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By J. B. Cheatham, M. D. Biggs

This paper presents a systematic method for determining the forces on a simplified roller bit. The kinematics of an actual roller bit drilling in rock is complex; nevertheless, it is desirable to obtain an accurate analytical model.. As a preliminary study, the roller bit is represented here by a simple two-dimensional bit and the rock by a Coulomb plastic material. Results from previous work, plus additional assumptions, are incorporated into a computer program to determine the forces required to move the bit in a specified manner. Example problems are worked by use of this program. By studying similar drilling problems and by supporting laboratory work, one could eventually obtain an accurate analytical model for drilling by an actual roller bit. This could lead to the compilation of a catalog of results that, in turn, would allow selection of the optimum drill bit for any given situation. INTRODUCTION

Jan 1, 1970

By K. E. Gray, M. S. Seth

In Part I of this work,1 equations of elasticity were formulated for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure. Equations of elasticity and the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant rate of pressure or a constant rate of flow is maintained at the wellbore. In this paper, the approach presented earlier is extended to finite reservoirs for the cases of (1) steady-state flow, (2) constant pressures at the well bore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Results of this work show that radial and tangential stress gradients are high near the wellbore but diminish rapidt; away from the well; the vertical stress gradient behaves in the same way but is less severe. Radial stresses are compressive or neutral, whereas tangential and vertical stresses may be tensile, neutral or com-pressive, depending upon the boundary conditions, the physical Properties of the system and the radial distance involved (vertical stresses are always compressive in an unbounded system1. For constant boundary pressures, both radial and tangential stresses increase with time whereas they both decrease for a closed outer boundary and constant pressure at the wellbore. The vertical stress decreases with time for both systems. For steady-state systems, radial displacement may be positive or negative, depending upon the dimensions of the system, the pressure differential and the porosity. Radial displacement may be positive or negative for a closed outer boundary but is positive for constant pressures at both boundaries. INTRODUCTION The importance, utility and complexity of a realistic appraisal of the stress state at and local to a wellbore were indicated in Part I. In this paper the analytical approach presented earlier is extended to finite, cylindrical reservoir geometry for the cases of (1) steady-state flow, (2) constant pressures at wellbore and outer boundary and (3) constant pressure at the wellbore and no flow at the outer boundary. Other than the outer boundary of the reservoir being finite, the physical system and assumptions pertinent thereto are the same as before. The reader may wish to review the mathematical development through Eq. 49 of Part I before proceeding here. SOLUTION FOR GENERAL BOUNDARY CONDITIONS THERMAL STRESSES AND DISPLACEMENTS Since normal stresses do not exist at the free boundaries of a system subjected to thermal stresses, the boundary conditions are

Jan 1, 1969

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By Y. C. Liu

Both the habit plane of martensite and the orientation relationship between the matrix and martensite platelets of different habit planes have been investigated in binary titanium alloys with molybdenum, chromium, and iron. The effect of the mode of deformation on the martensite habit plane was studied. A micrograph of an exposed mar-tensite platelet is presented. IN the study of martensitic transformation in Ti-Mn alloys,' two martensite habit planes—{334), and {344)8—were reported. The {334), habit was also observed in unalloyed titanium upon transformation,' although there is disagreement with respect to the exact indices. The other habit plane, {344),, has not been reported in martensitic transformation in any other alloys. The present investigation was made to determine whether other binary titanium alloys with P-stabil-izing elements would exhibit a crystallography of transformation similar to that of Ti-Mn alloys. Furthermore, since martensite platelets can be induced by deformation under certain conditions, it was of interest to investigate whether the mode of deformation, compressive or tensile, would influence the formation of martensite platelets on a specific plane in an alloy system which possesses two martensite habit planes. Experimental Procedure The material used for the preparation of the binary alloys of iodide titanium with molybdenum, chromium, and iron had the following purities: 99.99 pct iodide titanium, 99.9 pct molybdenum, 99.423 pct chromium, and 99.9 pct iron. The compositions of alloys listed in this paper are in nominal weight percentage. All specimens used were prepared and treated according to the procedure described in reference 1, unless stated. For the subzero temperature treat,ment the following experimental schedule was followed. After specimens had undergone the grain-growth treatment, they were quenched into an ice-water bath and were then metallographically examined. In specimens of higher alloy content, no martensitic transformation was observed. In those in which mar-tensitic transformation did occur, only specimens in which the martensite platelets existed as fine needles in localized regions were used. All specimens were reannealed 17 hr at 1200°C, quenched into ice water. and the capsule was broken. They were held in the ice water for from 5 to 10 sec, then transferred to a liquid-argon bath. This stepped quenching procedure was found to be more efficient than direct quenching into liquid argon. In the latter case, as soon as the hot specimen was immersed in the liquid argon, a protective, insulating layer of argon gas formed, and the specimen continued to glow vividly in the bath for some time. In the study of the habit behavior of martensite produced by deformation, specimens were deformed at room temperature either by compression, tension, or rolling. Martensite habit planes were determined by the two-surface analysis procedure described in reference 1. A stereographic net of 153/4 in. diam was used throughout the investigation. The method for determining the orlentation relationship between martensite and the matrix follows that used by Greninger and Troiano.' A diamond-polishing table with its auxiliaries was used in order

