Search Documents

By R. O. Williams

Measurements have been made of the internal energy of deformation in a Cu-A1 alloy and a Cu-Zn alloy as the deference between the work and the released heat. The method required the rapid compression of samples to reduce thermal interactions. The rate of energy storage is low initially but then becomes almost linear with strain. Both alloys stored about 60 cal per mole at a strain of 0.4 in the recrystallized condition. The fractional rate of storage increases at low strains reaching about 0.25 at a strain of 0.15 and then decreases slowly with increasing strains. As do pure metals, these alloys release appreciable energy immediately following deformation; in contrast with pure metals, however, the release continued for extended periods of time. This energy release is somewhat sensitive to the amount of deformation, the deformation temperature, and prior thermal & eatment. It is believed that this release is a composite of that observed in pure metals which has been attributed to dislocations and that due to the motion of vacancies which produces increased short-range order. IT is expected that changes brought about by deformation of a pure metal can be understood in terms of the three defects—dislocations, vacancies, and interstitials—along with the interactions possible between these defects. Frequently stacking faults are created and must also be considered. 1t is not immediately clear whether or not the stress fields which are created should be regarded as independent of dislocations. For alloys there is the important additional effect of atomic configuration, for example short-range order, which must also be considered and will, in general, interact with each of the above defects. While it is true that a complete understanding of pure metals is not yet possible, it would seem very valuable to establish the similarities and differences between pure metals and alloys. Such knowledge could contribute to the understanding of both. A study of the changes in internal energy resulting from deformation of two alloys is reported here. Although some information has been available for alloys almost as long as for pure metals, the volume of work has been substantially less. Sato' and Quinney and Taylor' were responsible for the earlier work, both using brass and annealing calorimetry. tizhnova' studied stored energy in Cu-Ni alloys by a method somewhat similar to the one reported here. Bever and his co-workers have made extensive studies of Au-Ag alloys4'5 and more recently CU-AU'U' using solution calorimetry. Clarebrough et a1.' have recently studied brass using annealing calorimetry. EXPERIMENTAL METHOD The present results were obtained by the rapid, adiabatic compression of a sample about 1/4 in, diam by 1/2 in. long between two tungsten carbide hammers. A vacuum provided thermal isolation and oil provided effective lubrication between the sample and hammers. The increase in internal energy is the difference between the mechanical energy and the heat liberated within the sample. The mechanical energy was determined from the velocity of the hammers (calculated from the height through which the hammers traveled) and was essentially constant for each deformation cycle. The heat was determined from the temperature increase of the sample which was measured by an embedded thermocouple. Specific heat data were calculated from Neumann's rule using tabulated data for pure metals.9 Since the fraction of the energy which is stored is large compared to that for pure metals, specific heat data of high accuracy are not required. Successive increments of deformation were carried out by repeating the procedure, the limit being determined mostly by the decreasing accuracy caused by the increasing corrections and the decreasing storage of energy. About five cycles were used to give a true strain of about 0.5 while the time interval between cycles was 1 to 2hr.

Jan 1, 1963

By J. D. Defilippi, E. M. Gilbert, K. G. Brickner

FCC chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Transformation to martensite is considered to be responsible for this behavior in some metastable Cr-Mn-N steels. However, very stable Cr-Mn-N steels also exhibit a ductile-to-brittle transition. The results of this study indicate that deformation faulting is the probable cause of the brittle behavior of stable Cr-Mn-N steels. Deformation faulting accounts for the ductile behavior of these steels in a tension test at -320°F and brittle behavior in an impact test at -320°F. Deformation faulting also accounts for the toPological features observed on the fracture surfaces of impact specimens of these steels. FACE- centered- cubic chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Many Cr-Mn-N steels transform to martensite during deformation,l-5 and several investigatorsl-3 have suggested that the brittle behavior of these steels is caused by martensite formation. However, very stable Cr-Mn-N steels also exhibit brittle behavior. Schaller and Zackeyl reported that a very stable Cr-Mn-N steel (less than 3 pct martensite formed at -320°F) exhibited a transition temperature higher than that for steels in which large volume fractions of martensite formed during testing. The explanation given by Schaller and Zackey for this observation was that in the very stable steel the martensite, because of its higher interstitial content, was more brittle than that formed in their other steels. This explanation was questioned by Tisinai and samans4 and Baldwin.6 Moreover, because the toughness of stainless martensite at cryogenic temperatures is generally very low, this explanation does not account for Thompson's7 observation that small additions of nickel (1 to 3 pct) greatly improve the toughness of high nitrogen (0.35 pct) Cr-Mn-N steels. The present paper summarizes the results of an investigation of the low-temperature brittleness in very stable Cr-Mn-N steels. The importance of the mode of deformation on the toughness of these steels is discussed. Table I. Compositions of the Steels Invertigated, Pet Steel C Mn P S Si Ni Cr N - A 0.09 14.70 0.018 0.011 0.47 0.22 18.40 0.54 B 0.12 14.90 0.001 0.008 0.48 0.14 17.80 0.38 C 0.12 14.95 0.004 0.005 0.62 3.95 18.43 0.38 MATERIALS AND EXPERIMENTAL WORK The compositions of the steels investigated are shown in Table I. Steels A and B had compositions within the limits of a proprietary Cr-Mn-N stainless steel,* whereas Steel C was similar in composition to the proprietary steel except for its 3.95 pct Ni content. All steels were hot-rolled to 1/2-in. thick plate. The plates were subsequently annealed for 1 hr at 2000°F and water-quenched. Standard longitudinal and transverse Charpy V-notch impact specimens were machined from the annealed plates. Duplicate longitudinal and transverse impact specimens were tested at 212", 80°, 32", 0°, -100°,-160°,-200°,-256", and -320°F. Longitudinal tension-test specimens were also machined from the plates and tested at a crosshead speed of 0.05 in. per min at the aforementioned temperatures. The fractured impact and tension-test specimens of all three steels were examined to determine whether martensite had formed during testing. Magnetic, X-ray, electron-diffraction, and electron-microscopy techniques were used to detect the presence of martensite in the highly deformed areas of these specimens. Metallographic examination of highly deformed areas of impact and tension-test specimens revealed the presence of dark-etching bands, such as those shown in Fig. 1. These bands were observed only in deformed samples and were thought to be associated with the low-temperature brittleness of the Cr-Mn-N steels. Accordingly, a sample 1 in. wide by 3 in. long was cut from the 1/2-in.-thick plate of Steel C. This sample was surface-ground to a in. and then cold-rolled 60 pct at -320°F. Thin foils were prepared from the cold-rolled sample and examined in a JEM electron microscope. Brightfield, dark-field, and selected-area diffraction techniques were used to determine the cause of the dark-etching bands. Fractographic experiments were also performed. Impact specimens Of Steels A, B, and C were broken at -320oF, and the fracture surfaces of these specimens were immediately shadowed with carbon. The carbon replicas were examined in a Siemens electron microscope, and attempts were made to correlate the topological features of the fracture surfaces with the deformation mechanisms that could be occurring during an impact test of these steels.

