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By R. M. Rose, D. P. Ferriss, J. Wulff

Single crystals of tantalum were grown by multipass zone melting in an electron beam apparatus. Tension tests of these crystals at 4.2 x 10&apos;* per sec-gave a resolved louler yield stress of 7300 psi at with a chisel edge; total uniform deformation increased from 1 to 2 pct at 77°K to over 20 pct at 300°K. This, and slip traces, indicated that deformation is more inhomogeneous at lower temperatures. Deformation occurred exclusively by slip in <III> directions, on planes in the <111> zones. Cross slip was frequent, particularly for those orientations where the resolved shear stress on the cross system was comparable with that on the primary plane. The existence and magnitude of the upper yield point were found to be sensitive to orientation. This effect was related to the circumvention of dislocations which were "locked" by interstitial atoms, by double cross slip, or composite slip, of screw dislocations. Prestrainirg at 300°K did not remove the upper yield point in subsequent tension at 77°K. Also, this treatment was found to cause yield points, where none existed for the unprestrained material. This behavior was also rationalized in terms of the circumvention mechanism. The mechanical properties of polycrystalline tantalum have been investigated by several workers,1"4 and may be summarized by pointing out the following features: a) Sharp rise of yield stress with decreasing temperature below room temperature. b) Response to strain aging at 300" to 400"C. c) Yielding with upper and lower yield-point phenomenon at and below room temperature. d) Low strain hardening below room temperature. e) Reluctance to twin except at very high strain rate. Furthermore, tantalum is ductile at ordinary strain rates as low as 4.2"K.&apos; This feature, in particular, makes tantalum unique among the high melting point, bee transition metals of Groups V and VI in the periodic system. Therefore, a more fundamental and detailed knowledge of the low-tempera- ture deformation of tantalum is required. Since high purity and the absence of grain boundary effects make such a study most productive and unambiguous, the method of electron beam zone melting was selected for the preparation of test specimens. This technique has the further advantage that crystals may be seeded in order to obtain any desired orientation. EXPERIMENTAL The electron beam zone-melting equipment was constructed as a modification of that described by Calverley, Davis, and Lever? All crystals were made by three passes of the molten zone at 4 mm per min to achieve an optimum purity commensurate with economy of time and material. Table I reports the chemical analyses of the starting and refined metal. It will be noted that there remain some 50 to 70 wt ppm of interstitial elements, while all substi-tutional elements have been removed by evaporation. Tungsten is picked up by evaporation of the cathode filament wire. Crystal seeding was normally successful within 3 deg, and the orientation of all crystals are given in the standard stereographic triangle in Fig. 1. Tensile bars were prepared from the crystals by centerless grinding to the shape in Fig. 2. Specimens were then electropolished to remove 10 pct of the diameter in order to remove worked material and to prepare a metallographic surface for subsequent deformation trace observations. All specimens were held in the split bushing grips as indicated in the cross section view of Fig. 2. All tests were made at a strain rate of 2 112 pct per min in an Instron testing machine.

Jan 1, 1962

By D. J. Carney, R. L. Stephenson

M. O. Holowaty (Inland Steel Co., Chicago)—Messrs. Stephenson and Carney should be commended on the presentation of this very interesting paper. They have introduced new ideas on sampling of sinter and have thereby made a valuable contribution to the qualitative evaluation of sinter. The paper undoubtedly presents a novel approach to the problem of sinter sampling and this is to be regarded as its main value. Sampling of sinter from the pallets prior to the discharge is by no means new. This sampling procedure was used in the past by Philbrook; Hamilton and Ameen and others. The sampling basket used by the authors of this paper, however, permits one actually to obtain a good sample of the sintering mixture. The basket which can also be described as a removable pallet goes then through the entire process of sintering and thus offers a sample which is positively representative of the batch in question. The authors&apos; method of evaluating physical properties of sinter seems to be not altogether clear, however. It is felt that the following points should be clarified: I—In the section describing the shatter test the authors state that a 5-lb sample was used in the actual tests. There is no mention of the initial size of sinter particles used and the method of obtaining this 5-lb sample from the sinter cake weighing about 100 to 120 lb. It is also surprising that the sample was dropped from a height of 3 ft instead of the conventionally used 6 ft. Unfortunately there is no mention of the number of drops to which the sample was subjected. 2—The tumbler test used by Messrs. Stephenson and Carney in testing the samples of iron ore sinter was performed in a standard ASTM coke tumbling drum. The drum measures 3 ft in diam and is equipped with two 3-in. lifter bars. The distance of fall in this testing drum is identical with the distance used in the previously described shatter test. The number of drops in the tumbling drum is approximately double the number of revolutions. The basic difference then between the drop-shatter test used by Stephenson and Carney and the tumbling test seems to be the number of drops to which the sample is subjected and the abrasive action to which the sinter particles are exposed in the rotating drum. In any case, the choice between the shatter test and the tumbler test seems to be only a matter of taste and convenience. 3—The authors of the paper state that "in order to insure getting results that were representative . . . the entire sample obtained by means of the sampling basket was used as the starting material for the tumbler test. If the sample broke in pieces, all the pieces were used regardless of their size." The initial size of the material is known to be a very important factor, influencing seriously the final size of the particles. This should be particularly important in case of hard sinters. It seems also very troublesome and inconvenient to charge 12-in. cubes of sinter weighing about 100 lb into the testing drum. This could be eliminated by taking a standard fraction of somewhat smaller particles.

