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By A. M. Sarem

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady - state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two - phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-pbase relative permeability as it does in two-phase flow. INTRODUCTION In the light of increasing demand for three-phase relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis 1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between I/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression for determining the outflow face saturation from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. PROPOSED METHOD The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three - phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Jan 1, 1967

By C. H. Benedict, H. C. Kenny

A 2000-ton ammonia leaching plant has been operated by the Calumet & Hecla Mining Co., at Lake Linden, Mich., continuousl~ since February, 1917, except from April, 1921, to April, 1922, during the period of depression following the European war. A description of this plant has been published elsewhere.1 The present article describes the operation of the plant since 1917, together with the changes in the process that have been found to be advisable. In spite of the fact that this plant and that of the Kennecott Copper Co. are the only ones operating on a large scale, much experimental work is being done on ammonia leaching, as applied to oxidized ores, and it is to aid these and other investigators that this detailed account is given. For the benefit of those unfamiliar with the original article, the following short abstract is given, as an introduction to a more detailed account of the process and the reasons for present practice. Rêsumê of Previous Article Leaching on a commercial scale began in July, 1916, and by Februsry, 1917, the plant of 2000 tons capacity was in commission. The ore treated is a conglomerate containing native copper and no sulfides or oxidized copper minerals. Before leaching, the ore is crushed by steam stamps and Hardinge pebble mills to pass a 28-mesh screen. Free copper is removed, by gravity concentration, on Woodbury jigs and Wilfley tables, and colloidal slime for oil flotation is removed by quadruplex Dorr classifiers. The leaching sand remaining contains about 2 per cent. + 28-mesh material and 15 per cent. — 200-mesh and carries from 8 to 14 lb. of copper per ton, depending on the grade of ore worked. The solvent employed in leaching is a water solution of ammonium carbonate,

Jan 1, 1924

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

IN 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group -SO4- or _S03- are excellent collectors for cassiterite and promise to be selective.1 The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000gram Denver cell. EXPERIMENTAL METHODS Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously described.5-10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these tests determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver Submachines.--Melbourne tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By Yves Dardel

The literature concerning the remelting of alunlinum and its alloys is very rich. Unfortunately the majority of the papers on this subject have no scientific value, for the theories or explanations are too often in opposition to the laws of physical chemistry. Furthermore only a few of the methods of purification are considered in the literature. Hence it has seemed necessary to the author to sketch a general theory of the purification of secondary aluminum. The purpose of the purification is to eliminate the impurities that the charges, and the atmosphere of the furnaces bring into the bath during the successive remelt-ings. Indeed scrap as well as metal can be used when soiled with oil, greases, water, or others, if it has been sufficiently dried and contains oxides. At the melting point of the metal, the oils and greases are decomposed into their constituent elements H², O2, H²O, co², CO, CH,, and others. These gases are added to the corresponding gases in the atmosphere of the furnace. The impurities introduced into the metal during the remelting will accordingly be the products resulting from the action of these gases on the liquid bath. The quantity of hydrogen that is soluble in aluminum and its alloys is given by the relation of sieverts3 as a function of its partial pressure PH2 in the atmosphere m = K vPH² [I] where K is a constant, which depends only upon the temperature and increases with it. The experiments of Rijntgen and Braun4, RÖntgen and M611er5, Bircum-shaw6 and Winterhagerl have rendered it possible to determine the value of K, when the temperature is less than 1.000°C. One obtains: log K = - 4,702.5T + o 238 [2] Besides its usual significance, the term Ph~ represents also the internal pressure of dissolved hydrogen, since in the equilibrium, that is1 when no gas exchange Occurs between the two phases, the Pressures of hydrogen in the metal and in the atmosphere must be equal. Eq I shows that when the partial pressure of H2 increases the amount of dissolved hydrogen in equilibrium increases, and that, if the contrary Occurs, the quantity of H² should diminish. However, if for any reason the diffusion of hydrogen is hindered and the total amount of dissolved gas remains constant while the temperature decreases, the internal pressure of H² increases until it reaches the value of the hydrostatic pressure. At this point, bubbles of hydrogen appear in the bath and escape out of it. The amount of hydrogen in the metal is then limited by a a depending On the hydro- static pressure, which is practically equal to one atmosphere. Indeed hydrogen does not accumulate in the form of a hydride appearing as a separate solid phase. However1 even the mechanism of the solubility is not yet elucidated. One does not know exactly as yet, whether the