Jan 1, 1970

By B. C. Allen

The interface energies of chronzium, molybdenunz. hugsten, and their solid-solution alloys Cv-35Re, MO-33Re, and UJ-25Re were studied at 0.6 to 1.0 of the absolllte liquidus ter)zpe,vature using fiz&apos;e )izethods. Liquid surface tension, yv , was deter mined clsing the pendant-drop and drop-weight methods. Results are, respectizlely, 1700, 2370, and 2480 +100 dynes per ct for the rhernium -containing alloys and essentially the same as tlwse reported for liquid chro)riln, trolybdenum, and tungsten. Average solid slrjace energy, rsv< xias ))zeasured using tlre fiber-extetlsion method. The ratio of ysS, the acerage high-angle grain-boundary energy, to ySV cclas jolnd fronz grain-bolzdary grooue angles fort)zed at the surface in an inert atrfizosphere. Absolllte iute?:face energies were deterawined using ?nultip/rase equilibria involzing suitable liquids of known surface tension (tin, silver). Interpretation of the experimented results in view of pvobable tenzperatzcre, orientation, and purity effects giz,e the follouling approximations in ergs per sq ctn: ysv (i2lo. Mo-33Re) - 2100, ySS (Mo, Mo-33Re) - 800, rr (defornzation twins in MO-33Re at 1200"C) - 800. ysV (Cr. Cr-35Re) - 2400. YSS (CY, Cr-35Re) - 1000. Probably Ylv- YSV- 2500 for tungsten and W-25Re, giving yss (It&apos;, W-25Re) - 900. The interface energies of solid and liqid ch?&apos;omiu?.z, nolybdenu?rr, and tungsten are not geatly aff&apos;ected by rhenium and therefore are not a ttlajor factor in the ductili zing rhenium effect in Croup VI-A metals. THE interface energies of the refractory Group VI-A metals, chromium, molybdenum, and tungsten, are not well-established. The objective of this investigation was to study the liquid surface tension, solid surface energy, and grain-boundary energy of these metals and compare them to those found for the bcc solid-solution alloys, Cr-35e,&apos; 0-33e,&apos; and -25e. Five techniques were used to measure interface energies in high-purity polycrystal rod, wire, and sheet at 0.6 to 1.0 of the absolute liquidus temperature. The alloys were chosen to see if there was any connection between interface-energy behavior and the ductilizing rhenium effecL4j5 EXPERIMENTAL WORK Materials. A description of the materials used is presented in Table I. Chromium rod was prepared by arc melting iodide process crystals supplied by Chromallo Cor., hot extruding, and warm swaging to 0.63-cm-diam rod.6 The sheet was prepared by rolling as-extruded rod to 95 pct reduction in area from a hydrogen furnace at 800" to 900°C and surface grinding off 0.02 cm from each face. Cr-35Re rod was prepared by arc melting sintered rhenium powder and iodide chromium crystals, warm rod rolling to 50 pct reduction in area in cans, and swaging to 60 pct reduction in area at 1100" to 1200°C. Some of the rod was warm-rolled to sheet and then surface-ground. Portions of swaged chromium and Cr-35Re were further reduced by swaging and drawing to 0.013-cm-diam wire by the General Electric Co. Mo-33Re and W-25Re rod, sheet, and wire were provided by Chase Brass and Copper Co. The molybdenum sheet consisted of two lots, both essentially the same except for the carbon content. Liquid Surface Tension. The liquid surface tension of Cr-35Re, Mo-33Re, and W-25Re was measured by a combination of pendant-drop and drop-weight methods using techniques already decribed." Following out-gassing, molten drops were formed on the ends of centerless-ground Mo-33Re and W-25Re rods by electron bombardment at 5 x 106 mm. Similar drops were formed on outgassed Cr-35Re rods by induction heating under 1 atm of 99.995 pct Ar. Solid Surface Energy. Solid surface energy was measured by conducting microcreep experiments on molybdenum, Mo-33Re, chromium, and Cr-35Re wires at 2350°, 2306, 1550°, and 180O°C, respectively. In preparation, gage marks -2.5 cm apart and -0.001 cm deep were circumferentially scribed on the wire with a razor blade. Weights of the wire material were then attached. Five to seven reasonably straight wires were hung in a container made out of the wire material. The free end was placed through a small hole in the removable top and secured by bending a small portion 90 deg. The containers not only tended to provide vapor-solid equilibrium for the wires but also protected them from gaseous impurities. They were nominally 2.5 cm in diam by 5 cm high and were made from extruded chromium rod, Cr-35Re arc casting, molybdenum bar stock, or welded Mo-33Re sheet. After deg re as ing, the assembly was outgassed at a relatively low temperature to 2 x 10"5 mm and then recrystallized 2 to 8 hr at the creep temperature in a rhenium-element resistance furnace. The static argon atmosphere was gettered by tantalum radiation shielding. Specimen temperature was measured optically to 25"C using calibration with known melting points and blackbody conditions. The wires generally developed a stable bamboo-type structure according to Fig, l(b), (c), and (d) and retained their gage marks [upper portion of Fig. l(d)]. One or two of the weights were clipped off to provide a low load for the creep anneal. To minimize the possibility of bending or breakage, the wires remained attached to the top of the annealing container which was held to keep the wires vertical. The distance between gage marks was