Jan 1, 1954

By D. W. Frommer, M. M. Fine

Mineral dressing research showed that iron concentrates of commercial quality could be produced from the Pea Ridge deposit near Sullivan, Mo. Magnetic separation and flotation, on a laboratory scale, yielded concentrates ranging from 60.0 to 71.4 pet Fe at recoveries of 89.9 to 97.6 pct. Early in 1957 St. Joseph Lead Co. announced discovery of three new centers of iron ore deposition in east central Missouri.&apos; The discovery resulted from exploratory drilling in the vicinity of a magnetic anomaly or high. A deep hole, drilled into the Pre-Cambrian porphyry to determine the cause of anomaly, penetrated a magnetite-rich deposit.&apos; The magnetic surveys that revealed the anomalies were begun by the Missouri Geological Survey in 1929 and were continued into the 1930&apos;s.3 At that time an area in Crawford County known as the Bourbon magnetic high was located. A second anomaly, similar in size and intensity, was discovered about six miles to the northeast in Franklin County in the vicinity of Sullivan. This area was not studied in detail until the early 1940&apos;s. To determine the cause of the anomalies, the USBM drilled four holes at the Bourbon site in 1943-1944.4 The most productive hole penetrated four mineralized zones having a total thickness of 127.5 ft. These zones contained magnetite in rhyo-lite porphyry at depths between 1600 and 2000 ft. Additional iron ore below 2000 ft was considered a possibility at the time. Some years later, the USGS, Missouri Geological Survey, St. Joseph Lead Co., and others cooperated in sponsoring an aeromagnetic survey of the Bourbon-Sullivan area which resulted in discovery of a third high, about eight miles distant at Pea Ridge. This deposit, with an estimated reserve of 50 to 100 million tons of iron ore, is considered the main find, although other orebodies in the same general area are of definite interest.&apos; When this discovery was announced, St. Joseph Lead also revealed plans to exploit the deposit jointly with Bethlehem Steel Co. A new corporation, Meramec Mining Co., was established, and 1962 was set as the target date for completing physical plant.2 Annual production goals of 2 million tons of beneficiated and pelletized iron ore were proposed. Preparation of the site for shaft sinking was begun in June 1957. Orebody and Character of Samples: Drilling to date has established the Pea Ridge orebody as a crescent-shaped pipe about 300 ft wide. Some drillholes were bottomed at 2800 ft in very good iron ore.6 he orebody is predominantly magnetite, although hematite and a mixture of hematite and magnetite occur in the upper areas and peripheral walls. Drillhole cores representing ore from different areas and depths of mineralization were grouped into composites for testing. These composites consisted of: 1) medium grade mixed hematite and magnetite, 2) high grade mixed hematite and magnetite, and 3) high grade magnetite. The medium grade ore came from three holes with depths of i350 to 1900 ft. The high grade mixed hematite and magnetite cores came from the 1790 to 2812-ft interval of one hole. Partial chemical analyses of the three samples, given in Table 1, reveal that all are excessively high in phosphorus and sulfur, and sample 1 is

Jan 1, 1960

By R. V. Higgins, A. J. Leighton

A fast method is needed for calculating thoroughly the performance of two-phase flobr~ in reservoir rock with complex geotrietry. The authors present such a method and .slzow its accuracy by romparison with laboratory performrrnce of a five-spot pattern. In making the performance c.alculations, the octant of the five-spot pattern was divided into four channels. The computer tinle required for the culculation was one rllinrcte. This is rorighly about minute per channel. INTRODUCTION By using an electronic computer it is now possible to make reservoir performance calculations in which fewer assumptions and more significant variables are included than was possible with a desk calculator. These performance calculations include such variables as the properties of the reservoir rock and its contained fluids, properties of the rock-fluid system and even different well-spacing patterns. Usually, the more variables that are included the higher the computer cost—and time on the computer is expensive. As a result, a short procedure is needed so the many variables will be included and accurate performance calculations will result. If a reservoir is composed of alternate layers of permeable and impervioi~s rock, and if each conducting layer has a different relative permeability, the combined computer cost for calculating each layer by the present long computer programs (which includes different well-spacing patterns and other variables) would be expensive. The performances of complex spacing patterns in a field often are studied by a potentiometric model, but in these model studies the analogy is to the flow of only a single phase. This paper presents a procedure to calculate the performance of a five-spot pattern with two phases flowing using a potentiometric model as a guide for the dimensions of channels and other related data. The time required to calculate the complete performance is about one minute on the IBM 7090 or four minutes on the IBM 704. The procedure can be extended to calculate the performance of more complex well spacings or an entire field with little modification. The procedure has been tested on the performance of the laboratory water floods of a five-spot pattern reported by Douglas, et alThe range of viscosity ratios in the laboratory experiments is from 0.083 to 754, which is extensive. The accuracy of the performance calculations is excellent as shown by the plotted points in Fig. I. The recovery as influenced by the geometry of the five-spot, taking into account the deviation from true radial character, has been predicted by Aronofsky and Ramey." The authors used a potentiometric model to determine the sweep efficiency to breakthrough of the flooding agent. Dyes, Caudle and Erickson,&apos; by means of a laboratory model, show the influence of mobility ratio on recovery after breakthrough of the injected material. Dyes, et ai, used the X-ray shadowgraph technique and miscible phases in their studies. Craig, Geffen and Morse from the analysis of the performance of their laboratory model correlate many variables, including average saturation of a flooding agent determined by permeability relationship. Craig, et al, used X-ray shadowgraphs to determine the sweep efficiencies in sandstone models. In this report the sweep efficiency is not needed, and the important effect of continuously changing saturation gradients before and after breakthrough

By J. L. Thompson

There are two basic forms of the LPG-slug process: the gas driven and the water driven. The pressure required for miscibility between gas and LPG prohibits the use of the gas-driven LPG process in shallow reservoirs. The water-driven LPG slug process normally exhibits good sweep efficiency. However, displacement of the LPG by water is poor. An improvement in this process appears possible by injecting a slug of carbon dioxide between the LPG slug and the water drive. Laboratory experiments were conducted in homogeneous linear systems to determine the effect of pressure on the various displacement zones. In the carbon dioxide-LPG displacement zone, the effect of pressure on the displacement efficiency is negligible above the miscibility pressure. However, the displacement efficiency decreases linearly with decreasing pressure below the miscibility pressure. With water displacing carbon dioxide, it was found that the recovery of carbon dioxide after water breakthrough can be predicted from its solubility in water. A displacement test was conducted with LPG and carbon dioxide slugs large enough to avoid interference between the oil-LPG, LPG - carbon dioxide and carbon dioxide - water displacement zones. Under these conditions, essentially complete oil and LPG recovery was obtained. However, a substantial amount of carbon dioxide was left in the core at water breakthrough. INTRODUCTION It has been shown in homogeneous linear systems that essentially complete oil recovery can be obtained by displacement with a miscible fluid such as LPG. Economic considerations dictate that the valuable LPG also be recovered. Methods proposed for recovering the LPG include (1) displacement with natural gas at a pressure high enough to make the two fluids miscible1 (the disadvantage of this method is that the required pressure of about 1,500 psi is too high for shallow reservoirs) and (2) displacement of the LPG with water2 (principal disadvantage is that a large amount of LPG remains in the formation because of poor displacement efficiency). This paper treats an improvement in the water-driven LPG slug process3,4 where carbon dioxide is injected between the LPG and water. Carbon dioxide is completely or at least partially miscible with propane and soluble in water; thus, displacement efficiency is improved at both ends of the carbon dioxide slug. To minimize effects of other variables, all experiments were conducted in linear core systems. GENERAL PROCESS DESCRIPTION The displacements of propane by carbon dioxide and carbon dioxide by water are considered separately, assuming enough of each is injected to prevent mutual interference. Displacement descriptions are confined only to the part of the pore volume containing mobile fluids unless otherwise specified. The schematic representation is given in Fig. 1. Starting at the producing well, a zone containing only oil is followed by a zone containing a single-phase mixture of propane and oil. The concentration of propane increases in the direction of the injection well and ultimately grades to pure propane. Then follows a zone containing a mixture of propane and carbon dioxide in continuously varying proportions until 100 percent carbon dioxide is reached. In this zone, the concentration of carbon dioxide in the immobile water phase also varies from zero to full saturation. Whether the displacement of propane by carbon dioxide is of complete or partial miscibility depends on pressure and temperature (Fig. 2). If the horizontal line representing the prevailing pressure intercepts the boundary curves of the phase envelopes for the prevailing temperature (i.e., if the pressure is lower than the critical