Jan 1, 1949

By Yves Dardel

THE literature concerning the remelting of aluminum and its alloys is very rich. Unfortunately the greater part of the papers about this subject have no scientific value, for the theories or explanations are too often in opposition to the laws of physical chemistry. Furthermore only a few of the methods of purification1,2 are considered in the literature. Hence it has seemed necessary to the author to sketch a general theory of the purification of secondary aluminum. The purpose of the purification is to eliminate the impurities that the charges and the atmosphere of the furnaces bring into the bath during the successive remeltings. Indeed scrap as well as metal can be used when soiled with oil, greases, water, .. , if it has been sufficiently dried and contains oxides. At the melting point of the metal, the oils and greases are decomposed into their constituent elements H2, 02, H2O, C02, CO, CH4, and others. These gases are added to the corresponding gases in the atmosphere of the furnace. The impurities introduced into the metal during the remelting will accordingly be the products resulting from the action of these gases on the liquid bath. The quantity of hydrogen that is soluble in aluminum and its alloys is given by the relation of Sieverts3 as a function of its partial pressure PH2 in the atmosphere [m = K _%/PH, [I]] where K is a constant, which depends only upon the temperature and increases with it. The experiments of Röntgen and Braun4, Röntgen and Möller5, Bircumshaw6 and Winterhager7 have rendered it possible to determine the value of K, when the temperature is inferior to 1.000°K. One obtains: [log K = - 4,702.5 + 0.238 [2]] Besides its usual signification, the term PH2 represents also the internal pressure of dissolved hydrogen, since in the equilibrium, that is, when no gas exchange occurs between the two phases, the pressures of hydrogen in the metal and in the atmosphere must be equal. Eq I shows that when the partial pressure of H2 increases the amount of dissolved hydrogen in equilibrium increases, and that, if the contrary occurs, the quantity of H2 should diminish. However, if for any reason the diffusion of hydrogen is hindered and the total amount of dissolved gas remains constant while the temperature lowers, the internal pressure of H2 increases until it reaches the value of the hydrostatic pressure. At this point, bubbles of hydrogen appear in the bath and escape out of it. The amount of hydrogen in the metal is then limited by a maximum depending on the hydrostatic pressure, which is practically equal to one atmosphere. Indeed hydrogen does not accumulate in the form of a hydride appearing as a separate solid phase. However, even the mechanism of the solubility is not yet elucidated. One does not know exactly as yet, whether the

Jan 1, 1947

By R. Scot Clark

The reactively sputtered silicon dioxide capacitor -was developed for use in the monolithic integrated circuit, thereby requiring the capacitor to be fabricated on an oxidized silicon slice. The silicon dioxide film is formed by reactively sputtering silicon in a 50 pct Ar-50 pct 0, atmosphere and the physical properties are indistinguishable from silica. A practical upper limit of capacitance per unit area of 0.25 pf per sq mil is reached with the capacitors fabricated from the Si0, film. Methods shown to enhance this value are double stacking the thin-film capacitors and addition of aluminum to the silicon cathode during sputtering to form an aluminosilicate dielectric. A major contribution to the field of diffused integrated circuits would be the addition of auxiliary passive devices for replacement of diffused passive devices which are currently being fabricated for many integrated circuits. This accomplishment would increase the flexibility of the diffusion process in order to concentrate more on transistor parameters rather than on fabricating diffused resistors and capacitors. To pursue this technique, a thin-film SiOz capacitor was developed which has _ proven applicable to many integrated circuits. Although the SiOl capacitor has an application, the major deterrent from extending the integrated circuit into many useful areas such as low-frequency linear application is the low dielectric constant of SiO, and the low usable capacitance in an integrated circuit. This paper will cover the sputtering techniques used for forming the SiO, film, the physical and electrical properties of sputtered SiO,, and yield information concerning the application of these capacitors to integrated circuits. REACTIVE SPUTTERING Reactive sputtering is simply the sputtering of a metal or semiconductor in glow discharge in the presence of a reactive gas. The material to be sputtered is seen in Fig. 1 as the cathode of the system and is bombarded with positively charged ions of the ambient gas. In this investigation, the ambient gas is composed of 50 pct Ar and 50 pct O2 at a pressure of approximately 2.5 X l0-' Torr. The ions are accelerated toward the cathode in the cathode dark space by the electric field and upon striking the cathode effect a momentum energy transfer to the surface atoms. The transferred energy is sufficient to dislodge a surface atom or atoms and these particles diffuse through the glow discharge to the collector or anode. Several mechanisms of oxidation in the reaction chamber can be considered during reactive sputtering. 1) The surface of the cathode is oxidized and the oxide is subsequently sputtered. 2) Oxidation and sputtering occur simultaneously. 3) Sputtering of the cathode material is followed