Jan 1, 1967

By Carl F. Lutz, Robert F. Mehl

A layer of brass was formed on 0 brass using a vapor-solid reaction technique. The variation in composition with distance within the phase layer and across the a -ß interface was determined by an electron probe. The diffusivities were calculated as a function of concentration; the diffusion coefficient in brass was found to change by a factor of twenty-five over a compositional range of 8 at. pct. An explanation is proposed to account for the large change in the diffusivity, based on possible stresses in the diffusion zone; it is suggested that the concentration dependence of the thermodynamic factor might decrease the activation energy with increasing zinc content. ALTHOUGH the body of data on diffusion coefficients (D- values) in terminal solid solutions and in isomorphous systems is quite large, there is but little quantitative information for intermediate alloy phases. This paper recounts measurements of D-values for the ? phase in the Cu-Zn system. The experimental method employed consists in the forming of alloy layers and determining and analyzing the concentration-distance (c-x) curve. The experimental method employed could have been applied to several systems; the Cu-Zn system was chosen because the D-values in the a and ß phases are well known, and can thus be used for purposes of comparison. The rates of growth, of intermediate alloy layers are known for a number of systems. In nearly all cases the thickness varies parabolically with time, as to be expected if the rate of growth is controlled by the D-values. In a few cases, nonparabolic behavior has been noted.1 Nonparabolic growth may be the result of a) a variation of the composition at the phase interface with time, b) interface-controlled kinetics, c) short diffusion times coupled with long vacancy lifetimes (in vacancy diffusion),2 and d) crystal reorientation during diffusion in anisotropic systems.3 In the Al-Ni system4 and in the Al-u5 system parabolic growth kinetics are slowly approached after an initial transient period. In general those phases stable at a given temperature in a system A-B appear as separate phase layers when A and B are put in contact and given a diffusion he at-treatment. In most cases the compositions at the interface of adjacent phase layers are those read from the phase diagrams for the termini of the respective phases. This discontinuity in concentration is taken as independent of time, and the growth of one phase at the expense of another is assumed to be independent of interface kinetics, i.e., the rate of interface movement is controlled by volume diffusion in the phases concerned. wagner6 has given many solutions for multi-phase diffusion processes, assuming that the chemical diffusion coefficient, D, is independent of concentration, as have others. Jost7 has pointed out that the familiar Boltzmann-Matano solution is as valid for a (c-x) curve exhibiting concentration discontinuities at phase boundaries as for the usual single-phase case. Heumann and associates8,9 have applied this solution to the multi-phase case, but lacking concentration data within the several layers were forced to assume linear concentration gradients, thus calculating only average D-values. The purposes of the present study were: 1) to determine the dependence of D on concentration, 2) to calculate the intrinsic diffusion coefficients D?Cu and D?Zn, 3) to establish the time-law for the movement of the interface, 4) to determine the concentration limits at the ß-? interface, and, 5) to attempt to clarify the mechanism of diffusion. EXPERIMENTAL PROCEDURE The ? phase is exceedingly brittle; conventional solid couples and conventional sectioning methods were thus inapplicable. Vapor-solid couples were accordingly employed. Unfortunately the equilibrium vapor pressures of Zn for the ? phase are unknown; to escape this awkwardness, samples were enclosed in a capsule containing powder of an alloy of known composition, sufficiently large in quantity as to be effectively an infinite source, maintaining the concentration of Zn at the sample surface constant with time. The sources of Zn-vapor which can be employed in reaction with Cu, or a brass, or ß brass, to form a layer of ? brass satisfactorily wide in concentration range, are alloys of the phases ?, or ? + E or ? + d (depending on the temperature).

Jan 1, 1962

By P. G. Chamberlain, E. R. Podnieks, R. E. Thill

Although published data on the physical properties of rock are voluminous, information is often lacking on the environmental conditions under which such data were acquired. Efforts are frequently directed to improve specimen tolerances and preparation procedures; but investigators often overlook giving the rock environment equally careful control during the testing program. Generally, tests are conducted at existing laboratory room conditions, and the prepared rock specimens are frequently, if not most commonly, air-dried for various lengths of time before testing. The standard testing atmosphere recommended by the American Society for Testing & Materials (ASTM)1 is 73.4°F and 50% relative humidity. To maintain a rock at 50% relative humidity for testing purposes, however, requires special equipment and preconditioning procedures, as this study demonstrates. Relatively small variations in the moisture content of a specimen, for example, due to the coolants or lubricants used during specimen preparation, can cause significant variations in the physical properties measured. Such moisture variations may occur in the rock specimen even after it is air-dried, since laboratory humidity conditions commonly fluctuate from day to day. For these reasons, this study emphasizes procedures for preconditioning and maintaining a controlled environment during testing. Although the effects of moisture or temperature on rock properties have previously been studied, their combined effect on rock properties is unknown. In this study, uniaxial compressive strength, Young&apos;s and stiffness moduli, and longitudinal wave velocity were determined and compared under controlled conditions of temperature, moisture, and pressure for 11 environments considered to be of particular interest in laboratory, in-situ, and even simulated lunar environments. The following environments were selected for this program: -250°F under dry, 50%

