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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 G. R. St. Pierre, M. J. Pool, R. Speiser

The activities of chromium in solid Cr-Ti solulions contaitning from 10 to 90 at, pct Cr were measured over the temperatutre range 1250" to 1380°C. The Knzudsen effusion technique with direct weighing of the Knudsen cell was used. This was possible because the vapor pressure 0f chromium is about 600 times greater than the capor pressure of titanium so that the amount 0f titanium effusing could be neg-Lected. the activities of titanium were determined by g-raphical integration of the Gibbs-Duhertz equatiotz. The solutio~ls sllcdied exhibited positive deviations from Raoult's law, but they approached ideality as the temperature was raised from 125 to 138t C. The integral free energy of mixing was calclated from the activity values. AF has a maximum value of - 1.66 kcal a1 1390°C and a composition oj 55 at. pcl Cv. The free energy of formation of 'TiCr, is —0.76' lzcal a1 1250°C. The heats and entropies of mixing usere determined using the second law and thus tile mlues could be in error by a considerable amount. The Cv-Ti system is not a regular solution. ThE increasing emphasis on application of various models to alloy formation and solution behavior has led to an intensified interest in the thermochemistry of alloys. In a majority of the cases where different models have been applied the alloy system used was a simple one. However, the amount of data available on more complicated systems is small and in order to fully understand the behavior of metallic solutions more experimental work has to be carried out on these systems. The Cr-Ti system is reasonably complex and even though this system was being investigated as early as 1937 by Kroll,' no previous work has been done on the thermodynamic properties of either the liquid or solid state. This research was undertaken to determine the thermodynamic properties of solid Cr-Ti alloys. EXPERIMENTAL PROCEDURE The experiments on the Cr-Ti system were carried out in a water-cooled metal vacuum system. This system is composed of a brass vaporization chamber wound with copper tubing for cooling purposes, a brass liquid-nitrogen trap, an oil diffusion pump, and a Duo-Seal forepump. The pressure in the system is measured with an ionization gage. The interior of the vaporization chamber is shown schematically in Fig. 1. The Knudsen cell is supported by the molybdenum tripod, and a magnetically operated shutter is provided to protect the Pyrex sighting glass against deposition of metallic vapors in the intervals between temperature measurements. Heating is accomplished by means of a 20-kw 450-kc Westinghouse oscillator. The susceptor in this case is 10-mil tantalum seamless tubing which also forms the outside of the sample container. The remainder of the sample container consists Of an im~ervims re-crystallized alumina crucible and a 10-mil-thick tantalum lid. Two holes are drilled in the lid. The diameters of these holes were measured with the calibrated stage of a "Tukon" microhardness tester. The thicknesses were measured with a micrometer. A Leeds and Northrup disappear ing-filament optical pyrometer was used to measure the temperature. This is sighted through the smaller of the two holes in the lid and corrections for the emissivity of the sample were not necessary since the ratio bf cell length to hole diameter was large enough to insure a hohlraum. The pyrometer was calibrated at the ~~t~~~l Bureau of Standards, and the correction for the Pyrex sighting window was determined in the laboratory. The titanium used in this investigation was obtained from Mallory-Sharon and the chromium from The Union Carbide Metals Co. The reported purities were

Jan 1, 1968

By T. D. Murphy, G. V. Henderson

The element silicon, with its usual partner, oxygen, plays the same role relative to inorganic materials as carbon and hydrogen play with respect to living organisms. The crystallographic structure of silicon dioxide (SiO2) consists of one atom of silicon well-nigh inseparably bonded to four contiguous atoms of oxygen, a gas of but slightly more than half its atomic weight, forming a three-dimensional network of SiO4 tetrahedra (Dietz, 1968). This wispy arrangement is the fabric of the mineral quartz which is one of the harder, more abrasive, and chemically stable raw materials to be found in Mother Nature's cupboard. Most of us are vaguely familiar with the observation that nearly 60% of the lithosphere to an approximate depth of 10 miles is composed of these two elements, which proportion actually rises to about 75% if the atmosphere, hydrosphere, and biosphere are included (Parker, 1967). Elemental silicon is a brittle steel-gray metalloid with a density of 2.42 and does not occur in nature. In its limited commercial form, which is still brittle and metallic in appearance, its density drops to 2.33. It combines with oxygen to form the gaseous oxide SiO, or the solid dioxide Si02 (analogous to its congener carbon in CO and CO2); a tetrachloride SiCI4 (analogous to CC14); or, combining with oxygen and one or more metal ions, forms the largest rock-making family of all, the silicates. Further, next to the feldspars, quartz is the most abundant known mineral and, in some form or another, accounts for roughly 12% of surficial terrestrial rock. It is this so-called "free silica" to which your attention is chiefly directed in this chapter. In any such consideration of silica, its several crystalline phases with their attendant differing physical properties appear worthy of delineation. Alpha quartz is the only one of this interesting polymorphic family that is thermodynamically stable at normal pressures and temperatures up to about 573°C. The low phases of tridymite and cristobalite can exist in the so-called metastable state below 117° to 200ºC but seldom occur in nature in these two different crystal forms (Sosman, 1965). Opaline silica, now considered by most researchers to be a variety of cristobalite, occurs in abundance and is the only exception. The three remaining polymorphs, keatite, coesite, and stishovite, also are metastable under ambient conditions. Keatite, however, is not known to occur naturally and has only been synthesized in the laboratory. The other two have been identified in submicron sizes and in microscopic amounts, occurring naturally as a result of high order shock-wave pressures generating quite elevated temperatures --such as might accompany the impact of a large meteorite on a hard sandstone terrain (Chao et al., 1962). An intriguing characteristic of these silica minerals, and one which has very practical applications, is their extremely variable densities. The classic 2.65 specific gravity of alpha quartz drops to 2.20 in tridymite, cristobalite, and lechatelierite (natural silica glass), as well as in many man-made glasses of commerce which are merely noncrystalline or amorphous solids in the form of super-cooled liquids which can no longer change their shapes (Pauling, 1950). It rises again to 2.50 and 2.93 for keatite and coesite, respectively, and finally becomes a reported 4.35 for stishovite-nearly a 50% range in density for the known physical combinations that silica naturally assumes (Frondel, 1962; Konnert et al., 1973; Pecora, 1960). Pursuing its esthetic aspects, briefly, silica is well-represented among gem stones which, to qualify as such, must have the attributes of beauty, durability, and rarity (Jahns, 1983). As quartzose gems usually have but one or, at

