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By T. H. Janes

NATURAL abrasives of some type are found in all countries of the world. In order of their hardness the principal natural abrasives are diamond, corundum, emery, and garnet, which are termed high grade, and the various forms of silica, including pumice, pumicite, ground feldspar, china clay and, most important, sandstone. The properties qualifying materials for use as abrasives are hardness, toughness, grain shape and size, character of fracture, and purity or uniformity. For manufacture of bonded grain abrasives such as grinding wheels, the stability of the abrasive and its bonding characteristics are also important. No single property is paramount for all uses. Extreme hardness and toughness are needed for some applications, as in diamonds for drill bits, while for other purposes the capacity of the abrasive to break down slowly under use and to develop fresh cutting edges is of greatest importance, as with garnet for sandpaper. In dentifrices, soaps, and metal polishes, of course, hardness and toughness are objectionable. First among the natural abrasives, industrial diamonds are essentially of three types: l—bort, which includes off-color, flawed, or broken fragments unsuitable for gems; 2—carbonado, or black diamond, a very hard and extremely tough aggregate of very small diamond crystals; and 3—ballas, a very hard, tough globular mass of diamond crystals radiating from a common center. Bort comes from all diamond-producing centers, carbonados only from Brazil, and ballas chiefly from Brazil, although a few of this last group come from South Africa. By far the largest producer of industrial diamonds is the Belgian Congo; the Gold Coast, Angola, the Union of South Africa, and Sierra Leone supply most of the remainder. There is no production in Canada, which imports $6 to $9 million worth of industrial diamonds annually. Industrial diamonds find innumerable uses in modern industry. They are used for diamond drill bits for the mining industry; in diamond dies for wire drawing; in diamond-tipped tools for truing abrasive wheels and for turning and boring hard rubber, fibers, and plastics; and in diamond-toothed saws for sawing stone, glass, and metals. High-speed tool steels, cemented carbides, and other hard, dense alloys can be cut, sharpened, or shaped efficiently only with diamond-tipped tools and diamond grinding wheels. .. Second only to the diamond in hardness is corundum, an impure form of the ruby and sapphire gems consisting of alumina and oxygen (Al²O³) with impurities such as silica and ferric oxide. Corundum generally crystallizes from magmas rich in alumina and deficient in silica, as in the nepheline syenites of eastern Ontario. Grain corundum is used in the manufacture of grinding wheels; very coarse grain is used in snagging wheels. Both types of wheels are employed in the metal trades, where the hardness of corundum, coupled with its characteristic fracturing into sharp cutting edges, makes it an ideal cutting tool. The finest corundum (flour grades) is used for fine grinding of glass and high-precision lenses. From 1900 to 1921 Canada was the world's leading producer of corundum. Following this period the deposits located in northern Transvaal of the Union of South Africa supplied more and more of the world's requirements, and since 1940 South Africa has provided almost the entire output, which has ranged between 2500 to 7000 tons a year during the last decade. Minor amounts have also been produced in Mozambique, India, and Nyassaland. Opportunities for Mining Corundum Corundum deposits in southeastern Ontario are of three types, which may be described as follows: 1—Scattered, irregularly-shaped deposits of coarse-grained corundum which could be mined by means of small pits. About 10 groups of such deposits are known. Although the tonnage of individual deposits of this type is not great, it has been estimated that several years' ore supply is available for a small tonnage operation. Deposits average about 9 pct corundum. 2—Large irregular deposits of coarse-grained corundum which would require mining by adit with possibly a scavenger operation on the remains of former surface deposits. The Craigmont deposit of this type produced about 20,000 tons of corundum concentrate during operations between 1900 and 1913. Most of the readily available surface ore was removed by operators during that time. Reserves of ore above road level have been estimated to average 7 pct corundum, but none of the so-called reserves have been blocked out, or even indicated, by diamond drilling. From 1944 to 1946, 2025 tons of

