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By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l'wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown

By Charles H. Behre

This paper deals with recent geologic studies in the slate belt of Northampton, Lehigh and Berks counties, Pennsylvania. The work was conducted under the auspices of the Pennsylvania Topographic and Geologic Survey. Three years have now been spent in detailed consideration of the economic geology of this region. In the field, particular attention was paid to the bearing of geology on quarry development and property valuation and the object of this paper is to summarize the results from that viewpoint. Excellent studies of a somewhat similar nature have already been carried out by Bowles,' but with the emphasis upon the details of quarrying and fabricating methods, rather than upon the geologic relations. The Northampton-Lehigh-BeRks District Location The region here discussed lies in east-central Pennsylvania and extends southwestward from Delaware River, on the New Jersey line, to the Schuylkill in north-central Berks County. It is an elongated belt occupying the northern sections of the three counties mentioned and lying along the southern edge of Blue Mountain. Its length is about 50 miles and its average width five or six, though in places it attains a maximum of 10 miles. There are no large cities in the region, but about 10 miles south are Reading, Allentown, Bethlehem and Easton. Railroads serving the slate belt are the Delaware, Lackawanna and Western, and the Pennsylvania along the Delaware River, the Lehigh Valley and Central of New Jersey along the Lehigh, and the Pennsylvania and Philadelphia and Reading on the Schuylkill. In addition, two railroads—the Philadelphia and Reading and the Lehigh and New England—cut obliquely through the slate region to reach the more isolated communities. Transportation facilities are thus excellent. The slate deposits of these three counties are conspicuously unified, both economically and geologically. In general type of marketable

Jan 1, 1928

By Joachim J. Hauser

Experiments on latent hardening were peyformed by compressing single crystals along a direction perpendicular to the tension axis. The slope and length of easy glide in the tension test were found to depend only on prior deformation in the same slip plane. Prior deformation on a different slip plane changes the stress level of the resulting stress-strain curve. The yield points appearing upon reloading after prior extension and unloading were related to the end of easy glide. SEVERAL researchers have studied the latent hardening due to deformation of a crystal by slip on a slip System after prior deformation. These experiments can be divided into those in which the prior deformation was on the same plane as the subsequent and those in which the two deformation processes were in different planes. In the former category are the experiments of Buckley and Entwistle,1 Parker and washburn,2 and Haasen and Kelly.3 The latter case has not been studied systematically; it was the main purpose of this investigation to produce this type of latent hardening and explain the results in terms of the existing theories of work hardening. In general, tension producing slip on a certain slip system can be preceded by tension, transverse compression or longitudinal compression, each with predictable dislocation movement and intersection. The intersection of dislocations can lead to glissile or sessile jogs, Cottrell-Lomer locks and other sessile dislocations. The effect on the stress-strain curve could depend on which combination of the former mechanisms is operating. Haasen and Kelly3 have studied the yield points which occur in aluminum and nickel single crystals upon reloading after prior unloading in a tension experiment. They attributed this effect to the anchoring of dislocations occurring during unloading. As Cottrell and stokes4 have shown that dislocations cutting through the "forest" could only lead to reversible changes, they attributed the anchoring to the formation of sessile dislocations during unloading. However, different kinds of sessile dislocations could be formed during unloading, and it was the purpose of this experiment to determine whether Cottrell-Lomer locks are responsible for the yield effect and for the end of easy glide. The case where a longitudinal compression is followed by tension along the same axis is commonly referred to as a Bauschinger test. This type of effect was studied by Buckley and Entwistle1 on aluminum single crystals and by Parker and washburn2 on zinc single crystals. In such a test, the tension and the compression activate the same slip plane with opposite slip directions. The use of sideways compression in the present experiments permits the activation of different types of slip systems and the study of their effect on the easy glide region and on the transition between the elastic and easy glide region. The theory of seeger5 for the flow stress in fee materials is applied to explain the latent hardening. EXPERTMENTAL PROCEDURE All the single crystals used in this investigation had an axial orientation close to <210>, called the "0.5" orientation. This is the orientation for which the tensile axis is 45 deg from both the slip plane and the slip direction. The single crystals were grown from the melt under a helium atmosphere using milled graphite boats,=at a rate of 8.6 mm per min. The silver used in the experiment was 99.98 pct pure. The single crystals had a square cross section about 0.9 by 0.9 cm and a length of 14 cm. The orientation of the specimen was determined within ±2 deg by the Laue back-reflection method. The specimens were annealed at 940&apos; ± 2°C in a helium atmosphere for 24 hr and then furnace cooled over a period of 7 hr. The specimens were electropolished in a solution of 9 pct KCN in water. The specimens were tested in a soft-type tensile machine (the load is prescribed) up to 3 pct strain. The stress was increased continuously at approximately 30 g per mm2 per min. The strain was measured over a 5 cm gage length with a mechanical extensometer employing an optical lever. The strain and stress were measured with accuracies of i 2 X 10-5 and ± 2 g per mm2, respectively. The remainder of the stress-strain curve up to 20 pct strain was obtained in a hard-type tensile machine (the strain rate is prescribed). The strain and the stress were measured in that machine with an accuracy of ±2 pct. The compression tests were performed in the hard-type machine using accurately machined steel blocks without lubrication. The blocks were used so as to apply a uniform compression over a length of 13 cm. The strains were measured on the hard-type machine and with a micrometer.