Jan 1, 1957

By I. H. Van Horn

IN the development of the incandescent electric lamp one aim of the investigators has been to establish the fundamentals of lamp design, so that the performance of any new lamp may be accurately predicted. The study of the temperature relations in lamps has done much toward establishing these fundamentals. Fig. 1 gives the typical FIG. 1.-ARRANGEMENT OF PARTS IN MAZDA B AND MAZDA C LAMPS. arrangement of the lamp parts in both the Mazda B (vacuum) and Mazda C (gas-filled) lamps. The outstanding differences are the filament form and the bulb shape. The ideal lamp is one in which the filament operates at a uniform temperature throughout its length. In practice, it is necessary to disturb this uniformity by the introduction of supports and terminals. The amount of cooling at the supports and terminals affects the over-all efficiency of the filament as a light producer. The life of the lamp is ordinarily proportional to the maximum and not to the average filament temperature. The Holborn-Kurlbaum type of optical pyrometer has

Jan 9, 1919

Jan 1, 1964

By J. M. Uys, T. B. King

WalSH, Chipman, King, and rant' have measured the water content (as hydrogen) of actual steel-making slags. An average water content of 290 ppm was found for basic open-hearth tapping slags and 114 ppm for acid open-hearth slags. Upon equilibration of these slags at 1550°C with a 25 pct H20-75 pct Nz atmosphere, the water content increased to about 410 and 300 ppm for the basic and acid slags, respectively. Walsh et al. concluded that an acid slag was thus relatively far removed from equilibrium, and that basic slags showed a closer approach to equilibrium, with the water vapor in the furnace atmosphere. Herasymenko2 contended that these conclusions were unjustified, as the oxygen pressure used in the equilibration experiments, ;bout 5 x X atm, was quite different from that found in the furnace. Consequently, during the experiments the slag composition would have changed due to oxidation of ferrous iron. As an extension of Walsh's work and to attempt to clarify this matter, the solubility of water in a basic open-hearth slag was measured as a function of oxygen pressure. Similar measurements were also made on synthetic silicates in the "Fe0"-Fe203-SiO, system. The experimental technique has been described previously by Walsh et a1.l and Uys and King.3 Samples of the basic open-hearth finishing slag, contained in 10-cc platinum crucibles, were equilibrated at 1550°C with atmospheres of different oxygen pressure but constant water-vapor pressure, Ph~o = 0.192 atm. Calculations, as well as measurements, indicate that this figure approximates the water pressure of the combustion gases in a steam-atomized, oil-fired open hearth. Oxygen pressures in the open hearth can vary from 10"2 atm in the combustion gases to between l0-' and 10" atm in the steel bath. The former figure depends on the combustion practice and the latter on the carbon content and temperature of the bath. The oxygen pressure of the slag should lie somewhere between these extremes and is expected to be closer to that of the steel bath than that of the combustion gases. Oxygen pressures were therefore varied between 10" and 6 x l0 atm. At the lowest pressure the slag "puffed up" when quenched (indicating possible loss of water) so experiments were not conducted at lower oxygen pressures. The results are shown in Fig. 1, which includes the water content of the slag "as sampled". The results show that the water content of the slag increased appreciably on equilibration with water vapor at 0.192 atm pressure and that the water solubility apparently decreases with increased oxygen pressure. The solubilities found are comparable to those of the Li20-Ca0-Si02 system.3 Work with synthetic slags in the "Fe0"-Fe203-SiOz system was performed at 1500" C, with Ph20 = 0.192 atrn and for oxygen pressures varying between 10"2 and 10-lo atm. Samples for chemical analysis were prepared as described by Larson.4 The results are shown in Fig. 2. Some low-silica melts tested at low oxygen pressures "puffed up" when quenched and analyzed less than 100 ppm water; these results are not included in Fig. 2. The melts containing 40 mol pct silica also showed a tendency to "puff up" during the quench, when they were tested at the lowest oxygen pressure. These results indicate that, at constant silica content, the solubility of water decreases somewhat with increased oxygen pressure. The effect is, however, small considering the wide range of oxygen pressures studied. Also, at constant oxygen pressure (above about lom5 atm) the solubility increases

