be proposed which can explain these properties. ELECTRICAL PROPERTIES OF GaAs-GaSb HETEROJUNCTIONS After interface alloying. in preparation for the electrical and electro-optical experiments, ohmic contacts were made by conventional means. For example. Kovar tabs clad with tin were alloyed to n-GaAs or similar tabs clad with Au-Zn were alloyed to p-GaAs. The units were mounted and then etched. All four combinations of conductivity types

Jan 1, 1965

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' 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 H. M. Davis, J. H. Keeler

Densities of SAE 1020 (I) and ingot iron (II) decreased with cold rolling to minima at 60 pct reduction, whereas high-purity iron (III) was unaffected. I recovered promptly with annealing; II, sluggishly and incompletely. Hydrogen occlusion of III or II was barely affected by 60 pct cold reduction, but that of I was increased a hundredfold. IT has been reported of iron that its density is decreased and its occlusive capacity for hydrogen is increased by cold work. One of the most interesting aspects of each of these properties is that the changes brought about by cold work are not necessarily eliminated by annealing and recrystallization. Yet recrystallization is generally accepted as restoring to their original condition the properties or characteristics altered by cold work. A number of investigators have reported a decrease in density with cold reduction. Two1, 2 have shown that annealing after cold reduction may not return the density to its original value. It has been suggested' that cracks or flaws in inclusions produced during cold drawing contribute to the lowering of the bulk density of the metal. Extremely high-purity copper has been reported as not exhibiting a density decrease with cold reduction. On the other hand, calculations' indicated that grain distortion by itself can produce expansion of the order of magnitude of the changes observable. Maier" showed that both the density of iron and that of copper passed through a minimum with increasing cold reduction. Although much information is available on the subject of hydrogen in steel0, 7 and it is well known that plastic deformation of a metal may increase its occlusive capacity,8-12 most of the reports pertain to charging the metal with hydrogen by cathodic deposition or with acid. Darken and Smith,'" who employed acid charging, emphasized the great influence of cold work on the occlusive capacity of iron for hydrogen and showed the inability of a prolonged high-temperature annealing treatment to restore the occlusive capacity of cold-worked steel to the value exhibited in the hot-rolled condition. It has been reportedm that an "endothermic" metal*