Jan 1, 1962

By J. E. Burke

RECENT investigations have elucidated many of the phenomena of the grain growth process, but have also revealed some conflicting and unexplained results. Beck and his co-workers1,2,3 have shown that grain growth continues with continued heating at one temperature until the average grain size approaches the thickness of the specimen, Plotting the logarithm of the average grain diameter, D, against the logarithm of the annealing time, t, they find the straight line relationship given by the equation: [D=Ktn [11] with possible small deviations at short annealing times. K and n are constants at constant temperature. On the other hand, Walker4 finds that, in alpha brass, the rate of growth falls off more rapidly than indicated by Eq I after long annealing, so that an equilibrium grain size is approached. Burke5 showed, using Walker&apos;s data, that time and temperature for grain growth are apparently related through an activation energy, H, according to the relationship: [t, Hr i &apos;_ III t„ = R \T, - ~) [2]] where t1 and t2 are the annealing times necessary for the average grain size to increase from Do to D at temperatures T1 and T2 and R is the gas laws constant. In the case quoted, H had the value 60,000 cal per mol. The apparent validity of this relationship, at least up to 700°C, and the approximate value of H were later confirmed by Beck.&apos; The results obtained by Beck, Kremer, Demer and Holzworth2 for aluminum and aluminum-magnesium alloys could not be satisfied by such a relationship, since the slope of the isothermal curves increased with increasing temperature. These data indicate and Beck, Holzworth and Hu6 later demonstrated experimentally that the only apparent factor controlling the rate of grain growth at constant temperature is the grain size. While many of the phenomena have been elucidated, a reasonably quantitative explanation of the process is lacking. There exists uncertainty even as to the primary driving force for grain growth, although there is a considerable body of indirect evidence that the interfacial energy of the grain boundary is responsible.7,8,10 Making implicit use of this assumption, several authors14,15 have pointed out that grain boundaries should migrate toward their center of curvature. Harker and Parker&apos; have advanced this concept furthest, and show that one can expect grain boundary migration to occur only when the grain faces are curved, or when they meet at non-equilibrium angles. When the face is curved toward a grain A, for example, the atoms in the surface of grain B, on the other side of the boundary, are on the average more surrounded by the atoms of their lattice than the atoms on the surface of grain A. Because of thermal motion, the atoms at the interface will sometimes be attached to grain A and