Jan 1, 1955

By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.' The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

Vermont State Geological Survey, Burlington, Vt. G H. Perkins, State Geologist Most of the file reports of the State Geologist of Vermont were destroyed in a flood at Montpelier two or three years ago Full sets of 17 volumes may be seen only in libraries. The Annual Report for 1928 and the Annual Report for 1930 may still be had, as well as a few copies for the following years: 1901-2, 1907-8, 1909-10, 1915-16, 1921-22, 1923-24. These are distributed without charge. Flood-damaged copies of the two vols, Geology of Vermont, by Hager and Hitchcock, cost $3 plus postage For any of these volumes address State Librarian, Montpelier, Vermont.

Jan 1, 1933

Senator Smoot recently introduced his bill providing for the leasing of oil and coal lands. This bill provides only for the leasing of these lands from the Government and advocates government ownership of all government coal and oil lands. Under the provision of the bill as now proposed, 50 per cent. of all money received under the measure is to be paid to the state in which the land is located. The money must be used, however, for the construction and maintenance of roads and for schools. The last leasing bill was defeated when it was about to become law largely because of the fact that it allowed the sale of coal lands.

Jan 9, 1919

By O. P. Arora, I. L. Caplan, H. von E. Doering

ThE interpretation of X-ray and electron diffraction data obtained in plastic deformation studies of hcp a titanium requires knowledge of angular relationships between crystallographic planes and directions. Rarey el 01.' have calculated both interplanar angles and angles between directions for a number of c/a ratios. This information, although useful for approximate applications, does not provide exact data for specific hcp metals. Recently, Hu2 has tabulated interplanar angles specifically for hcp titanium. The present study augments the existing data on titanium by providing the angles between plane normals and rational crystallographic directions in addition to interplanar and interdirectional angles. These angular relationships were calculated on an IBM 360 Computer using a Fortran IV program.* Cal-

Jan 1, 1969

By James R. Cudworth

ENGINEERING has been taught at the University of Alabama for over a hundred years. The School of Mining and Metallurgy was authorized by the Board of Trustees in 1887 and four students were graduated in 1888. In 1919 the legislature directed that all mineral industry instruction in the state should be centralized at the University and designated the department of mining of the College of Engineering as the Alabama School of Mines and made financial provisions for carrying on both instructional and research work for the benefit of the mining industry of the state and for cooperation with the U. S. Bureau of Mines, which had established its Southern Experiment Station on the campus.

Jan 12, 1950

CHARLES E. WILSON'S second quarterly report "Meeting Defense Goals" was encouraging on the outlook for the mining industry, as prolonged demand for minerals seems assured; but for the individual engineer things are not so rosy. Ten percent of the gross national product is going for defense but the gross national product has been increased by 9 pct since the national emergency was declared apparently a commendable rate of progress. The increased production does not seem to have had the stabilizing effect on prices it should and housewives have been revising domestic budgets upward on a quarterly basis. Government economists have reached the conclusion that more taxes and wage and salary freezing are necessary to counteract inflation.

Jan 8, 1951

By F. Milton Lewis, Roshan B. Bhappu, James L. Coburn

Part one of this article, published in the September 1976 issue of MINING ENGINEERING, described procedures for analytically evaluating the physical and chemical properties of an ore; it also described various types of equipment that are available to the minerals engineer for designing required comminution operations. Part Two of this article illustrates the practical application of these principles to the design of a sound comminution system for a known set of ore characteristics. This exercise is aimed at giving the young engineer a review of the methods and procedures that are available for designing comminution systems. To illustrate these methods, a large-tonnage porphyry copper ore body with the following characteristics is selected:

Jan 11, 1976

By N. J. Feola, E. P. Klier

NOTCH properties of titanium materials have been extensively investigated in the impact test.'-" For the most part the impact strength meas- ured suggests a ductile-brittle transition that lies at relatively high temperatures, thus indicating a possible notch sensitive condition at ambient temperatures. Recently it has been shown' that the impact strength for unalloyed titanium, as for aluminum alloys, may be a nonsensitive index of notch sensitivity as provided by the notch strength as measured in the notch tensile test. The notch strength for unalloyed titanium was found to depend on the nitrogen and carbon contamination levels. In the present work the levels to which oxygen, nitrogen, and carbon contaminants can be tolerated without leading to excessive em-

Jan 1, 1958

By Glenn Allen

SAN FRANCISCO Mines of Mexico, Ltd. owns and operates an extensive group of claims in the San Francisco del Oro-Santa Barbara district, about 15 miles southwest of Parral, Chihuahua. The property comprises the mines, aerial tramways, flotation mill, power plant, shops, offices, assay and testing laboratories, modern hospital, water and sanitary system, quarters for miners, mechanics and operators, a well housed colony for Mexican staff employees and residences for foreigners. Each colony has a club house and mess and tennis courts. The employees have constructed a nine-hole golf course. In other words, the property is self-contained and completely integrated for production of lead and zinc concentrates from complex sulfide ores.

Jan 1, 1930

By J. H. Fletcher

AIR has been cooled, heated, washed; humidified and dehumidified for many purposes and in many industries. At a number of metal mines air is conditioned to reduce the high humidity and unbearable heat found in deep workings, and at some mines air is washed to allay siliceous dust. Steam is introduced into the intake air at many coal mines, particularly in winter, for the purpose of keeping loose coal dust so moistened that the hazard of an explosion is lessened. This paper will describe a further successful application of air conditioning in a coal mine, where, for over three years, all intake air has been cooled to a constant temperature for the sole purpose of preventing roof falls.

Jan 1, 1931

By C. C. Templeton, J. C. Rodgers

A key step in feed water treatment for generating wet steam for thermal oil recovery is the removal of calcium and magnesiunt hardness by cation-exchange series softening. Knowing the solubility of any scale forming salts in brines at elevated temperatures is necessary for fixing the level to which the feed water must be softened. Such calcium sulfate solubility data, previously not available above 392F, were determined by the authors in a flow equilibrium apparatus mud will be reported elsewhere. These data were used to develop a method for predicting the solubility of anhydrite in hot water or steam droplets for saturated steam pressures as high as 2,000 psig (637F). (The calcium sulfate solubility product is represented by a combination of two factors, one reflecting the effects of ionic strength and the other accounting for the effects of complex ion formation in either calcium-magnesium-rich or sulfate-rich brines.) The method is applied to a calcium-magnesium-rich brine If moderately high salinity from a pilot hot-water flood, I nd to several sulfate-rich, low-salinity feed waters and l lowdown (cooled steam droplets) samples from steam s ak operations. The predicted calcium hardness levels corresponding to the calcium sulfate solubilities agreed reasonably well with the results of laboratory solubility determinations run on the field samples. Further testing of the method is needed for brines of other composition classes. Existing field cation exchange softeners in the cases tested are performing adequately since all the samples were found to be undersaturated with respect to calcium sulfate at their operating temperatures. Introduction Prevention of scaling caused by precipitation of calcium sulfate (anhydrite) is of considerable concern in connection with thermal recovery processes using wet steam or hot water. To avoid anhydrite precipitation in a heated system, an engineer must keep the product of the calcium and sulfate concentrations in the water or steam droplets below the value of the solubility product of anhydrite for the temperature and brine composition in question. Usually it is most practical to keep the concentration product lower than the solubility product by keeping calcium low in the presence of high sulfate, or by keeping sulfate low in the presence of high calcium. This can be done by a choice of combinations of natural waters and water treatment processes (such as series cation exchange softening to remove calcium). Until recently, few anhydrite solubility data, particularly for solutions containing other salts, were available for temperatures above 392F (211 psig steam); Marshall, Slusher and Jones' studied the CaS0,-NaCI-H,O system up to 392F and surveyed the work of previous investigators. To model natural brines, one needs to study the solubility of anhydrite in aqueous solutions of sodium chloride, sodium sulfate, calcium chloride, magnesium chloride and their mixtures. Since steam pressures as high as 2,000 psig (637F) may be involved in thermal oil recovery projects, a solubility study was conducted between 482 and 617F.' Discussed in this paper is the application of these data to the prediction of anhydrite precipitation in some practical steam soak and hot-water injection projects. Any simple method for predicting the solubility of an inorganic compound over a wide range of temperatures and solution compositions must be based on some assumptions, and therefore must yield approximate results. On the one hand, natural brines contain too many ionic species for all to be included in a simple scheme; on the other hand, there is no adequate theoretical basis for the exact prediction of solubility in even simple solutions of mixed electrolytes. However, it is possible at a given temperature to base a reasonable prediction scheme on two phenomena:'-' the increase in solubility with increasing total concentrations of all ions (as measured by the ionic strength; see the Appendix), and an increase due to formation of cornplexes between calcium ions and sulfate ions and between sulfate and magnesium ions. Stiff and Davis' developed such a scheme for predicting the solubility of gypsum (CaSO, ¦ 2H,O) in brines at temperatures u~ to 212F. However, for the higher temperaturei of present interest, the stable solid phase is anhydrite (CaSO,). This study involves a two-part method for predicting anhydrite solubility products. First, one predicts a value K, for a given ionic strength I and a given temperature T corresponding to mo./msr, = 1 from data of the CaS0,-NaCI-H,O system. Second, one determines a group of factors F .= F(Ca) • F(Mg) • F(SO,), where the individual factors account for increases in the solubility product due to complex formation by high concentrations, respectively, of calcium, magnesium and sulfate. Combining the two parts, one obtains the solubility product in molalities as