Jan 1, 1983

By G. E. Keller, G. D. Coe

Several methods have been devised for rapid determination of sulfur in coal using a high-temperature combustion furnace. The fundamental principles of the various methods are similar but the techniques vary widely. The method described herein is no different in principle from some of its predecessors but varies considerably in technique. Originally devised to overcome the low-accuracy criticism leveled against the others, the tube-furnace method has proved successful for limited applications. Work is being done to widen the applicability of the technique. Subsequent to the work of A. Vita1 in 1920, a number of investigators have published data dealing with the rapid determination of sulfur in coal using a high-temperature combustion furnace.2-5 These, together with several unpublished methods, involve wide differences in technique although they are all similar in principle. Investigation of typical details of procedure showed that poor precision or accuracy could be attributed to one or more of the following: 1) inadequate quantity of sample to be representative, 2) a delivery tube temperature too low to confine condensation to a washable area of the tube, 3) no provision for back washing the delivery tube, 4) incomplete absorption of the sulfur compounds due to inadequate bubbler, and 5) the false assumption that all of the sulfur is evolved as sulfur dixoide. The method herein discussed is no different in principle from some of its predecessors; the differences are in technique. Although the method is rapid—a determination can be completed in 5 min— accuracy has riot been sacrificed in order to achieve speed. MATERIALS AND EXPERIMENTAL WORK Fig. 1 shows the arrangement of the equipment. A metered volume of oxygen is passed through calcium chloride for removal of moisture, then through Ascarite for removal of carbon dioxide, and thence through a glass tee to the feed end of the combustion tube. Connected to the side arm of the glass tee is a rubber tube that is closed with a pinch clamp during combustion of a sample. The products of combustion are expelled through a Vycor bubbler, the end of which is submerged 3 cm below the surface of a 1 pct hydrogen peroxide solution contained in a 300 ml high-form beaker. At the completion of the 4-min combustion period the contents of the beaker are titrated to a yellow end point, using a methyl red indicator, with 0.05 N sodium hydroxide (or sodium tetraborate). The pinch clamp on the tube leading from the tee in the oxygen line is then opened and mouth suction applied to draw the hydrogen peroxide up into the bubbler past the ell, almost to the rubber tube connecting the bubbler to the combustion tube. This washing of the bubbler is repeated until no further acid reaction with the indicator is obtained. The hydrogen peroxide-sul-furic acid solution is then titrated to the final yellow end point. Test work conducted at the Robena Laboratory disclosed the following critical conditions that had important bearing on the precision of the method: Weight of Sample: Several series of tests wherein the sample weight ranged from 0.1 to 0.5 g of -60 mesh coal showed that the lowest variance (standard deviation squared) resulted from the use of 0.5-g samples; the variance was slightly greater when 0.3-g samples were used, and with less than a 0.3-g sample weight the variance increased rapidly with decrease in weight. Although the use of a 0.5-g sample invariably resulted in a very slight explosion as soon as the sample entered the hot zone of the combustion tube, this did not detract from the precision of the method. Temperatures: Mott and Wilkinson5 found that a combination of low temperature (1250°C) and low oxygen flow rate (less than 700 ml per min) tended to give high results due to formation of oxides of nitrogen. Although the method herein employs a much higher oxygen rate than 700 ml per min, as an additional precaution to assure accurate results, 1315°C (2400° F) is recommended as the most desirable furnace temperature. The temperature of the elbow of the bubbler should be at least 75°C to minimize condensation

Jan 1, 1961

By C. H. Li, R. J. Stokes, T. L. Johnston

Dislocation half-loops, artificially introduced by sprinkling with carborundum, were subjected to stress using three-point loading. The different stages of loop expansion and multiplication were then correlated with the macroscopic stress-deflection curve. Loop expansion started at approximately one-third of the "yield stress," defined here as the motivation stress. Above one-half of the "yield stress" simple multiplication commenced while about two-thirds of the yield stress gross multiplication developed short slip-line segments. These values were not affected by the age of surfaces exposed to both dry and wet air. Slip was not detected on unsprinkled crystals below two-thirds of the "yield stress." Thus the stress to activate intrinsic sources, defined here as the activation stress, was approximately twice the motivation stress. This relationship was independent of the strain rate used. It is concluded that lattice resistance takes the form of a viscous drag rather than a static type of force. THE importance of surface condition and environment as one of the more significant factors controlling the mechanical properties of ionic solids has recently received renewed attention.1-4 In some materials, notably the alkali halides, exposing freshly cleaved specimens to the atmosphere results in a progressive hardening and embrittlement of the crystals. This has been attributed to the surface layer becoming "aged," thereby restricting the motion of dislocations in such a way that pileup and eventually fracture results. It is necessary therefore in studying the mechanical properties of ionic crystals to inquire first into the density and distribution of dislocations in the normal cleaved surface and to understand the role these dislocations play in the onset of plastic flow. Knowledge of the effect of environment on this behavior will then assist in understanding the mechanism of embrittlement on aging. In the work reported here a method is described for studying the initiation of plastic flow from dislocation sources in the surface of magnesium oxide crystals. Preliminary results are described of the influence of surface age on this behavior. EXPERIMENTAL TECHNIQUES The magnesium oxide used in this investigation was obtained from the Norton Co. and had a nominal purity of 99.5.pct. Single-crystal specimens, having dimensions typically 1/4 by 1/8 in. cross section and 1 in. in length, were prepared by cleavage over (100) planes from the parent crystal. They were deformed under three-point loading with 3/4 in. spacing between the two end supports and a constant rate of deflection at the center of 0.001 in. per min. The maximum strain rate therefore was 1.5 X 10-5 sec-1. Reasons for choosing this particular form of loading will become apparent in a later section. In addition, a number of confirmatory type tests have been performed at higher loading rates where the maximum strain rate was increased to 1 x 10-3 sec -1. Following deformation the crystals were etched to reveal the dislocation distribution. In a previous paper5 we described a satisfactory etching solution consisting of 5 parts of saturated ammonium chloride, one part of sulfuric acid, and one part distilled water. Immersion of the crystals for 1/4 hr at room temperature developed reproducible conical etch pits at the points where dislocations emerged through the surface. It should be mentioned that dislocations freshly introduced by room temperature deformation gave sharply pointed etch pits which generally distinguished them from the almost flat-bottomed pits obtained on "grown-in" dislocations. The distinction is obvious in the photomicrograph included in Fig. 5(b). Annealing crystals at 1000°C for 12 hr on the other hand gave sharper etch pits on the grown-in dislocations and the distinction was no lower -possible; a similar observation has been reported for lithium fluoride. We have succeeded furthermore in chemically polishing magnesium-oxide crystals. Boiling in fresh 85 pct ortho-phosphoric acid for only 1 min resulted in a microscopically smooth surface which could again be etched to reexamine the dislocation distribution. This boiling time was sufficient to remove the surface damage introduced by cleavage (see next section). SURFACE DISLOCATION SOURCES There are a number of ways by which dislocations may be introduced into cleaved surfaces to act later