Jan 1, 1954

By B. E. Sundquist

The various methods based on solution models for obtaining free energies of mixing from miscibility-gap data have been applied to a number of binary-alloy systems. For nine of these systems there exist experimental thermodynamic data that permit a comparison of the results to experiment. It was found that the method of van der Toorn and Tiedema almost invariably leads to results that are physically unacceptable and that vary drastically with small changes in the miscibility-gap parameters. The subregular solution model is found in all cases, except the Al-Zn, Fe-Cr, and Cu-Pb systems, to exaggerate the free energy of mixing by 30 pct or more. The model developed by Lumsden is found to give results that are often in excellent agreement with experiment and which exaggerate the free energy of mixing by no more than 30 pct. These results and others give evidence that the Lumsden treatment of the effect of unequal atomic sizes and of imperfect configurational randomness due to deviations of AB bond energies from the mean of AA and BB bond energies is adequate for most systems. ANALYTIC expressions are frequently proposed for the dependence on composition of the activities of the components of a solution. Because the development of solution theory is incomplete, these expressions contain parameters which must be determined by experiment. The measurement of activities is often difficult and consequently such measurements are less readily available than are measurements of phase equilibria which, under certain conditions, can also be used to evaluate these parameters. For example, suppose it is known that two structurally dissimilar phases, each of known composition, in an n-com-ponent system are at equilibrium at a given temperature and pressure. n equations can be set up in terms of these parameters expressing the equality of the chemical potential of each component in the two phases. In addition, one can write the Gibbs-Duhem equation for each phase that also contains these parameters. Thus, if these n + 2 equations contain n + 2 parameters, these parameters can be determined (at the temperature in question) from the phase diagram alone. If the average number of parameters in each expression for the activity of a given component in a given phase is V then there will be 2nV parameters involved. Equating 2nV to n + 2 shows that, for n + 2, V = 1. If the temperature dependence of each parameter were to be expressed in some explicit form one could use equilibrium conditions at a number of temperatures to increase V. The situation is much improved when the two phases in equilibrium are structurally similar. It can then be assumed that, stably or metastably, two phases will become one at higher temperatures. Thus the number of parameters involved becomes nV instead of 2nV. Hence, V = 2 for n = 2 using only one temperature. (It is implied here that the activity expressions used are valid over the entire composition range.) In this investigation only the equilibrium of two structurally similar, two-component phases (miscibility-gap systems) will be considered. The various proposed solution models will be applied to a number of these systems and the results compared with available experimental results. All of the analytic expressions that have been proposed for the free energy of mixing of a two-component system are of the form where ?Gmix is the free energy of mixing per mole of solution, N1 and N2 are the mole fractions of components 1 and 2, respectively, and f(Ni, T) is some function of composition and temperature. In the "ideal" solution model f = 0. In the "regular" solution model f = a constant. Since these two models permit only a symmetric equilibrium diagram they will not be considered further here. The simplest model that permits a nonsymmetric miscibility envelope is the so-called "subregular" solution model proposed by Hardy.1 This model gives where the Ci(T) are functions of temperature only. The same expression for f is obtained from the "linear a function" model proposed by Darken and Gurry2 and applied to miscibility-gap systems by Wriedt.3 This model requires that the a function defined by be a linear function of composition (yi is the activity coefficient of component i). This model is not purely hypothetical for it has been found2 to hold true for a number of systems. It is readily shown3 that the f(Nl, T) obtained from this model is of the form given in Eq. [2]. It will be noted that the subregular solution model contains only two parameters and hence both of them can be determined at any desired temperature below the critical temperature, Tc, for a miscibility-gap systems in the manner described previously. At T, the two constants can be determined by equating the second and third derivatives of ?Cmix with composition to zero. Another two-parameter model was proposed by Lumsden4 who set

Jan 1, 1967

By P. W. Rainier

THE Chivor emerald field is situated on the eastern slope of the Andes in the Department of Boyacá, at an elevation of about 8000 ft. above sea level. It overlooks the Llanos (plains) of the Orinoco and is watered by many streams flowing into the Rio Meta, the Orinoco's largest tributary. The Rio Meta is navigable from the Orinoco to a point within about 50 miles of the Chivor district and may eventually prove to be the reasonable outlet for the future development of this part of the country. The topography of the district is extremely rugged and mountainous (Fig. 1), the difference in elevation between two points on a mining claim 1 km. square being sometimes as much as 4000 ft. The ground is covered with dense forest growth and the available timber is suitable and sufficient for mining purposes, but it is becoming gradually depleted by Indian clearings as the country around the mines becomes settled. The many streams combined with the rough topography give good possi-bilities for hydroelectric power. The center of population nearest to Chivor is Bogota, the capital of the republic and a city of some 300,000 inhabitants; the distance is two and one-half days' travel. The first stage of the journey from Bogota, is accomplished by rail to Chocontá, some 4 hr. travel. From Chocontá the journey is made in the saddle, one night being spent in Guateque. The latter is a small town and the nearest post office to the mines, being some 10 hr. ride distant. The roads are mere bridle paths, in parts hazardous and almost impassable in the wet season. All supplies brought to the mines, other than those produced locally, are carried by pack mule; mule freight from Chocontá costs 3 centavos1 per pound. The climate of the Chivor district is healthful and bracing. The wet season begins in March and concludes in November, the remaining months being dry. The annual precipitation is about 150 in. The temperature throughout the year is nearly constant, varying from about 45° F. to about 65° F. shade temperature. The rains are cold and unpleasant, and for the greater part of each day in the wet season the country is shrouded in dense mist. A fire can with comfort be kept burning in a living room all the year round. There are a few slight

Jan 1, 1929

The Mexican Government is building a mill at Churunibave in Sonora to handle lead, zinc, and copper ores. This development was sparked by increased mining activity in Mexico and Arizona caused by the Korean war. Pickands Mather, acting for a group of iron ore producers, is negotiating an agreement with Steep Rock Iron Mines, Ltd. to explore and perhaps lease iron ore property covering more than 1000 acres in the Steep Rock Lake area in Western Ontario. Plans call for the early commencement of an exploratory program. Other members of the group by Pickands Mather are Bethlehem Steel, Youngstown Sheet & Tube, the Steel Co. of Canada, and Interlake Iron Corp.