Jan 1, 1948

By Pierre I. Desré, Donald T. Hawkins, Ralph Hultgren

The torsion effusion method has been used to measure the vapor pressure of thallium over pure thallium in the temperature range 931" to 996&apos;k The resulting 100 cal per g-atom is in excellent agreement with previous values. Vapor pressures of T1 above seven Ag-Tl alloys ranging from 33 to 90 at. pct T1 were measured at 979K. Calculated silver activities show a positive deviation from Raoult&apos;s law, approaching ideality near the liquidus. Measured thallium activities scatter less than previous measurements using the electromotive force technique. Values for the silver component were calculated by Gibbs-Duhem integration. This paper reports the results of a study of the liquid Ag-T1 system by the torsion effusion method. The method has been discussed in detail previously1 and will be only briefly summarized here. The sample is contained in a cell which is suspended on a torsion wire. Vapors effusing from orifices on opposite sides of the cell exert a torque on the wire. The torque is related to the vapor pressure by the following relation: where D is the torsion constant of the wire, 4 the angle of torque, fl and f2 the correction factors determined by Freeman and seamy2 to account for orifice length, a1 and a2 the areas of the orifices, and ql and q2 the distances of the orifices from the axis of rotation. By using the same cell for pure thallium and the alloy, it follows that: so that most systematic errors are eliminated in determining the activities. EXPERIMENTAL 99.999+ pct T1 was obtained from the American Smelting and Refining Co. and 99.999 pct Ag was obtained from Cominco American, Inc. Seven Ag-T1 alloys, ranging in composition from x^\ = 0.33 to 0.90, were prepared by melting together weighed amounts of the pure metals in sealed, evacuated Vycor tubes and quenching the melts in water. The apparatus and graphite cells were the same as those used by Hawkins and Hultgren3 in their study of the Pb-Sn system. RESULTS Ten measurements were made on pure thallium in the temperature range 931" to 996K, and the results are presented in Table I. Values of were calculated using tabulated Gibbs (free) energy functions.4 No dependence of on temperature or orifice size was found, indicating that equilibrium was attained. Data for the Ag-T1 alloys are shown in Table 11. Values were smoothed with respect to composition by a plot of where . DISCUSSION The value = 43,520 * 100 cal per g-atom for pure thallium (95 pct uncertainty limit) is in excellent agreement with previous investigations.4 In the Ag-T1 system, this study shows positive deviations from Raoult&apos;s law at all compositions. Fig. l gives the phase diagram according to Hansen, and Fig. 2 presents the activity values measured in this study as well as those from electromotive force measurements at 950°K by Terpilowski, Kundys, and slaby.&apos;

Jan 1, 1969

By B. D. Lichter

The lattice parameters of zirconium and zirconium-oxygen solid solutions (hcp) were determined from measurements of back-reflection X-ray photograms obtained at 29°C using a symmetrical focussing camera. The following linear equations between parameters (c,a) in angstrom units (10-8 cm) and atom ratio (m) of oxygen to zirconium were obtained: c = 5.14764 + 0.2077m a =3.23168 + 0.1099m. The linear equations given are valid over the range 0 to 5 at. Pct 0. The accuracy of individual parameter measurements approaches the limiting accuracy determined by the spectral broadening of the incident characteristic radiation, and exceeds the accuracy of previously reported values. THE present work was undertaken in order to determine the lattice parameters of zirconium-oxygen solid solutions with an accuracy that allows quantitative determination of oxygen in zirconium. The results indicate that this is possible if very careful measurements are made, since the parameter change is only a few hundredths of a percent per at. pct 0.1, 2 In the present investigation the desired accuracy was achieved with large-grained samples using a back-reflection focussing camera and maintaining good temperature control during exposure. In addition a digital computer was used for calculation of the parameters by means of an analytical extrapolation.37 Suitable diffraction photograms were obtained from large-grained samples by using a modification of the technique described by Graf and Monteil.5 This consists of simultaneous rotation and oscillation of the specimen about two mutually perpendicular axes during exposure. Whereas, normally the upper limit of grain size is about 50 µ for useable diffraction photograms, this technique allows extending the upper limit of grain-size to exposure of a single crystal. EXPERIMENTAL Preparation of Alloys for X-ray Diffraction—Zir-conium, designated as hafnium-free, Westinghouse "Grade 1," was swaged from l/2-in.-diam crystal bar to 3/8-in.-diam rods. Substantially all of the hydrogen was removed from the zirconium by annealing at 1200°C in a high dynamic vacuum. The rods were then swaged to 0.2 in. diam without intermediate annealing, and 2 in. lengths were cut for alloying with oxygen. Samples for chemical analysis were taken from portions of the rods between each 2 in. length. Chemical analysis of the dehydroge-nated zirconium is given in Table I. Commercial tank oxygen (99.5 pct 0) was condensed in a liquid nitrogen-cooled trap, and part of the condensate was slowly reevaporated into 5-liter storage flasks. Nitrogen remained as a reactive impurity, and the calculated maximum increase in nitrogen content after a 5 at. pct 0 addition to zirconium was 50 ppm by weight. However, chemical analyses of several of the prepared alloys indicated that the maximum increase in nitrogen content was 10 ppm. The storage flasks, a Sieverts-type gas burette and manometer, and associated traps, pumps, and pressure gauges were connected through a glass high-vacuum manifold to comprise the gas addition system. A fused silica tube, connected to the mani-