Jan 1, 1965

Visitors frequently put the question to Kalgoorlie gold miners; "Why don't you concentrate your mining operations?" A mine may be drawing ore from over a hundred different working places which are spread out over several thousand feet of strike and on many different levels. The answer to this question is that "finished" can rarely be written for a section of the mine. The intricate web of mineralization in faults, shears and fractures is an endless puzzle, each solution opens up new avenues to be explored. After the last ore is taken from a stope, a program of drilling may continue for several weeks on different possibilities. Perhaps no ore is discovered and drilling is abandoned, but it is not unusual for another search to begin later in that same area on a new theory with successful results. Wherever a slightly richer mineralization is found, it is needed to "sweeten" the mill heads. Over seventy years ago gold was discovered in the dry wastes of Western Australia. Rich deposits of alluvial gold were found at first and as these were worked out they led to the discovery of the lode ores, which were leaner and harder to extract.

Jan 10, 1964

By Howard L. Hartman

There is reason to believe that ventilation systems so far devised for use with continuous mining machines fall far short of success. This is vividly demonstrated to anyone who has observed in a continuous miner section the localized ignitions of pockets of gas and the generation of dense clouds of dust by the cutting head of the machine. The alarming frequency with which major ignitions and disasters continue to occur in modern mechanical mining and the rise in incidence of pneumoconiosis serve as reminders that our ventilation systems are far from achieving the ultimate in providing protection from either short-term explosions or long- term dust diseases, both of which take lives. Human safety is the main concern in ventilation. But in this day of high-priced labor, let us not forget human comfort, either, for this is a major factor in motivation toward high productivity. The failure or inadequacy of most mine ventilation systems in providing the kind of working conditions at the face that are conducive to productive as well as safe operation is an indictment of our environ- mental control program in mining generally.

Jan 3, 1962

By Joseph M. Chelini

A cash-flow factor is any figure acquired in an evaluation that effects the cash flow potential of an eventual operation. Table I is a list of some of these cash-flow factors. There are more, such as, the payments and penalties in a smelter schedule if the concentrate would be sent to a smelter. During an evaluation it is necessary to maintain a two-way flow of communication between the evaluation people and financing people. To accomplish this, it is necessary to translate the vocabulary of the evaluating people into the vocabulary of the financing people, or geologic and engineering jargon into dollars and cents. This is done by cash-flow studies in which cash-flow factors are input, which when logically manipulated using accepted rules and procedures of accounting, provide an output in dollars and cents.