Jan 3, 1951

By F. C. Bond

SIZE of grinding media is one of the principal factors affecting efficiency and capacity of tumbling-type grinding mills. It is best determined for any particular installation by lengthy plant tests with carefully kept records. However, a method of calculating the proper sizes, based on correct theoretical principles and tested by experience, can be very helpful, both for new installations and for guiding existing operations. As a general principle, the proper size of the make-up grinding balls added to an operating mill is the size that will just break the largest feed particles. If the balls are too large the number of breaking contacts will be reduced and grinding capacity will suffer. Moreover, the amount of extreme fines produced by each contact will be increased, and size distribution of the ground product may be adversely affected. If the balls added are too small, grinding efficiency is decreased by wasted contacts that are too weak to break the particles nipped; these largest particles are gradually worn down in the mill by the progressive breakage of corners and edges. Ball rationing is the regular addition of make-up balls of more than one size. The largest balls added are aimed at the largest and hardest particles. However, the contacts are governed entirely by chance, and the probability of inefficient contacts of large balls with small particles, and of small balls with large particles, is as great as the desired contact of large balls with large particles. Ball rationing should be considered an adjunct or secondary modification of the principle of selecting the make-up ball size to break the largest particle present. Empirical Equation In 19521,2 the author presented the following emerical equation for the make-up ball size: B - ball, rod, or pebble diameter in inches. F = size in microns 80 pct of new feed passes. Wi - work index at the feed size F. Cs - percentage of mill critical speed. S — specific gravity of material being ground. D == mill diameter in feet inside liners. K - 200 for balls, 300 for rods, 100 for silica pebbles. Eq. 1 was derived by selecting the factors that apparently should influence make-up ball size selection and by considering plant experience with each factor. Even though Eq. 1 is completely empirical, it has been generally successful in selecting the proper size of make-up balls for specific operations. But an equation based on theoretical considerations should be used with more confidence and have wider application. The theoretical influence of each of the governing factors listed under Eq. 1 was accordingly considered in detail, as described below, and a theoretical equation for make-up ball sizes was derived. Derivation of Theoretical Equation Ball Size and Feed Size: The basis of this analysis is that the largest ball in a mill should be just sufficient to break the largest feed particle into several pieces, excluding occasional pieces of tramp oversize. In this article the size F which 80 pct passes is considered the criterion of the effective maximum particle feed size. The smallest dimension of the largest particles present controls their breaking strength. This dimension is approximately equal to F. As a starting point for the analysis it is assumed that a 1-in. steel ball will effectively grind material with 80 pct passing 1 mm, or with F- 1000µ or about 16 mesh. The breaking force exerted by a ball varies with its weight, or as the cube of its diameter R. The force in pounds per square inch required to break a particle varies as its cross-sectional area, or as its diameter squared. It follows that when a 1-in. ball breaks a 1-mm particle, a 2-in. ball will break a 4-mm particle, and a 3-in. ball a 9-mm particle. This is in accordance with practical experience, as well as being theoretically correct. Confirmation of this reasoning is supplied by the Third Theory of Comminution," which states that the work necessary to break a particle of diameter F varies as F. Since work equals force times distance, and the distance of deformation before breaka4e varies as F it follolvs that the breaking force should vary as F½ These relationships are expressed in Table I, with a 1-in. ball representing one unit of force and breaking a 1-mm particle. This establishes theoretically the general rule used in Eq. 1 that the ball size should vary as the square root of the particle size to be broken. Ball Size and Work Index: The work input W required per ton" varies as the work index Wi, and the