Jan 1, 1972

By R. A. Flinn, R. D. Pehlke, D. R. Glass, P. O. Hays

Knowledge of the depth of penetralion of an oxygen jet into the bath of the oxygen converter and of the correlation of penetration with driuing pressuve, lance heighl, and nozzle throat area is vital to the understanding of converter operation. If the penetration is too shallow, then severe and hazardous slopping takes place. On the other hand, if the jel penetrates entirely Lhvough lhe bath for an apprcciublc period of time, bottom damage occurs. In addilion to measurement of the penetralion of the jel, knou~ledge of the circulatory movement in the bath is also of interest in order to evaluale various theories oj-concerter operating behavior which have been published. In this investigation, experimental converters were buill of IOU- , 300-, and 4000-lb capacity. Four independent methods were used to determine penelralion: the onset of bottom marking, a nitrogen bubbler probe, observation througlt an optical syslew built into the oxygen lance, and direcl viewing of the jet issuing from the bottom of the vessel. Good correlation zuas obtained, and empirical relalions for pvedicling perletration were found. These relations were conjzrmed by bottom marking tests in 55- and 110-ton vessels. Within the operaling conditions employed in these tests, the depth to which a single oxygen jet penetrated zuas found lo vary according to the relatiorl ThE technical literature is replete with data concerning the successful use of the basic oxygen furnace or converter in steelmaking. Experimental data are lacking, however, on the vital factors of the depth of penetration of the jet into the bath and the induced circulation. Commercial operating conditions usually have been the result of cut and try experiments in lance manipulation until satisfactory results were obtained. There have been, however, two hotly argued opposing theories concerning desirable depth of penetration and these are exemplified by the Schwarz and Miles patents1,2 on one hand and the Suess patent3 on the other. The Schwarz patent teaches that the jet, issuing from the nozzle at supersonic speed, penetrates deeply "so that the reactions between the iron and the oxygen and between the oxygen and the rest of the smelting components take place in the center of the bath". Specific operating suggestions are given by Miles.2 By contrast, the Suess patent calls for surface Circulalion was investigated by lour methods: by direct observation in 200-lb open baths, by the use of graphite rudders in the 300- and 4000-lb converlers, by direct observalion through an oplical system in the lance, and by various models al room temperature. All were in excellent agreement and indicated that the motion of the bath ulas up at the center, radially outluavd at the surface, and down at the sides. Experi-ments in small and in commercial vessels indicate that it is essential to operate with a jet penetration of approximately 50 pct of the bath depth. Surface blowing results in low oxygen eficienty and in hazardous conditions which may render the process inopeuable. RejYactory dartzage al the bottom of the vessel is only encountered when the jet penetrates to the bottom, and this can be avoided by properly applying the penetration formula. The application of this en/pirical formula in commercial peraations is best when limited to combinations of lance size, pressure, and height which are typically encounteved in the use of a single-hole lance. blowing so that "...the oxygen jet does not penetrate deeply into the molten metal bath and is confined to an impingement area at the central portion of the bath surface". These references are given merely to illustrate the basic differences between the two schools of thought and to point out the need for measurement of penetration for the sake of the operator. For example, it is shown later that inefficient and even dangerous conditions can arise if improper blowing conditions are used. Differences are also evident between the two schools of thought as to the mixing, circulation, and agitation which is to be accomplished by the jet. The Schwarz patent states that "surface contact is not sufficient in most cases to bring about quick reaction, the same as the blowing of the gas over the bath surface or the mere blowing of the gas onto the bath surface". The patent goes on to call for active mixing. In contrast the claims of the Suess patent call for "discharging a stream of oxygen ... to an extent to avoid material agitation of the bath by the oxygen stream". In this patent the circulation is said to be downward in the center and up at the sides of the vessel. A number of investigators4-12 have explored penetration and circulation in transparent models. In general, it is agreed in these tests that the circulation is upward at the center (along the sides of the jet cavity),

Jan 1, 1968

By Bauer, Alan

In considering blasting it is necessary to consider the drilling and explosives since one is generally concerned with the total cost of muck of a certain size in the pit or through the crusher. To get a current idea of the drilling situation in open pit mines plotted in Fig. 1 are the drilling costs per ton of material vs. hole diameter for rotary drill holes in large limestone, iron ore and taconite operations. The exception is the 2-in. diam hole which was drilled with a percussion drill in limestone.

Jan 1, 1968

By C. R. Whitney, G. N. Maniar, D. R. Muzyka

Previous results have shown that Pyromet 860, an Fe-Ni-base heat-resistant alloy, is stable at temperatures as high as 1500°F for aging times as long as 100 hr. This Paper describes the results of long-time creep-rupture testing at 1050" to 1400°F at various stress levels. Times as long as 37,660 hr were employed. The effects of time, temperature, and stress on the precipitates and their morphologies were studied by optical and electron microscopy, X-ray and electron diffraction, and microprobe techniques. phase, containing cobalt, nickel, and molybdenum, was detected after extended exposures from 1200" to 1400°F and careful study was performed to describe the kinetics of its formation in this alloy. µ phase formation apparently has little effect on the elevated-tem-perature properties of Pyromet 860. For times as long as 500 hr at 1300°F and below, with µ phase present, m significant effects on ambient temperature properties were noted. For longer times at 1300°F and after 1400°F exposure, the effects of u phase on ambient temperature tensile strength properties are not clear due to y&apos; effects and grain boundary reactions. Electron-vacancy, N,, numbers were calculated using different methods described in literature and correlated with the present findings. In the selection of alloys for use in gas turbine applications, structural stability ranks as a primary criterion. High-temperature strength and cost are also of major concern. With these factors in mind, Pyromet 860 alloy, an Fe-Ni-base superalloy was designed. This alloy combines the cost advantages of Fe-Ni-base alloys such as A-286, 901, and V-57 with improved strength and structural stability&apos;1,2 and no tendency to form the embrittling cellular 77 phase. A previous study3 reported on the stability of Pyro-met 860 at temperatures from 1375" to 157 5°F and times up to 100 hr. That study showed that the y&apos; precipitates increased in size and separation and decreased in number with an increase in time or aging temperature. No deleterious phases were found to occur. In the present work, samples from four production heats were subjected to long-time creep-rupture testing at 1050" to 1400°F at various stress levels. Various heat treatments were used on the starting samples and tests were run up to 37,660 hr. The effects of time, temperature, and stress on the precipitates and their morphologies were studied by optical and electron microscopy, X-ray and electron diffrac- tion, and microprobe techniques. Electron vacancy numbers, Nv , calculations were made by TRW.4 Experimental results are correlated with the Nv data used to predict occurrence of intermetallic phases such as a phase. EXPERIMENTAL PROCEDURE Mechanical Tests. Material for the present study came from four production size heats of Pyromet 860 alloy, weighing from about 3000 to about 10,000 lb. All of these heats were made by vacuum induction melting plus consumable electrode vacuum remelting. The nominal analysis for this alloy is compared with the actual analysis of the four heats in Table I. Sections of these heats were forged to 9/16-in. round bar,3/4-in. square bar, 3-in. round bar, 4-in. square bar, and a gas turbine blade forging about 16 in, long, about 6 in. wide, and weighing about 20 lb. In general, all forging of this alloy is done from a 2050°F furnace temperature. Longitudinal test blanks were cut from the centers of the smaller bars, from mid-radius positions for the 3- and 4-in. bars, and from the air foil of the gas turbine blade and heat-treated according to the procedures outlined in Table 11. Heat treatment A is the "standard treatment" recommended for this alloy for best all-around strength and ductility. Heat treatment B is a modification of treatment A for improved tensile strength at moderate temperatures. The treatment coded C was designed for treating large sections according to a procedure previously described.&apos; Heat treatment D was developed to yield optimum stress relaxation characteristics at 1050°F for a steam turbine bolting application. After heat treatment, the test blanks were machined either to plain bar creep specimens with a gage diameter of 0.252 in., to combination smooth-notched stress-rupture bars with a plain bar diameter of 0.178 in. and a concentration factor of Kt 3.8&apos; at the notched section, or to notch-only specimens. All specimens conformed to ASTM requirements. Metallography. Most of the creep-rupture tests were continued to failure. A few bars were fractured as smooth or notch tensiles after creep-rupture exposures. After fracturing, ordinary metallographic sections were made primarily in gage areas adjacent to fractures to represent a "high-stress" region and through specimen threads to represent a "low-stress" region. All metallographic sections were made in a longitudinal direction with respect to the test specimen axes. For optical microscopy, the samples were etched in glyceregia (15 ml HC1, 5 ml HNO,, 10 ml glycerol). For XRD analysis, the phases were extracted electrolytically in two media: 20 pct &Po4 in H20 for selective extraction of y&apos; and 10 pct HC1 in methanol for carbides and other phases.

