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

Magnesium, the eighth most abundant element in the earth's crust, is found widely distributed in a variety of minerals. Among the more commercially important ones are magnesite (MgCO3), brucite (Mg[OH]2), dolomite (CaMg[C03]2), and the salts magnesium sulfate and chloride often found in natural brines. Among other commercially important magnesium-containing minerals are olivine ([MgFe]2Si04), talc (H2Mg3[Si03]4), and serpentine (H4Mg3Si2O9). These are valuable because of desirable characteristics given them by the magnesium content and its placement in the particular crystal structure. These minerals are the raw materials for a host of products including magnesium metal and several grades of magnesia or magnesia-containing materials for refractories, fluxes, fillers, insulation, cements, decolorants, fertilizers, and chemicals. Considering only those minerals valued for their magnesia or magnesium content, over 85% of the material tonnages are processed to be used as refractories. Dolomite, which is used in enormous tonnages for its physical properties in construction, has an important use as a refractory raw material in its own right and, after calcination, as a precipitant for magnesium hydroxide, which is an intermediate for the production of magnesia or magnesium metal. Magnesia from the reaction of calcined dolomite (or limestone) with seawater or magnesium-containing brines has supplanted much of the production of magnesia from mined magnesite, particularly in the United States. The best known of the minerals directly and widely exploited for magnesia content is magnesite, one of the calcite group of rhombohedral carbonates which includes calcite (CaC03), siderite (FeCO3), and rhodochrosite (MnCO3) among others. The members of this group enter into a wide range of substitutional solid solutions when the positive ions have similar radii. The radii of magnesium and iron ions are within 6% of each other; hence, magnesite and siderite form a complete series of which breunnerite (ferroan magnesite) is a well-known end member. However, the radius of calcium ion is 36% larger than that of magnesium ion, and only limited substitution exists at each end of the MgCO3-CaCO3 series. Dolomite is not a member of the calcite group, but results when calcium and magnesium ions alternate in equal number in an ordered structure among carbonate ions. The result of these relationships is that calcite and dolomite, often found intermixed with magnesite, occur commonly as identifiable crystal entities which can often be separated to a varying degree from the magnesite by various beneficiation techniques. Magnesite, when pure, contains 47.8% MgO and 52.2% CO.. The pure mineral is sometimes, but rarely, found as transparent crystals resembling calcite, but, preponderantly, magnesite contains variable amounts of the carbonates, oxides, and silicates of iron, calcium, manganese, and aluminum. Magnesite may be either crystalline or amorphous (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black with shades of yellow, blue, red, or gray. The color is not a fundamentally significant indicator of purity, but in a given deposit, an experienced person can often roughly grade magnesite by assessing color and crystallinity. The crystalline form of magnesite occurs in

Jan 1, 1983

By G. W. Doepel, W. P. Sibley

A three-dimensional, multilayer, mathematical model has been developed for predicting performance by mis-c.ible displacement. Areal and vertical coverage, total gas-oil ratio, propane-oil ratio and oil-recovery factor for the multilayer system are computed as functions of hydrocarbon pore volumes of solvent injected. The technique has been programed for use on the IBM-7090 digital computer and was used in calculating perfortnance for continuous miscible displacement of a five-spot, 50-layer .system. Results reported are based on the use of published laboratory data for a single, uniform five-spot layer. However, the technique is sufficiently generalized to calculate performance of any system of layers of any pattern configuration and mobility ratio, provided data are available to describe perfortilance of a single layer. The technique has also been adapted for predicting oil recovery resulting from various gas-driven slug sizes. The results presented for both continuous and slug-type injection show, that permeability variation has 0 significant effect on oil recovery but that solvent composition, within the range studied, has a lesser effect on oil recovery. INTRODUCTION Experience from many of the miscible-phase displacement projects currently in operation indicates that the injected solvent flows preferentially through the more permeable zones in the reservoir. This preferential solvent flow in the high-permeability streaks results in a reduction of vertical coverage (C,) and an attendant decrease in oil recovery. The multilayer technique presented in this paper uses areal coverage (C.,) data for a single layer from the literature and from laboratory measurements of displacement efficiency (herein referred to as microscopic coverage, C,,) to calculate areal coverage (C,) and vertical coverage (C,) for the multilayer system. Oil recovery for the multilayer system is obtained as the product of (Ca) (Cm) (Cv). It is assumed that C, in a single layer is 100 per cent; therefore, (C,) (Cm) is a measure of oil recovery from that layer. Data presented in the literature for a single layer generally deal only with areal coverage and/or microscopic coverage —but seldom specifically with oil recovery. Nevertheless, this technique is flexible in that either Ca and C,, of an individual layer or a direct measurement of oil recovery for the layer may be used. In developing this technique, the problem arose concerning a method of determining the relative amounts of solvent that will enter each layer during any increment of solvent injected. To solve the problem, a dimensionless equation was derived for expressing solvent injected into each layer as a fraction of total injection. A finite-difference method was applied in integrating the equation to determine oil recovery for the system of layers as a function of pore volumes injected. The technique subsequently was programed for solution on a digital computer. The method was applied to predict performance of a deep California reservoir under continuous miscible displacement and has been extended for calculating oil recovery as a function of slug size for gas-driven slug injection. The technique may be applied to any petroleum reservoir that can be adequately represented as a layered system, by considering permeability variation,1-3 permeability range and average permeability. Each layer is then assigned its appropriate permeability, porosity and hydrocarbon saturation. RESERVOIR VOLUME CONTACTED BY SOLVENT It has been recognized for some time that high microscopic coverage (C,) can be obtained by injecting a miscible agent, such as propane, into an oil reservoir. These high values of C,,, have been demonstrated in the laboratory and are normally between 80 and 100 per cent, depending on solvent and reservoir oil composition as well as on reservoir temperature and pressure. In miscible-phase displacement, because there is no interface between solvent and oil, effective permeability to solvent is the same as that to oil. (This assumes that oil saturation has not changed and that water is immobile.) Consequently, mobility ratio (M) simply reduces to that of viscosity ratio . Perrine4 and Habermann5 have shown that large