Jan 1, 1969

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent investigations1. a data on relative grain boundary energies in silicon iron have been obtained. The present investigation is a continuation of this work along similar lines for the purpose of obtaining additional information on boundary energies. One aim has been to extend the data for a (110) series, which was formerly studied,' to small differences in orientation, since a recent theory3,4 based on a dislocation model of grain boundaries predicts a E. ? (A-ln ? )* form of energy curve for small differences in orientation. Another aim has been to provide data for a (100) series—all grains having (100) planes parallel with the surface of sheet speci-mens—and to compare the results with the predicted form of energy curve. Finally, information on the nature of approach to equilibrium conditions was to be obtained through observations on the movements of grain boundaries. Recently published papers2,3,5 have treated the mathematical problem of expressing equilibrium conditions for grain boundaries for the general case when boundary energy depends upon boundary orientation. The equilibrium equations, which relate equilibrium angles and grain boundary -free energies, contain additional terms that express the variation of energy with boundary rotation. It has been necessary in the present investigation, however, to neglect these additional terms since no data for their evaluation were available. Dropping the additional terms leads to the following approximate equations which were used: E12/sin ?3 = E18/sin?2 =E28/sin?1 or those of the form: E28 + E13 cos ?3 + E12 cos ?2 = 0 Experimental Procedure Except for sample F1, all specimens were made from two lots of silicon iron called C and L respectively. The compositions of these are listed in table I. In the preparation of 12 three-grain specimens for the present investigation, a controlled grain growth technique, which has been described previously,' was used. After preparation, the specimens were notched at the boundaries to shorten them as a means of providing more rapid approach to equilibrium in the anneals. Initial grain boundary angles were determined from micrographs taken at X500. Seven anneals, totaling about two days at 1300°C and two to four days at 1400°C, were run in an atmosphere of pure dry argon as described in a previous paper.' Boundary changes generally could be followed without metallographic surface preparation, because thermal etching occurred during the anneals. These observations indicated angle changes of as much as 35" in some instances, with the major changes occurring during the first anneal. Annealing was discontinued when the angles reached stationary values. Fig. 1 gives a schematic diagram for purposes of defining crystallographic and boundary directions for three grains with common plane parallel with the sheet. Differences in orientations (expressed by A) are the angles between [00l] directions. They can be calculated with the aid of the ?'s. The grain boundary angles can be calculated from the w'S. Results Results are given in table 11. Types of crystal-lographic planes refer to those parallel with the sheet. Orientations are given in terms of [00l] direc-tions as shown in fig. 1. Except for grain 3 of specimen H6, which was unintentionally tilted 7" out of a (100) plane, all grains generally were within 1" or 2" of the plane specified. The directions of boundaries were measured generally to within 1" on both upper and lower surfaces, and the average direc- tions were determined for use in calculating the grain boundary angles. Variations in grain boundary directions refer to deviations from average directions. Boundaries near the junction point for all specimens generally were very close to perpendicu-