Jan 1, 1970

By Frederic L. Kadey

Diatomite is a siliceous, sedimentary rock consisting principally of the fossilized skeletal remains of the diatom, a unicellular aquatic plant related to the algae. Thus, it has-been formed by the induration of diatomaceous ooze, and consists mainly of diatomaceous silica, a form or variety of opal which is first formed in the cell walls of the living diatom. Diatomaceous silica is not generally regarded as a synonym or the equivalent for diatomite, although it has been so used at various times. Accurately, diatomaceous silica is the preferred name for the principal mineral component of which the rock, diatomite, is composed. The terms diatomaceous earth and kieselguhr are used as synonymous with diatomite. The designations tripoli, tripolite, infusorial earth, etc., were used at one time but are now obsolete. With the changing nomenclature, these terms that were at one time correct when proposed and used for generations would be considered incorrect if used today in the light of current knowledge. The designation diatomite is reserved for those accumulations of diatomaceous silica that are of sufficient quality, size, and minability to be considered of potential commercial value. Processed diatomite possesses an unusual particulate structure and chemical stability that lends itself to applications not filled by any other form of silica. Foremost among these applications is its use as a filter aid, which accounts for over half of its current consumption. Its unique diatom structure, low bulk density, high absorptive capacity, high surface area, and relatively low abrasion are attributes responsible for its utility as a functional filler and as an extender in paint, paper, rubber, and in plastics; and as an anti-caking agent; thermal insulating material; catalyst carrier; and chromatographic support; polish, abrasive, and pesticide extender to name a few representative applications. The United States is the principal producing country, although diatomite is found in numerous other locations.

Jan 1, 1975

By R. D. Pehlke, J. V. Gluck

A study was made of&apos; the effects of up to five additional solutes on the thermodynamic activity of zinc in dilute solution with molten bismuth in the range 450" to 650°C. The experimental measurements were made in a multielectrode galvanic cell apparatus employing fused LiCl-KCl as the electrolyte. The solute additions included indium, lead, tin, cadmium, copper, silver, antimony, or gold. A range of positice and negative interactiotls with zinc was covered. The experinzer~tal observations were cowlpared with the activity coefficients calculated usitlg either Wagner&apos;s first-order Taylor series rnodel or a proposed second-order solution itrteraction model. hi general, the truncated first-order Taylor series proposed by Wagner gaue good results for "dilute" solutions (XBi > 0.90) contaitzing up to six solutes. The second-order model, which includes a second-order cross-interaction term, produced a slight improvement in predictions for solutions with XZn = 0.015 and a significant improvement for solutions with XZn = 0.050 hear the limit of Henry&apos;s law region). Seveval of the quaternary solutions studied contained a total solute content of 0.215 mole fraction, and fairly good success was achieved in predicting the activity coefficient 01- zinc. ThE study of thermodynamic interactions between dilute solutes in liquid metallic solutions has occasioned much recent interest. It is useful to recall in this respect that Wagner&apos;s well-known expression for the activity coefficient&apos; is a practical application of the problem of representing a given function, i .e., In ?, by means of a sequence of polynomials. No specific physical model of a solution is involved in its use. As suggested by Wagner, a Taylor Series is used to expand In ? about a point of infinite dilution with respect to all solutes. The partial differential coefficients of the series have been termed "interaction parameters". Various authors&apos;-6 have proposed formalisms for parameters, the definitions being designed to meet some specific experimental or physical condition. A usual assumption is that terms above first-order in the Taylor Series may be neglected. In that case, the logarithm of the activity coefficient is expressed as a linear function of solute concentrations. The resulting expression is presumed valid for any number of additional solutes as long as the solution can be regarded as "dilute". This assumption can be termed "the hypothesis of additivity". However, experimental tests of that hypothesis for quaternary or higher-order solutions have been extremely limited. Primarily such tests have been confined to studies of effects of added metallic elements on either the activity of carbon or the solubility of gases in liquid iron.7-13 The only known previous study of an all-metal system is the limited work of Okajima and pehlke14 on the effects of multiple solute additions on the activity of cadmium in liquid lead. The present investigation is a portion of the work to determine the effects of various solute additions on the activity of zinc in dilute solution with molten bismuth in the range 450" to 650C It was shown for such ternary solutions that second-order Taylor Series terms could be evaluated at the same time as first-order terms, with no additional experimentation required. A second-order solution model was described which, under certain conditions, is a rigorous representation of solute activity in a ternary solution. (In the sense employed in this paper, the term "model", as distinguished from "equation", is taken to mean an empirical correlation or formalism, but not a hypothetical physical system per se.) Presumably such a model could be extended to produce a better representation of In ? in solutions of even higher order. The feasibility of a generalized Taylor Series approach to solution interactions and inclusion of second-order terms also has been discussed recently by Lupis and Elliott in independent work concurrent with the present investigation. In addition, they discussed empirical means of estimating certain second -order coefficients.17 The utility of such solution models rests on the ability of a truncated series to represent adequately the experimental facts in multicomponent solutions. Questions that arise include: Do the second-order terms really make a significant contribution? How far away from "dilute" solution may such models be applied? Are the types and varieties of the additional solutes important? among others. In order to provide some answers to these questions, an experimental study was made of the effects of two or more additional solutes on the activity of zinc in dilute solution with molten bismuth. Comparisons were then made with calculated activity coefficients obtained using the previously determined ternary interaction parameters. INTERACTION MODELS As an example of the approach to defining activities in multicomponent solutions, consider the Taylor Series expansion for a quaternary system, i.e., three dilute solutes. Writing terms through second order, the result is:&apos;&apos;