Jan 1, 1963

By B. A. Kulp, R. R. Reeber

Lattice parameters for the wurtzite form of' CdS mere measured by powder X-ray diffraction techniques over the temperature range 26° to 1000 K'. A negative thermal -expansion coefficient was determined parallel and perpendicular to the c axis below 13.5°K. Near 808°K, the curves of the a, parameter, the differential thermal expansion, and the resistivitv vs absolute temperature exhibited a reversible discontinuity. j\. direct determination of the lattice parameters of CdS over an extended temperature range is of particular use in interpretation of the effects of high pressure on the band structure of semiconductor materials. For example, Langer' has studied the effects of pressure on the absorption edge of CdS from 77°K to room temperature. In order to properly interpret his results it is necessary to know the change in lattice constants as a function of temperature for the wurtzite, zincblende, and rocksalt2 modifications of this material. Thermal-expansion measurements for CdS, wurtzite phase, have previously been determined over a limited temperature range.s74'5 The zincblende phases, of other compounds with similar bonding, have been investigated by Novikova et a! .'' Previous thermal-expansion measurements for metals with hexagonal symmetry have for the most part used bulk sample techniques for low-temperature result. Most X-ray measurements at low temperature have been on materials with cubic symmetry.'jQ The use of X-ray powder-diffraction techniques offers a convenient and accurate method of measurement over a wide temperature range. The X-ray method, besides measuring unit cell size, also provides information about change in structure type and the nature of some of the stacking defects present. I) EXPERIMENTAL PROCEDURE The thermal expansion was measured by X-ray powder-diffraction techniques. Lattice parameters for the range 300" to 1000°K were determined in a 19-cm Unicam camera. From 26" to 300°K a 34-cm back-reflection camera with the Van Arkel" film arrangement was used. The sample was bonded to a copper cold finger below a helium, hydrogen, nitrogen, oxygen, dry ice, or ice brine bath in a metal cryistat. che inner bath was surrounded by another one for radiation shielding. Nitrogen was used in this outer bath for the very low-temperature runs while dry ice and acetone was used for the 195°K point. CuKa X-rays, filtered with a nickel foil, entered the cryostat through a 0.001-in.-thick aluminum window. During a typical 9-hr exposure the sample was continuously rotated through a 30-deg arc. Heat losses from the sample holder limited the minimum temperature attained to 26°K with helium in the inner dewar. Temperature calibration between 25" and 125°K was determined with an Allen Bradley 300-ohm carbon resistor. The resistor was attached to the back of the copper finger with a thin layer of silicone grease. Liquid He, HZ, N2, and O2 baths were used to calibrate the resistor. Temperature variation is estimated to be *2"K with a slightly higher uncertainty at room temperature and 264°K. The thermal expansion of high-purity germanium from 373" to 900°K was measured as a calibration for the Unicam camera. This value was compared with the known value1' for the thermal expansion. A discontinuity in the thermal-expansion coefficient of the CdS a, parameter was observed. Similar discontinuities in the resistivity and differential thermal analysis at the same absolute temperature indicate that the temperature error is *5°K in the temperature range above 500°K. Temperature errors in the Unicam camera below 500°K are appreciably higher due to large gradients in the resistance furnace. II) SAMPLE PREPARATION The CdS was Eagle Picher ultrapure grade. The crystallite size range of the as-received powder