Jan 1, 1951

By G. R. Countryman, G. H. Thomas, I. Fatt

Procedures are described for scaling up turbulent friction pressure drops of inelastic fluids and laminar friction pressure drops of inelastic/elastic fluids in circular ducts. The laminar scale-up calculation method does not require the use of arbitrarily defined flow models, and can be performed directly from laminar capillary viscometry data, or by means of a numerical solution of the integral equation for Poiseuille flow, inputing true shear rate-shearing stress data from other simple shearing experiments. e.g. Couette and plane Poiseuille flows. The turbulent scale up procedure, based on the Dodge-Metzner correlation for inelastic fluids, requires evaluating the characteristic rheological parameters at the existing wall stress under laminar flow conditions. Since the wall stress is the quantity sought in a pipe flow scale-up problem, a trial-and-err or solution is indicated, and therefore a calculation method has been developed and programmed for a medium-size magnetic-drum-memory digital computer. Laminar flow data from other somces may also be adapted to this turbulent scale-upmetbod for inelastic fluids. Comparisons between predicted and experimentally observed friction losses for generalized Reynolds numbers ranging from 3 — 32.000 indicate an error band width of less than 10 per cent in circular tubes ranging in size from 0.5 to 1.89 in. in diameter. INTRODUCTION Considerable effort has been devoted to the problem of establishing an accurate procedure for predicting the laminar and turbulent flow behavior of non-Newtonian materials in pipes from data obtained with small scale laboratory or pilot plant equipment, as evidenced by the variety of reviews on the subject.1-3 Although there does not appear to be a universally accepted scale-up method for laminar flow, the various methods currently employed can be divided into two principal categories depending upon whether a functional relationship between shear rate and shearing stress is assumed, or whether a generalized correlation is adopted. The methods of Hedstrom4 and of Weltmann are typical of the first category, while the generalized correlation of Metzner and Reed6 illustrates the second category. Under appropriate conditions either approach yields a reasonably satisfactory description of laminar flow behavior. In contrast, the prediction of non-Newtonian transitional and turbulent friction losses is much more complex. For example, certain types of materials have been observed to sustain laminar flow at much higher flow rates than Newtonian liquids. When turbulence does develop, the level of agitation is damped to such an extent that the friction factor is lower than that of the original low viscosity Newtonian medium. Extremely broad transition regions and "diameter effects" have also been noted in the turbulent flow of certain chemically complex materials.' Aside from the latter complications, which are attributed in part to viscoelasticity, the existence of a variety of scale-up procedures for predicting transitional and turbulent friction losses is due principally to the chioce of viscosity parameter used in the definition of the Reynolds number. In contrast, Dodge and Metzner have demonstrated that the friction factorReynolds number relationship for inelastic fluids can be satisfactorily generalized provided the fluid property parameters are evaluated at the existing wall shearing stress.* However, the quantity usually sought in a pipe flow scale-up problem is the wall stress, and hence a trial-and-error procedure is required when dealing with non-power law materials. In this report we discuss two calculation methods: (1) for determining the wall stress, and hence the friction pressure drop, for inelastic fluids under conditions of turbulent flow by means of an iterative procedure, and (2) for predicting laminar friction pressure drops without recourse to arbitrarily defined flow models.