Jan 1, 1968

By Douglas W. Fuerstenau, Kalanadh V. S. Sastry

A mathematical model is developed for flotation in a countercur-rent column where continuously generated air bubbles rise through a downward flowing pulp. The model is based on the assumption of axially dispressed plug flow of both the liquid and air-bubble phases. An appropriate flotation-rate expression, which takes into account the changing concentration of solid particles on the bubble surface, is formulated and applied to the column flotation process. Although a complete solution of the resulting equations is not possible for the general case, solutions for specific limiting cases have been obtained. From these, it is possible to predict theoretically the dependence of the column performance on certain variables. Specifically, concentration profiles as a function of height in the column have been calculated for various values of the characteristic dimensionless parameters. The effect of axial dispersion on the perforance of the equipment is pointed out. In recent years, there has been considerable progress in delineating the fundamental physicochemical principles underlying the unit operation of flotation and in advancing methods for kinetic analysis and process modeling of flotation.&apos; In general, nearly all such process research has been concerned with the analysis of conventional flotation equipment and circuits. From these investigations, the possibility of developing and designing flotation apparatus for more efficient separation appears limited with conventional equipment. How- ever, recently there has been an attempt to apply coun-tercurrent flow techniques to flotation in the context of a flotation column.- some of the results from pilot-plant studies2 indicate possibilities for success of this process at least in obtaining higher-grade concentrates though not higher recoveries. A flotation column operates on countercurrent principle in which bubbles continuously generated at the bottom of the column rise through the downward flowing slurry. A schematic diagram of the flotation column is shown in Fig. 1. The physicochemical principles of bubble-mineral attachment, using this flotation column, are essentially the same as those which prevail in conventional equipment, the only differences being in the flow patterns of the various phases. The salient operating feature of the column as compared to those of a conventional cell is that neither mechanical nor turbulent pneumatic agitation is employed. The column is

Jan 1, 1971

By Jasper L. Stuckey

It is not known when kaolin mining was first begun in North carolina, Evidence, in the form of excavations and primitive tools, indicates that some of the deposits were worked in prehistoric times. It has been suggested that the prehistoric mining was for mica, but the workings were all in altered or partly altered pegmatite material and the dumps do not represent the amount of material removed. some of the early openings may have been made in search of kaolin or semi-kaolinized feldspar which was sold to English1 traders along the coast and used in some Of the early English porcelains. In 1744,2 an application was made for an English patent to produce porcelain from an earthy mixture obtained from the Cherokee Nation in North America. It is well established, however, that the occurrence of kaolin in western North Carolina was known in England by 1767. In that year, Josiah Wedgewood sent T. Griffiths3,4 to what is now Macon County, North Carolina, to secure a supply Of kaolin for use in England. Griffiths diary, now in Etruria Museum, Stokes-on-Trent, contains a most interesting account of his experience. Kaolin was discovered at St. Austell, England, shortly after the voyage Of Griffiths, which probably accounts for the lack of further interest in American kaolin. Between 1767 and 1888, there are no records of kaolin mining in North Carolina. In the latter year, however, mining was begun near Webster, Jackson County, and, in the intervening period, has become an important industry. &apos;Or some 20 years, kaolin mining was carried On chiefly in Jackson, Macon, and Swain Counties. About 1904, it was begun in the Spruce Pine district and for the past 20 Yea&apos;s most of the kaolin mined in the State has come from Avery, Mitchell, and Yancey Counties. Distribution The kaolins of North Carolina are limited in occurrence to the Piedmont Plateau and Appalachian Mountain area of the State. While kaolins are widespread in the Piedmont Plateau, having been prospected for in Rutherford, Cleveland, Gaston, Granville, Lincoln, Catawba, Ire-dell, Richmond, Moore, Randolph, and Montgomery Counties, the production from that area has never been important. The known deposits of commercial importance are limited entirely to the mountain area of the State. While kaolins occur widely distributed throughout the mountain area and have been prospected for in many counties of that area, commercial production has come chiefly from two districts. One of these includes Jackson, Macon, Swain, and Haywood Counties. The other includes Avery, Mitchell, and Yancey Counties. Geology With few exceptions, all the known kaolin deposits in North Carolina contain

Jan 1, 1948

By Jasper L. Stuckey

It is not known when kaolin mining was first begun in North carolina, Evidence, in the form of excavations and primitive tools, indicates that some of the deposits were worked in prehistoric times. It has been suggested that the prehistoric mining was for mica, but the workings were all in altered or partly altered pegmatite material and the dumps do not represent the amount of material removed. some of the early openings may have been made in search of kaolin or semi-kaolinized feldspar which was sold to English1 traders along the coast and used in some Of the early English porcelains. In 1744,2 an application was made for an English patent to produce porcelain from an earthy mixture obtained from the Cherokee Nation in North America. It is well established, however, that the occurrence of kaolin in western North Carolina was known in England by 1767. In that year, Josiah Wedgewood sent T. Griffiths3,4 to what is now Macon County, North Carolina, to secure a supply Of kaolin for use in England. Griffiths diary, now in Etruria Museum, Stokes-on-Trent, contains a most interesting account of his experience. Kaolin was discovered at St. Austell, England, shortly after the voyage Of Griffiths, which probably accounts for the lack of further interest in American kaolin. Between 1767 and 1888, there are no records of kaolin mining in North Carolina. In the latter year, however, mining was begun near Webster, Jackson County, and, in the intervening period, has become an important industry. &apos;Or some 20 years, kaolin mining was carried On chiefly in Jackson, Macon, and Swain Counties. About 1904, it was begun in the Spruce Pine district and for the past 20 Yea&apos;s most of the kaolin mined in the State has come from Avery, Mitchell, and Yancey Counties. Distribution The kaolins of North Carolina are limited in occurrence to the Piedmont Plateau and Appalachian Mountain area of the State. While kaolins are widespread in the Piedmont Plateau, having been prospected for in Rutherford, Cleveland, Gaston, Granville, Lincoln, Catawba, Ire-dell, Richmond, Moore, Randolph, and Montgomery Counties, the production from that area has never been important. The known deposits of commercial importance are limited entirely to the mountain area of the State. While kaolins occur widely distributed throughout the mountain area and have been prospected for in many counties of that area, commercial production has come chiefly from two districts. One of these includes Jackson, Macon, Swain, and Haywood Counties. The other includes Avery, Mitchell, and Yancey Counties. Geology With few exceptions, all the known kaolin deposits in North Carolina contain