Jan 1, 1961

By N. J. Grant, Hans Brunner

ThE materials used in this investigation were furnished by the Aluminum Co. of America and consisted of high-purity alurhinum (99.995 pct) and two aluminum-magnesium alloys containing approximately 2 and 5 pct Mg. The compositions of these alloys are listed in Table I. The materials were received as hot rolled 3/8-in. diam rods and were made from the same heats as the materials which were previously used in this laboratory.&apos;j3 The rods were cold swaged to 1/4-in. diam by 1 in. long, and then had two parallel flats machined over the gage length 0.085 in. apart. The test bars were annealed for 10 min at 700° F, and strained 1 pct in tension at room temperature. They were electropolished (80 pct acetic acid; 20 pct perchloric acid, 70 pct concentration) at a temperature of 60°F at approximately 20 v. A grid, transverse or square, spaced 0.2 mm apart, was impressed by rolling a fine threaded screw (128 threads per in.) across the flat surfaces. The depth of the grooves was less than 5 p. For final annealing and grain size control the specimens were enclosed in aluminum foil and sealed in Vycor tubes. Annealing conditions varied from 1 hr at 700° F to 5 days at 1050° F, depending on the alloy content, to give for most of the specimens a final grain size of about 1 mm. This treatment was followed by electropol-ishing as described above. For the test series presented in Figs. 4 and 5 round specimens were used instead of flat ones, and fine machining marks served as marker lines instead of the impressed grid lines. Electropolishing was omitted. The major advantage is that the spacing of the machining marks is only about 1 u as compared to the 200 u of the impressed grid lines, permitting higher precision in strain measurements. Unfortunately the strain annealing necessary for grain size control also resulted in some preferred orientation of the grains. The preferred orientation of three arbitrary specimens was measured by X-ray diffraction methods and the averaged results are shown in Fig. 1. The possible effects of the preferred orientation on the test results will be discussed later. The testing temperatures were 410°, 515", 725", and 940° F, with one exception in the case of the 5.1 pct Mg alloy. Since the solubility limit of this alloy is 520°F, a test temperature of 545°F was cho-se sen instead of 515°F. The selection of the test temperature was based on two considerations: 1) at 900°F and above, extensive grain boundary migration made it more difficult to measure grain boundary sliding; 2) at 400°F and below, there was so little grain boundary sliding that it was again difficult to make precise measurements. The stress was chosen to give a creep rate of approximately 2.7 pct per hr in connection with Figs. 2

Jan 1, 1961

By A. C. Emery

The physical and chemical properties for the metalliferrous feed materials to the Imperial Smelting Process blast furnace are defined and the means of achieving these properties by the sintering or briquetting routes discussed. Modern sinter plant performance data is included with a plant flow sheet showing draughting patterns. The necessity for ensuring an adequate SO2 content in sinter machine gases when roasting sulphide materials to enable conversion to sulphuric acid in a contact acid plant is described. The ability of the process to consume limited quantities of oxide materials, residues from other processes and other secondary sources is discussed. The argument for a briquetting route is developed out of this limitation and the merits of cold and hot briquetting examined. Development work on the hot briquetting route for this purpose is briefly described and several flow sheets outlining possible applications for hot briquetting to different raw material situations including the preparation of low lead charges for the furnace are presented.