By V. J. Berry, J. D. Pendergrass

Well pressure transient tests provide a means for directly obtaining information about formation pressure and reservoir flow capacity. Such tests have also been proposed for determining presence and location of faults or other reservoir closures and for measuring oil in place. For mathematical convenience, most theoretical studies have considered the reservoirs to be homogeneous. Definitive information is not yet available to show whether the actual presence of nonuniformities will make pressure transient behavior different from that of a uniform reservoir. The conclusions reached from actual transient tests are questionable, therefore, insofar as they rely on the original assumption of homogeneity. One type of nonuniformity commonly assumed to exist is that of stratification. In most reservoirs the strata are thought to be in vertical communication. Equations for the transient flow of a single-phase, compressible fluid in a one-well, bounded, circular reservoir have been solved for several situations involving crossflow between multiple strata of various thicknesses and permeabilities. The results show that except for the very early flow period, which usually is too short to be analyzed, the transient performance observed at the well is substantially identical with that of a homogeneous reservoir having the same dimensions and having the same steady-state flow capacity. Thus, stratification does not adversely affect interpretation of well transient tests. This conclusion holds for all commonly encountered combinations of reservoir thickness and external radius. Deviations are observed for unusually thick reservoirs whose outer radii are relatively small. The results of these studies also show that the presence and the amount of stratification cannot be simply diagnosed from reservoir pressure transient data when there is crossflow between strata. INTRODUCTION The last decade has brought wide acceptance of the transient well pressure test for determining reservoir parameters. Following the original work of Hurst and van Everdingen,1 the mathematical theory was thoroughly explored. Numerous authors have suggested how to determine static reservoir pressure, permeability-thickness product, original oil in place and reservoir limits for different reservoir geometry. The same mathematical techniques have been used to predict the transient performance of a reservoir over a long period of time. Most of the theoretical work has been for homogeneous, isotropic systems. Some results have also been presented for a homogeneous, anisotropic reservoir.2 Petroleum reservoirs are not homogeneous. The deposition process seems to favor creation of a stratified formation. This concept is sufficiently well accepted so that the most natural extension of the transient flow theory beyond the homogeneous case is to a stratified formation. Results for a stratified reservoir with no vertical communication between layers can be obtained from the results for a homogeneous reservoir. Lefkovitz, et a1,3 have given a thorough treatment of the two-layer case. Two recent papers4,5 have treated the case of a two-layered reservoir with vertical communication or crossflow, between layers. Russell and Prats4 find that, after a relatively short time, the two-layered reservoir with crossflow exhibits a simple exponential pressure decline. From this time forward, the behavior is not distinguishable from the behavior of a homogeneous reservoir having the same steady-state flow capacity. The results of Katz and Tek 5 are equivalent. Russell and Prats4 also speculate that a multi-layered reservoir with crossflow will behave as a homogeneous system after long enough production time "... providing the contrast in kh between layers is not too great". They also suggest that, at intermediate times, "... the relative positions of the layers with respect to each other will have a great influence on the production behavior and on the time at which the previously mentioned large-time approximation might be valid". Katz and Tek5 remark upon the mathematical difficulty of treating a reservoir having many layers or strata. If relative position of the layers is also