Jan 1, 1960

By G. Das, S. V. Radcliffe

The substructural features developed in tungsten as a function of annealing temperature (up to 2200°C) and type of material [undoped and doped powder metallurgy (PM) tungsten and electron beam melted tungsten] have been investigated by transmission electron microscopy. For doped PM tungsten wires, characteristic "par-ticulate" substructural features developed rapidly with increase in annealing temperature above 700°C. The features consisted of parallel rows of elongated or circular shapes (500 to 1000A diam) lying along the direction of the wire axis and were identified as internal voids by diffraction contrast experiments. In recrystallized doped PM rod, larger voids were observed and were identified by precision dark field analysis to be cubic in shape and bounded by (100) planes. In marked contrast with both the doped PM materials, recrystallized undoped PM rod exhibited only very occasional and randomly arranged voids. Furthermore, no voids were observed in either material after electron beam melting. The high concentration of voids in the doped PM materials is attributed primarily to vaporization of doping additions or their pvoducts situated at the original grain boundaries , whereas the few voids in undoped material are considered to be traces of microporosity which were not eliminated during sintering. A tentative mechanism is suggested for the dezlelopment of the voids in relation to the processing sequences (sintering and working) and to the subsequent annealing. In recent years, a characteristic substructural feature consisting of rows of small elongated or circular regions of light contrast lying along the direction of working has been seen in thin foil electron microscopy studies of annealed sheet, wire, and rod tungsten. These features were present in the published micrographs of sheet by Weissmann et al.1 and of wire by Meieran and Thomas2, although the authors did not draw attention to them. Wronski and Fourdeux3 observed similar features in sintered rod tungsten (it was not specified whether or not the material was doped*) and interpreted them on the basis of their ap- particles, based on extraction replica evidence from the fracture surface of the initial hot-rolled slab material from which the sheet was prepared. No diffraction contrast experiments on the features were reported in any of these studies. The present investigation was undertaken with the primary objectives of: a) identifying the nature of these substructural features in tungsten by electron diffraction contrast experiments, since the contrast for voids can be expected to differ from that for crystalline or glassy particles, and b) elucidating the origin of the features and their development. For the latter purpose, doped and undoped powder metallurgy tungsten was obtained as rod and wire to represent different stages of reduction during final processing. These materials were examined both in the as-processed condition and after annealing to successively higher temperatures. In addition, the same doped and undoped materials were examined after vacuum melting in rod form. I) MATERIALS AND PROCEDURE Doped powder metallurgy (PM) tungsten wire (commercial purity 99.9 pct W) was obtained in the as-drawn and surface ground condition (0.030 in. diam "ground seal rod"). Doped and undoped tungsten rod (0.075 in. diam) representing an earlier stage of final processing was obtained from the same commercial source (Refractory Metals Division, General Electric Co.). Lengths of both the doped and undoped rod materials were single-pass melted in an electron-beam zone refiner to examine the effect of vacuum melting on the substructure. Annealing was carried out in a tungsten crucible in a tantalum strip resistance furnace under a vacuum of l0-15 mm Hg. Longitudinal sections of the wire and rod materials were examined by light and electron microscopy. The preparation of thin foils suitable for electron transmission from 0.030 in. diam tungsten wire and the rod specimens was carried out by means of a high-precision microjet technique developed to provide lack of jet stability and precise control of the area thinned. The method is described in detail elsewhere.' The foils were examined in a JEM 6A electron microscope using a goniometer stage (±20 deg tilt, 360 deg rotation) and operated at 100 kV. To minimize contamination problems a 200 µ condenser aperture was used in conjunction with a useful beam current of 50 µA. II) RESULTS AND DISCUSSION A) Diffraction Contrast Analysis. In order to determine the optimum conditions for the development of the substructural feature, a series of isochronal 30 min annealing experiments were carried out on specimens of the doped PM tungsten wire. The transmission electron microscopy analysis showed that the as-drawn wire, Fig. 1(a), consists of 'fibers' whose long axis is closely parallel to the wire axis of (110). The fiber width averages some 0.5 µ. Dense disloca-

Jan 1, 1969

Jan 1, 1923

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962

By O. C. Holbrook, George G. Bernard

A new theoretical treatment has been obtained for the behavior of pattern waterflood injection wells when closed in. Two cases are treated: Case I where oil and water are assumed to have the same properties, and Case 2 where they arc different. In applying the method, one plots log (p — p,) vs closed-in time, where p is well-bore pressure at any tims and p, is static pressure. The value of p. is determined by trial and error as that value which makes the plot linear at large time. A value for the permeability-thickness product can be determined from the intercept of this linear part, and a value of the skin factor from the injection pressure at time of closing in. Application of the method to data from water floods at three fields seems to give reasonable results. For the case of unit mobility ratio, it is proved that this new method should give the same value for permeability-thickness product as the conventional pressure build-up method. In addition, the new method gives correct values for static pressure, whereas the conventional method does not, often indicating negative static pressures. The new method may be used in cases where the surface pressure persists after closing in as well as in cases where it does not. INTRODUCTION It is of considerable interest and importance to be able to determine the characteristics of the reservoir in an area surrounding a water injection well. Thus, if we can determine early in the life of an injection well that there is a considerable "skin effect", remedial measures can be started before a full-scale pattern flood begins. Similarly, if it can be shown that a gradual buildup of skin effect is occurring with time, measures to free the water of plugging material can be taken. Determination of static pressure in the water-injection well may show that the water is entering a thief zone and not the desired reservoir. Finally, determination of the permeability of the sand around the injection well will allow estimation of the future relation between injection pressure and rate. It should be possible to determine average reservoir permeability, skin effect and static pressure from pressure fall-off data. However, at the time we began work on this subject, it was thought that no adequate theory on which to base such determinations' was available. According to the conventional method which considers the reservoir to be filled with one fluid of small compressibility (see Van Everdingen, Joers2, and Nowak2), shut-in pressure is plotted vs log where is injection time, and At is closed-in time. The physical significance of injection time, may well be questioned in this case, since in a reservoir completely filled with a single fluid (as required by this theory) and with input and output rates equal, the pressure behavior after an initial transient is independent of t,. Attempts by our Tulsa area to use this theory led to negative values of static pressure in most cases. Because of these limitations of the method discussed above, it was decided to attempt to develop a new theory of pressure behavior in water injection wells, one which would apply when there is a gas saturation, as is so often the case in water floods. In the following treatment the assumptions and basic equations are given first, then the method of application of the equations. A complete example is given to clarify details of application. All difficult mathematics has been placed in the appendices so that the reader can follow the text without difficulty. However, if he wishes only to apply the results without knowing the basis for them, he can learn how to do this from reading only the sections entitled "Plotting of Experimental Results" and "Example." ASSUMPTIONS AND BASIC EQUATIONS Statement of Problem It will be assumed that a horizontal layer of constant thickness contains in its pore system a mixture of oil, gas and water. While water is being injected into this pore- system through a well at constant rate, an oil bank is built up, gas being expelled from the space taken by the oil as shown in Fig. 1. The saturations within each

