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By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By Robert Bell

THE " Tar-Sands." is the name which has been given to the extensive horizontal deposit of fine Cretaceous sand, blackened by tarry petroleum, which forms the banks of the last or lowest 130 miles of the Athabasca river before it terminates in Athabasca lake. The Cretaceous strata, to which these sands belong, extend northwesterly from Dakota all the way to this lake and for 500 miles beyond it. The Athabasca river forms the uppermost section of the Athabasca-Mackenzie, one of the great rivers of the world. It rises on the Pacific side of the Rocky mountains, westward of Edmonton, and flows north of east to a point called Athabasca. Landing, 100 miles north of Edmonton, where it turns northward and runs about 280 miles before it falls into the west end of Athabasca lake. The section of this river-system which discharges the lake just named into Great Slave lake, is called Slave river, and below the latter lake it becomes the Mackenzie river. Along the section of 280 miles of the Athabasca river above mentioned, the Cretaceous strata consist of bluish-gray and drab-gray marls, on top, from Athabasca Landing to Drowned rapid, 110 miles down stream; then heavily bedded gray sandstones, 225 ft. in greatest thickness, underlying these, form the banks for about 40 miles further. The strata appear to be horizontal, but they really clip very slightly to the southward. At Drowned rapid, we see the first of the tar-sands resting on almost horizontal beds of bluish-gray limestone of Devonian age. In some places the limestone is associated with shaly or marly bands. Notwithstanding the great hiatus between the two series, the horizontal tar-sands lie conformably upon the almost level upper beds of the limestone wherever the two formations are seen together, all along the river, throughout a

Mar 1, 1908

By A. Chakravarti, C. C. Harris

First-order kinetics adequately describe the recovery of a single floatable species. The conditions under which cell behazior can be simulated by a single-phase model are discussed; deviations from the multiphase model are accountable. The rate coefficient depends upon operating conditions besides particle size and mineralogy and the physicochemical properties of the pulp constituents. The model for a real flotation system combines the first -order, single-phase model with a distribution of noninteracting species. Methods for determining the distributions are discussed. Applications of the procedure to flotation studies are outlined. The mathematical description of flotation as a rate process can be traced to Garcia1 who reported cases in which the fraction of solid remaining in a cell in semi-batch operation, F (for Notation used throughout, see Table l), decays exponentially with experimental time T. F = e-k>r. (1 The differential equation leading to Eq. 1 is dF ----= -k,F (2) dT which is recognized as the algebraic analog of the chemical kinetics first-order reaction equation.' This has led to suggested mechanisms for flotation and mathematical relationships other than first order: with very little foundation other than analogy. The flotation rate coefficient kl can be accounted for as the product of several probabilities concerning bub-ble-particle attachment and detachment, aggregate entry from pulp into froth and return from froth to pulp, and removal from froth as concentrate. These factors clearly contribute to the magnitude of the overall flotation rate, and there are others also, but describing flotation merely as the overall probability of consecutive gross events hardly appears a significant advance in understanding. More recently, it has been described in terms of a stochastic process, which promises to provide a more satisfactory approach? The present paper will be more concerned with a phenomeno-logical description of the flotation process than with an account of the internal mechanics of the process. This is not a statement of priorities, or a judgement of the relative importance of these options but rather an assessment of what is presently possible. Previous investigators'" have developed methods for interpreting semi-batch flotation data in terms of species distribution. These methods have been used in an attempt to explain flotation behavior in response to changes in operating conditions." Inspection of examples given in the literature" reveals discrepancies between theory and experiment, and data obtained in the Colum-