Jan 1, 1977

By Charles George, Ronald Faul

The cementing process has been used in approximately 2.5 million oil and gas wells to seal, protect and isolate various downhole formations against communication. It has been adapted to other more specialized situations such as solution mining and sealing salt storage reservoirs. The technical literature contains very few papers specifically dealing with the cementing process for these applications, yet there have been many special projects in various parts of the world that are novel. These will be highlighted in this review. This paper also presents a comprehensive review of the various techniques used in cementing wells drilled for the recovery of soluble salts and brines. It also covers the application of cementing techniques to a large number of wells drilled for the storage of hydrocarbons in South Louisiana.

Jan 1, 1985

By Victor V. Damiano

THOMPSON1 proposed a very convenient nomenclature in which an imaginary regular tetrahedron was used to facilitate the analysis of dislocation interactions in fcc materials. The faces of the tetrahedron were constructed parallel to four different sets of (111) planes, and the six edges of the tetrahedron then represented the six 1/2 [110] Burgers vectors. The lines which joined the midpoint of a tetrahedron face with the ends of one of its edges represented the Burgers vectors of the partial dislocations into which the six 1/2 [I101 Burgers vectors dissociate. Using Frank&apos;s2 notation, all of the dislocations and their partial dislocations were identified and numerous possible interactions were postulated. The case of hexagonal crystals is unfortunately more complex, but it appears convenient to introduce a system similar to that of Thompson1 to describe the various slip planes and Burgers vectors encountered in cph structures. The system proposed has limited application but serves to identify the following slip systems {0001} <l20>, {1010} <1120>,

Jan 1, 1963

By F. J. Smit

The Tintic Division of Kennecott Copper Corporation operates the Burgin Mine in the East Tintic District near Eureka, Utah, approximately 75 miles south of Salt Lake City. The Division was organized in 1963 to develop concealed replacement orebodies in the area located by Bear Creek Mining Company, Kennecott&apos;s domestic exploration subsidiary. Several accounts of the discovery of these orebodies and the general geology of the area have been given (1, 2). The ore is very complex and of varying degrees of oxidation and alteration. The principal metal values are lead, zinc, silver, and cadmium. The Burgin No. 2 shaft was sunk in 1963 to provide access for mining the orebodies. Much of the ore mined after this shaft was sunk was high grade and shipped directly to smelters, but concurrently it was recognized that concentration would be required to upgrade the lower grade ore in the deposits. Accordingly, in January 1967, authorization was received to construct a 500 tpd concentrator. From the beginning it was expected that the characteristics of the mill feed would vary widely and unpredictably as mining progressed. This paper summarizes the characteristics of the ore, the test work upon which the plant design was based, the engineering and construction, and the present operation of the facility eighteen months after startup. ORE CHARACTERISTICS The Burgin ore is a complex assemblage of minerals from replacement of limestone. The replacement and alteration occurred in at

Jan 1, 1970

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport&apos;s scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By James A. Barr