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of liquid Mg-Ge alloys have been determined between 1000°and 1500°K by an isopiestic method. Germanium specimens, heated in a temperature gradient and contained in covered graphite crucibles of special geometry, were equilibrated with magrtesium vapor in closed titanium tubes. The crucible design allowed free access of magnesium vapor to the samples during the equilibration to form alloys of magnesium and germanium, but prevented magnesium losses from the crucibles on quenching the titaniuin tubes to terminate the experimental runs, thus preserving the equilibrium alloy compositions. The activities and partial molar enthalpies of magnesium and the integral thermodynamic properties of the system were calculated from the experimental data. THE Mg-Ge phase diagram' shows one congruent melting compound, Mg2Ge, of essentially stoichio-metric composition, two eutectics, and very limited terminal solid solubilities. Very little information is available on the thermodynamic properties of the Mg-Ge system. The free energy of formation of Mg,Ge was recently deter-mined2 by a Knudsen cell technique in the temperature range 610° to 760°C. The standard enthalpy of formation of Mg,Ge was measured calorimetrically by Bever and coworkers.3 The present study was undertaken as part of a general investigation of the thermodynamic properties of the homologous series of Mg-Group IVB systems, i.e., Mg-Pb,4 Mg-Sn,5 Mg-Ge, and Mg-Si. An isopiestic technique was used which was developed by the authors5 for investigating the thermodynamic properties of liquid Mg-Sn alloys. Specimens of the nonvolatile component, contained in covered graphite crucibles, are heated in a temperature gradient in an evacuated and sealed titanium reaction tube, and equilibrated with magnesium vapor of known pressure. The method employs crucibles of special geometry which preserve the high-temperature equilibrium composition of liquid alloys having a highly volatile component such as magnesium on termination of the experimental runs by quenching the crucibles to room temperature. EXPERIMENTAL PROCEDURE First reduction germanium of 99.999+ pct purity (Eagle-Pitcher Co., Cincinnati, Ohio) and 99.99+ pct magnesium metal (Dominion Magnesium Ltd., Toronto, Canada) were used. The graphite crucibles were machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non-reactivity of graphite with germanium at the temperatures used in this study had been previously established by Scace and Sleck.6 The experimental procedure has been previously described in detail.5 The selection of a particular crucible geometry for a run was determined by a combination of imposed experimental conditions, the principle being that more tightly covered crucibles were required to preserve alloy compositions during quenching when higher magnesium pressures and higher specimen temperatures were used. Depending upon the composition range of the equilibrated alloys the source of the magnesium vapor was either pure magnesium or a two-phase mixture of Mg2Ge + Ge-rich liquid of known magnesium pressure. The experimental runs can be divided into the following three groups on the basis of crucible geometry and magnesium source material. Crucibles with Small Holes and Pure Magnesium Reservoirs. The crucible dimensions were identical to those of the Mg-Sn investigation5 except that the hole diameters were reduced to 0.010 in. because of the higher temperatures and higher magnesium pressures involved in the Mg-Ge system. During an equilibration run, magnesium vapor diffused from the reservoir to each specimen through the small holes, one drilled through the crucible lid and two others drilled through graphite baffles positioned vertically inside the crucible between the lid hole and the specimen. Since the magnesium pressure was high, i.e., in the range 117 to 277 Torr, during the equilibration time of approximately 24 hr, equilibration was not impeded by these holes. A specimen composition at equilibrium was fixed by the relative temperatures of the specimen and the reservoir, and by the thermodynamic properties of the system. Upon brine quenching the titanium reaction tube to end a run the vapor pressure of magnesium above the liquid alloys decreased exponentially with decreasing temperature, and the small cross-sectional areas of the holes (4.9 x 10"* sq cm) drastically reduced magnesium losses from the crucibles. Because of its low vapor pressure, germanium losses from crucibles during a run were at most 0.2 mg for pure germanium and correspondingly less for the alloys. This crucible geometry satisfactorily retained the equilibrium alloy compositions on quenching for magnesium-rich (from 3 to 33 at. pct Ge) alloys provided their temperatures were below the melting

Jan 1, 1967

By S. G. Epstein

Using the capillary-reservoir technique, electromi-gvation rates of cadmium and indium in liquid bismuth were measured at several temperatures. The electric mobility of cadmium Jrom 305° to 535°C and indium from 310° to 595°C can be expressed as a function of temperature by the equations UIn = 1.52 x 10-3 exp sq caz per v-sec Migraion of both solutes was cathode-divected at a rate rnore than four tiMes tHAt previously found for siluer in liquid bisnmth. The electric mobilities of cadmium and indiulrz in liquid bismuth at 500° C are nearly identical with their respective mobilities in mercury at room temperature. AS part of a systematic study of the variables which are considered to control electromigration in liquid metals, the electromigration rates of cadmium and indium in liquid bismuth have been measured. Mass transport properties of silver in liquid bismuth have been reported previously,&apos; and measurements of tin and antimony in liquid bismuth are forthcoming. Comparisons will be made with literature values for these same solutes in mercury.2&apos;3 This series of solutes was selected to determine the effect of the solute valence on its electromigration. Silver, cadmium, indium, tin, and antimony have nearly equal atomic masses but have chemical valences ranging from +1 to +5. They are all fairly soluble in bismuth above 300°C and all have radioactive isotopes, which are an aid in making analyses. EXPERIMENTAL TECHNIQUE Electromigration of cadmium and indium in liquid bismuth was measured by the modified capillary-reservoir technique previously described.&apos; In this method irradiated cadmium or indium is added to bismuth to form alloys containing about 1 wt pct solute (<2 at. pct solute). Several quartz or Pyrex capillaries: 1 mm ID and 5 cm long, vertically oriented, are simultaneously filled in the reservoir of the liquid alloy. A direct current is passed through two of the capillaries, which contain tungsten electrodes sealed in the upper end. The other capillaries sample the reservoir during the experiment. After a measured time interval the capillaries are removed from the reservoir and rapidly cooled. The glass is then broken away from the solidi- fied alloy, which is then weighed, dissolved in acid, and analyzed for solute content by chemical and radiochem-ical techniques. An electric mobility (velocity per unit field) can be calculated from the amount of solute entering or leaving each capillary by the simplified expression1 in which Ui is the electric mobility of the solute, ?mi the solute weight change, Ci the solute concentration of the reservoir, I the current, p the alloy resistivity, and l the duration of the experiment. This expression is valid as long as the experiment is terminated before a concentration gradient develops across the capillary orifice. Earlier experiments showed that the concentration gradient formed initially at the electrode changes with time and eventually reaches the orifice, due to back-diffusion. This condition produces a solute exchange between capillary and reservoir by diffusion or convection, opposing the electromigration, which results in a lower measured value for the electric mobility. To determine if the concentration gradient had reached the orifice, the capillaries used in some of the experiments were sectioned at 1-cm intervals and the solute content of the alloy from each section was radiochemically determined. A typical concentration profile for an experiment with indium in bismuth is shown in Fig. 1; cadmium in bismuth showed similar behavior. As illustrated in the graph, very little back-diffusion has occurred in the capillary containing the cathode, since the concentration gradient is confined to the upper 1 cm of the capillary. In the capillary containing the anode, however, the concentration gradient is much broader, extending nearly to the orifice, even though the net change in solute concentration is nearlv the same in both capillaries. Since cadmium and indium probably lower the density of bismuth when alloyed, depletion of the solute from the alloy adjacent to the anode would increase the density of the liquid in the uppermost region of the capillary. This would give rise to convective mixing within the capillary, causing the broadened concentration gradient. Conversely, the alloy adjacent to the cathode should have a reduced density as the solute concentration is increased by migration, explaining the "normal" concentration profiles found in these capillaries. This disparity was not found for electromigration of silver in bismuth. Both metals have similar densities at the operating temperatures, and nearly symmetrical concentration profiles were found in the two capillaries of each exueriment. This density effect was also apparently encountered when an attempt was made to measure diffusion coefficients for indium in liquid bismuth by the same technique which was successfully used to measure diffusion of silver in bismuth.&apos; Capillaries 1 mm ID and 2 cm