Jan 1, 1948

By R. K. Hopkins

For a great many years fusion welding has been used in and around petroleum refineries, but it is only within six or seven years that the more important pressure vessels have been constructed by this process, because before that time the properties of fusion welds would not with-stand such rigorous service. Since the adoption of fusion welding for the construction of this equipment, the refiner has required pressure vessels suitable for operation over a very wide range of conditions. On the one hand, vessels must operate at extremely high temperatures, in the range of 950° to 1000° F., and on the other vessels must be suitable for operation at sub-zero temperatures down as low as -75° F. Also, vessels are required suitable for operation at pressures upwards of 1000 lb. per sq. in., and as low as a 29-in. vacuum. In addition, vessels are required to withstand the attack of very corrosive mediums. It has been a rather difficult task for the fabricator to meet all of these require-ments, but as a result of the extensive research carried on by steel manu-facturers and several fabricators of class I vessels, practically all of these demands have been met. In order to meet the refiners&apos; requirements for this wide range of conditions, the fabricator has worked closely with the metallurgist. This has enabled him to choose the proper base metal for each service condition, but it has been the fabricator&apos;s problem to develop a welding rod and welding technique, as well as a heat-treatment, that would produce in the welded vessel characteristics in and around the weld comparable to those in the base metal. Where corrosion is not a serious problem, and where the operating temperatures are not too high, ordinary carbon steel has served very well. But when corrosion is serious, and/or when the temperatures are either very high or very low, it is necessary to use some form of alloy steel to give satisfactory service.

Jan 1, 1935

By Langtry E. Lynd

The predominant tonnage use of titanium is as a white pigment, in the form of rutile or anatase, which are allotropic modifications of titanium dioxide. Because of its whiteness, high refractive index and resulting light scattering ability, titanium dioxide is unequaled as a white pigment for paints, paper, rubber, and a wide variety of other materials. Consumption of titanium dioxide pigments for these uses has been rising steadily for many years, United States consumption in 1956 amounting to about 486,000 tons, worth $250,000,000. Production was off a little in 1957 and 1958. An outstanding development in the titanium field in recent years is the expansion of titanium metal production. Virtually nonexistent before 1948, United States production of pure titanium metal sponge reached a high in 1957 of about 17,200 tons, worth about $77,000,000. United States titanium sponge metal production in 1958 was cut back to about 4,600 tons because of reductions in military requirements. Another major use of titanium, in the form of the mineral, rutile, is for welding rod coatings. United States consumption of rutile for this purpose in 1958 amounted to about 11,000 tons, worth $1,100,000. Titanium-Bearing Minerals Although several minerals contain titanium as a major constituent, only a few of these occur in sufficient quantities and concentrations to be of commercial importance. These are ilmenite (FeTiO3), rutile (TiO2), and alteration products of ilmenite which have been referred to as weathered ilmenite, leucoxene, or arizonite. The other polymorphs of titanium dioxide, brookite and anatase, occur in a few deposits, of which only one has been of even minor importance. Considerable concentrations of titanite or sphene (CaTiSiO5) and perovskite (CaTiO3) are known, but do not compete with ilmenite and rutile deposits in grade or size. Rutile is very widely distributed as an accessory mineral in most rocks, but large deposits of commercial importance are rare. A few rock deposits have been worked for rutile but only one, in Virginia, is in operation (1959). Development of one in Mexico was discontinued recently. At present, the main sources of rutile are the beach and dune sands of Australia and Florida. A major use of rutile is for the manufacture of titanium tetrachloride, which is the intermediate compound universally used in titanium metal manufacture. Another main use of rutile is for welding rod coatings. Although the whiteness and brightness of titanium dioxide pigment is due to the high refractive index of rutile or anatase, natural rutile is too impure to be used directly as a white pigment, is too expensive to use for manufacturing pure oxide pigment, and is too scarce to provide the required tonnages. Instead, the cheaper, more abundant, mixed oxide of iron and titanium, ilmenite, which is readily decomposed by sulfuric acid, is used for manufacture of rutile and anatase pigments. Ilmenite is mined from both rock and sand deposits. Rock deposits contain ilmenite in massive or heavily disseminated form along with magnetite or hematite and are almost invariably associated with anorthositic and gabbroic rocks. Ilmenite also occurs as an accessory mineral in a great many igneous and metamorphic rock types. Concentrations of

Jan 1, 1960

By Allan Martin, R. A. Swalin

Diffusion rates of manganese, aluminum, titanium, and tungsten in nickel were measured at temperatures between 1100° and 1300°C. Activation energies, Q, and values of the frequency factor, Do, were calculated for each system. Values of Q were found to be within 15 pet of that for self-diffusion of nickel in agreement with present theories of diffusion. ONE of the most interesting problems in diffusion concerns factors governing the order of diffusion coefficients of various solutes in a common solvent metal at low solute concentrations. An early suggestion by Rhines and Mehl&apos; was that diffusion coefficients might each approach that of the self-diffusion coefficient of the solvent itself. Later Thomas and Birchenall&apos; pointed out correlations between the order of the diffusion coefficients and the freezing point depressions of the solvent by the various solutes. Other correlations have been sought. To settle this question it seems likely that much more data will be needed and, in particular, data collected at low solute concentrations. This type can be obtained by special analytical techniques as well as by use of radioactive tracers. The following study was made of diffusion of manganese, aluminum, titanium, and tungsten in a common solvent, nickel, at relatively low solute concentrations: 1—Production of alloys of nickel with manganese, aluminum, titanium. and tungsten at concentrations of the order of 1 atomic pet. 2—Use of pressure-welded diffusion couples in cylindrical form. 3—Diffusion anneals in the temperature range of 1100" to 1300°C. 4—Lathe sectioning of the diffused couples. 5—Spectrophotometric analyses of lathe turnings for the solute being studied. 6—Calculation of the diffusion coefficient for each of the solutes as a function of temperature. 7—Interpretation of results with current theories of diffusion. Experimental Work Materials—Two types of nickel were used in this research. The grade designated as Vacuum melted Mond nickel was used for all diffusion systems except the Mn-Ni system for which the Vacuum melted electrolytic nickel was used. Analyses of the two grades are given in Table I. The manganese used in making alloys was 99.9 + pet pure, aluminum 99.99 pet pure, titanium 99.9 pet pure, and tungsten of C.P. grade powder. Alloys used in this investigation were prepared by melting in vacuo or under a low pressure of argon. After melting, all heats except those of nickel-manganese were poured into a cylindrical copper mold 3 in. long and 1 in. ID. In the case of nickel-manganese, the alloys were solidified in the melting crucible. For nickel-aluminum heats alumina crucibles were used and for all other heats, zirconia crucibles.