The writer&apos;s first experience with flotation was during World War I, in the bene-ficiation of Alabama graphite schist ores. One plant used a cone with a peripheral overflow; dried ore was distributed by a rotating disk onto the surface of the water. No reagents were added&apos; The flake-graphite film floated along with some fine silica. Dewatering screens separated the flake. Naturally unit capacities were low but results were satisfactory. Minerals separation mechanical flotation machines were used in another graphite mill. pine oil was added directly to the head cells, with very good results. All the graphite concentrates from both types of flotation were carefully refined after drying by passing through burr mills, followed by very close sizing on sifters. In March 1927, the writer ran a very successful flotation test on minus 28-mesh, deslimed, Tennessee brown phosphate "sand,"† using a mechanical laboratory machine built in the shops of the Anaconda Copper Mining Co., through the courtesy of Ernest Klepetko. The machine was soon converted to a subaeration type, with improved results. This phosphate research program was greatly enlarged and led to the formation of the phosphate Recovery corporation. The development of nonmetallic flotation followed rapidly. The first flotation machine for bene- ficiation of phosphate was installed in January 1928, in a pilot mill, by International Minerals and Chemical Corporation, at Mulberry, Florida. These machines were Minerals Separation, 24-in., sub-,,,tion types, with weir control of pulp between cells. The sand bleeders were very small—about 1¼-in. diameter. As the feed flake. Is to 25 per cent plus 28-mesh material, the cells choked up frequently. This was corrected by cutting a 2 by 6-in. bleeder opening above the impellers, at grid level, which short-circuited the coarse fractions directly into the feed of the next cell. The matter of size classification and grinding was a considerable problem, which does not come within the scope of this article. Because of the troubles noted above, cascade-type roughers were installed in the second flotation plant, built about 1930. Experimental cells had been tried in 1928. General plant layout is shown in Fig. 1 and details of the cascade construction in Fig. 2. The cascade installation in plant NO. 2 gave good results and eliminated troubles due to choke-ups and coarse feed. The capacities and metallurgical results equaled those of the modified 24-in. Minerals Separation flotation machines in plant No. I The objections to the cascade installation are the floor space and mill height required. In 1939 an improved Minerals Separation machine was tested in parallel with the cascades. Extensive tests indicated

Jan 1, 1947

By James A. Barr

The writer&apos;s first experience with flotation was during World War I, in the bene-ficiation of Alabama graphite schist ores. One plant used a cone with a peripheral overflow; dried ore was distributed by a rotating disk onto the surface of the water. No reagents were added&apos; The flake-graphite film floated along with some fine silica. Dewatering screens separated the flake. Naturally unit capacities were low but results were satisfactory. Minerals separation mechanical flotation machines were used in another graphite mill. pine oil was added directly to the head cells, with very good results. All the graphite concentrates from both types of flotation were carefully refined after drying by passing through burr mills, followed by very close sizing on sifters. In March 1927, the writer ran a very successful flotation test on minus 28-mesh, deslimed, Tennessee brown phosphate "sand,"† using a mechanical laboratory machine built in the shops of the Anaconda Copper Mining Co., through the courtesy of Ernest Klepetko. The machine was soon converted to a subaeration type, with improved results. This phosphate research program was greatly enlarged and led to the formation of the phosphate Recovery corporation. The development of nonmetallic flotation followed rapidly. The first flotation machine for bene- ficiation of phosphate was installed in January 1928, in a pilot mill, by International Minerals and Chemical Corporation, at Mulberry, Florida. These machines were Minerals Separation, 24-in., sub-,,,tion types, with weir control of pulp between cells. The sand bleeders were very small—about 1¼-in. diameter. As the feed flake. Is to 25 per cent plus 28-mesh material, the cells choked up frequently. This was corrected by cutting a 2 by 6-in. bleeder opening above the impellers, at grid level, which short-circuited the coarse fractions directly into the feed of the next cell. The matter of size classification and grinding was a considerable problem, which does not come within the scope of this article. Because of the troubles noted above, cascade-type roughers were installed in the second flotation plant, built about 1930. Experimental cells had been tried in 1928. General plant layout is shown in Fig. 1 and details of the cascade construction in Fig. 2. The cascade installation in plant NO. 2 gave good results and eliminated troubles due to choke-ups and coarse feed. The capacities and metallurgical results equaled those of the modified 24-in. Minerals Separation flotation machines in plant No. I The objections to the cascade installation are the floor space and mill height required. In 1939 an improved Minerals Separation machine was tested in parallel with the cascades. Extensive tests indicated

Jan 1, 1947

By E. W. Engelmann

A NEW and interesting type of drier has been developed and operated at the Magna plant of the Utah Copper Co. for the past year for the drying of a filtered concentrate in the molybdenum recovery plant of this company. The several units installed have ranged from 12 to 30 in. in width, and from 14 to 30 ft. long. Their economy was immediately apparent after the first one was installed. The machine is not only low in capital cost, but has proved efficient for the drying of fine concentrate at low operating cost. The Utah vibrating drier consists of a steel conveyor trough supported on flexible reeds from a structural steel foundation anchored in concrete. The steel pan, which is also the drying surface, is vibrated by a heavy Utah electromagnetic vibrator fastened either to the head or discharge end of the pan. The vibration thus obtained agitates the material and causes it to be conveyed over the heated surface.