Jan 1, 1959

By R. L. Dietrich

Magnesium alloy sheet has less ability to accept bending at room temperature than most of the heavier metals. In work designed to improve the bend properties, the preferred orientation of the sheet is of major importance as it is in all studies of the properties of wrought magnesium products. When rolled into sheet, all of the common magnesium alloys form an orientation texture having the basal (002) planes approaching parallel to the surface of the sheet. This texture is only slightly affected by annealing. Magnesium single crystals are highly anisotropic, and, as might be expected, so are magnesium alloy wrought products in which a strong preferred orientation is developed. It is therefore not surprising that bend properties are affected by orientation. Ansel and Betterton1 reported that the orientation of AZ3lXt sheet varies from surface to center and that bend properties are improved by etching away the sharply oriented material at the surface of the sheet to reach the more broadly oriented structure below. This paper covers a study of that orientation, either during the rolling process or by treatment of the finished sheet, in an effort to improve the bend properties and toughness of sheet. Literature The orientation texture of magnesium and magnesium alloy sheet has been studied extensively. Early determinations2 showed that pure magnesium sheet has a preferred orientation in which the basal planes are parallel to the sheet surface within very narrow limits. J. C. hIcDonald3 and J. D. Hanawalt4 reported that sheet containing a small amount of calcium develops a "double" texture, that is, the majority of the basal planes are a few degrees from parallel to the surface and there is a noticeable vacancy at the parallel position. Bakarian5 made careful quantitative pole figures of both pure magnesium sheet and MI alloy SEPTEMBER 1949 sheet which show these features. In all of these studies, however, the orientation was determined by transmission methods in which the resulting pattern is an average through the thickness of the sheet. The tendency of wrought metal to exhibit a different orientation at the surface from that in the center has been reported by many investigators. G. von Vargha and G. Wasserman6 found that with copper, aluminum, iron, and brass the textures of rolled compared to drawn wires were the same at the center but differed markedly at the surface. It was also reported by investigators7 that the orientation of rolled aluminum varies from surface to center. Har-greaves8 found that the surface texture of AM503 (magnesium alloy similar to MI) sheet was different from the center texture. It is reported by Edmunds and Fuller9 that zinc alloy sheet sometimes had a thin layer at the surface with a strong orientation of the basal planes parallel to the surface, which, if present, impaired the bend properties of the sheet. Part1 Surface Orientation ofMag- nesium Alloy Sheet and the Effect on Properties Attempts to correlate the bend properties of magnesium alloy sheet with tension ductility over short gauge lengths proved unsuccessful and the subsequent investigation showed that nonuniformity in orientation is a con- tributing factor as the properties of the surface material have a much more important effect in bending than in tension. A program to study the relationship between surface orientation at the surface and bend properties was then undertaken. First, the effect of etching away the surface of sheet on the bend properties and the orientations at the various depths were studied. Sheet samples of M1, AZ31X, and AZ61X were etched in dilute nitric acid to remove the surface material for various depths to 0.015 in. As may be seen in Table 1, the minimum bend radius improved considerably as the surface layers were etched away but it was necessary to etch the sheet quite deeply, much more so than was found necessary by Edmunds and Fuller9 on zinc sheet. It is also apparent that the amount of etching required is a function of the sheet thickness. In all of this work, radii were measured as R/t, the radius divided by the sheet thickness, in order to eliminate the effect of the reduction in sheet thickness produced by the etching. To determine the orientation texture of the sheet, X ray reflection patterns were taken using copper radiation with the bearn striking the specimen at an angle of 17' to the surface, which is the Bragg angle for the (002) planes of magnesium. Two exposures were made of each specimen, one with the beam perpendicular to the rolling direction and the other with the beam parallel to the rolling direction. The symmetry of the preferred orientation in magnesium sheet is such that these two photographs gave an approximation of the pole figure sufficiently accurate for qualitative work and it was not thought worthwhile to make complete pole figures. These X ray patterns show that the orientation has a much narrower spread at the original surface of the sheet than below the surface. The narrow spread is found in sheet having the majority of the basal planes (002) parallel to the surface, and since this is an unfavorable position for slip, it is