Jan 1, 1968

By H. I. Aaronson, C. Laird

The kinetics of thickening and of lengthening of ?&apos; plates in an Al-3.93 pct Cu alloy in the temperature range 203" to 300" C were determined by means of transmission electron microscopy. The rate of thickening was found to be less than that allowed by volume diffusion control at all temperatures, by amounts which increased with decreasing temperature, in agreement with the predictions of a general theory of precipitate morphology.1 Thickening was treated on the basis of the ledge mechanism. Ledges were deduced to spread across the broad faces of ?&apos; plates at volume dzjrfusion-controlled rates, as anticipated from the disordered structure of their edges. Lengthening of 8&apos; plates, on the other hand, took Place more rapidly than allowed by volume dzjrfusion. This occurred despite clear morPhological evidence of a bmrier to growth at the edges of these plates. It was concluded that the misfit dislocation structure comprising the barrier requires that lengthening take place by a jog mechanism. The tnisfit dislocations, however, also serve as diffusion short circuits, and allow high overall lengthening rates to be achieved. In Part I&apos; it was shown that, within the range of aging temperatures and times studied, the broad faces of 8&apos; plates formed in Al-4 pct Cu are fully coherent with the a, matrix. Virtually .all of the dislocations present in these faces were found to have developed as a result of plastic deformation in the a phase. Such dislocations are thus "intruders", rather than the more usual misfit-compensating variety. The edges of 8&apos; plates were confirmed, by extension of the earlier studies of Mat-suura and Koda,3 to be made up of edge-type misfit dislocations, in sessile orientation with respect to lengthening of the plates. These interfacial structures should cause 8&apos; plates to thicken and to lengthen at rates less than those allowed under the condition of volume diffusion control, such as would be expected if the interphase boundaries had disordered structures.&apos; The narrow width of 8&apos; plates, the reproducible crystallography of their broad faces, and the appearance of these plates in cross section as octagons rather than as circular discs2 provide qualitative support for these deductions. The present study of the rate of thickening and the rate of lengthening of 8&apos; plates was undertaken in order to examine them on a quantitative basis. I) THICKENING KINETICS OF THE BROAD FACES OF?&apos; PLATES A) Literature Review. The measurements now available on the thickening kinetics of single-phase precipitate plates consist of one plot of the thickening of a proeutectoid ferrite plate in an Fe-C alloy,&apos; showing (as predicted) thickening rates less than those allowed by volume diffusion control. B) Experimental Procedure. Details of the preparation of the 4-3.93 pct Cu alloy used in this study have been previously reported.4 As in Part 1,&apos; transmission electron microscopy was the observational tool employed. A general description of the apparatus and procedures of the electron microscopy studies is given in Section I of Part I. In thin foils, 0&apos; plates tend to form at and parallel to the foil surface.&apos; A direct investigation of the thickening process by means of hot-stage transmission electron microscopy was therefore not feasible. It was thus necessary to use the conventional method of aging individual bulk specimens for a wide range of different times at the various temperatures studied. In each specimen, the thicknesses of a number of plates were measured. Since thin foils prepared from "bulk-aged" material contain a large proportion of grains with orientations near (001) , it was relatively easy to find, near the edges of the foils, the characteristic multifold patterns of intersecting extinction contours which indicate regions where the foil is exactly at an (001) orientation. The thicknesses of large numbers of plates were measured along the (200) branches of the "stars" so that the 8&apos; plates were precisely parallel to the optical axis of the microscope. Wherever possible, intersecting extinction contours were adjusted with the parameter s > 0 to improve the visibility of the plates in bright-field illumination. These precautions, in combination with taking the measurements at the thinnest parts of the foils, minimized the errors in the measurement of the thickness of the plates resulting from inexact parallelism to the electron beam. Since the plates were very thin, it was not easy to measure their thickness on the photographs. The techniques of enlargement and of microdensitometry were employed to minimize errors from this part of the measurement. A further source of possible error, that the plates can appear thicker because of contrast associated with mismatch normal to the plane of the plate, was also considered. The images of the plates were usually thinner than those of dislocations, however, and no anomalous changes in apparent plate thickness were observed when regions of foil containing plates were tilted through various diffracting conditions. Any error from this cause must therefore be small. Other sources contributing errors were: a) the microdensitometer traces per se and the subjective estimates of their peak limits, and b) slight fluctuations in magnification associated with small changes in the current of the objective lens of the electron microscope. The overall error probably amounted to no more than 5 to 10 pct. In order to obtain readily interpretable data on thickening kinetics, it is essential that the diffusion fields of adjacent ?&apos; plates not be allowed to overlap. Calculations&apos;-&apos; showed that this condition is definitely not ful-