Jan 1, 1938

By R. L. Hadley, G. Derge

The amounts of oxygen in liquid iron-titanium alloys up to 50 pct Ti were measured and the oxide phases in equilibrium with these alloys were determined by using TiO² crucibles. A minimum of about 0.003 pct 0 occurs at less than 1 pct Ti. The various liquid and solid oxide phases can be arranged on a ternary isotherm. THREE characteristics of titanium contribute to the interesting aspects of its reaction with oxygen in liquid iron: 1—It forms a number of stable oxides. 2—All oxides have large negative free energies of formation. 3—The pure metal exhibits high solubility for oxygen. In addition, the use of titanium as a stabilizing and strengthening element in alloys suggests a need for investigation of its reactions in amounts greater than those normally required for deoxidation. These higher compositions are also of interest because they occur during the addition of ferroalloys and produce deoxidation products before dilution is achieved. Titanium Deoxidation in the Literature While the use of titanium as an alloying element and deoxidizer has been common for several decades, the first detailed study of its deoxidizing characteristics was carried out by Wentrup and Hieber&apos; in 1939. These authors determined the extent of deoxidation possible with titanium and identified, by microscopic examination, the products formed. They found that titanium in excess of 0.2 pct did not reduce the oxygen content of iron below 0.004 pct at 1600°C. They identified the spinel FeO-TiO² at low titanium concentrations and Ti2O³ in melts containing more than 0.2 pct Ti. A portion of the area surveyed by Wentrup and Hieber has been investigated recently by Evans and Sloman² using X-ray diffraction for inclusion identification. They concurred in general with the findings of Wentrup and Hieber, but reported the existence of Ti³O5 as a deoxidation product in the range near 0.1 pct Ti. Comstock, Urban, and Cohen³ discussed the deoxidation of iron with titanium, correlating the data of Wentrup and Hieber with free-energy data for the titanium oxides. Scatter at high titanium values was considered attributable either to the formation of an oxide exhibiting high solubility in liquid iron or to the entrainment of solid oxide particles leading to high apparent solubility. Chipman&apos; has calculated the deoxidation curves for titanium based on free-energy data for titanium oxides. These calculations (Fig. 1) and those of Comstock, Urban, and Cohen involve assumptions as to the activity coefficients of oxygen and titanium in liquid iron, since such data have not been determined. Investigation of the deoxidizing characteristics of chromium" and vanadium0 have shown that these elements decrease the activity coefficient of oxygen in liquid iron, leading to a tendency toward relatively high oxygen values and experimental scatter in highly alloyed melts. Experimental This investigation involved two major objectives: 1—determination of the composition of the oxide phases in equilibrium with liquid Fe-Ti alloys, and 2—establishing the pattern of oxygen solubility in liquid Fe-Ti alloys at titanium concentrations in excess of that required for attainment of minimum oxygen content. Raw Materials Ingot iron was used having the following composition: 0.02 pct C, 0.017 pct Mn, 0.01 pct Si, 0.02 pct S, 0.006 pct P, and 0.03 pct 0. The titanium used