Jan 1, 1950

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By R. M. Hays

Prior to use of this model siphon finisher, the only means of evaluating metallurgical performance of the siphon finisher was by pilot plant studies. These are costly and require large quantities of material. A model siphon finisher and a test procedure which permits the evaluation of siphon finisher metallurgical performance has been developed. Metallurgical results between the model siphon finisher and pilot plant or commercial units show fairly good correlation. The upgrading of magnetic taconite concentrates by hydraulic concentration has been practiced for several years. In the 1940's, Braund1 used a multistage upflow classifier to upgrade magnetized magnetic concentrates. In present taconite plants, the SiphonSizer, marketed by Dorr-Oliver, Inc., has been particularly suitable for upgrading magnetic concentrates. When the hydraulic SiphonSizer is used to upgrade the concentrates in the finishing portion of the overall flowscheme, the unit will be called a siphon finisher to distinguish this application from classification. Prior to this work the only means of evaluating the metallurgical performance of the siphon finisher was by pilot plant studies which are costly and require large quantities of material. Therefore, it was desirable to develop a model siphon finisher and a test procedure which would simulate siphon finisher performance and require only small samples of material. This model would permit the evaluation of small samples such as drill core samples and be useful in evaluation of commercial siphon finisher design and performance. THE SIPHON FINISHER The siphon finisher, as shown in Fig. 1, is a tank equipped with a system of water jets which distribute the hydraulic water uniformly across the bottom of the vessel with an energy release for agitation in the teeter bed. The feed to the siphon finisher is intre duced through a feed well in the center of the unit. The silica and middling particles overflow a peripheral weir into the overflow launder. The magnetite fraction is discharged by a siphon or a modulated discharge valve. The siphon or the discharge valve is usually operated automatically by a float assembly which is responsive to the depth of the teeter bed. Various interface sensing devices have also been

Jan 1, 1968

By N. O. Johnson, J. Boyer, D. H. Sargent, R. B. Frahme

Although the Western bentonite industry has grown rapidly, it is facing major challenges to sustained growth. The fundamental penalty of costly overland transportation to both domestic markets and to US seaports is of increasing importance; as both substitute materials and foreign bentonites present more formidable competition in the historic market areas of drilling muds, foundry sands, and iron ore pelletizing; and as foreign demand grows more rapidly than domestic demand. The Western bentonite industry is facing these challenges by altering its transportation patterns, by upgrading of products, and by emphasizing customer service and stringent quality control.

Jan 1, 1980

By N. O. Johnson, J. Boyer, D. H. Sargent, R. B. Frahme

Although the Western bentonite industry has grown rapidly, it is facing major challenges to sustained growth. The fundamental penalty of costly overland transportation to both domestic markets and to US seaports is of increasing importance; as both substitute materials and foreign bentonites present more formidable competition in the historic market areas of drilling muds, foundry sands, and iron ore pelletizing; and as foreign demand grows more rapidly than domestic demand. The Western bentonite industry is facing these challenges by altering its transportation patterns, by upgrading of products, and by emphasizing customer service and stringent quality control.

Jan 9, 1979

The centenary of Julia Ward Howe, author of "The Battle Hymn of the Republic," is of particular interest to the members of the Institute because of the very active part that has been taken in the affairs of the Institute by her son, Dr. H. M. Howe. By an order of the Board of Education, the one hundredth anniversary of Mrs. Howe's birth, May 27, was observed in the public schools of New York City with the singing of the fatuous battle hymn. Boston, the city of her adoption, celebrated her centenary by a service in the Church of the Disciples, where Governor Coolidge made an address, and in which John Andrew Post took a prominent part. General Pershing sent a letter, which was read by the Rev. Abraham Mitrie Rihbany, in which he said: "It is a great privilege to bear witness to the widespread effect of ?The Battle Hymn of the Republic? on the morale of the fighting men. It is unique in its religious fervor and enthusiasm and whenever sung it can have but the same effect which it produced when it was first sung in the Civil War."