Jan 1, 1971

By Jules E. Jenkins

IN the past quarter century the seismograph has played an increasingly important role in evaluating vibratory effects transmitted to adjacent communities by industrial blasting operations. In this period research has advanced through two major phases—from falling pin seismometers to three-component recording seismographs. The initial phase of this research is now regarded as the era of recording, during which the seismograph merely recorded occasional events. It has emerged from this stage into the era of control and analysis and in this later period has been recognized as a full-fledged industrial tool. Although the falling pin machines of earlier years indicated probable amplitudes of industrial blasting vibrations, they gave no reliable measure of such displacements, nor did they provide essential information concerning direction or frequency of motion. The first contribution of the three-component recording seismograph was the weight-for-distance formula developed by the U. S. Bureau of Mines. This empirical formula enabled users of commercial explosives to determine beforehand the probable vibratory effects of a blast when the weight of the explosives charge and the distance from the shot point were known. This formula has withstood the test of time and is still applicable for blasts detonated by instantaneous methods. The second major contribution of the three-component recording seismograph followed the introduction in 1945 of short period or millisecond delay detonation. This might be described as a two-stage contribution, the first of which revealed a 50 pct reduction in the vibration magnitude when millisecond detonation was used rather than instantaneous discharge. This second part of this double contribution led to the discovery of the vibration dip phenomena, see Fig. 1. In Fig. 1 the horizontal coordinates indicate the displacements amplitude in inches, and the vertical coordinates, the explosive weight in pounds. The top curve is that of the U. S. Bureau of Mines for instantaneous detonation. Its curvature conforms to the two-thirds power of the explosive weight as provided in the weight-for-distance formula; hence the vibratory effects increase in proportion to an increase in the explosive charge. If the other curves shown below are temporarily disregarded, it may be considered that the entire area below this top curve represents both useful and waste energy. As mentioned previously, when millisecond delay detonation was first investigated it was found that in general the U. S. Bureau of Mines curve could be decreased by about 50 pct, or to the position of the middle curve. At the outset it was assumed that this curve would likewise increase in some proportion to the explosive charge, as did the top curve, that is, the curve would indicate a continuous upswing. As seismographic data accumulated this assumption was found to be erroneous in part. It was discovered that

Jan 1, 1957

By A. William Johnson

It was pointed out in an earlier paper1 that our understanding of the atomic mechanism by which diffusion occurs in metallic alloys is scarcely in an advanced state. This unsatisfactory condition is the result not of any lack of interest, but of the difficulty of designing experiments that .will yield suitable data. The diffusion coefficient of an alloy, measured in the usual way, is simply a number specifying the rate of homogenization of a nonhomo-geneous metal; this number, of itself, can furnish neither the rate at which the individual atoms move nor information as to the mechanism by which they move. It does not necessarily follow, however, that such information cannot be obtained, even if the path to be followed is still not clear. Much success has been attained in the study of diffusion in ionic crystals. A number of experiments, for which there are few counterparts in connection with metals, yield information often indicating a detailed mechanism by which diffusion probably occurs. From such work, quite acceptable theories of lattice imperfections have been developed by Wagner, Schottky, Frenkel, Jost and others.2 It is postulated that real crystals of stoichiometric composition contain, in equilibrium, certain imperfections of which the most importarlt types are: (I) vacant cation sites, with an equal number of interstitial ions; (2) vacant anion sites, with an equal number of interstitial ions; (3) equal numbers of anions and cations in interstitial positions; (4) equal numbers of vacant anion and cation sites. The classification of a particular crystal according to this scheme then follows from studies of the variation of electrical conductivity with pressure of the electronegative component surrounding the crystal, with ion size, and with temperature; other physical phenomena, such as the Hall effect, have aided in establishing the classification. The relative mobility of the anion and cation may be determined by chemical analysis of the salt at the electrodes following electrolysis. With such information, and knowing that one ion never occupies the lattice site normally belonging to an ion of opposite sign, it is usually possible to ascertain the diffusion mechanism. It is clear that the same experiments are not applicable to metal crystals, and substitute experiments that yield as much information have not yet been devised. Much can be learned, however, about the mobilities of the two* kinds of atoms in alloys by the use of radioactive metals as indicators. Only one such experiment has been performed in the past. In 1933, Seith and Keil,3 in an effort to explain the great difference between the rate of diffusion of gold in lead and of lead in lead, measured the rate of diffusion of radioactive lead in 3 gold-lead