Jan 1, 1965

By R. A. Wood, R. I. Jaffee, H. R. Ogden, D. N. Williams

Strain-induced porosity has been found to occur in titanium and other materials at tensile strains greater than the uniform elongation of the material. Porosity in titanium increases with increasing strain and temperature, being most severe at 300° to 800°F. Strain-induced porosity is believed to be a normal part of the mechanism of deformation in ductile materials. DURING the past few years there have been numerous references to the occurrence of voids in laboratory test specimens of metals subjected to strain.l-7 These voids have been referred to as intercrystalline cracking, strain-induced porosity, intergranular cav-itation, voids, and porosity. They appear to occur at grain boundaries or interfaces, and are generally associated with large amounts of strain and have been found mostly in creep specimens and to a lesser extent in tensile specimens. Because the phenomenon does not occur unless the material has been strained,

Jan 1, 1960

By Sumner M. Anderson

Any discussion of outside support to Latin American mineral industries must concede at once the pre-eminent role of U. S. industry and business. American capital has developed the great copper resources of Chile and Peru, the lead-zinc of Peru and Mexico, the bauxite of Surinam and Jamaica, the petroleum and iron ore of Venezuela. American consumers have provided the market for their products. U. S. companies operating south of the border have trained Latin American geologists, engineers, chemists, and skilled labor—including metal, mineral, and fuel technicians—to new and greater competence. The industrial demands of World War II drastically altered world economics and concepts of U. S. foreign mineral requirements. In this country discovery of vital mineral resources fell far behind the alarming depletion rates, and there was new appreciation of the actual and potential importance of the world's less extensively explored areas. During the war and afterward, the task of supplying the nation's mineral requirements became greater than private industry could carry alone, and the Government assumed a position of continuing support. In Latin America, as elsewhere, this support applies in three categories: banking, procurement, and technical assistance. The first two are now generally accepted as necessary Government functions; the third has often been misunderstood and misinterpreted, although it has given rise to legitimate controversy. There have been major accomplishments in all three categories, as well as some errors of judgment. Since the beginning of World War 11, U. S. Government financing, procurement, and technical assistance have been applied on a large scale to a wide range of commodities and services throughout the free world. The present discussion—under the separate headings mentioned—will concern only the support related to a single industrial group in a single geographic area. During the War Federal banking was conducted on an emergency scale by temporary agencies created to meet the abnormal circumstances. Unfortunately, there are no readily available data on these activities that would permit evaluating loans and credits extended for mineral projects in Latin America. The only agency operating in this field since World War II is the Export-Import Bank, under its own authority and to some extent from credits authorized by the Office of Defense Mobilization. The Bank can offer more capital—on more favorable terms—than is available from most Latin American banks, and its staff of engineers evidently can appraise loan applications more favorably than commercial banks in this country are willing to do. The risks seem to be justified, as defaults have been well under 1 pct of total loans. From V-J day 1945 to the end of 1957, mineral loans to Latin America have been authorized for projects totaling $541.63 million in eight countries. In order of magnitude of credits, they have been made to Brazil, Peru, Chile, Mexico, Argentina, Venezuela, Guatemala, and Bolivia. In order of magnitude by industries. they are for development and expansion of steel mills, copper, manganese, nitrate plants, iron ore, zinc plants, sulfur plants, cement plants, tungsten, coal, and lead. Loan Distribution: By far the largest loans have been $307.9 million for iron and steel projects in Brazil, Chile, Mexico, Argentina, and Peru: $100.4 for developing the great low-grade copper deposits of southern Peru; and $55.3 million for developing manganese deposits in the Territory of Amapa, Brazil. Others range from $20.8 million for a zinc smelter in central Peru to $19 thousand for iron-mine trucking equipment in Chile. It has been noted that 59 pct of the loans have been to foreign companies, 14 pct to companies of mixed foreign and American capital, and 27 pct to American mining companies. About 40 pct of the total authorizations has been disbursed so far. In addition to these amounts, the Strategic Materials Division of the Economic Cooperation Admin-