Jan 7, 1919

By J. Geertsma

In order to obtain a better insight into the pressure-volume relationship of reservoir rocks a theory of pore and rock bulk volume variations is presented. The theory is independent of the shape of the pores but is restricted to isotropic porous media built up of continuous homogeneous matrix material. The main conclusion obtained from this theory is that only three elastic constants and three viscous constants are required for describing pore and rock bulk volume variations if the porosity is explicitly introduced into the treatment. In addition, reasonable approximations are introduced for various types of reservoir rock, e.g., sandstones, limestones, and shales, which lead to further simplifications of the basic formulas. In consequence there is then a further reduction in the number of deformation constants which have to be determined experimentally. It is shown how measurements of these remaining deformation constants can be performed most conveniently. Finally the application of the theory to reservoir studies is discussed and the translation of experimental results obtained in the laboratory into reservoir behavior is considered. INTRODUCTION The decline of fluid pressure in connection with the withdrawal of fluid from an underground reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock results in a decrease of both the pore volume and the total volume of the fluid-filled formation. Whereas the variation in volume of the reservoir fluids with pressure is usually known from PVT analysis, that in the volume of the porous medium is rarely measured, as it is considered of minor importance in reservoir engineering. Nevertheless, certain experimental results' suggest that in a number of cases the neglection of the variation in pore volume may introduce errors into material balance calculations of reservoirs producing above the bubble point. Only a few experimental results on the compressibility of porous rocks have been published. The compressibility of pure quartz and of calcite can be found in a paper by Adams and Williamson'. Botset and Reed' carried out some experiments on the compressibility of loose sands, while Carpenter and Spencer' measured the compressibility of a number of consolidated sandstones, which data were supplemented by Hughes and Cooke5. Hall' finally reported a number of experiments designed to study the influence of the porosity on the compressibility of oil-bearing formations, from which it appeared that, particularly in the low porosity range, the compressibility of the pore volume is important enough to be taken into account. Difficulties, however, arise in applying these experimental results to field cases. This is partly due to the fragmentary nature of the published data. Yet even if more complete data were available, the need for a theoretical background would be strongly felt. Such a background can be partially found in studies carried out by Biot,6,7 who published a theory of elastic deformations of porous materials and their influence on fluid displacement within the pores, by Lubinski8, who studied the stress distribution in an elastic porous medium neglecting pore compressibility, and by Gass-mann" who mathematically analysed the elasticity of packings of spheres. The contributions of Biot intro-duce a number of deformation constants which are impractical for reservoir rocks from an aspect of experi-mental determination. The theory developed by dass-mann is correct but difficult to read. It appeared, how-

Jan 1, 1958

By Eugene A. Alexandrov

The Minister of Geology of the Soviet Union P.Ya. Antropov, recently visited China and claims that this country occupies one of the foremost places in the world in reserves of tin, tungsten, molybdenum, antimony, iron ore, coal, and phosphates. Occurrences of economic value of chromite, nickel, gold, beryllium, tantalum, niobium, rare earths, and asbestos have also been reported. MINERAL RESOURCES Coal: The inferred reserves of coal are estimated at at 1,500 billion tons. A considerable part of the coal reserves is represented by coking coal, 80% of which is bituminous. Thicknesses of coal seams range up to 150 ft in the principal deposits located in northern and northeastern China. The total output of coal in 1958, 270 million tons, was produced by an army of 20 million people mainly in small mines operated by the agricultural communes. Modern hydraulic mining is applied besides primitive, obsolete methods and equipment