By W. M. McCardell, W. O. Winsauer

The abnormal conductivity found in shaly reservoir rocks containing an electrolyte is shown to be a consequence of the electrical double layer in the solution adjacent to charged clay surfaces. This increased conductivity results from a higher concentration of ions in the double layer than in the solution in equilibrium with the double layer. It is shown that the magnitude of the increased conductivity of a shaly reservoir material is influenced by the concentration and type of ions in the equilibrium solution as well as by the colloidal nature of the rock. INTRODUCTION An important factor in the quantitative interpretation of the electric log is the resistivity factor of reservoir rock. The resistivity factor is defined as the resistivity of the rock when completely saturated with an electrolyte divided by the resistivity of the electrolyte itself.&apos; In the normal case, the resistivity factor for a particular rock sample is independent of the resistivity of the electrolyte and reflects the pore geometry of the rock.&apos; In 1949. Patnode and Wyllie&apos; showed that in some cases the resistivity factor is not constant, but instead varies with the resistivity of the electrolytic solution. It was shown that clean sands behave normally—i.e., that the resistivity factor does not vary with resistivity of the electrolyte — but that sands con- taining shale and clay may exhibit abnormally low resistivity factors when the solution used to saturate them is of fairly high resistivity. At low resistivities of the electrolyte, the resistivity factor for a shaly sand appeared to approach a normal behavior. It is evident that the resistivity factor of a shaly sand is dependent upon factors other than pore geometry when the solution used to saturate it is of high resistivity. Patnode and Wyllie, and later de Witte,&apos; assumed that the conductivity of a shaly sand saturated with an electrolyte could be represented as the sum of two quantities. One of these was assumed, in effect, to be the conductivity which would be expected if the sample were a clean sand. and the other was assumed to be a conductivity inherent in the sample itself. The latter was supposed to be constant for a given rock sample regardless of the solution used to saturate it. The source of this added conductivity was ascribed to "conductive solids." In actual practice: the effect of the abnormal behavior of shaly sands is of minor importance except when the resistivity of a formation such as a sand is high. Thus the effect is more important when the sand is saturated with a dilute brine than when it contains a more concentrated electrolyte. The effect is also more important when the sample contains oil or gas than when it contains only saline water. Recently it has been suggested that the porosity of a stratum may be estimated from the electric log by use of the resistivity of the invaded zone." This is the zone flushed with the filtrate from mud used in drilling the well. which is ordinarily very dilute brine. When the method is applied to shaly sands, the effect of abnormal conductivity becomes of importance. This report describes an investigation of the mechanism responsible for the abnormal behavior of the resistivity of shaly rock saturated with conducting solutions. The investigation

Jan 1, 1953

By S. A. Braley

THE first commercial production of bituminous coal in the United States was in 1820, and formation of acid in the areas from which the coal was removed began at that time. Thus it is 130 years since the development of mine acid began. The coal operator has had to deal with the acid water produced in his mines, and his losses from corrosion of pumps and equipment have been tremendous. Other industries and the public have been forced to spend large amounts for their water requirements because of the acid discharge from the mines. There are many contradictions in the literature on this subject probably because of variations in the analytical procedures followed and differences in the methods of calculation and reporting. The opinions previously expressed may be summarized as follows: The production of mine acid has been looked upon as a simple chemical reaction wherein the oxygen of the air has reacted with pyrite to produce ferrous sulphate and free sulphuric acid. This reaction appears in many chemistry texts and generally has not been considered worthy of further study. Since the measurement of hydrogen ion concentration or activity was developed and expressed in terms of pH, indicator and instrumental methods for pH determination have become readily available, making it natural to think of it as a measure of acid content. Special purpose analytical methods applicable to potable waters, sewage effluents, and boiler waters, based in general upon the determination of what may be regarded as impurities, have been applied to more concentrated solutions constituting mine discharges, without reference to the fact that these specialized procedures had been developed to serve as operating guides for water-treatment plants. It has been assumed that the pounds of acid deliv- Table I. Showing pH and Titratable Acid of Varying Concentrations of Ferrous and Ferric Sulphates Ferric Ferrous ion Acldfty Ion Acidity (Fe+++) ppm CaCO3 We++) ppm CaCOa ppm PA equiv. PPm pH equiv. 11.200 1.80 30,000 11,200 3.98 20,000 5,600 2.01 15,000 5,600 4.15 10,000 2,800 2.21 7,500 2,800 4.41 5,000 1.120 2.48 3,000 1,400 4.68 2.500 560 2.60 1,500 140 5.00 250 280 2.65 750 28 5.00 50 112 2.81 300 56 3.07 150 28 3.38 75 ered by a mine was roughly a constant varying with the number of acres mined, and that the concentration of the acid in the drainage was inversely proportional to the volume of flow. Increased flow was thought to result in a dilution of the acid produced. When the Sanitary Water Board of the Commonwealth of Pennsylvania established a fellowship at Mellon Institute, the first approach to the problem was to review some of the chemical reactions involved and their relation to acid production. Since the sulphates of iron were among the principal constituents of coal-mine drainage, the first studies were based upon solutions of chemically pure ferrous and ferric sulphate. These are both neutral salts, that is, the iron and the sulphate are equivalent, but they produce acid reactions in water solution because as salts of strong acids with weak bases, they hydrolyze to form acid solutions. Solutions of each salt, of varying concentrations, were prepared and the pH, titrable acidity and iron and sulphate