Jan 1, 1959

By J. E. House, C. J. Lewis

In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-pregnant sulfuric acid leach solution is contacted with an organic extractant dispersed in kerosene; the uranium enters the organic phase and associates itself with the organic extractants. Simultaneously an-ions or cations, as the case may be, leave the organic extractant phase and enter the aqueous phase. The two phases are then allowed to separate by virtue of their immiscibility. Based on the data available, a generalized procedure for the recovery of molybdenum from the sodium carbonate scrub liquor of acid leach uranium mills using secondary and tertiary amine extractants is presented, as is another generalized procedure for the recovery of molybdenum from the bleed stream of alkaline leach uranium mill circuits. Such economic appraisal as can be made at this stage of the development is also indicated. Molybdenum occurs in most uranium ores. Whether the uranium is solubilized by the acid leach route or by the alkaline leach process, some of the molybdenum present in the ore is solubilized along with the uranium. Molybdenum in uranium mill pregant solutions may cause processing difficulties, among which may be mentioned the poisoning of resins, the precipitation of organo-molybdenum complexes, or the build-up of molybdenum in recycle streams. While the uranium milling industry has been successful in applying measures to overcome the problems arising from the presence of molybdenum in the circuits, such measures nevertheless add to the cost of producing uranium yellow cake concentrate. Table I shows the analysis of typical uranium pregnant leach solutions. Uranium recovery by solvent extraction is presently practiced only in conjunction with acid leach circuits, and it may be noted that of about 16,000 tons of uranium ore daily processed by sulfuric acid leach, more than half of this tonnage follows the solvent extraction route. Uranium mills leaching ore with sodium carbonate-sodium bicarbonate solution (the so-called alkaline leach circuit) do not use solvent extraction. In this case the uranium pregnant solution is sufficiently pure to permit the direct precipitation of uranium concentrate with subsequent recycle of the alkaline leach solution. While solvent extraction procedures may be developed which are economically attractive for the alkaline leach uranium process, this has so far not been the case. The earlier uranium mill solvent extraction circuits used organo-phosphate extraction reagents, among which di-2-ethylhexyl phosphoric acid was popular. It should be borne in mind that uranium in its sulfuric acid leach solution exists in an equilibrium involving uranium in both anion and cation forms: uo + 2S0 = [uo2(so4)2] For this reason uranium may be extracted by either cation extractors or anion extractors and this is likewise true of molybdenum. However, the organo-phosphate extractants also load ferric iron which is usually present in the uranium acid leach solution. For this reason, it is necessary to reduce this solution substantially to the ferrous state ahead of solvent extraction using organo-phosphate reagents. The amines, being anion extractors, selectively reject iron and thus render the iron reduction step unnecessary. In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-

Jan 1, 1961

By J. C. Martin

Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators in which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the aduantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. INTRODUCTION In recent years, computers have been used to calculate the performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The situation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; and, for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow re1ations.l-3 In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation.l.2. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir's thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoir. This requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats' et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats' assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. DISCUSSION SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate: (1) that the fluids along any line perpendicular to such a reservoir's upper surface are in static capillary equilibrium (vertical equilibrium); (2) that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; and (3) that hydrostatic pressure gradients exist along any line perpendicular to the reservoir's upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together.