By S. T. Yuster

An analysis has been made of the factors responsible for tilted fluid contacts in petroleum reservoirs. The factors are static and dynamic with the former being controlled by those variables responsible for the capillary rise of fluids, and the latter include rate of formation tilt and hydraulic circulation. The explanation that rate of formation tilt may be responsible for tilted contacts appears untenable. The role of some of these factors in the migration, fractionation. accumulation and possibly the prospecting for oil is indicated. INTRODUCTION While it is generally considered that the segregation of gas, oil, and water in a petroleum reservoir results in approximately horizontal planes separating these phases. there are factor; which modify this simplified picture to a very great extent. Some of these factors are static. and the departure of the fluid interfaces from horizontal may represent a static equlibriun. Some of these factors may be dynamic and the interface positions may be non-equilibrium and represent a steady .state condition. Of course combinations of these two situations may also exist. The reasons most commonly given for this behavior are hydraulic circulation of fluids, change in character of the formation, and a rate of tilt of the formations more rapid than the rate at which the fluids may re-establish an equilibrium. Russell's Principles of Petroleum Geology' contains an extensive discussion of tilted fluid interfaces and their importance in the migration and accumulation of petroleum. Russell cites examples of tilted water tables at Lance Creek, Wyo.; Rock River, Wyo.: Cut Bank. Mont.; Cushing, Okla.: and Graham; Okla. Also given was the Wasson Field of West Texas which has saucer shaped oil-water and gas-oil interfaces with the saucer being deeper in the case of the oil-water contact. The Bradford Field in Pennsylvania has a tilted water table. San Ardo. Coalinga None and some other California field.; have tilled contacts. A recent paper by King Hubbert discuses the effect of hydraulic circulation of the water underlying the oil in a given stratun and it- implications in the accumulation of and drilling for the oil. The foregoing would indicate that tilted fluid interfaces are not uncommon and that it would be of importance to underbtand the forces which are responsible. Further. it would be of interest to examine certain idealized models of situations which may cause tilting with the thought in mind of deriving relatinnships between the important variables. These relationships may only hold exactly for the model* assumed but the results may apply semi-quantitatively to actual formations and at least indicate trends. The discussion will be divided into the effect of static factors and the effect of dynamic factors. STATIC FACTORS It has already been mentioned that one reason given for tilted contacts is a variation in formation properties. Specifically this is a change in the pore size of the formation capilaries. If the internal surface of the reservoir is preferetially wet by water, capillarity will cause the water 10 rise to a greater extent above the free water table in a small capillary than in a large one. Consequently the water-oil contact will be higher in the lower permeability sands than in the higher permeability sand.;. The free water table may be defined as the position the oil-water interface would take if capillarity were absent. Since the phenomenon is the capillary rise of water in an oil environment, a derivation of this shold give a relationship between the variables. Fig. 1 is an idealized model of the situation with a uniform bore circular capillary ubstitttting for the tortuous non.circular formation pore. The upward force.; on the column of water will be equated to the forces downward to give the equilibrium situation. forces upward = force downward where r is the radius of the capillary in ceritimetera. a is the interfacial ten4on oil-water in dynes per centimeter, 0 is the

Jan 1, 1953

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By Robert C. Emmett, Donald A. Dahlstrom

FOR many years gravitational classification has been employed as a basic tool in beneficiation of minerals and coal. While improvements have been made to increase efficiency and fields of application, the basic flow pattern has remained relatively unchanged in most gravitational classifiers. Feed slurry is introduced into a settling pool wherein the coarser solids settle against either an upward or horizontal fluid current, or a combination of both, and are withdrawn in a concentrated underflow stream. The finer solids below the classification point possess too low a settling velocity and thus are primarily swept out through a weir overflow by the bulk of the fluid. Because of its simplicity, efficiency, and low power and maintenance costs, gravitational classification finds a wide acceptance for separations in the range of 20 to 325 mesh. Two factors resulting from the basic flow pattern employed in gravitational classification present difficult problems for certain installations. If classification at 60 to 200 mesh of separation is desired, capacity in terms of gallons of overflow per minute per square foot of settling pool area must be low to allow required solids to settle to the underflow. If a thousand or more gal per min of feed slurry must be handled, either a very large classifier or a number of smaller units must be employed, taking up floor space and head room. Examples of this are the large classifiers, wetting tanks, or settling tanks used in the coal industry for recovery of process water from fine solids. Units as large as 50 or 60 ft in diam and 60 ft high, requiring substantial amounts of steel, are not uncommon. A second factor is the lack of self-regulation in gravitational classification. As overflow rate increases, mesh of separation increases correspond-ingly. This normally heightens difficulties of bene-ficiation. If a fine mesh of separation is required at varying feed rates, the problem is more than doubled in complexity. One of the primary advantages of gravitational classification is low power requirement. Gravity feeds or very low pressure heads are employed. However, fluid energy is still present in the inlet stream and provision must be made to dissipate it properly to obtain uniform upward or horizontal currents. Rather than waste this energy, it would be desirable to utilize it to secure a greater degree of self-regulation and simultaneously increase classification capacity per square foot of area. A free vortex could be realized by a tangential entry of feed, resulting in generation of centrifugal force to complement force of gravity in its action. With greater force it should be possible to gain finer separation at any overflow rate per square foot of settling pool area as compared with conventional gravitational classification. Furthermore, as feed rate increases, centrifugal force will also increase and at least partially offset faster currents sweeping solid particles to the overflow. A more stable classification point should result. The liquid-solid cyclone is the most common application of a free vortex in the beneficiation field.' Many previous papers have emphasized uniformity of flow pattern within the cyclone which is largely responsible for the sharp classification that can be obtained.'-4 If a free vortex can be maintained in a non-pressurized vessel with a free surface it may be possible to realize a third advantage of sharper classification. This open-top cyclone would then achieve a minimum energy loss comparable to that with conventional classifiers, and a mesh of separation coarser than 150 mesh, extending the range of application of the free vortex. This is not presently possible with ordinary cyclones. To test the applicability of the free vortex to gravitational classification, a 30-in. diameter open-top cyclone was constructed at Northwestern University. The cylindrical section was 30 in. high and the conical section included an angle of 60". The feed nozzle was a standard 4-in. pipe entering tan-gentially, with centerline 17 1/2 in. below the top of the cyclone. The conical section was flanged near