Jan 5, 1972

By W. J. Moore, E. M. Swiggard, H. Shenker

Beryllium is the most soluble of the double-acceptor impurities in germanium; the solubility is at least 1 x 10 19 atoms cm3. Photoconductive, optical, and electrical measurements were made on a set of Ge:Be samples grown without other intentionally added imp~ivities. The excited-states spectrum of beryllium in germanium was determined both in zero field and in magnetic fields up to 30 kc. It was found that the absorption 0-f lines in the vicinity of the G line increased markedly with increasing magnetic field. The ioniza-tion energy of neutral beryllium in germanium was determined to be 24.3 * 0.1 mez: using the excited-states spectrum. An infrared detector using a Ge:Be element was found to have a normalized detectivity D* (50 p, 1000 cps, 1 cps) of 9 X ldO cm-~ps"~-w-'. The Ge:Be sambles exhibited low-field breakdown and inibzirity band conduction effects at low temperatures. WHILE the properties of most dopants in germanium have been thoroughly investigated, the properties of beryllium in germanium have had relatively little attention. Much of the work that has been done' has been concerned with the properties of singly ionized beryllium in germanium. The purpose of the present work was to determine the photoconductive and electrical properties of beryllium-doped germanium (Ge:~e) with a small concentration of other electrically active impurities. Ge:Be is of special interest since beryllium is the most soluble of the known double-acceptor impurities in germanium. MATERIALS PREPARATION A set of &:Be crystals with beryllium concentrations between 5 x 1013 and 1x 10'' cmm3 and without other intentionally added impurities was grown in a hydrogen atmosphere by the horizontal zone-refining techniques described by Swiggard and Shenker.2 The segregation coefficient of beryllium in germanium was found to be about 0.07 and its maximum solubility was found to be greater than 1 x 10'' atoms cm-3 which is in agreement with previous results.' Most of the crystals were found to have a small net concentration of shallow acceptors; for example, a crystal having a beryllium concentration of 1.1 X 1016 cm-3 was found to have a net concentration of shallow acceptors of less than 1.5 X 1013 cm-3. Ingots designed to have a beryllium concentration of 1 x 1017 cm-3 or less exhibited a loss of electrically active beryllium. That is, the beryllium concentration was lower than expected and the decrease of the beryllium concentration along the length of the ingot was much larger than expected. It is hypothesized that this effect is due to the oxidation of the beryllium by the residual oxygen in the system. This effect is similar to but not as severe as the effect observed with boron in germani~m.3, 4 OPTICAL ABSORPTION SPECTRUM The excited-states spectrum of neutral beryllium atoms in germanium was studied by measuring the infrared optical absorption spectrum. A typical spectrum is shown in Fig. 1; the labeling of the absorption lines follows that of Fisher and Fan.* The spacings between the observed lines and the D line are nearly equal to the corresponding spacings for the other ac -ceptors in germanium.5-7 By the use of the theoretical result67' that the neutral impurity ionization energy is 2.53 mev larger than the energy of the D line, the ionization energy of neutral beryllium in germanium was determined to be 24.3 * 0.1 mev at 4.2"K. This method yields a more precise value of the impurity ionization energy than the usual Hall effect method.' The absorption spectrum of Ge:Be was also measured as a function of magnetic field using a magnetic field parallel to the incident radiation and using unpolarized radiation. A typical spectrum taken at 30 kG is shown in Fig. 2. An unexpected observation is that the absorption of the lines in the vicinity of the G line (there is a strong possibility that some of these lines may be associated with lines other than the G line) increases with magnetic field. RESISTIVITY AND HALL DATA Measurements of Hall voltage vs temperature were made on several of the samples. The thermal activa-

Jan 1, 1968

By C. A. Heiland W. E. Pugh

The principle underlying the majority of magnetic intensity variometers is a comparison of the force to be measured with another force of known magnitude. The known force may be (a) of a magnetic nature, such as magnetic fields produced by magnets or coils, or (b) of a mechanical nature, such as (1) the elastic forces of wires, or (2) the force of gravity, such as employed in bifilar magnetometers and magnetic balances. In instruments of such type, usually a magnetic system is employed, free to move about either a horizontal or vertical axis, on some sort of a suspension. If the earth's magnetic field alone were present, such a system would adjust itself into the direction of the field or that of its components. Owing to the simultaneous action of the comparison force, however, the magnetic needle assumes a position that differs from the direction of the magnetic force; for all such instruments, the angle of deflection is given by tan = FIX, where F is the known and X the unknown earth magnetic force component. In other words, the magnetic system merely serves as an "indicator" for the position of balance of the two forces. Considering the matter from this point of view, it is not immediately obvious why the temperature of such a magnetic system should modify the results. In magnetic instruments, we may distinguish two different effects of temperature: (1) a magnetic effect and (2) a mechanical effect. The first is due to the fact that the magnetic moment of a magnet drops with an increase in temperature. This drop is characterized by the temperature coefficient of the magnetic moment (see equation 1). The second effect is due to the change in the torsion of suspension wires with temperature or to the expansion of lever arms of masses acting on magnetic balances.