Jan 1, 1952

By B. F. Buie

For over 200 years meerschaum has been a significant item of trade between the Near East and countries to the west. Best-known for its use in making smoking pipes and cigar and cigarette holders, it is also used in making a variety of decorative and ornamental items. It is easily carved, and is given an attractive, lustrous finish by rubbing. No published specifications are known, but compact form, purity, uniform whiteness or light color, and uniform, porous texture appear to be requisites. Fig. I a shows the appearance of a piece of crude meerschaum from Turkey; Fig. lb a carved item; and Fig. lc, d, and e show the fibrous and porous texture as revealed by the scanning electron microscope. Neither a major industrial mineral nor a precious stone, meerschaum nevertheless holds a record of long-and continuing-association with art and personal affairs of man. It is also a mineral to which modem methods of exploration and production probably could be profitably applied. An interesting account of the preparation and use of meerschaum in the early part of this century is given by Sterrett (1907). Geology and Mining Mineralogy Meerschaum is recognized now to be the compact variety of sepiolite, the claylike variety of which is one of the minerals included in the chapter on clays. The word meerschaum, from the German meaning "sea foam," was in earlier times used synonymously with sepiolite, a word of Greek origin suggestive of the resemblance of the compact variety-then the only variety known-to cuttlefish bone. At one time meerschaum was used as the commercial name, and sepiolite for the scientific name. However, to think of meerschaum as the name by which sepiolite is known commercially is no longer valid, in view of the recent emergence of the earthy variety as a competitor of bentonite and other clay materials. Present tendency is to restrict the term meerschaum to the compact variety, and to use the term sepiolite as a more general name to include both the compact and earthy varieties. This is the terminology followed in this publication. Meerschaum typically is white to light gray, has a hardness of 2 to 2 ½ , conchoidal to irregular fracture, and specific gravity varying with porosity from about 2 to less than 1. The composition is somewhat variable,- but is near that determined by Schaller (1936) for sepiolite as 2MgO.3SiO2.4H2O. A more modern for mula based on X-ray determination of the crystal structure is given by Caillére and Henin (1961) as (Site) (Mg9)030(OH)6(0H2)46H20. The reason for the firm, compact nature of meerschaum, in contrast with the earthy variety of sepiolite, is not fully understood. It may be due to the presence of a very minor amount of some bonding material such as silica. Scanning electron microscope (SEM) photographs of a specimen from Turkey (Figs. lc-le) indicate that the meerschaum is composed predominantly, if not entirely, of crystalline fibers which merge into sheetlike forms in a complex, intertwined mass. Detailed X-ray and crystal structure data, as well as some data on thermal stability range, are given by Caillère and Hénin (1961) for the sepiolite family of minerals. Mode of Occurrence and Origin Most authors have attributed the origin of meerschaum to alteration of serpentine or other magnesian minerals. The occurrence in alluvium and other surficial deposits does not necessarily indicate that the alteration was supergene. In fact, hydrothermal origin appears more likely for some deposits, though not for all.

Jan 1, 1983

By J. R. Morison, M. P. O’Brein, J. W. Johnson, S. A. Schaaf

The force exerted by unbroken surface waves on a cylindrical object, such as a pile, which extends from the bottom upward above the wave crest, is made up of two components, namely: 1. A drag force proportional to the square of the velocity which may be represented by a drag coefficient having substantially the same value as for steady flow, and 2. A virtual mass force proportional to the horizontal component of the accelerative force exerted on the mass of water displaced by the pile. These relationships follow directly from wave theory and have been confirmed by measurements in the Fluid Mechanics Laboratory of the University of California, Berkeley. The maximum force exerted by breakers or incipient breakers is impulsive in nature, reaching a value much greater than that produced by unbroken waves but enduring for only a short time interval. This impulsive force represents the ultimate development of the accelerative force and is produced by the steep wave front and large horizontal acceleration at the front of a breaker. This impulsive force greatly exceed. the drag force computed from the particle velocities of the breaker. The reader is cautioned that these preliminary results are applicable only to single piles without bracing and are likely to be modified somewhat where multiple piles are driven, one within the influence of the other or where multiple piles are connected by submerged bracing. This paper is essentially a preliminary report submitted at this time because of the current importance of wave forces in the design of offshore structures. An extended series of additional experiments is planned for the near future. Theoretical Relationships For the sake of simplicity of treatment, the theory will be developed from the equations for waves of small amplitude. The horizontal displacement of a water particle is described by the equation 2p cosh — (d + z) H L 2pt X =----------------------sin ----- . , (1) 2 2pD T sinh------ L The horizontal component of the orbital velocity is obtained by differentiation with respect to time as 2p cosh — (d + z) pH L 2pt u = ------------------- cos— .... (2) sinh- L The acceleration of the water particles at any position is obtained by again differentiating with respect to time as 2p cosh — (d + z) 9 u -2vH L 2pt -----=----------------------------sin ----- . . (3) 3 t T2 2pd T sinh------ L where H = wave height — ft L = wave length — ft d = still water depth — ft z = depth below the still water measured negatively downward — ft. T = wave period — sec t = time — sec The force exerted on a differential section, dz, in length is pD2 s u pD 1 dF= [CM (p/4) st + Cn/2 u2] dz • • (4) where D = pile diameter — ft p = water mass density — slugs/ft3 C, = coefficient of mass C,, = coefficient of drag Substituting for a s u/s t arid u2 from Eqs. (3) and (2), the force per unit length at any position z is dF p2 pD H2 &apos; / = — [- fM sin ? ± fD cos2 ? ] . . . (5) dz 2T2 fM D fD 2pt Cm = pA/H:CD = A2;? = T [+ cos2 ? for 0 < ? < p/2 cosh— (d+z) 3p L — < o < 2p Sin L -cos2 ? for p/2 <? <3p/2 The sin 9 term (inertia) i- negative for 0 < 0 < p and positive for p < ? < 2p. Values of A and A&apos; appear in Fig. 1

Jan 1, 1950

By C. E. Violet, R. J. Borg, E. M. Howard

The miscibility gap in the Au-Ni system has been determined by Mossbauer spectroscopy, with used as a probe. The phase boundaries were determined from the compositional dependence of both the isomer shift and Curie temperature. X-ray diffraction measurements were also used to confirm the Mossbauer results. 1 HE purpose of this research is to demonstrate the application of Mbssbauer spectroscopy to the determination of phase boundaries and to redetermine the miscibility gap by an independent and novel technique. The techniques evolved in this study are readily applicable to other polyphase systems and are generally as quick and accurate as the more conventional methods, e.g., metallography, X-ray diffraction, thermal analysis, and so forth. To be sure, not all polyphase systems will lend themselves favorably to Mijssbauer investigations, but this is a problem met in the use of conventional methods as well. The Mbssbauer spectrum responds to a different set of physical parameters, and consequently provides an entirely independent method of analysis. It is especially useful if the system has either a ferromagnetic or an antiferromagnetic transition. The Au-Ni system was selected because alloys containing more than -60 at. pct Ni become magnetically ordered at low temperatures; also the miscibility gap is quite well established (see Ref. 7 for a compilation of pertinent references, also Fig. 11, and thus provides a reliable test of this novel procedure. As Fe is the most commonly used Mijssbauer isotope, there exists a wealth of information concerning its behavior in iron-containing alloys and compounds. However, as yet there have been relatively few experiments using it as a probe to investigate nonferrous systems. By choosing a nonferrous alloy system, we are able to demonstrate that its use is not restricted to systems containing iron as one of the major constituents. Wertheim and ~ernick&apos; have used the same method to investigate Cu-Ni, and demonstrated that one can obtain a systematic variation in the isomer shift and magnetic hyperfine field. However, we believe this to be the first time these techniques have been used to establish phase boundaries. Two hyperfine interactions were measured and used to determine the phase boundaries, viz., the magnetic hyperfine splitting and the isomer shift which in this alloy system are both strong functions of composition. Calibration curves were established based upon single-phase solid solutions obtained by quenching from temperatures well above the maximum of the miscibility gap, see Fig. 1. Solid solutions containing 25, 50, 65, 75, 85, 92, and 96 pct Ni as well as pure nickel were used in the calibration procedure. Fig. 2 shows the Curie temperature, TC, and the isomer shift, v,, as determined from the Mbssbauer spectra, and variation in lattice parameter as determined by X-ray diffraction, as functions of composition. The compositions of the two-phase systems quenched from temperatures within the miscibility gap are obtained by comparing their respective values of TC and v0 with the calibration data. I) EXPERIMENTAL Mbssbauer sources were made by fusing the component metals in a tungsten arc melter, which has a water-cooled copper hearth. Both nickel and gold were 99.999 pct pure, and the melting was done in an atmosphere of purified argon. The alloys were rolled, diced,