Jan 1, 1956

By Dr. Hermann Wedding

Albert Ludwig Serlo was born February 14, 1824, at Crossen-on-the-Oder. After completing his school-studies and his training as a mining official, he received in 1851 an appointment as Royal Manager of salt-works (Salinenfactor) and member of the Administratioll of Salines at Konigsborn, near Unna, Westphalia. The issue of new regulations for the training of higher State officials in the Department of Mining, Metallurgy and Salines, led him to pass in 1856 a special examination for the rank of Assessor, in consequence of which he was called to Berlin, to serve for a few months as an assistant in the Ministry of Commerce, which had charge of mining, etc. In the same year he became Bergmeister and member of the mining administration at Bochum, Westphalia, and in 1858 Oberbergrath and member of the provincial administration, called the Oberbergamt, having its headquarters located at Dortmund. In 1861 he was appointed Director and head of the newly-reorganized mining

Jan 1, 1900

By J. H. Swisher

HIGH-temperature anneals in wet hydrogen are widely used in research as a technique for decarburiz-ing Fe-C alloys. This technique is also used commercially in processing low-carbon steels for magnetic applications. The results of some calculations to be presented show that for temperatures up to 1100°C there is a critical temperature for maximizing the decarburization rate of alloys containing about 0.1 pct C. The low-temperature portion of the iron side of the Fe-C phase diagram1 is reproduced in Fig. 1. Preliminary calculations show that the critical temperature is between 727" and 905°C. In this range, the alloy contains two phases during heat treatment, ferrite and austenite. Decarburization therefore occurs by a process termed "diffusion accompanied by a phase change".&apos; For intermediate stages of decarburization, the carbon concentration profile in a flat plate is shown in Fig. 2. The carbon content increases linearly from zero at the surface to a value, cB , at the two-phase boundary. cB is known from the phase diagram, see Fig. 1. At the interface where x = 5, the carbon content increases to ci, the initial concentration in the alloy. smith3 has derived an equation which describes the rate of movement of the boundary. With a rearrange-

Jan 1, 1969

By H Pray, H. W. Russell, Paul D. MILLER

It is known that austenitic chromium-nickel steels that have free carbide in the grain boundaries are subject to intergranu-lar corrosion. It is difficult to detect such a susceptible condition in a fabricated article because present test methods require a sample section for examination and in most cases this is difficult to obtain. The question of the nature and prevention of intergranular corrosion in austenitic stainless steels has been ably discussed by Bain and co-workers1-3 and by other investigator4-10 The present methods of study subject samples to corrosive conditions in such reagents as the Strauss solution, a mixture of copper sulphate and sulphuric acid. Such tests usually require at least 72 hr. to run. Various methods of measuring the degree of sensitization have been employed, such as the measurement of electrical resistivity, magnetic measuremerits, measurement of the degree of cracking produced on bending over a malldrel, and microscopic studies. The detection of carbides at the grain boundaries by metallographic polishing and etching methods is tedious and requires a skilled operator. A recent report on such methods of carbide detection is given by the American Society for Testing Materials Subcommittee VI of Committee A.-1011 and by Arness.12 The present investigation was undertaken to develop a simple test procedure for detecting carbide precipitation or susceptibility to intergranular corrosion. The test is designed for use in the plant and for the testing of fabricated structures. Carbide precipitation, the factor leading to susceptibility to corrosion, is produced by heating the alloy in the temperature range 800° to 1600°F., as in welding, in improper annealing or in service where such temperatures are met. The connection between such precipitation and susceptibility to corrosion has been thoroughly discussed, as has been the use of stabilizing addition elements to prevent precipitation. Experimental Method A small area of the steel under test is subjected to an anodic treatment in a cell that can be &apos;lamped Onto a a Or an actual structure. The cell and electrical circuit used are illustrated in Fig. I. The cell C is lead, joined to the steel plate D and insulated from it by a short piece of rubber tubing E. The cell is forced tightly against the steel plate by a spring Or clamping device. The seal formed by the rubber against the steel plate is sufficient to retain the liquid bath inside the cell. The spot treated can be made any shape desired, depending on the shape of the rubber gasket. The cell illustrated polishes a circular spot about 3/8- diameter&apos; The bath consists of 60 per cent (by weight) sulphuric acid to which is added 5 ml. per liter of Glycyrrhiza extract (U.S.P.). The cell requires about 2 to 2.5

Jan 1, 1941