Jan 1, 1969

By John S. Brown

IN 1925 the writer undertook a detailed statistical study of all producing areas in the Joplin district as a basis for evaluating programs and measuring objectives. For this purpose, the published figures in the yearly volumes of Mineral Resources were used, supplemented for earlier years by publications of the Missouri Geological Survey and other local and less official sources. When all else failed, the available data were projected backward to hazard a reasonable guess as to the unrecorded early output of important areas. Fortunately, the proportion of such prehistory production is not a large factor in any of the totals. These results were used during the next few years to measure the relative importance of various producing areas and to predict the peak period of development of the all-important Picher field. For the purpose of this review, the charts have been completed to the end of 1950. During World War 11, the U. S. Bureau of Mines became interested in a similar study and issued comprehensive statistical tabulations of data up to 1945 ( Info. Circular 7383), which have been checked against the figures used herein. This tabulation, however, does not include all the earlier data used by the writer nor does it offer any estimates of the wholly unrecorded era in the beginnings of the earlier camps. The area covered in this study is shown in Fig. 1 on which are indicated the relative location and approximate outlines of the principal producing camps. This also shows the approximate yield to date of each major camp in terms of combined lead and zinc concentrates. The output of zinc concentrates is roughly seven times that of lead. Hence, the economy of the district has depended primarily on the price of zinc, with lead as an important byproduct. Over much of the productive period, lead concentrates averaged about twice the value of zinc concentrates per ton, and in certain mines or areas the proportion of lead to zinc was substantially above average. The Joplin district is largely flat prairie but is partly moderately dissected, partially wooded land with a relief generally less than 100 ft. The rocks are almost flat-lying, nearly parallel to the surface, and the chief ore formation is the Mississippian Boone limestone, including its cherty phases. This formation either outcrops in the producing areas or is covered by a thin veneer of Pennsylvanian shales. Virtually all the ore occurs within 400 ft of the surface, and a large part at less than 300 ft in depth. Most of the land was divided into small farms or town lots before mineral development; tracts seldom exceeded 160 acres, and averaged considerably less. Mineral rights followed the surface ownership, segregation was rare, and a system of leasing for mineral development became well established early in the region&apos;s history, many landowners deriving small to sizable fortunes from royalties. Because of the shal-lowness of the ore and other factors, prospecting and mining was cheaper than in almost any comparable mining district in the United States. This situation, coupled with the widely divided land ownership, offered a fertile field for promoters and speculators and led to the rise of many small mining concerns. Only in its later history, under stern economic compulsion, has control tended to centralize in a few companies. Under these conditions, any important new discovery or successful development had much the effect of a gold rush or an oil boom. Every property in the area was leased quickly, promptly drilled, and, if ore was found, it was soon on the market. Many companies and individuals participated, and the average producing lease-hold probably was about 40 acres in extent. Any important field thus was attacked by anywhere from 10 to 100 or more producers. Production zoomed, eventually steadied or wavered, and ultimately subsided, leaving a desolation of tailings mountains, cave-ins, empty housing, and wreckage. The object of this paper is to depict the pattern of this process, so far as metal production is concerned, and to note the way in which it reacted to economic and political pressures. Production Charts In Fig. 2 is charted the production record, in tons of lead and zinc concentrates combined, of eight of the principal camps, which together account for approximately 99 pct of the total district production, over the years from 1870 to 1950. This period covers all but the very minor beginning of mining history. Two important camps are divided by state lines; hence, it has been necessary to combine production records for the two portions, based on estimates that may be slightly in error. Certain camps are sub-dividable into important units for which separate figures are available in whole or in part and have been charted as fractions of the major unit. The corresponding price of zinc is shown above all the charts. Three camps, Aurora, Neck City, and Galena, show a remarkably symmetrical graphic pattern, which is interpreted as the norm. The curves rise steeply to a peak, level off for an irregular interval, and then drop sharply to zero on a slope corresponding roughly to that covered by the initial rise. The three portions of these charts seem appropriately characterized by the designations of youth, maturity, and decline. On the whole, with some irregularities, the production in each of the three periods seems to be almost equal. A fourth camp, Granby, fails to conform to the normal pattern. It exhibits a very long period of reasonably uniform, stabilized production corresponding to maturity, followed by a rather precipitate decline. Its youth is hidden in the era of prehistory. This habit of steady, long-continued production at an even keel is attributable to the fact that this camp, more than any other, was controlled largely by a single principal owner at any given period over most of its history and this permitted the imposition

Jan 1, 1952

Jan 1, 1923

By Morris Muskat

A theory is presented for calculating the performance history of complete water-drive systems producing from idealized stratified formations. The general equations are applied to systems where the permeability stratification is either of the exponential or linear type. Calculations were carried through for different degrees of permeability stratification, but with special emphasis on the effect of the mobility ratio between the produced oil and the invading water on the resultant performance. These results are also expressed graphically as curves for the initial water breakthrough recovery, for the different degrees of stratification, as a function of the mobility ratio, and of the composition of the produced fluid stream as a function of the cumulative oil recovery. For several typical cases the latter has also been plotted as a function of the cumulative oil and water throughflow. The general result is that when the mobility of the oil is lower than that of the invading water the channelling tendency resulting from the permeability stratification becomes aggravated as the higher permeability zones become flooded out. Situations of this type would obtain when producing low gravity or highly viscous oils. Conversely, if the mobility of the oil is high compared to that of the invading water, the flooding of the high permeability zones will lead to a retarding and choking effect, and the gross bypassing phenomena will be partially suppressed. These conditions would correspond to those of flooding high gravity or low viscosity oils. A discussion is given of the various basic assumptions made in the analysis, including that of ignoring the stripping phase of the production history as implied by relative permeability concepts. INTRODUCTION The physical ultimate recoveries from oil reservoirs are basically determined and limited by the physical oil displacement processes associated with the reservoir producing mechanism. In practice, however, the economic ultimate recoveries are further limited by the mobility of the reservoir fluids and the uniformity and continuity of the producing formation. In fact, it is the differential depletion between the component parts of the composite reservoir which ultimately determines the total recovery at the time of field abandonment. While this observation applies to both the solution gas drive and gravity drainage mechanisms, in which use is made only of the energy contained within the original oil-bearing reservoir, it is of even more paramount importance under operations wherein the energy associated with extraneous fluids provides the ultimate oil expulsion mechanism. Whether the invading fluid is the water from an edgewater drive, water injected for pressure maintenance, gas injected for pressure maintenance, or gas returned to the formation in a cycling program, it is often the continuity and uniformity of the producing section which will control the economic efficiency of the operations. The importance of the problem of reservoir non-uniformity does not, of course, lessen its complexity or the difficulties of its solution. In fact, these are inherently such that the concept of a "general" solution is virtually meaningless. About all that can be reasonably hoped for is the analysis of specific and well-defined types of non-uniformity which may give some degree of approximation to actual reservoir conditions. Since variations in the nature of the reservoir which depend only on the position along the streamlines will not lead directly to major differential depletion development within the reservoir, the types of non-uniformity considered thus far have involved stratification assumptions. That is, the producing section has been replaced by a multi-layer "sandwich," each uniform areally, and differing from the others only in its basic physical constants as to thickness, porosity and permeability. The fluid motion in the composite system is thus approximated by a parallel superposition of the independent fluid movements in the individual strata. For the specific application to cycling operations the theory of the effect of permeability stratification has been developed for both discontinuous&apos; and continuous types of permeability stratification. Among the latter, treatments have been given of systems in which permeability distributions are governed by exponential, linear&apos; or probability3 functions. In all these studies complete dynamical equivalence was assumed between the injected dry gas and the displaced wet gas. The overall effective permeability of each stratum was therefore considered as constant and independent of the degree of invasion of the injected fluid. In the case of the displacement of oil by water, the assumption of dynamical equivalence between the water and oil will be strictly valid only by accident. Even if the oil viscosity should be the same as that of the water, the effective permeability to the oil in the presence of the connate water will in general be quite different from that of the water behind the water-oil interface flowing past the trapped residual oil. As a result the effective permeability for the stratum as a whole and rate of water invasion will change with time as the intrusion continues. The differential fluid motion in the individual strata will thus also vary with time. Qualitatively, it is easy to predict the resultant effects. If the permeability to viscosity ratio of the invading fluid exceeds that of the fluid displaced, the stratification and bypassing effect of the perme-