Jan 1, 1954

By B. M. Larsen, T. E. Brower

IN an earlier paper1 we discussed a simple, rapid method of taking samples of liquid steel and analyzing them for oxygen, which, though possibly not absolutely accurate (as is likewise true of all other methods), certainly yields results that are satisfactorily consistent. Accordingly, samples from hundreds of heats in different shops were analyzed for oxygen, with results sufficient in number to be handled statistically and permit estimation of some general trends. Measurements were made in acid as well as in basic open hearths, throughout the refining period, to learn how stirring, blocking, adding ore or lime or sand, affects the oxygen content of the bath; we also followed the changes brought about by tapping, teeming, and deoxidizing. Some of these results, discussed in an earlier paper.2 bring out the dominant role of the carbon-oxygen reaction in regulating degree of oxidation both of metal and of slag, also the marked variability of concentration of dissolved oxygen [0] in excess of that which would be in equilibrium with carbon and with carbon monoxide at a partial pressure of one atmosphere. As a logical beginning on this complex problem, we take up in the present paper the variability of this excess oxygen, ?[O], when other factors are as constant as they ever are in open-hearth operation; namely, toward the end of the refining period, when the bath may be regarded as in the comparatively steady state it approaches in absence of disturbing factors. This condition was chosen because by that time the significant reactions, except carbon oxidation, between slag and metal have come to substantial equilibrium; this facilitates interpretation of the complex situation and thus permits more definite conclusions to be drawn. This excess concentration of oxygen, ?[0], in the metal is needed, of course, to make the steelmaking process go at a reasonable rate; alternatively it may be regarded as a measure of the virtual pressure increment above one atmosphere, or of the degree of supersaturation, of carbon monoxide in the metal. According to our measurements, the excess concentration ?[O] in liquid steel varies from about 0.009 to 0.035 per cent oxygen by weight. It is quite sensitive to change of conditions, being altered temporarily by operations such as stirring with green poles, additions of ore, lime, or sand; but as the disturbance works itself out, it resumes a level within the intermediate range characteristic of the steady state. The conditions most common in average furnace practice are covered by the following : [ ] as in a reasonably steady state-that is, when it is boiling normally, is at proper temperature with a well-shaped slag, and has been free from disturbing effects during the preceding half hour-?[O] returns from

Jan 1, 1946

By A. G. Lyle, J. D. Runkle, G. A. Gillies

THE evaluation of data obtained by selective flotation from even a simple ore is a very difficult process, and when the ore tested is complex the process becomes extremely difficult and cumbersome. The authors, in the course of an investigation into the selective behavior of various flotation reagents on nonmetallic minerals§ were confronted with an aggravated form of this difficulty, owing to the large mass of data that had accumulated over a period of years. They finally devised a method whereby the results of the various flotation tests could be correlated and interpreted by means of graphs representing recoveries and rejections of the component minerals in the ore. This method of graphical analysis proved so useful in nonmetallic flotation that it was afterwards applied to sulphide flotation, where it yielded equally satisfactory results. Since this method of analysis leads to very definite conclusions as to the effect of changes in reagents and flotation procedure, it is felt that a wider application of the method might assist the industry by reducing the amount of test work required, and possibly increase the accuracy of the final analysis. GRAPHS In Fig. I, four curves are plotted on the same graph with cumulative percentages as ordinates and cumulative weights as abscissas. In this instance the four curves are named, respectively: the barite-recovery curve, the limestone-rejection curve, the silica-rejection curve, and the summation curve. In these tests barite was the mineral concentrated, therefore a barite concentrate was produced. Definitions Before explaining the curves in detail it might be advisable to define several new terms, such as "percentage rejection," "summation index," and "summation curve," as well as the word "test," which has been used in a special sense. A "test" will include all the operations performed upon a batch of ore from the time it is placed in the rod mill until the last product has been assayed. Thus a test may be a comparatively simple procedure producing only one concentrate and a tailing, or it may be a very complicated procedure producing five or more concentrates of a specific mineral as well as a tailing. The number of concentrates produced will depend entirely upon whether the collector was added to the pulp in the flotation cell in one lot or was added in five or more portions. Percentage Rejection.-The ability of a selective flotation collector to reject an undesired mineral is just as important as its ability to collect the desired mineral. The percentage rejection curves shown on the graphs give this factor due consideration and its value is calculated as follows: Suppose a concentrate contains 5 per cent of an undesired mineral. This indicates

Jan 1, 1942

By W. W. Odell

THE sulfur content of coal is perhaps more important in the manufacture of illuminating gas than in any other coal-using industry. Whether the gas is made by the distillation of coal in retorts or ovens or by steaming incandescent coal or coke in the water-gas process, a portion of the sulfur present in the fuel always passes into the crude gas. Practically all the sulfur that remains in the finished gas is transformed into sulfur dioxide (SO2) when the gas is burned. Sulfur dioxide is a pungent suffocating gas and, if present in the air in any perceptible amount, is deleterious to health and comfort and damaging to house furnishings. So universally is this recognized that laws regulating the amount of sulfur that may be permitted to remain in the gas are very generally in force. The capacity of a plant to purify gas frequently limits the selection of coal for gas making. This condition may arise from different causes. Some plants were originally designed to handle a certain grade of low-sulfur gas coal, and very little leeway was allowed for growth or for the use of inferior coals. Other plants, when built, had ample capacity to purify gas from relatively higher sulfur coals, but their output has grown so rapidly that their purifying capacity is now limited and only- the low-sulfur coals can be handled. There is a great quantity of coal in the United States that would satisfy the requirements of the gas manufacturer, were it not for the high sulfur content. The coals containing less than 1 per cent. sulfur are becoming scarcer year by year and, in time, the gas industry will probably be compelled to use coals that are now considered out of the question.