Jan 1, 1934

By Demitri B. Shimkin

Minerals - A Key to Soviet Power, by Demitri B. Shimkin. Harvard University Press. $8.00, 452 pp., 1953. -The book is an economic evaluation of the position of the Soviet Union in respect to mineral wealth and development. Various sources are drawn upon, including the reports issued after completion of the various five year plans. The book is of considerable reference value despite the confusion which beclouds information concerning Soviet mineral progress. The theoretical study is the joint product of some of the staff of the Harvard University Russian Research Center. The author's approach to metals and nonmetals in the Soviet Union is systematic and he presents a great deal of data covering the period 1926 to 1950. Indicated weaknesses in the mineral economy are highlighted. Some considerable space is given to Soviet mineral future.

Jan 5, 1953

By Kenneth A. Gutschick, Robert S. Boynton

Lime has become a very general loosely used term that includes virtually all finely divided types of limestone as well as burned forms of lime. However, actually (and according to Webster) lime is only calcined limestone (known as quicklime, calcium oxide, or calcia). It also embraces the secondary product of quicklime-namely hydrated lime or slaked lime (calcium hydroxide). Fundamentally there are two basic types of limestone-high calcium and high magnesium (dolomitic). The dolomitic quicklimes and hydrated limes correspond to their "high calcium" counterparts in terminology. The only difference is that the dolomitic types are a combination of the elements, calcium and magnesium, whereas high calcium limes contain only 0.5 to 2 pct of magnesium. Both types, which are made through calcination at high temperatures, are shown chemically as follows: [ ] In the above reactions either type of limestone is burned (calcined) in furnaces known as lime kilns so that the carbon dioxide content of the stone is expelled as a gas. With high calcium limestone 44 pct of the weight of the stone is lost; with dolomitic limestone the loss is 48 pct. Also, both reactions are chemically reversible since quicklime absorbs carbon dioxide readily and in so doing transforms itself back to the original carbonate form. Most quicklimes correspond in size to the original rock, which varies from one to eight inches, depending upon the type of kiln employed. Slight shrinkage occurs during calcination. A few limestones when calcined will decrepitate (break down) into a fine powdery form; however, chemically it is the same as the pebble or lump-sized material. For some uses the lumps of quicklime are pulverized and packaged. Since quicklime has great affinity for moisture and carbon dioxide, it is perishable. When it absorbs moisture and CO2 slowly from the atmosphere, the resulting product is "airslaked." Consequently, it must be stored in dry, moisture-proof areas that are free from CO2. Because of its fugitive nature, it is usually consumed within a few weeks after manufacture. A more stable form of lime is hydrated lime-commercially made by adding water to the quicklime until the lumps break down into a fine, white powder. This product, which is usually packaged, can be stored more safely; and many of its uses are interchangeable with quicklime. The irreversible chemical reactions of hydrated lime for both high calcium and dolomitic types are: [ ]

Jan 1, 1960

By R. C. Hassinger, D. V. von Rosenberg

Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. INTRODUCTION Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial** concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption.l,2 Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. BACKGROUND In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors3-5 have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. A more