Jan 1, 1957

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967

By Claudia Gasparrini

Gold, silver and platinum-group elements occur normally in very low concentrations in their ores. Because their market value is in many situations high enough to justify their full recoveries, mineralogical studies before any routine recovery is attempted are particularly important for the description of their manner of occurrence and decision on the appropriate recovery techniques. Gold and silver, although sometimes treated by similar metallurgical processes, may require different approaches and treatments because of the different manner in which they occur in their ores: gold has a relatively simple mineralogy limited to native gold, electrum and less often tellurides. Silver has a very complex mineralogy including over 200 different minerals. On the other hand, gold is more often than silver recovered from ores where its fine grain size requires the breaking of the host minerals by chemical methods. Mineral, grain sizes and host minerals all affect the metallurgy of the platinum-group elements..

Jan 1, 1984

By L. R. Duncan, O. M. Wicken

Magnesium, the eighth most abundant element in the earth&apos;s crust, is found widely distributed in a variety of minerals. Among the more commercially important ones are magnesite (MgCO,), brucite (Mg[OH],) , dolomite (CaMg[CO,],), and the salts magnesium sulfate and chloride often found in natural brines. Among other commercially important magnesium-containing minerals are olivine ([MgFe],- SiO,) , talc (H,Mg,[SiO,],) , and serpentine (H,Mg,Si,O,) . These are valuable because of desirable characteristics given them by the magnesium content and its placement in the particular crystal structure. These minerals are the raw materials for a host of products including magnesium metal and several grades of magnesia or magnesia- containing materials for refractories, fluxes, fillers, insulation, cements, decolorants, fertilizers, and chemicals. Considering only those minerals valued for their magnesia or magnesium content, over 85% of the material tonnages are processed to be used as refractories. Dolomite, which is used in enormous tonnages for its physical properties in construction, has an important use as a refractory raw material in its own right and, after calcination, as a precipitant for magnesium hydroxide, which is an intermediate for the production of magnesia or magnesium metal. Magnesia from the reaction of calcined dolomite (or limestone) with sea-water or magnesium-containing brines has supplanted much of the production of magnesia from mined magnesite, particularly in the United States. The best known of the minerals directly and widely exploited for magnesia content is magnesite, one of the calcite group of rhombo- hedral carbonates which includes calcite (Ca- CO,) , siderite (FeCO,) , and rhodocrosite (MnCO,) among others. The members of this group enter into a wide range of substitutional solid solutions when the positive ions have similar radii. The radii of magnesium and iron ions are within 6% of each other; hence, magnesite and siderite form a complete series of which breunnerite (ferroan magnesite) is a well-known end member. However, the radius of calcium ion is 36% larger than that of magnesium ion, and only limited substitution exists at each end of the MgC0,-Cam, series. Dolomite is not a member of the calcite group, but results when calcium and magnesium ions alternate in equal number in an ordered structure among carbonate ions. The result of these relationships is that calcite and dolomite, often found intermixed with magnesite, occur commonly as identifiable crystal entities which can often be separated to a varying degree from the magnesite by various beneficiation techniques. Magnesite, when pure, contains 47.8% MgO and 52.2% CO,. The pure mineral is sometimes, but rarely, found as transparent crystals resembling calcite, but, preponderantly, magnesite contains variable amounts of the carbonates, oxides, and silicates of iron, calcium, manganese, and aluminum. Magnesite may be either crystalline or "amorphous" (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black with shades of yellqw, blue, red, or gray. The color is not a fundamentally significant indicator of purity, but in a given deposit, an experienced person can often roughly grade magnesite by assessing color and crystallinity. The crystalline form of magnesite occurs in

Jan 1, 1975

By H. H. Rachford, D. S. Howard

In the withdrawal of fluids from tilted aquifers it is of value to be able to predict pressure patterns during the course of the pressure decline. As an example of this, in the displacement of fluids from oil reservoirs being produced by water-drive, prediction of the reservoir pressure is an important factor in fixing production rate. The prediction of pressure patterns in the depletion of an inclined aquifer has conventionally been made by solving the well known flow equations for the pressure Patterns in a horizontal aquifer, and correcting these patterm for the pressure difference due to the hydrostatic head associated with the vertical distance between a point in the horizontal aquifer and the corresponding point in the tilted aquifer. Inasmuch as the equation describing flow in tilted strata is different from that for horizontal flow. there was question as to the validity of the simple corrective procedure current1y in use. To examine the magnitude of error made using this procedure, an inclined aquifer was chosen for which the error was expected to he large, and the equation for flow in this tilted stratum was solved numerically. The results of the conventional procedure of correcting the solution of the equation for horizontal flow was compared with the solution of the correct equation by studying the difference between predicted pressures by the two methods. Three forms of the hydrostatic head correction were studied. The results for all three forms of the head correction are similar. The error in the approximate solution is quite dependent on the position of the horizontal aquifer with respect to the inclined one. The error is greatest at the producing end ad increases with amount of fluid withdrawn. The magnitude of the errors is not large if a good choice is made for the position of the horizontal datum. The most satisfactory position for the datum in all cases is near or slightly about the mid-point of the inclined stratum. Use of the best approximate method studied with the best datum tested yielded predicted pressures in error no greater than 7 psi. INTRODUCTION The movement of water by expansion from an aquifer to displace fluids from a contiguous oil reservoir was first recognized over 20 years ago.9 Since that time much work has been done to relate this mechanism to reservoir behavior mathematically. The result of this effort on the part of many workers has led to an understanding of underground fluid movement which has enabled us to follow and predict the behavior of the water-drive reservoir. One reason that good progress has been made in the application of mathematics to the study of pressure patterns and water movements in aquifers has been that the differential equation which describes this process is of a relatively simple form. The equation for the isothermal, horizontal, viscous flow of water through homogeneous sandstone is identical with that for the diffusion of heat through homogeneous solids, and this equation and means of obtaining solutions for it with many types of boundary conditions have been studied extensively. That this work has been highly successful is clearly emphasized by the large number of solutions developed for problems of interest both by methods of formal mathemat-

Jan 1, 1957