Jan 9, 1919

By S. Frederick Ravitz, Kenneth E. Fisher

Four liquids are ordinarily present in the lead blast furnace during lead smelting. At the bottom is the lead bullion, which is metallic lead containing about one per cent of impurities, including gold, silver, copper, bismuth, arsenic and antimony. Above this is the speiss, which consists essentially of arsenides and antimonides of iron and copper. The speiss is followed by the matte, which consists principally of sulfides of iron, copper and lead1. The top layer is the slag, of which the major constituents are silica, lime, alumina, zinc oxide and iron oxide. Similar products are obtained from the dross furnace, which treats the dross obtained in decopperizing lead bullion. The distribution of gold and silver among these various products is of considerable importance in the smelting of lead. In general, the matte and speiss cannot be treated in the lead smelter, and usually are sent to a copper smelter. It is usually desirable, therefore, to keep their gold and silver contents as low as possible, and to collect the precious metals in the bullion. If the bullion, speiss, matte and slag exist together in equilibrium, the gold and silver should distribute themselves among these four liquids in a definite manner, which, other conditions being equal, should depend only on the amounts of gold and silver in the charge to the furnace. It is thus apparent that a knowledge of whether such equilibrium exists is necessary before attempting to study the effects of various compositions of matte and speiss on the distribution of gold and silver among the furnace products2. Moreover, systems consisting of four liquids in equilibrium are very rare, and are of considerable scientific interest. In order to ascertain whether equilibrium existed, the distribution of gold and silver among the four liquids was determined. The speiss,

Jan 1, 1937

By L. K. Oliver, Marshall

The use of model studies for the development of invasion patterns for cycling is .illustrated by model studies obtained with a recently developed apparatus in the solution of actual cycling problems. Introduction Depletion of a gas reservoir by cycling under pressure maintenance may be divided into three general phases. In the first phase, injection of dry gas is used to move all possible wet gas to producing wells prior to breakthrough of appreciable quantities of dry gas into producing wells. In the second phase, injection moves additional wet gas to producing wells while moderate quantities of dry gas are being produced. The third phase consists of production without injection to deplete the commercial gas reserve which remains after the cycling operation. Thus, in the first phase, a portion of the reservoir is invaded by dry gas, and the dry gas usually displaces something less than 100 pct of the wet gas from the invaded portions of the reservoir. The second phase enlarges the invaded portion of the reservoir and, at the same time, increases recovery from that zone invaded by dry gas in the first phase of the cycling operation. The result is an early yield of a substantial quantity of the liquefiable hydrocarbons in the reservoir with a minimum of the retrograde losses which occur in some reservoirs. The overall recovery from such an operation is usually high. The summation of the paths taken by dry gas in a cycling operation can be termed an invasion pattern. The use of electrical models to predict invasion patterns has been the subject of several contributions to the literature.1-3 The results of such model studies as applied to actual cases has been discussed by Kelton4 and Miller and Lents.= Recently, an improved apparatus for conducting potentiometric model studies has been developed, as described by Lee.V he purpose of this paper is to present model studies or invasion patterns obtained with this instrument in the solution of actual cycling problems. The percentage of displacement of wet gas within the invaded portion of the reservoir in cycling, increase in recoveries of wet gas by continuing cycling after dry gas breakthrough, recoveries of wet and dry gas by production after cycling, or economic factors in cycling are beyond the scope of this paper. Discussions which follow will be limited entirely to the development of suitable invasion patterns for cycling under pressure maintenance and the use of model studies therein. Discussion OF Results In using model studies to predict invasion patterns in cycling, some factors which influence the results are the following:

Jan 1, 1948

By Marshall, L. K. Oliver

The use of model studies for the development of invasion patterns for cycling is .illustrated by model studies obtained with a recently developed apparatus in the solution of actual cycling problems. Introduction Depletion of a gas reservoir by cycling under pressure maintenance may be divided into three general phases. In the first phase, injection of dry gas is used to move all possible wet gas to producing wells prior to breakthrough of appreciable quantities of dry gas into producing wells. In the second phase, injection moves additional wet gas to producing wells while moderate quantities of dry gas are being produced. The third phase consists of production without injection to deplete the commercial gas reserve which remains after the cycling operation. Thus, in the first phase, a portion of the reservoir is invaded by dry gas, and the dry gas usually displaces something less than 100 pct of the wet gas from the invaded portions of the reservoir. The second phase enlarges the invaded portion of the reservoir and, at the same time, increases recovery from that zone invaded by dry gas in the first phase of the cycling operation. The result is an early yield of a substantial quantity of the liquefiable hydrocarbons in the reservoir with a minimum of the retrograde losses which occur in some reservoirs. The overall recovery from such an operation is usually high. The summation of the paths taken by dry gas in a cycling operation can be termed an invasion pattern. The use of electrical models to predict invasion patterns has been the subject of several contributions to the literature.1-3 The results of such model studies as applied to actual cases has been discussed by Kelton4 and Miller and Lents.= Recently, an improved apparatus for conducting potentiometric model studies has been developed, as described by Lee.V he purpose of this paper is to present model studies or invasion patterns obtained with this instrument in the solution of actual cycling problems. The percentage of displacement of wet gas within the invaded portion of the reservoir in cycling, increase in recoveries of wet gas by continuing cycling after dry gas breakthrough, recoveries of wet and dry gas by production after cycling, or economic factors in cycling are beyond the scope of this paper. Discussions which follow will be limited entirely to the development of suitable invasion patterns for cycling under pressure maintenance and the use of model studies therein. Discussion OF Results In using model studies to predict invasion patterns in cycling, some factors which influence the results are the following:

Jan 1, 1948

By W. D. Robertson, E. Scala

Electrical resistivity of a number of pure liquid metals and alloys has been measured as a function of temperature and composition. The data show a close correspondence between the liquid and solid states with respect to thermal, structural, and compositional relationships. STUDY of diffuse scattering of X-rays by liquid metals1 has demonstrated that some degree of order persists above the melting point and that the atomic constitution of liquids is more analogous to the solid state than to a gas. Consideration of the change in various thermodynamic properties that accompanies transformation from solid to liquid leads to the same general conclusion.² evertheless, specific knowledge of the constitution of the liquid state is limited when compared with that of the solid and gaseous states owing, in part, to the difficulty of interpreting the X-ray data and in part to the indirect character of deductions based on thermodynamic data. Of the structure-sensitive physical properties, electrical resistivity of liquid metals is perhaps the most easily interpretable, particularly when comparison is made with the solid state. According to the available data, most of which was obtained prior to 1914, cubic metals exhibit a normal linear and positive temperature dependence in the liquid state and the data have been accepted without question. The divalent metals, zinc and cadmium, are apparently exceptional in that resistivity is not linear with temperature and it passes through a minimum. Mercury also exhibits a nonlinear temperature dependence but the slope is always positive. Important comparisons with magnesium could not be made at the time the following work was undertaken because the necessary experimental data were not available. Data on liquid solutions are very limited and are largely from a single source."-" Based on Bornemann's work, Norbury7 pointed out that the resistivity of liquid copper alloys appeared to be dependent on the valence of the solute and that the increase due to the solute was of the same order as in the solid state. However, large extrapolations were involved and no quantitative relationship was developed. Therefore, before proceeding with additional deductions regarding the resistivity of liquid metals and interpretation in terms of structure, it appeared necessary to verify and extend the previous work with particular emphasis on divalent metals and the effect of alloying elements of different valence in dilute liquid solutions. The present work includes: 1—A determination of the resistivity of high purity liquid magnesium, tin, indium, copper, zinc, and cadmium as a function of temperature. 2—The effect of 1 atom pct of copper, cadmium, aluminum, tin, antimony, and

Jan 1, 1954

By Enid C. Plante

This paper deals with the flotation of the mineral fluorite (calcium fluoride) and of two associated gangue minerals, calcite and quartz. The aim of the investigation was to produce "acid-grade" fluorite, which must contain less than one per cent of silica. Several reagents are used successfully in practice for floating fluorite from its ores. Oleic acid is the most widely used collector, usually at temperatures above 60°C, with sodium silicate as a dispersant for quartz and quebracho or tannin to depress calcite. Sulphides (e.g., galena) are often removed first by xanthate flotation. Many investigators23 report results in which more than 80 pct of the fluorite is recovered in a concentrate assaying 96 pct or more of fluorite and less than I pct of silica. This investigation was undertaken with the intention of floating the gangue, which is the minor constituent of the ore, from the fluorite. Hence emphasis was first placed on the cationic compounds that float quartz. No satisfactory separations were obtained in this way, and other reagents were investigated to discover whether these were more effective than oleic acid in floating fluorite from quartz in the usual way. The first part of the paper describes experiments with several long-chain collectors available commercially. Most of this work has been by captive-bubble and cylinder flotation tests, with some batch tests in a flotation machine. The second part describes the use of sodium cetyl sulphate as a collector for fluorite and includes laboratory tests and extension of the work to batch tests in the flotation machine. A method for determining the adsorption of sodium cetyl sulphate on fluorite has been developed and is described. Theory of Collection by Paraffin-chain Salts It may be assumed that these compounds are adsorbed at the mineral surface in one or more of three ways outlined by Kolthoff:12 1. Exchange adsorption between lattice ions in the mineral surface and collector ions in solution. Closely related is adsorption by the collecting mechanism postulated by Taggart,17 in which there is metathesis between the collector and the mineral cation or anion. 2. Exchange .adsorption between adsorbed gegen ions (p. 67, ref. 19) and collector ions in solution. 3. Adsorption of nonelectrolytes (polar-nonpolar) without displacement of adsorbed ions. With cationic collectors, inorganic cations in the solution (e.g., hydrogen ion) compete with the collector ions and therefore act as depressants, while inorganic anions have the same effect with anionic collectors. From this follows the general conclusion that ions of the same charge as