Jan 1, 1969

By M. A. Dayananda

Based on the Kirkendall frame of reference, a method is proposed for the determination of atomic mobilities of all the diffusing species in a multicorn-ponent system with a single diffusion couple. The method is based on an atomic mobility model developed on the concept of negligible interactions among the intrinsic fluxes. It is shown in the model that mobilities can be obtained directly from the cumulative intrinsic fluxes past the Kirkendall interface. The proposed method replaces the need for a prior determination of interdiffusion coefficients far the calculation of mobilities. Relations between intrinsic diffusion coefficients and mobilities are derived and the mobility calculations are illustrated with diffusion data in Cu-Zn-Mn alloys at 850°C. ThE concept of "intrinsic flux" with respect to a fixed lattice was introduced "i Darken1 to explain toa Kirkendall effect2 demonstrated by the motion of inert markers during isothermal diffusion in single-phase binary solid solutions. Based on this concept, intrinsic diffusion studies have been made in various binary metallic systems3,4 employing such a lattice frame of reference, commonly referred to as the Kirkendall interface. Similar approaches, both theoretical and experimental, have been presented5"10 to study intrinsic diffusion in multicomponent systems. Based on the direct integration of Fick&apos;s law extended to multicomponent diffusion, Philibert and Guy8 proposed a method for the determination of intrinsic diffusion coefficients. For an n-component system, this procedure requires an experimental study with (n — 1) diffusion couples, all having their Kirkendall interfaces at the same compositio;, where n(n — 1) intrinsic diffusion coefficients are defined. This technique has been employed for ternary diffusion studies by Dayananda and Grace" and Guy and Leroy.11 A different approach is recommended by Ziebold and Cooper,12 who have derived relations between interdiffusion coefficients and atomic mobilities employing fluxes referred to the local center of volume. Their analysis is based on the simplifying assumption of negligible interactions among intrinsic fluxes. This assumption has been considered satisfactory for dilute solutions.5"7 The use of this analysis for the calculation of mobilities requires an initial determination of interdiffusion coefficients with a set of diffusion couples having intersecting diffusion paths. It is the purpose of this paper to propose a method that would permit a direct determination of mobilities of all components of a multicomponent system from a single diffusion couple. This method is based on a mo- bility model developed with diffusion fluxes referred directly to the Kirkendall interface, generally identified by inert markers. gen erall, like that of Ziebold and Cooper,12 employs the simplifying assumption that the flux of each component relative to a fixed lattice is caused only by the driving force of its own chemical potential gradient. THE KIRKENDALL INTERFACE Inert markers are employed in diffusion couples to locate experimentally the position of the Kirkendall interface. They are initially placed at the weld interface for "sandwich" couples, or at the original vapor-solid interface for vapor-solid couples. Studies of marker motion in binary systems3&apos;4 with both types of couples indicate that markers remain in a plane of constant composition and move with this plane para-bolically with time. Parabolic marker movements were also observed in ternary Cu-Zn-Mn couples by Dayananda and Grace.10 It is reasonable to expect a similar marker behavior even for diffusion couples with a higher number of components.

Jan 1, 1969

By W. P. Evans, R. W. Buenneke

Warren and Averbach&apos;s multiple order, Fourier method was applied to solid specimens of SAE 1045 steel. The material was hardened to three hardness levels and specimens of each hardness were shot peened to three intensities. Particle size, root-mem-square strain, mean strain, md macro residual stress were determined for each. Microstrains caused by either hardening or peening varied markedly over microregions. In general, increasing the hardness or peening intensity increased the rms strain and decreased the particle size. Similar effects were observed by varying hardness and peening intensity independently. At a Rockwell hardness of C 50, peening had little effect on line broadening, but both mean strain and macro residual stress increased. Mean strain was independent of column length. Induced macro residual stress by peening was affected most by initial hardness, but not by specific peening intensity. The purpose of this work is to establish the state of residual strain and particle size by X-ray diffraction in hardened and cold-worked plain carbon steel and attempt to relate these X-ray measured parameters to fatigue performance. X-ray line broadening (and its micro implications), along with X-ray residual stress (and its macro implications), may be basic indicators of the inherent fatigue resistance of the material. X-ray line broadening is caused by variable lattice strains and small particle size. Both are a result of plastic deformation which accompanies hardening or cold working processes. Therefore, X-ray line broadening is a good measure of both. warren1 has recently reviewed the Warren and Averbach2,3 Fourier analysis of line broadening. Strain and particle size effects can be separated because broadening due to particle size is independent of order of the diffraction peaks, while broadening due to strain is not. Microstrain is obtained as a root-mean-square strain averaged over discrete distances within the crystals causing diffraction. These distances are quite small, varying from 10 to 10081, and may be interpreted as the gage length over which the strains are averaged. Because of their variable nature, the X-ray line is broadened. The plot of rms strain vs distance (or column length) within the specimen gives a measure of their variability. Small particles also cause X-ray line broadening as already mentioned. A particle is interpreted as a region within a crystal or grain which diffracts X-rays coherently. This region is one of given orientation and may be bounded by a small angle grain boundary, dislocations, a twin boundary, or a stacking fault. The present work covers measurement of X-ray line broadening and macro residual stress on an SAE 1045 steel, quenched and tempered to various hardnesses. Various amounts of cold working were produced by shot peening the surfaces to various Almen intensities. Particle size, root-mean-square strain, and mean strain were calculated from the Fourier coefficients of the X-ray diffraction profiles in a direction normal to the peened surface. No effort was made to separate the various causes of particle size broadening. Macro residual stresses were reported in directions parallel to the peened surface. I) X-RAY METHOD The Fourier coefficients were determined for the 110 and 220 X-ray profiles. They were corrected for instrumental broadening by the method of Stokes,4 using an annealed reference specimen of similar geometry presumed to be free from broadening due to small particles and distortions. The nth Fourier cosine coefficient, A,, is related to a particle size coefficient, Ap, and a distortional coefficient, ADn, by the equation:

Jan 1, 1963

By Glenn C. Waterman

Richard Strong (Oliver Iron Mining Div., U. S. Steel Corp.)—Mr. Waterman states (p. 59, Trans., January 1954): "Core-sludge combining factors have been calculaied for any combination of core-sludge recovery on the basis of several logical assumptions: 1—The sludge sample loses reliability geometrically as sludge recovery drops. 2—The sludge sample should not be used if the percentage of sludge return is less than the percentage of core recovered. 3—A core sample should receive a weighting at least equal to the percentage of core recovery." Assumptions 1 and 2 seem justified at Chuquicamata and most geologists would agree to the validity of assumption 3. However, contrary to the statement quoted above, the core sample does not in general receive a weighting at least equal to the percentage of core recovery when the Chuquicamata methgd is used. Furthermore, the basic Chuquicamata method is identical to the Longyear or relative volume core-sludge assay combining method. Finally, the Chuquicamata method does not, in its present form, reflect true geometric loss in sludge sample reliability according to the relationship L = AR (N-1) The basic equations representing the two steps of the Chuquicamata method can be combined algebraically as follows (using the symbology of the original article except as noted): Vol A + B Assay 2 = ASA = Assay 1 Vol A VolB Core Assay [I] Vol A CA.F + ASA (100 —F) Combined grade =[21 100 Pct where F and (100 — F) are the core and adjusted sludge assay factors from Fig. 3. Substituting Eqs. 1 and 2 and collecting terms Combined grade = Vol B Vol A + B CAF (100—-F) + Assay 1 (100-F) Vol A Vol A 100 pct Eq. 3 is a unified and general statement of the Chuquicamata method. The true core factor includes not only the factor F from Fig. 3 but also the quantity VolB ------------- (100 — F), which is implicit in the value of Vol A the adjusted sludge assay. This quantity is real and positive for all values of F and core recovery less than 100. Therefore the true core factor is always less than F except when F is equal to 100. If sludge recovery is 100 pct, Eq. 3 can be further simplified as follows: Let F = percentage of core recovered. Let Vol A = Vdh (100 Pct — Pct CR) where Vdh is the total volume of the sampled interval and let Vol B = (Vdh — Vc.) Pct CR where V, is the core volume in the sampled interval at 100 pct core recovery. Then combined grade = Vo V. CA Pct CR- + Assay 1, 100 Pct — Pct CR Vdh Vdh [4] 100 Pct Eq. 4 shows that when sludge recovery is 100 pct the laboratory sludge assay receives significant weight in the Chuquicamata method, even at 100 pct core recovery. The maximum weight assigned to the laboratory sludge assay depends on drillhole size, as follows: Eq. 4, with suitable changes in symbology, is identical to Royce&apos;s formula 8,&apos; which is a statement of the Longyear or relative volume method of combining core and sludge assays. If Mr. Waterman&apos;s assumption 3 is of paramount concern to the geologist, the Royce method (for core recoveries of 60 pct and above) or a method employing the percentage of core recovered as a core weighting factor are the only recognized methods known to the writer which achieve the desired result. A modification of the latter method embodying Mr. Waterman&apos;s assumptions 1 and 2 would result from applying the factors from Fig. 3 directly to the laboratory core and sludge assays.

Jan 1, 1956

By E. H. Rennhack, J. F. Libsch

Definite transition behavior was found in unalloyed titanium at 0.13 pct 0 equivalent. The addition of 0.5 Sn, 1.0 Al, 0.5 Al, and 1.0 Sn lowers the tvansition temperature of titanium at oxygen equivalents exceeding 0.22, 0.29, 0.40, and 0.51, respectively. Metallographic evidence indicates that progressive amounts of oxygen restrict deformation at low temperatures resulting eventually in brittle fracture. The presence of tin or aluminum is thought to alter the atomic distribution of oxygen within the titanium lattice in such a manner as to facilitate some degree of slip and twinning. 1 ITANIUM-like iron and zinc experiences a transition from ductile to brittle fracture with decreasing temperature. The presence of sufficient quantities of the interstitial elements, carbon, oxygen, and nitrogen in solid solution, has been shown to progressively lower the room-temperature impact resistance of titanium with increasing interstitial content.1"1 Ogden,et al,2 reported finding no transition from ductile to brittle fracture with decreasing temperature in iodide titanium. However, a definite transition was found to occur at 0.36 pct 0 equivalent in an alloy containing 0.47 pct carbon in solid solution. The oxygen equivalent in this case was obtained by assuming the effects of carbon, oxygen, and nitrogen in combination on the impact properties of titanium to be additive on the same basis as their separate effects on tensile strength, namely: Oe = 2/3 (pct C) + pet 0 + 2 (pet N) They concluded that the tendency toward transition behavior is dependent on the total interstitial content in solid solution and not on any one particular interstitial element. Rennhack,4 however, recently found transition behavior in iodide titanium at an oxygen equivalent of 0.17 pct. Ogden, etal3, reported that the strengthening effects of carbon, oxygen, and nitrogen in titanium decrease with the addition of tin. They showed that tin additions increase the tolerance of titanium for the interstitials, that is, 10 pct Sn permitted individual additions of up to 0.4 wt pct of the interstitial elements without any significant loss in ductility. Aluminum tends to decrease ductility and impact strength of titanium for a given interstitial ~ontent.3 Van Thyne and Kessler5 found that the solid solubility of carbon in titanium doubled in the presence of 10 pct Al. The precise effects of tin and aluminum in the nrespncp of rorvfen nn the impact properties of titanium had previously not been determined. The high oxygen tolerance of titanium containing tin may provide a suitable means for improving the impact properties of titanium containing the interstitial elements, particularly oxygen. Unlike tin, however, aluminum has a high affinity for oxygen and will reduce rutile titanium dioxide (TiO2)by a thermit-type reaction.6 Thus, the atomic distribution of oxygen in titanium might be different in the presence of aluminum. The present work was undertaken to: 1) Determine the effect of oxygen on the transition behavior of unalloyed iodide titanium. 2) Determine the effect of small amounts of tin and aluminum on the transition behavior of iodide titanium in the presence of oxygen and other interstitial~. EXPERIMENTAL Three different lots of iodide titanium were employed to prepare the alloys studied in the present work. Their chemical composition is presented in Table I. The compositions of the tin and aluminum used for alloying are shown in Table 11. Oxygen additions were made using calcined rutile titanium dioxide (TiO2)of 99.7 pct purity. Alloy Preparation—Four titanium-base alloys containing separate additions of 0.5 and 1.0 pct each