By B. H. Caudle, R. L. Slobod, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.' These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.'! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By F. W. Jessen, R. W. Durie

The development in the laboratory of mall salt cavities illustrated that the rate at which salt dissolved was affected by the rate at which fresh water was injected into the cavity. Experiments carried out with small salt cores indicated, however, that the rate of salt removal with forced convection was not significantly different from that with natural convection, provided the flow was in the laminar range. The rate of salt removal was apparently controlled by the water salinity, which was indirectly determined by the rate at which fresh water was injected. With turbulent flow at the salt surface, the rate of salt removal could be increased several-fold with the same salinity in the cavity. A quantitative evaluation of the rate of salt removal under natural convection was attempted by using techniques developed for the analogous heat convection system. The values of the rate of salt removal obtained experimentally were considerably greater than the calculated values due to surface irregularities. To determine the effect of these irregularities, the rate of salt removal was found for a smooth surface by experimentally determining the rate of salt removal as an irregular surface developed and then extrapolating this trend back to initial time. Excellent agreement between the experimental and calculated values then were obtained. INTRODUCTION Underground cavities leached from massive salt formations have been used extensively for many years for storing LPG products. The development techniques for storing methane gases in the liquid state at a low temperature leads to speculation that underground salt cavities of controlled geometry may be quite important in this field. In any case, the increasing number of salt cavities used for storage indicates an impending need for a better knowledge of the washing process to efficiently develop maximum storage volumes within specified regions. It is the purpose of this paper to discuss some aspects of -the mechanism of the dissolution of salt in the formation of cavities of controlled geometry. Although no attempt is made to resolve the problems that may be associated with the storage of methane in the liquid state in salt formations, the fact that salt cavities can be formed at reasonable cost would appear to justify investigation in this direction. Further, underground cavities have the advantage of allowing storage at higher pressures (and hence higher temperatures) than surface installations. Although the thermal conductivity of salt is somewhat higher than frozen earths, 0.017 cal/(sec) (cm)(c) for salt at 32F vs 0.005 cal/(sec) (cm) () for ice at this temperature, this disadvantage is offset by the higher storage temperature in underground cavities. For example, at atmospheric pressure, the temperature of liquid methane would be —258F. In a storage cavity at 2,000 ft, the pressure would be approximately 1,000 psia, which would allow a storage temperature of -9OF. The formation temperature would be roughly 110F at this depth, hence the total temperature differential would be 200F. Under surface storage conditions the corresponding temperature difference would be some 333 F (75 F + 258 F). The results of this difference can be compared more readily by substituting the appropriate values of thermal conductivity, temperature difference, heat capacity and density into the solution of the diffusion equation for the unsteady linear conduction of heat. For the underground salt storage, the heat flux is 15cal/(sec) (sq cm), where t is the time in seconds from the initiation of the cooling. For the surface system, and using the thermal properties of ice at the average temperature, the corresponding figure is 21cal/(sec) (sq cm). Hence, the heat losses through ice under surface conditions would be some 30 per cent higher than the underground salt storage. This ratio would vary, considerablv. Of course, for other conditions, but it indicates that an advantage over surface facilities may be obtained by storage in underground salt cavities.