Jan 1, 1949

By Enid C. Plante

THIS paper deals with the flotation of the mineral fluorite (calcium fluoride) and of two associated gangue minerals, calcite and quartz. The aim of the investigation was to produce "acid-grade" fluorite, which must contain less than one per cent of silica. Several reagents are used successfully in practice for floating fluorite from its ores. Oleic acid is the most widely used collector, usually at temperatures above 60°C, with sodium silicate as a dispersant for quartz and quebracho or tannin to depress calcite. Sulphides (e.g., galena) are often removed first by xanthate flotation. Many investigators23 report results in which more than 80 pct of the fluorite is recovered in a concentrate assaying 96 pct or more of fluorite and less than I pct of silica. This investigation was undertaken with the intention of floating the gangue, which is the minor constituent of the ore, from the fluorite. Hence emphasis was first placed on the cationic compounds that float quartz. No satisfactory separations were obtained in this way, and other reagents were investigated to discover whether these were more effective than oleic acid in floating fluorite from quartz in the usual way. The first part of the paper describes experiments with several long-chain collectors available commercially. Most of this work has been by captive-bubble and cylinder flotation tests, with some batch tests in a flotation machine. The second part describes the use of sodium cetyl sulphate as a collector for fluorite and includes laboratory tests and extension of the work to batch tests in the flotation machine. A method for determining the adsorption of sodium cetyl sulphate on fluorite has been developed and is described. Theory of Collection by Paraffin-chain Salts It may be assumed that these compounds are adsorbed at the mineral surface in one or more of three ways outlined by Kolthoff :12 I. Exchange adsorption between lattice ions in the mineral surface and collector ions in solution. Closely related is adsorption by the collecting mechanism postulated by Taggart,17 in which there is metathesis between the collector and the mineral cation or anion. 2. Exchange adsorption between adsorbed gegen ions (p. 67, ref. 19) and collector ions in solution. 3. Adsorption of nonelectrolytes (polarnonpolar) without displacement of adsorbed ions. With cationic collectors, inorganic cations in the solution (e.g., hydrogen ion) compete with the collector ions and therefore act as depressants, while inorganic anions have the same effect with anionic collectors. From this follows the general conclusion that ions of the same charge as

Jan 1, 1947

By Colin C. Harris, Nathaniel Arbiter

Flotation kinetics is the study of the variation in amount of froth overflow product with flotation time, and the quantitative identification of all rate con- trolling variables. With such variables maintained constant, the algebraic relationship between the proportion of mineral floated and flotation time is a flotation rate equation. This contains the constant values of all the rate determining variables implicit in one or more rate constants which must be evaluated from experimental data. The form or forms of the rate equation can either be deduced from assumptions or facts established about the mechanism of the process, or, more commonly, determined empirically or by analogy with similar rate process. (See pages 215 to 226 and 221 to 227.) The earliest contributions on flotation kinetics came in the mid- ~hirties,3,27,31 with interest increasing in recent years. The broad goal of these studies is the reduction of the total variability of a flotation system to equations among the individual variables, or among a lesser number of dimensionless groups.43 Although the goal is at present far from realization, its attainment will yield many practical advantages. The quantitative under- standing of the process should lead to improvements both in metallurgical results and flotation cell design. It should lead also to reliable methods for scaling-up* of laboratory and pilot plant results to full size operation without the need for expensive and time-consuming mill tests on commercial machines. Finally, this type of quantitative information will assist the automation of flotation cells and circuits as well as control by computers. Replacing present methods of control based on post-mortem assays and trial and error manipulation of reagents and cell variables by control through exact process analysis should yield higher levels of grade and recovery through reduction of the large variability of present-day results. CHEMICAL ENGINEERING ANALOGIES: Industrial flotation always involves flow of pulp through a series of stirred tanks. It thus bears formal analogy to many chemical engineering processes, the kinetics of which in flow systems has been studied for many de- cades.38,39,73,83 It will be useful to review these studies before considering flotation kinetics. Batch and continuous treatment are classified in Fig. 1. Batch operation in the true sense is unknown in flotation where concentrate is always removed

Jan 1, 1962

By Arvid E. Anderson, Frank K. Cameron

The weathering of copper-bearing ores with the formation of a water soluble salt and the recovery of the metal by leaching and evaporation precipitation, are processes long known, which have at various times been utilized with more or less commercial success. It is commonly assumed that the technical principles involved are quite simple and their application to a particular case easy. If these assumptions were true, we should anticipate a long list of uniformly successful leaching operations, which is not the case, and one would be justified only in calling attention to either unique or peculiar features of any particular enterprise; whereas, in studying the problems of the recovery of copper from the old workings of the Ohio Copper Co. in the light of available descriptions of other leaching projects, we have not found the assistance hoped for to guide us to the best realization of our own opportunities. It appears desirable, therefore, to call attention to these guiding principles, together with a description of the facts of accomplishment. Justification lies in the fact that the leaching and precipitation of copper at the Ohio Copper Co. mine in Bingham Canyon, Utah, is successful. This success is measured by an average monthly production of 600,000 Ib. of copper at an average operating cost, to date, of 3.85 cents per pound at the company's workings, or 6.32 cents per pound after paying shipping and smelter charges on the finished copper. A total of 17,076,099 Ib. of copper had been shipped to the smelter from the beginning of operations, August, 1922, to April 1, 1925. Probably these results can be bettered with further study and realization of the factors involved and the devising of methods of meeting them. It is now an assured fact that the enterprise will have a relatively long and continuously profitable life and that its reserves will not, nor cannot, be suddenly and permanently depleted. It is particularly noteworthy that the financing of this enterprise has been entirely from its earnings. The few hundred dollars necessary for the first experiments and production were obtained by the sale of used, and no longer needed, equipment from a mill belonging to the company; and all funds since required throughout the growth and development of the enterprise, from a few troughs with a production of 2000