Jan 1, 1969

By P. Somasundaran, I. J. Lin

There are several methods described in the literature for the determination of the order and the rate constant for the flotation of minerals. These often involve some type of computational or graphical procedures. A relatively simpler method developed on the basis of a technique used by Chang" in chemical kinetics is described in this paper. Chang's technique, like most others in chemical kinetics," is based on the law of mass action which states that the rate of a chemical reaction is proportional to the active masses of the reacting substances at any given time. Application of this law to the flotation of minerals would involve the adaptation of the terms "flotation" for "chemical reaction" and "floatable amount of the minerals" for "the active masses of the chemical reactants." There are indeed a large number of physical processes controlling the actual flotation rate. The most inefficient one of these could be considered equivalent to the slowest reaction in a series of chemical reactions. If variables such as aeration rate and agitation are kept at constant levels, the rate of flotation under free flotation conditions (i.e., conditions under which the suspension is dilute) will be given by the following equation: where C is the concentration of the floatable minerals in the pulp at any given time t, K is the rate constant, and n is the order of the reaction. If we represent the floated fraction of the floatable mineral at time t as m (0 m - 1) and C at t = 0 as Ca, integration of Eq. 1 yields

Jan 1, 1974

By S. Arthur Krom

Recent experiments indicate that the usual type of concen-trating-table is not only poorly adapted to produce the desired results, but also is based upon an incorrect principle, namely, the use of riffles to perform the work of stratifying the various minerals. We have heard a good deal about riffles for concentratiug-tables; exhaustive experiments have been made to discover the proper form of riffle, or to prove the superiority of this or that form; disputes and patent-litigation have arisen over the matter of riffles, and thus marly have been led to believe that the riffle is the saving-device upon which the process of concentration depends. In the present paper it is proposed to show that the riffle is greatly overrated as to the part it performs in the concentration of minerals, and that, in the near future, it may possibly be eliminated entirely from that process. The experiments in question have shown that the troublesome riffle can be considered of secondary importance at the most, and should be so classed in the construction of a concen-trating-table built upon the right lines. The action of any form of riffle on a concentrating-table is such as to upset and retard the process of settling and stratifying the various minerals on the table-deck. From the deck of a riffled table no concentrates can be delivered until the deck is " bedded," that is, until a suffcient amount of metallic values has been fed to the table to spread over a large portion of the deck, forming a substratum of the heavier minerals. This substratum must be maintained by the feed within quite narrow limits, and directly proportional to the rate of discharge from the table, in order that the bed shall not be lost. On the other hand, the riffles having a very limited carrying-capacity, considerable care must be taken not to overfeed a riffled table, in which case the table proceeds, in mill parlance, to rob itself. As soon as the space between the

Jan 1, 1912

By H. B. Charmbury, D. R. Mitchell

Everyone in the coal industry from top management to the preparation engineer is vitally interterested in recovering as much salable coal as possible from the run-of-mine product. Coal losses from a preparation plant occur in the solid refuse material being discharged from the plant and in the bleed-off slurry from the water circuit. The refuse is generally hauled from the plant in solid form by trucks, conveyors, or aerial trams to the refuse or culm banks or it may be crushed and transported by hydraulic methods to refuse ponds or dams. The loss of coal in refuse material and the extent of this problem has been covered in another paper. The loss of salable coal in the plant bleed-off slurry is one of the water circuit problems in coal preparation plants. Slurries originate at various places in the processing circuits and are usually disposed of by transportation to waste ponds known as slurry ponds. Even though the combustible material discharged as slurry and refuse from the plant is labeled a loss, the loss must only be considered temporary. There is a tendency at the present time to examine refuse and slurry losses and to reprocess these materials to recover valuable coal.