Jan 1, 1965

By R. L. Slobod, B. H. Caudle, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.' These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.'! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By Donald A. Corrigan, John Chipman

It is shown that the heat of solution of nitrogen in liquid-iron alloys is Proportional to the interaction coefficient. This proportionality forms the basis for a method of predicting nilrogen solubility at any temperature when the interaction coefficient is knoun at 1600°C ov when the solubility is known at some one temperature. A method for predicting the solubility of nitrogen in liquid steels, including alloy steels, was proposed some years ago by Langenberg.' Since the data available at that time were restricted to temperatures of about 1600°C, his predictions were similarly restricted. More recently, Nelssonz devised an approximate method for estimating nitrogen solubilities at higher temperatures. It is the purpose of the present paper to present a method by which the solubility of nitrogen at any temperature within the steelmaking range may be predicted from the known interaction coefficients at 1600°C. Nitrogen in iron and in all of the alloys to be considered here is known to obey Sieverts' Law; hence the activity of nitrogen in an alloy of fixed composition is proportional to its concentration, here expressed in weight percent. The activity of nitrogen is defined as equal to its weight percent in the binary Fe-N solution at any temperature. Its activity coefficient in any alloy is the comparison being made at equal values of T and PN2. In all alloys the activity coefficient changes with composition, log fN being a linear function of the percent of alloying element at low concentrations. In the following calculations the alloy compositions are restricted to those in which this linear relation is exhibited. For most systems this is a fairly wide range, for example up to 5 pct V and to 10 pct Cr or Ni. For this composition range. complex alloy is the same as that in the Fe-N-j ternary solution. Langenberg's method of prediction was based on Eq. [3], the values of log fN for various additions being taken from a graph. Instead of using the simple addition indicated in Eq. [3], he used a more complex method suggested for Fe-S-j alloys by Morris and Buehl.3 For the composition ranges in which Eq. [2] is valid the two methods are equivalent. Nelson extended the prediction to other temperatures on the assumption that logfN is inversely proportional to absolute temperature. It may be shown that inverse proportionality would result if the partial molal entropy of nitrogen were unaffected by addition of the alloy element, an assumption which Nelson designated as a "regular" solution. It has been shown recently by the authors4 that this assumption is not a good approximation. The heat of solution of nitrogen (N2) in an alloy may be obtained if the solubility is known as a function of temperature. Measurements of this nature have been reported recently by Beer5 for Fe-Mn alloys, by Nelsson2 for Fe-C, by El Tayeb and parlee6 for Fe-V, and by Pehlke and Elliott7 for many alloys embracing a wide range of compositions. In connection with the work of the last named authors it is noted that their Fig. 22 gives the heat effect per half mole rather than per mole of N2. In using their data we have shifted some of their values slightly by using the best straight line in preference to their curve. Their data, supplemented by others from the literature, are summarized in Table I. In Fig. 1 the heat of solution of nitrogen is shown as a function of composition for the several alloy systems. The difference between the heat effect in the alloy. AH; and that in pure