Jan 1, 1926

By Walter Rosenhain

In selecting solid solutions for the subject of this lecture I have been guided by several considerations. The bodies known under that somewhat paradoxical name play a most important part in all types of alloys; consequently, a deeper knowledge of their constitution must 'be of fundamental importance to both metallurgical science and practice. Further, having been asked to deal with some of the more theoretical aspects of metallurgy, I have been tempted to describe certain considerations, which I believe to be novel, in regard to the nature of solid solutions. These considerations constitute a theory that requires much experimental confirmation, but they have passed the stage of speculations, for experimental evidence has become available and one inference after another, that can be derived from the theory, is found to be in accord with well-known facts. In putting before you these ideas and inferences, it must be understood that detailed quantitative proof of every step cannot be furnished. Our conclusions must therefore be stated with the reservation that their acceptance must depend on the manner in which the discovery of fresh facts may either confirm or confound them. If we wish to understand the structure of solid solutions we nust carefully realize the manner in which these bodies are formed in alloys. The formation of solid solutions is by no means confined to alloys, but it is desirable to confin5 attention, at the outset, to intermetallic solid solutions. It is not easy to formulate a precise definition of the term "solid solution." It may be said that a solid solution is a crystalline body formed from a liquid solution or from an intimate mixture of solids, or of liquid and solid, that retains in the solid state an admixture of the two substances (solvent and solute) as intimate as that which exists in a liquid solution. The term is undoubtedly paradoxical, for one usually associates solution with a liquid, but the difficulty cannot be evaded by using such a term as solidified solution, for this might refer to a solution that has set, or congealed, without undergoing crystallization. The German term mischkry stall avoids the difficulty and appears to

Jan 1, 1923

By Walter Rosenhain

In selecting solid solutions for the subject of this lecture I have been guided by several considerations. The bodies known under that somewhat paradoxical name play a most important part in all types of alloys; consequently, a deeper knowledge of their constitution must 'be of fundamental importance to both metallurgical science and practice. Further, having been asked to deal with some of the more theoretical aspects of metallurgy, I have been tempted to describe certain considerations, which I believe to be novel, in regard to the nature of solid solutions. These considerations constitute a theory that requires much experimental confirmation, but they have passed the stage of speculations, for experimental evidence has become available and one inference after another, that can be derived from the theory, is found to be in accord with well-known facts. In putting before you these ideas and inferences, it must be understood that detailed quantitative proof of every step cannot be furnished. Our conclusions must therefore be stated with the reservation that their acceptance must depend on the manner in which the discovery of fresh facts may either confirm or confound them. If we wish to understand the structure of solid solutions we nust carefully realize the manner in which these bodies are formed in alloys. The formation of solid solutions is by no means confined to alloys, but it is desirable to confin5 attention, at the outset, to intermetallic solid solutions. It is not easy to formulate a precise definition of the term "solid solution." It may be said that a solid solution is a crystalline body formed from a liquid solution or from an intimate mixture of solids, or of liquid and solid, that retains in the solid state an admixture of the two substances (solvent and solute) as intimate as that which exists in a liquid solution. The term is undoubtedly paradoxical, for one usually associates solution with a liquid, but the difficulty cannot be evaded by using such a term as solidified solution, for this might refer to a solution that has set, or congealed, without undergoing crystallization. The German term mischkry stall avoids the difficulty and appears to

Jan 1, 1923

By Arthur Knapp

The practical application of mud-laden fluids in wells has been the subject of many papers.' However, there seems to have been little investigation of what actually happens when mud-laden fluids are applied to a loose porous sand. The assumption is that the fluids penetrate the sands and that there is some plastering action. The degree of penetration and the relation of plastering action to wall stability is not generally known. This paper describes a series of experiments made in an attempt to observe, in laboratory apparatus, the action of mud-laden fluids under conditions simulating those to be found in a well. For the purposes of this discussion all fluids containing solid matter in suspension are mud-laden fluids. Series I: Penetration of the Pores of Uncemented Sands The subject of the penetration of porous formations by water is discussed in detail in Water-Supply Paper No. 67 of the U. S. Geological Survey. No attempt was made to repeat the experiments described therein. The results of the first experiment of this series are given simply to show the capacity of the apparatus used. The conditions in this first experiment were maintained throughout the remainder of this and the second series, except where noted. The experiments of Mills, McCoy, and others on subsurface flows, adjustments, migrations, etc., deal with the oil, water or gas within the porous beds.V he experiments described herein deal with the conditions immediately surrounding the bore hole.

Jan 1, 1923