Jan 3, 1960

By R. C. Patterson

IN view of the circumstance that very few important changes have been made within the last 15 or 20 years in the equipment of rod and wire mills, the description of a new process introduced by Grenville Mellen, of Llewellyn Park, N. J., to take the place of the present laborious system of producing rods of lead, zinc, brass, copper, aluminum, etc., may be interesting to members of the Institute. This new process consists in the production of cast rods at one operation in a small continuous casting machine. The hot liquid metal is transferred from the melting crucibles directly into an endless chain of mold blocks in the machine, where solidification takes place, and the rod comes out continuously in a solid form at one end as long as the molten metal is supplied. The operation of these mold blocks so as to produce a solid rod of uniform structure constitutes an important part of Mr. Mellen's invention. The machine (Figs. 1 and 2), 12 ft. in height over all, 2 by 3 ft. in horizontal- cross-sectional area, and 6,000 11). in weight, has a framework of cast iron, holding in position two endless chains of mold blocks, which are made in sections and join in center alignment. The mold orifice is made up of these mold sections, into which the liquid metal flows. The molding chains are composed of steel blocks, grooved on one face to form the molding cavity, and linked together with flexible joints. Each block is carried on four rollers which guide the chain around the end sprockets and carry it in its course through the machine. The accuracy of alignment requisite to the production of a perfect rod in the mold groove formed by these sections is secured by careful machine work, and by building the four ways, down which the alignment takes place, so that two of the sides are fixed permanently, while the opposite sides are held to their position by spring pressure. The guides carrying the molds, while in casting position, are water-cooled square tubes.

Jan 5, 1915

By John. C. Reed

THIS paper presents briefly some of the principal results of 3 ½ months field work during the summer of 1938 in the Chichagof mining district, southeastern Alaska. The report is preliminary and presumably will be followed later by a more complete report to be published by the Geological Survey. The paper is concerned principally with the structural geology of a block of steeply dipping graywacke as revealed underground in the Hirst Chichagof and the Chichagoff mines, the two principal mines of the district. The two mines have produced about $16,000,000 worth of gold and silver. The attitude of the graywacke, which is locally cut by dikes and sills of aplite, is remarkably uniform and trends about N. 62° W. The average dip is about 67° SW. The graywacke is cut by large faults, the best known of which are the Hirst and the Chichagof, whose average trends are about N. 30° W. and average dips about 75° SW. The faults at some places split into the bedding of the graywacke and at others are deflected from their normal trends for considerable distances along the bedding. The relative movements along the faults was northwest and up at about 30° for the south-west or hanging-wall sides. The ore bodies are elongate quartz lenses in the faults. Most of the quartz is mineralized but locally large quartz masses are too low grade to be mined. The emplacement of the ore bodies appears to have been structurally controlled in large part by the intersections of the faults with the bedding surfaces. Places where the faults split or are deflected appear to have been particularly favorable places for ore deposition. There has been some post-quartz movements along the faults but it is thought that such movements have not been extensive enough to greatly modify the original positions and shapes of the ore bodies.

Jan 1, 1939

THIS paper presents briefly some of the principal results of 3 ½ months field work during the summer of 1938 in the Chichagof mining district, southeastern Alaska. The report is preliminary and presumably will be followed later by a more complete report to be published by the Geological Survey. The paper is concerned principally with the structural geology of a block of steeply dipping graywacke as revealed underground in the Hirst Chichagof and the Chichagoff mines, the two principal mines of the district. The two mines have produced about $16,000,000 worth of gold and silver. The attitude of the graywacke, which is locally cut by dikes and sills of aplite, is remarkably uniform and trends about N. 62º W. The average dip is about 67º SW. The graywacke is cut by large faults, the best known of which are the Hirst and the Chichagof, whose average trends are about N. 30ºW. and average dips about 75º SW. The faults at some places split into the bedding of the graywacke and at others are deflected from their normal trends for considerable distances along the bedding. The relative movements along the faults was northwest and up at about 30º for the south- west or hanging-wall sides. The ore bodies are elongate quartz lenses in the faults. Most of the quartz is mineralized but locally large quartz masses are too low grade to be mined. The emplacement of the ore bodies appears to have been structurally controlled in large part by the intersections of the faults with the bedding surfaces. Places where the faults split or are deflected appear to have been particularly favorable places for ore deposition. There has been some post-quartz movements along the faults but it is thought that such movements have not been extensive enough to greatly modify the original positions and shapes of the ore bodies.

Jan 1, 1939