Jan 1, 1960

By J. H. Wiggins

This paper first pictures the economic phase of evaporation losses and the actual evaporative conditions in handling and storing crude and gasoline in the United States; then follows a discussion of some of the theories of physics involved in evaporation loss and lastly an application of these theories to handling oil and gas on producing properties. GRANTING that about 600,000,000 bbl. of light oil will be produced in the United States this year and taking the Bureau of Mines' statement that 7 1/2 per cent. of the total crude production will be lost before the finished gasoline is shipped from the refinery, the volumetric evaporation will be 45,000,000 bbl. of the cream of the gasoline. This is a conservative figure and is equivalent to 1,890,000,000 gal. The real value of this liquid is at least 150 per cent. of the value of an equal volume of motor fuel. At only 10 c. per gal., the value lost is $189,000,000; at 15 c. per gal. the loss is $283,000,000. If 750,000,000 bbl. of light and heavy oil are produced here this year and the average price per barrel is $1.333, the gross return to producers will be $1,000,000,000 and the net returns about $200,000,000, if the cost of production is only $1 per barrel. Thus, the evaporation bill is about 20 per cent. of the gross income and is equal to the net income of the crude-oil producers. Two other comparisons with popular phases of the petroleum industry will help give an adequate conception of the evaporation problem. These are: cost of preventing evaporation compared to cost of cracked gasoline and volume of gasoline evaporated compared to volume of gasoline manufactured from natural gas.

Jan 7, 1924

By Arthur Knapp

Oil-well depletion curves, to be of value, should show when a well or lease may no longer be operated at a profit. The difference, at any time, between the total expenditures and the total income of a lease or well may be called the lease status. Plotting this lease status against time will give a curve subject to more accurate and different interpretations than the barrels-time curves. According to the hypothetical barrels-time curves shown in Fig. 1, well A, at the end of 16 mo., is producing twice as much oil as well B and will continue to produce for another year whereas well B will cease producing in about 6 months. Data fob Lease Status-time or Dollars-timb Curve Time Lease Months Status Lease purchased for $3000.............................. 0 — $ 3,000 No expenses chargeable to lease for 3 mo................. 2 — 3,000 Well A is started; cost of drilling for month is $16,000..... 3 — 19,000 Well is completed at additional cost of $10,000............ 4 - 29,000 Well A is brought in and flows 10,000 bbl. first month (we Fig. 1). Necessary to invest in tanks, boilers, pipe lines, etc.; difference between expenditures and receipts gives profit for month of $5,000............................ 5 — 24,000 Investment is small, cost of operating well A is small, so profits are $15,000................................... 6 — 9,000 Well ceases to flow so there is additional investment for pumping equipment and additional operating expense; net earnings from 6,000 bbl. of oil produced is $4,000. 7 ... Lease operation nor becomes normal and curve becomes smooth........................................... 8 — 500 9 2,000 10 4,500 11 6,000 12 7,700 13 8,700 14 9,000 15 9,500 16 10,000 A hypothetical lease status-time, or dollars-time, curve of this lease is shown in Fig. 2. At zero time, the lease is purchased for $3000, which is plotted below the zero dollar line, All subsequent entries are plotted

Jan 1, 1921

By L. B. Slichter

It has been estimated that rock exposures in most mining districts aggregate less than 1 per cent. of the total surface area.1 Conclusions concerning the hidden 99 per cent. necessarily have been based on knowledge of only a small fraction of the surface, and from this limited information the geologist has been obliged to deduce the approximate and general nature of the underlying formations. In the search for ore it is necessary to supplement this general picture with greater detail. Fairly accurate knowledge of relatively small zones is required. This knowledge is carefully sought in many different ways—detailed interpretations of geological history, the tracing of float, the use of test pits, of trenching, of drilling, and of other methods. Practical ingenuity, scientific brilliance, great perseverance and patience, and the expenditure of large sums of money have all been a part of this search. The problem of exploring beneath cover with economy, and of obtaining essential information which this cover hides, is obviously a difficult one. It is also a very important one, for geologist's inform us that already the story of the 1 per cent. exposed outcrops has been largely read.V here remains the nearly virgin field comprised in the hidden 99 per cent.: and the importance of this zone is bound to increase continually. In recent years, the problems connected with the exploration of this "99 per cent. zone" have attracted a constantly enlarging group of investigators and at present greater efforts than ever before are being made to resolve them. This work, in it's various special aspects, has enlisted, beside geologists, the cooperative efforts of chemists, physicists, and mathematicians. The progress made in this development should be kept before those directing explorations in order that due advantage may be taken of a changing situation. My subject concerns certain aspects of one of the older physical methods of exploration, the magnetic method. This method is familiar in principle to most of us, arid because of its age., is especially suitable for

Jan 1, 1929