Jan 1, 1960

By Robert E. Ogilvie, Zvonimir Ban

Oxidation experiments were conducted above 600°C to investigate the oxidation products formed on the surface of MoSi2. Results are presented which indicate that minor iron impurities play a key role in the oxidation behavior of MoSi2 above 600 °C. Based on considerations of the crystal chemistry of the oxidation products, MoSi2 with rhenium and iron additions was found to be resistant to oxidation in the pesting temperature range. AS early as 1914, Honigschmidtl observed that some silicides of molybdenum exhibited high resistance to oxidation at elevated temperatures. This fact did not arouse much interest until 1950, when Kieffer and cerwenka2 examined this property in more detail. They found that Mo-Si alloys with approximately 70 pct Mo (by weight) could be heated to 1600°C in an oxidizing atmosphere without any significant damage. The surface was found to be protected by the formation of an extremely thin silica glass layer which had no tendency to spa11 during subsequent thermal cycling. In 1955, Fitzer3 discovered that even solid bodies made of MoSi2 completely oxidized within a relatively short time when exposed to the air in the temperature range from 300° to 600°C. To describe this phenomenon he proposed the name "molybdenum disilicide &apos;pest&apos; ", clearly analogous to the previously observed "tin plague" ("tin pest") which, however, arises as the result of a phase transformation. Studies performed by Fitzer and, in particular, one published recently by Berkowitz, Blackburn, and Fel-ten,&apos; comprise the most extensive research to date on the pest phenomenon in MoSi2, as far as the fundamen- tal mechanism of the process is concerned. The first of these studies revealed the existence of a crystalline phase which appeared at the surface at 750°C and dissolved in the glassy silica layer at 1150°C. The logical assumption was that this phase was some reaction product of MOO3 and SiO2. The formation of a reaction product of this type seemed probable since it had been mentioned by Glemser and Lutz6 in a paper describing their studies of molybdenum oxides; however, this assumption was later disproved.8 It is our belief that information concerning the exact nature of this crystalline phase may be important for a better understanding of both pesting and the protection mechanism. Therefore, since the only available general description of the pest phenomenon was that of Fitzer, it was decided to reproduce his experiments. These experiments established that, in addition to the "pest" and "nonpest" temperature range, an intermediate region exists between 600" and approximately 650°C. This region is characterized by the appearance of a variable amount of yellow to orange colored crystals. The electron-beam microanalyzer was used to qualitatively determine their composition. Iron and molybdenum were found to be major constituents. This result can be explained based on the following facts: 1) iron, according to literature data,* is the most common impurity in molybdenum powder, and its content can be as high as 0.25 pct; 2) technical silicon powder usually contains iron; 3) steel ball mills are often used for the crushing and grinding of MoSi2. In order to clarify the exact role of iron, it was deliberately added to a stoichiometric mixture of molybdenum and silicon. The observed results corroborated the previous experiment, proving that iron (probably as some silicide phase) concentrates along the grain boundaries. I) EXPERIMENTAL PROCEDURE A) Oxidation of MoSi2 with Iron Additions. 1) Specimen Preparation. Specimens were prepared by both

Jan 1, 1967

By S. Kado, G. Derge, L. Yang

Self-diffusion coefficients of silver in molten silver have been measured by means of the capillary-reservoir method in the temperature range 1002" to 1105°C. The results can be .represented by the equation D = (7.10 i 0.06) X 10-4 exp [(—8150 ± 1130)/RT]. The heat of activation agrees within the limit of experimental uncertainty with that for the viscous flow. The validity of the Eyring and the Stokes-Einstein equations are examined on the basis of the self-diffusion coefficients obtained and the known viscosity data of molten silver. MEASUREMENT of the self-diffusion coefficient of silver in molten silver was made in the temperature range 1275° to 1378°K, using the capillary-reservoir method and &"&apos; as the radioactive tracer. The experimental arrangement is shown in Fig. 1. Silver of 99.99 pct purity (fine silver), was melted and degassed in vacuum in a graphite crucible situated inside a McDanel vacuum jacket. The crucible (4 in. tall and 1 in. ID) was protected both at the top and at the bottom with graphite shields and contained about 220 g of silver. The sample holder was a piece of graphite rod (1 in. long and 1/2 in. diam) with 4 capillaries drilled longitudinally into it. The holder was screwed onto a long graphite rod (12 in. long and 74 in. diam) which was connected to a steel disk hanging on a nylon string through a glass pulley. The steel disk kept the sample holder at the center of the McDanel tube and was heavy enough to overcome the buoyancy when the holder was lowered into the molten silver. By turning a handle connected to the pulley through a tapered glass joint, it was possible to raise or lower the sample holder without breaking the vacuum. Two such arrangements were constructed, sitting side by side in 2 Kanthal furnaces. One with non-radioactive silver in its crucible was used for the diffusion run and the other with radioactive silver in its crucible was used for filling the capillaries. To fill the capillaries with radioactive silver, the sample holder was degassed first and then lowered into the radioactive molten silver in vacuum. Purified argon gas was then admitted into the system to push the liquid silver into the capillaries. After cooling in argon, the filled capillaries were polished on emery paper to expose the top of the rod and used immediately as samples for the diffusion run which was carried out at the same temperature as that used for filling the capillaries. During the diffusion run, the samples were degassed in vacuum and lowered slowly into the nonradioactive molten silver before purified argon was admitted into the system. After a predetermined period of time, the samples were raised out of the melt and cooled in argon. The temperature of the melt was measured before and after the run with a chromel-alumel thermocouple inside a McDanel protection tube. Another chromel-alumel thermocouple attached to the outside wall of the McDanel vacuum jacket was used to indicate any fluctuation in the temperature of the furnace during the run, which was found to be less than ± 2°C for the longest run made (93 min). The temperature gradient inside the molten silver was found to be negligible. No significant difference was observed in the results obtained whether the melt was stagnant during the run or was stirred by raising and lowering the sample holder slowly a few times a minute for a distance of about 1/4 in. inside the melt.

Jan 1, 1959

By C. A. Siebert, S. H. Bush

Isothermal temper-embrittlement studies were conducted on a 5140 steel at various temperatures for times as long as 3000 hr. Specimens from the embrittled steel were subjected to impact tests, metallographic examination, microhardness, and lattice-parameter measurements. SEVERAL of the steels in the low alloy group are subject to a pronounced decrease in impact energy if held within, or cooled slowly through, a range of temperatures below the lower critical. This phenomenon, known as temper embrittlement, is quite pronounced in the chromium steels of which AISI 5140 is typical. This study considered the response of one heat of 5140 steel when embrittled isothermally at various temperatures for times as long as 3000 hr. Excellent reviews of the work done in the field of temper embrittlement have been written by Hollomonl and Woodfine.&apos; Both authors list the various theories which have been advanced to explain temper embrittlement. Some of the mechanisms considered were: 1—a transformation below 700°C; 2—an allotropic modification of iron; 3—precipitation from the ferrite of such compounds as carbides, nitrides, phosphides, or chromium oxides; 4—decomposition of retained austenite; 5—modification of special carbides; 6—grain-boundary segregation; and 7—selective distribution of carbides. The present study investigated the changes in hardness, Meyer&apos;s number, impact properties, micro-structure, and lattice parameter which occurred on embrittlement. Previous studies considered the influence of microstructure and of prior austenitic grain size3 on the response of 5140 steel to temper embrittlement. Equipment and Procedure All samples were taken from one heat of 5140 steel; the chemical composition of this steel was: 0.43 pct C, 0.86 pct Mn, 0.020 pct P, 0.019 pct S, 0.27 pct Si, 0.84 pct Cr, 0.10 pct Ni, 0.06 pct Mo, 0.10 pct Cu, and the remainder Fe. The material was received as % in. rounds. This stock was cut down to blanks measuring approximately 0.425~0.425~2.196 in. Heat Treatment: The rough blanks were normalized at 1600°F (870°C) for 1 hr, then austenitized at 1600°F (870°C) for 1 1/2 hr, and quenched into an agitated oil bath. The specimens were tempered at 1275°F (690°C) for 5 hr and water quenched. These tempered specimens were designated as the toughened state. Embrittling Treatments: The tempered bars were divided into sets and subjected to the various embrittling treatments listed in Table I. Temperatures from 750" to 1050°F were investigated for times of 1 to 3000 hr. Special tests to determine the effect of heating a short time at a higher temperature after long-time embrittlement at some lower temperature were also conducted. All specimens were water quenched at the end of the embrittling cycle, then ground and notched to obtain standard Charpy V-notch specimens. Impact Tests: The bars were fractured in a 260 ft-lb Charpy impact unit; specimens were fractured at temperatures ranging from —315°F to room temperature. Fixed temperatures used consisted of —315°F with liquid nitrogen, —115°F with dry ice and acetone, and 32°F with ice and water. Intermediate temperatures were obtained by suspending the bars in a jig over the liquid nitrogen, dry ice and acetone, or ice and water.