Jan 1, 1969

By Paul Billingsley

THE purpose of this paper is a comparison, based on genesis, of the ore deposits associated with the igneous rocks of the central Montana Rockies. Considered separately, without attention to their origin, the orebodies appear to be distributed haphazard, with no fundamental laws controlling their position and character. It is believed, however, that if all the factors be weighed, this apparent confusion will to a large degree disappear. The, first essential to such a comparison is detailed knowledge of the individual mines, as to their geographic position (see Fig. 1), their mineralogical character, and in particular the derivation of their ores.1 The authors of this paper have pursued such an investigation for the past 6 years, and have accumulated a mass of evidence that enables a preliminary correlation to be attempted. It appears that the majority of ore deposits are genetically related to one or another of the igneous

Jan 4, 1917

By L. W. Pommier, F. B. Brien, A. K. Bhasin

In the field of mineral processing, although many operations are applied to suspensions of ore particles in fluids, there is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. Previously proposed equations, based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids, are exam ined in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. As more knowledge is acquired in regard to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow predictions of conditions to achieve optimum results for engineering purposes. In the field of minerals processing, many operations are applied to suspensions of ore particles in fluids. The differential movement of solids of various sizes and densities in suspensions is of utmost importance to gravity concentration, wet classification, flotation, hydrometallurgy, and pipeline transport of solids. The subject is also of importance to other branches of engineering; for example, those involved with soil mechanics, ceramic slips, and oil-well drilling fluids. There is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The problems encountered in the direct application of the well-known Stokes and Newton's Laws to non-Newtonian systems have been examined in a previous paper.' Equations were proposed based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids. This present paper examines these equations in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. It is thought that, as more knowledge is acquired as to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow prediction of conditions to achieve optimum results for engineering purposes. The purpose of this paper is to make an initial assessment of the nature and magnitude of pertinent suspension variables. In order to avoid too voluminous a document, the examination of kinetics and mechanisms will be omitted at this time. THEORY A Newtonian fluid is defined as a fluid in which the stress is proportional to the rate of strain, 2 i.e.: H = viscosity; see Table I. for list of symbols The following equations are conventionally used to assess the motion of spherical particles moving under laminar and turbulent flow conditions through Newtonian fluids: When these relationships are applied in practice to suspensions, the liquid density is substituted by a composite suspension density, and viscosity is usually taken as that of the suspending liquid or an approximated "apparent viscosity." However, suspensions are non-Newtonian in character3 and thus, more than one viscosity parameter is required to describe their behavior. A number of models have been proposed for non-Newtonian fluids;2,4 among these the simplest is the Ostwaldde Waele or power-law model for incompressible fluids which for one dimensional flow may be reduced to:

Jan 1, 1970

By B. H. Caudle, L. G. Loncarie

Pilot flooding is one method of evaluating a proposed secondary recovery project. However, the amount and rate of oil recovery from an unconfined pilot area is not usually the same as from an equal area in a large-scale flood. This is true because fluids are free to move across the boundary of a pilot area. The result is that some of the oil produced in a pilot flood may come from outside the designated area and some of the displaced oil may leave the pilot area completely. This paper presents the results of fluid-flow model studies on a five-spot pilot flood. Mobility ratios between 0.1 and to have been studied. The effects of changing the ratio of injection to withdrawal rates are shown. INTRODUCTION A small-scale field test, or pilot flood, is an accepted method for evaluating the applicability of a secondary recovery operation and the economic potential of that operation for a reservoir. The pilot flood is carried on in the same manner, with the same injected materials and at the same pressures as would be used were the secondary recovery program to be expanded to a larger area of the field or to the entire field. If the reservoir fluid and reservoir rock properties are the same in the pilot area as in the rest of the reservoir, the production, injection and other pertinent data associated with the pilot test will represent and measure what should be expected from a full-scale development of this secondary recovery program. There is one major exception which, unfortunately, has been overlooked by many and which has been awaiting quantitative definition. This is the sweep-out pattern the reservoir engineer must use in interpreting the pilot flood and in extrapolating it to the full-scale development. The sweep-out area in a pilot flood is not contained within the five-spot pattern. Further, there is oil flow into and/or out of the five-spot during a pilot test. Thus, production data from pilots must be interpreted with this different flow system and sweep pattern in mind. We have studied the sweep-out pattern that will exist for some conditions of operation of pilot flooding a single five-spot (four injection wells and one producer). In our study, reported here, we have assumed that the reservoir is relatively homogeneous and of uniform thickness in the pilot area. The results of this study en-able the engineer to predict the recovery, injection requirements and project life for a full-scale operation from the pilot flooding data. The effects of various injection to withdrawal-rate ratios and mobility ratios in a relatively gas-free (10 per cent pore volume or less) system are shown. Experimental Method The technique used in this study was the same as that for the X-ray shadowgraph studies of sweep-out pattern efficiencies.' The model of the pilot and surrounding area was made from a uniform packing of round-grain sand consolidated with an epoxy resin. Fig. 1 shows the relation between the model and the pilot area. Only one-eighth of the pilot area had to be represented in the model because we assumed equal injec-