Jan 1, 1950

By A. D. Zunkel, A. H. Larson

Equilibrium arsenic contents of Pb-As alloys in contact with PbO-As2O3 slags containing less than 30 mol pct As2O3, were determined at 650°, 700: and 750 C in an inert at?rzosphere. In this temperature range, the arsenic content of the alloy increased with increasing temperature in the single-phase liquid slag region and decreased with increasing temperature in the two-phase slag region and the single-phase solid-solution slag region. The PbO-As2O3 phase diagram below 22 mol pct As2O3 was determined by thertrzal analysis and by application of a log ?As2O3/?PbO vS log XAs2o3 /x3pbO plot determined from the equilibrium actiuity data. The resulting phase diagram was not well-defined since the eutectic temperature was not detected in the thermal analysis experiments, although a region of terminal solid solubility of As2O3 was found. Results from the phase diagram determination are compared with an existing diagram in the literature. THIS experimental investigation is an extension of a study by the authors1 on the slag-metal equilibria in the systems concerned with commercial lead refining processes such as softening and dross fuming. The first part of this investigation was a study of the slag-metal equilibria in the Pb-PbO-Sb2O3 system. The only experimental work previously done on the Pb-PbO-As2O3 system was by Pelzel2,3 in which the phase diagram for the PbO-As2O3 system was determined below 50 wt pct As2O3 and the equilibrium constant for the reaction 3Pb + As2O3 + 3PbO + 2As was determined as a function of temperature. No slag-metal equilibrium data have been determined. It is due to the scarcity of information regarding the Pb-PbO-As203 system that this work was undertaken. This paper describes the determination of the slag-metal equilibria in the Pb-PbO-As203 system by equilibrating Pb-As alloys with PbO-As2O3 slags in an inert atmosphere, the effect of 1 wt pct additions of bismuth and copper on the slag-metal equilibria, and the PbO-As2O3 phase diagram both by thermal analysis and the use of the slag-metal equilibria data. EXPERIMENTAL Materials. The materials used in this investigation were analytical reagent-grade and assayed as follows: 1) 99.8 pct PbO (0.014 pct insoluble in CHJCOOH, 0.02 pct not precipitated by H2S, 0.1 pct CaO, and 0.08 pct SiO2); 2) 99.95 pct As2O3; 3) 99.99 pct Pb; 4) 99.0 pct As; 5) 99.99 pct Cu; and 6) 99.97 pct Bi. Room-temperature X-ray patterns revealed no detectable impurities in any of these materials. Apparatus for Equilibrium and Thermal-Analysis Determinations. The resistance-heated crucible furnace used in this investigation employed nichrome elements and was mounted so that it could be raised to surround the reaction tube during each experiment and, subsequently, lowered. A schematic diagram of the apparatus is shown in Fig. 1. Each charge was heated in a 3+-in.-OD by 31/2-in.-high 416 stainless-steel crucible placed in a 41/4-in.-1D by 18-in.-long fused-silica reaction tube which was closed at one end. On a shoulder around the crucible was placed a 3: -in.-OD by 12-in.-long open-end fused-silica condenser tube. The open end of the reaction tube was covered by a water-cooled brass cap with ports for 1) admitting an inert atmosphere to the system through a stopcock, 2) introducing a stainless-steel, motor-driven, paddle stirrer into the crucible, 3) evacuating the system with a mechanical vacuum pump, and 4) sampling the melt with Vycor sampling tubes. The brass cap was fitted to the open end of the reaction tube with a silicone gasket and collar clamp. The furnace temperature was controlled by a Barber-Coleman Capacitrol controller and a chromel-alumel thermocouple. Due to the corrosiveness of the melt, the controlling thermocouple also served as the measuring thermocouple. The temperature of the melt was calibrated against the controller temperature and was checked periodically during each test with a Vycor-enclosed calibrated chromel-alumel thermocouple. The temperature measurement and control can be considered accurate to ±3°C. Procedure. The charge placed in the crucible for each experiment consisted of 1000 g of Pb-As alloy and 300 g of PbO-As2O3 slag. The crucible was then placed in the reaction tube, the condenser tube was placed on the shoulder of the crucible, the silicone gasket and brass cap were fitted on the open end of the reaction tube, and the entire system was evacuated and filled with argon ten times. After the last flushing, a positive argon pressure of 1 psig was impressed on the system. The furnace was then raised to sur-

Jan 1, 1968

By R. S. French

THE purpose of this paper is to present data that have been obtained during the past two years concerning the effects of prior cold-work and temperature and time of anneal upon the recrystallization and grain growth of 70-30 cartridge brass. It was desirable to study certain of these phases so that an accurate picture of the principles of the subject could be shown. The work is not intended to provide explicit annealing data, but to provide material examples that may help to clarify analogous problems concerning this alloy. Specifications often set limitations upon the grain size of annealed materials because of the importance of grain size upon subsequent manufacturing operations. It was, therefore, worth while to study the variables that affect the recrystallized grain size of this material. C. H. Mathewson and A. Phillips,1 W. R. Webster,2 and others have presented annealing characteristic curves of this alloy. A recent typical curve presented by R. S. Pratt3 is shown in Fig. I. The tensile properties and grain sizes are shown as functions of the annealing temperature. Such curves serve as a useful guide in determining the physical properties of annealed material, but as they are made generally under carefully controlled laboratory conditions they do not indicate the performance of metal annealed in a mill muffle, where conditions are different and the amounts of metal require necessarily longer heating times and temperatures. Study of the effect of time and temperature upon grain growth and subsequent recrystallization was made with a coil of metal having the following analysis: 70.04 per cent copper; 0.007 lead; 0.007 iron; 0.00 tin; 0.00 silicon; 0.001 nickel; 0.000 phosphorus; balance zinc. The sample coil was obtained from metal that had been rerolled from hot-rolled mill stock, and was received at 0.228-in. gauge, soft, with a grain size of 0.125 mm. This material was then rolled 43.5 per cent to 0.125-in. gauge and annealed to a 0.053-mm. grain size. In this condition, samples were cut and used in all of the experimental work reported in this paper. TIME The first study was of crystal growth at a constant temperature over a moderate length of time. Material was cut from the stock coil at 0.129-in. size and rolled 75 per cent hard to 0.032-in. gauge. From this piece small samples were cut ½ by 2 in., suitable for grain-size determinations. Twelve samples were placed in an electric furnace uniformly across the width, approximately an inch from the floor, A thermocouple was wired to the center sample, so that the approximate metal temperature could be followed. At various