Jan 1, 1955

By A. R. Gregory, M. R. J. Wyllie

The literature reveals that scant attention has been paid to the systematic experimental determination of the formation factors of unconsolidated porous media. No experiments appear to have been made on the effect of increasing cementation on the formation factor of an initially unconsolidated porous medium. Measurements have accordingly been made of formation factors as a function of porosity for aggregates of spheres in the porobity range 12-56 per cent and of cubes, cylinders, discs and triangular prisms in the porosity range 30-45 per cent. The results are examined in the light of the theoretical equations of Clerk Maxwell. Fricke and Slawinski. Aggregates of unconsolidated spheres and beach sands have been artificially cemented with silica and the formation factor-porosity relationships determined. A theory is outlined which seeks to explain the results obtained and which postulates that formation factor and porosity data for consolidated sandatones may be used to determine the original porosity of the unconsolidated sands from which the consolidated sandstones were derived. It follows also that for consolidated sandstones F&apos; = C where F is formation factor, fractional porosity and C and k are constants. INTRODUCTION All schemes of electric log interpretation implicitly or explicitly require the use of formation resistivity factors or? as they are now generally called. formation factors. &apos;The originator both of the concept of formation factor and of the use of formation factor data in electric log interpretation was Archie.&apos; More recently it has been suggested that formation factors are of value in describing fluid flow in porous media. A full discussion of this problem together with adequate reference.: has been given by Wyllie and Spangler.&apos; In spite of the theoretical and practical importance of the subject, there appear to be remarkably few basic formation factor data in the petroleum literature. A wider search reveals that this situation is nut confined to the literature of the to industry. at various times over the last century, attempts have been made to compute the theoretical relationship between the formation factor and porosity of simple systems of unconsolidated particle.. However. the formulae derived are not all identical and the experimental evidence adduced in support of each i; not wholly convincitng. Most of the experimental work has been carried out on system. of unconsolidated spheres, although some attention has been given to systems of spheroids and cylinder. Other simple shapes have received neither theoretical nor experimental investigation. The writers feel that a better understanding of the formation factors of complex systems of practical importance requires a firm foundation of reliable experimental data applicable to simple systems. Accordingly, they have reviewed the relevant literature and have determined experimentally the relationship between the formation factor and porosity of unconsolidated aggregates of particles of regular geometrical shapes. Some experiments have also been carried out to investigate the effect of cementation on the formation factor-porosity relationship. PREVIOUS WORK Although the term formation factor was not used. the relationship between the resistivity of a solution containing dielectric solids and the resistivity of a similar solution not containing solids is an old and important problem. The formation factor of a system of dispersed spheres as a function of porosity was considered by Clerk Maxwell. Maxwell arrived theoretically at the following expression: where F is formation factor and fractional porosity. Lord Rayleigh&apos; also examined the problem of the formation factor of systems of spheres and cylinders and concluded that for spheres Clerk Maxwell&apos;.; expression gave a value of F whirl]. at low porosities particularly, was too small. However,

Jan 1, 1953

By Will Mitchell, Ford F. Miskell, C. L. Sollenberger

THE taconites in general are hard, tough ores, difficult to grind. Liberation of iron mineral constituents usually is accomplished by grinding the ore through at least 100 mesh, and often it has been found necessary to grind substantially through 325 mesh to achieve satisfactory recovery and grade in the concentration process. Because of the fineness of grind required and the enormous tonnages of material contemplated for treatment in the future, costs resulting from grinding media wear and power consumption, together with capital investment required for comminution, approach astronomical figures. Economy in any one of these elements per ton of material ground could very well reflect a considerable saving to the ferrous industry in yearly costs. With this in mind, the Research Laboratories of Allis-Chalmers Manufacturing Co. have launched a program to discover means of effecting this economy. The initial phase of the work as described here deals with a heat treatment of crushed raw ore, followed by thermal shock in cooling, for the preparation of rod mill feed. Several investigators 1-5 have noted an improvement in the grindabilities of ores treated in this manner. One investigator2 subjected low grade iron ores to heat treatment in an electric furnace. Basing his conclusions on screen analyses of crushed products, he observed that treated ore was more easily crushed than the untreated. He reported that observation of the treated and untreated ore through a microscope revealed cracks following the grain boundaries in treated ore, whereas no cracks were present in untreated ore. However, few if any have quantified the improvement in terms of total hp hours saved, reduction of wear of grinding media, or reduction of capital costs of grinding equipment involved. By means of Bond rod mill and ball mill grindabilities6 and by comparative wear tests, the conditions maintained during this investigation have been definitely evaluated. Heat treatment experiments have been made on a batch scale in a muffle furnace, followed by continuous scale experiments in a rotary kiln under various conditions of temperature, atmosphere, retention time, and quenching to determine the combination that would give the greatest improvement in the grindability of a taconite without affecting adversely the magnetic susceptibility of the magnetite. From these data, relative costs have been calculated for grinding both untreated and heat treated ore on a basis of plant capacity of 120 tons per hour. Heat requirements for a rotary kiln, as well as the kiln capacity required for the treatment, have been estimated. For these tests 50 tons of ore were obtained from the Aurora mine of the Erie Mining Co., Hibbing, Minn. The ore was reported&apos; to have been selected from the magnetic portion of the lower chert horizons. An average chemical analysis of this portion is shown in Table I and an approximate mineralogical analysis is shown in Table II. No attempt was made to differentiate between the various silicates because the compositions vary widely on the different horizons and depend on the degree of oxidation. Minnesotite, however, is the predominant silicate. The siderite grains were dispersed throughout the ore but were essentially associated with the rock-forming minerals. In a series of preliminary tests in which batches of -6 mesh ore were heat-treated in a muffle fur-

Jan 1, 1952

By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*