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1936

By R. S. Olson

An analysis of the wash thickener-two stage filtration circuit was undertaken to quantitatively describe the circuit performance. On the basis of information developed in this study, the factors of major importance in reducing soluble loss are: filter wash, wash zone size, filter capacity, filter feed pulp dilution, blow back, filter cloth, water to repulp, water to primary wash, water to feed pulp and thickener underflow. The wash thickener-two stage filtration circuit has been used in many hydrometallurgical plants to separate solute from leach solids. As many as 20 to 30 plant operating variables determine the performance of the wash circuit and hence the soluble loss. The complex relationships of these variables, with each other and with soluble loss, make the evaluation of their effect on mill performance difficult. An analysis of this type of circuit was undertaken to quantitatively describe the circuit performance. THE CIRCUIT The diagram in Fig. 1 represents the operation of the wash thickener-two stage filter circuit. This circuit provides for counter current, cross current or for a combination of countercurrent-cross current operation. The feed pulp stream, J, is intended to include any solution or water, other than primary and secondary filtrate, which enters the wash thickener. Except for filter washing, the operations in the circuit are simple mixing operations which can be described by material balance. The concentration of solute in the filtrate and cake solution after application of wash liquor cannot be described by simple material balance. The displacement washing equation, derived by Rhodes1 and extended by Choundhury and Dahlstrom,2 appears to best describe this case of miscible displacement in porous media. In a useful form, it is

Jan 1, 1963

Abbey, Robert Graham, District Mgr., The W. W. Sly Mfg. Co., 50 Church St., New York, N. Y. '21 Abbott, A. N Ave. Morelos 84, Cuernavaca, Morelos, Mexico '23 Abbott, Argyle Campbell, Geol 42 Everett St., Arlington, Mass. '29 Abbott, Clarence E., V.P., Charge of Raw Materials, Tenn. Coal, Iron & R. R. Co., 1242 Brown-Marx Bldg., Birmingham, Ala. '04 Abbott, Louis Benjamin, Chief Engr., Consolidation Coal Co., Watson Bldg., Fairmont, W. Va. '15 Abeel, George H., Jr., Cons. Min. Engr 1281/2 S. Canon Dr., Beverly Hills, Cal. '18 Abel, Raymond L., Asst. Prof., Dept. of Pet. Refin., Univ. of Pittsburgh. .Pittsburgh, Pa. '28 Abel, Walter D., Cons. Engr 650 S. Grand Ave., Los Angeles, Cal. '82 Abele, Louis T., Min. & Met. Engr., Supt., Texas Hill Mine Coulterville, Cal. '31 Abell, Leo M. Millicent, S. Australia '31 Abernathy, George Elmer, Prof. of Geol. & Min., Kansas State Teachers College, Pittsburg, Kan. '20 Aborn, Robert H., Research Lab., U. S. Steel Corp. Lincoln Highway, Kearny, N. J. '19 Abozeid, Mahmood, Dept. of Mines & Quarries Cairo, Egypt '26

Jan 1, 1932

By H. P. Willard, R. W. Gates

Basic Inc., has been mining magnesite and brucite for 27 years at Gabbs, Nev. This is a medium sized open-pit mine. The magnesite deposits are in north-western Nye County about 30 miles east of Luning, Nev., on the west slope of the Paradise Range, at an elevation between 5000 and 6000 ft. The magnesite and associated brucite is used to make magnesia refractories employed principally in the steel industry and magnesium oxide for various chemical uses.

Jan 10, 1963

Jan 1, 1969