Jan 1, 1944

By R. C. Padfield

Experience over a 3-year period in Bethlehem Steel Corporation&apos;s plants has demonstrated the reliability of open-hearth roofs of bonded sprung-arch constructzon with burned basic brick. The design principles lor constructing these roofs include a minimum hot-strength requirement for the basic brick, expansion allowances that extend the full roof thickness, structural members to control arch contour, and a specified minimum roof rise. The greater stability of bonded roofs is explained in terms of the basic stress patterns of ring constrution and bonded construction. PRIOR to the development of successful sprung-arch roofs of basic brick, the majority of open-hearth furnaces in the United States were operated with sprung-arch roofs built of silica brick. Although many silica roofs used on open-hearth furnaces were ring-arch construction, Bethlehem Steel Corp. used bonded-arch construction because of its greater stability. In ring construction, each ring of brick is separately keyed and comprises an independent arch with the straight joints between rings traverse to the longitudinal axis of the furnace. In bonded construction, the bricks are laid in rows starting from the skewbacks so that the straight joints run parallel to the longitudinal axis of the furnace. Each brick in a given row is laid so that it spans the joint between two bricks in the row beneath it. Thus, the transverse joints across the arch are broken and the arch rings are thereby interlocked or bonded. When basic roofs were first being developed, the basic brick that were available had low hot strength. Such brick could not be safely used in sprung-arch construction without some means of suspending them. With the development of higher firing techniques by brick manufacturers and the recently introduced direct bonded bricks with high hot strength, the use of burned basic brick in sprung-arch roofs became feasible. The availability of high hot strength basic brick coupled with the potentially lower cost and proven stability of bonded construction prompted Bethlehem&apos;s Research Department to study the possibility of using basic brick in bonded roofs. With the full cooperation of plant ceramic engineers and open-hearth superintendents, particularly in 3 years of fur-nace trials, we developed the design criteria for bonded roofs and the corresponding property requirements for the basic brick that are discussed in this paper. DESIGN PRINCIPLES OF SPRUNG-ARCH BRICK ROOFS Stresses in Fixed Arches. A sprung-arch open-hearth furnace roof is generally built on rigidly held skewbacks. The constraint of the fixed support at each end adds a bending moment to the horizontal and vertical reactions at the ends of the arch. Fig. 11 shows the positive direction of forces acting on an arch fixed at both ends. Fixed arches can be analyzed when the members are continuous and have elastic properties. However, brick are inelastic, and arches built with individual brick segments cannot carry tensile stresses. Therefore, for practical solution of brick arches, empirical formulas have been derived from elastic theory that place design restrictions on arch dimensions to avoid development of tensile stresses. McDowell2 cites three main conditions for stability in sprung brick arches: 1) the thrust line of the arch should be maintained in the middle third of the thickness to avoid tensile stresses and resulting open joints in inner and outer curves of the arch; 2) the angle between the line of thrust at any joint and a line perpendicular to the joint must not exceed the angle of repose between brick; and 3) the maximum pressure at any point must not exceed the strength of the arch materials at furnace operating temperatures. The first and third conditions are particularly important in designing sprung-arch basic roofs because of the comparatively low hot strength of basic brick. According to McDowell&apos;s equation, if the thrust line is maintained within the middle third of the arch thickness, the unit pressure is obtained as follows: where p = unit pressure in psi, F, = resultant thrust normal to skewback in pounds per foot, t = arch thickness in inches, and z = distance in inches of thrust line from arch axis. When the resultant thrust normal to the skewback acts along the arch axis, z equals zero and unit pressure is simply the thrust divided by the cross-sectional area. If the thrust line moves to the limits of the middle third of the arch thickness, beyond which tensile forces would develop, z then equals one-sixth of the arch thickness and the unit pressure is double that when the thrust line is acting

Jan 1, 1968

By Van Der Muelen P. A.

SOME time ago, the writer received from W. 0. Borcherdt, Manager of the, works of the Bertha Mineral Co. at Austinville, Va., several specimens of a dense yellowish slag-like material, containing cavities showing clear needle-like crystals, and representing a product formed by the fumes of zinc oxide and basic lead sulphate from the oxide furnace, attacking the firebrick lining of the flues. The matrix, which is of a greenish-yellow color, is made up chiefly of an amorphous glass, carrying numerous crystals, the latter being well-defined, clear, and transparent, but colored a very light yellow by small amounts of ferric oxide. A number of the crystals were carefully separated from the matrix and tested with the blowpipe. They have a fusibility of about 2, yield a globule of lead and a coating of lead oxide before the blowpipe on charcoal, and contain some zinc. Their hardness is 5 to 6. 1 Fig. 1. Under the microscope the crystals appear to be made up of a prism, with narrow faces, and a fairly large pinacoid, but unfortunately show no terminal faces (Fig. 1). Between crossed nicols they gave parallel extinction in. the three planes containing the crystallographic axes, and are therefore orthorhombic. The index of refraction is high. A number of the best crystals were measured on the reflection goniometer, the angles given below representing the average of measurements made on different individuals. mm = 46° 52&apos; mb = 66° 34&apos; a:b:c = 0.4334:1 :?

Jan 5, 1917

By Charles F. Park

Mining in the Pacific Coastal Region has passed through three stages of development. First came the gold rush days, a period when gold and silver were the objects of intensive search. Second was the development of the high-grade base-metal deposits and of the smaller and more refractory precious metal deposits. And third was the modern period that covers the discovery and development of the rarer metals, of large low-grade deposits, and of the industrial and nonmetallic minerals. Brief discussions of the salient geologic features of the region and of a few of the better known mineral deposits are given. The regional geology is favorable for continued exploration and discovery of new deposits and districts.

Jan 1, 1968