Jan 1, 1965

By K. C. Hong, R. B. Jensen

The problem of determining the optimum set of steam volumes and cycle lengths for a single well undergoing multicycle steam stimulation in order to maximize the cumulative discounted net income has been formulated mathematically and programmed for a digital computer. The mathematical fonnulation of the problem and the method for its solution are discussed in this paper. The oil production performance during each stimulation cycle was simulated by either a constant percentage or a harmonic decline. Using simple analytical expressions for production performance, the cumulative discounted net income and cumulative time of operation were related to the pertinent process and cost parameters and two principal process control variables (cycle length and steam injection volume). The discrete maximum principles was used to transform the equations for cumulative time of operation and cumulative discounted net income into a set of simultaneous equations. The simultaneous equations then were solved by trial and error on a digital computer to determine the set of cycle lengths and stem injection volumes that gives maximum cumulative discounted net income over the project life. INTRODUCTION Steam stimulation is a process for improving the oil recovery rate from wells producing high-viscosity crudes. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three phases: steam injection, soaking (steam condensation), and production. Significant increases in production rate following the stimulation operation result from heating the reservoir around the wellbore. As heat is removed with produced fluids and dissipated into nonproductive formations, the production rate declines, usually to near the prestimulation value. Typical production responses are given in case histories reported by Owens and Suter,l and are depicted in Fig. 1. Duration of the production phase is equal to the time for the oil production rate to decline to some specified value and is called the cycle length. (Cycle length is defined as the producing portion of the cycle and does not include the downtime required for steam injection and soaking operations.) Termination of the production phase coincides with the start of steaming for the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable. Models 2-4 have been developed to simulate behavior of a single well during one cycle of steam stimulation and have been used to investigate the effects of system and operating conditions on the production responses. However, these investigations have not shown how the models can be used to determine a most profitable set of operating conditions for a multicycle stimulation project. Perhaps these models are too complicated mathematically to be adapted readily to an optimization study. This paper presents a method for optimizing a multicycle steam stimulation project based on simple production performance models. First, the performance of a steam-stimulated well during each cycle was simulated by either a constant percentage or a harmonic decline model. Using these simple analytical expressions for production performance, the cumulative discounted net income (before tax) and cumulative time of operation for each cycle were related to the pertinent process and cost parameters and two process control variables—the cycle length and the steam injection volume. Finally, the profit function to be maximized was formed. The analogy between the above problem and problems of optimizing multistage decision processes that have been reported extensively in the chemical engineering literatures5-10 in recent years has led this investigation to the use of the discrete maximum principle.5-7 This principle was used to transform the equations for cumulative discounted net income and cumulative time of operation into a set of simultaneous equations characterizing the optimum operating conditions in terms of the two control variables. These equations

Jan 1, 1970

By Carl Wagner

This paper contains solutions of the differential equation of diffusion in binary alloys if the diffusion coefficient is an exponential function of the concentration of one of the components. THE general differential equation for one-dimensional diffusion in a binary system can be written as: where c is the concentration of one of the two components in any suitable units; x, the distance from a reference plane; t, time; and D, the diffusion coefficient. Hartley and Crank&apos; have pointed out that eq 1 with conventional length units for measuring the distance x holds only if the alloy can be regarded as a rigid framework. In general, this is not the case, especially if the lattice parameter varies appreciably with composition. If a modified coordinate system is used instead of an orthodox system based on the centimeter a:: length unit, eq 52 is obtained, which has the same general form as eq 1 and is generally valid. The necessary transformations are presented in the appendix. If&apos; D is independent of concentration, analytical solutions of eq 1 are known for numerous boundary conditions. If D depends on concentration, solutions based on known analytical functions are not available. Among others, Boltzmann2 and Matano3 have shown that the concentration c depends only on (x/t1/2) in the case of diffusion between two semi- infinite spaces with uniform initial concentrations: c = c, for x < 0, t = 0, i.e., x/tl/2 = — x [21] c = c2 for x > 0, t = 0, i.e., x/tl/2 = + a Moreover, Boltzmann and Matano have shown how D may be calculated as a function of concentration over the whole range of composition from c -c, to c = c2 if c as a function of (x/t1/2) for the initial conditions stated in eq 2 has been determined experimentally. Thus, for instance, in principle, the diffusion coefficient in silver-gold alloys may be calculated as a function of concentration for the whole range of composition from only one diffusion experiment with a couple of pure silver and pure gold welded together. If the diffusion coefficient D as a function of concentration c is known, a solution of eq 1 for boundary conditions as stated in eq 2 with arbitrarily chosen values of c, and C2 may be wanted. For instance, if the diffusion coefficient in an alloy A-B as a function of concentration has been derived from an experiment with a diffusion couple involving 0 and 30 pct B as initial. concentrations, the calculation of the concentration distribution in a diffusion couple involving other initial concentrations, e.g., 5 and 20 pct B, may be desired. This problem may be solved by numerical or graphical integration of eq l. The solution of an ordinary differential equation of second order, which results from using (x/t1/2) as an independent variable, can be computed quite rapidly if two conditions for the same value of the independent variable are given. In eq 2, however, two conditions are given for two

Jan 1, 1953