Jan 1, 1942

By A. William Johnson

It was pointed out in an earlier paper1 that our understanding of the atomic mechanism by which diffusion occurs in metallic alloys is scarcely in an advanced state. This unsatisfactory condition is the result not of any lack of interest, but of the difficulty of designing experiments that .will yield suitable data. The diffusion coefficient of an alloy, measured in the usual way, is simply a number specifying the rate of homogenization of a nonhomo-geneous metal; this number, of itself, can furnish neither the rate at which the individual atoms move nor information as to the mechanism by which they move. It does not necessarily follow, however, that such information cannot be obtained, even if the path to be followed is still not clear. Much success has been attained in the study of diffusion in ionic crystals. A number of experiments, for which there are few counterparts in connection with metals, yield information often indicating a detailed mechanism by which diffusion probably occurs. From such work, quite acceptable theories of lattice imperfections have been developed by Wagner, Schottky, Frenkel, Jost and others.2 It is postulated that real crystals of stoichiometric composition contain, in equilibrium, certain imperfections of which the most importarlt types are: (I) vacant cation sites, with an equal number of interstitial ions; (2) vacant anion sites, with an equal number of interstitial ions; (3) equal numbers of anions and cations in interstitial positions; (4) equal numbers of vacant anion and cation sites. The classification of a particular crystal according to this scheme then follows from studies of the variation of electrical conductivity with pressure of the electronegative component surrounding the crystal, with ion size, and with temperature; other physical phenomena, such as the Hall effect, have aided in establishing the classification. The relative mobility of the anion and cation may be determined by chemical analysis of the salt at the electrodes following electrolysis. With such information, and knowing that one ion never occupies the lattice site normally belonging to an ion of opposite sign, it is usually possible to ascertain the diffusion mechanism. It is clear that the same experiments are not applicable to metal crystals, and substitute experiments that yield as much information have not yet been devised. Much can be learned, however, about the mobilities of the two* kinds of atoms in alloys by the use of radioactive metals as indicators. Only one such experiment has been performed in the past. In 1933, Seith and Keil,3 in an effort to explain the great difference between the rate of diffusion of gold in lead and of lead in lead, measured the rate of diffusion of radioactive lead in 3 gold-lead

Jan 1, 1942

By Clement K. Chase

ION exchange recovery of uranium has been proved successful in many operating plants in various parts of the world. First used in column plants processing clear liquors, ion exchange has more recently been applied in basket resin-in-pulp systems. A logical further development is the application of truly continuous processing techniques to the ion exchange recovery of metals, since previous systems have been semicontinuous at best. Column ion exchange is a valuable technique and has been used extensively in South Africa and elsewhere. However, it requires clear liquors. To produce these clear liquors, considerable investment in filter plant and clarification equipment is necessary. In the cases where it is very difficult or impossible to produce clarified liquors, column ion exchange is not so useful. Moreover, some liquors suffer from post-precipitation after clarification, which can become a serious problem.

Jan 9, 1957

By H. D. Outmans

The author applies the theory of hydrodynamic stability to fluid flow in porous media and concludes that the displacement of miscible liquids is stable if the stability coefficient, as defined by Eq. 19.2 or Eq. 27.0, is positive. The conclusion is invalid, however, since it is based on a faulty argument. To demonstrate this, the reader is referred to Eqs. 4.1 through 4.5 of the paper which describe, in differential form, the first-order disturbances c, u, v, w and p. In these same equations, cx, cz, gl, g3 and are functions of the stable concentration c. This concentration c is known and depends on x, z and t (the author assumes cy = 0). It follows that cx, cz, gl, g3 and µ are also functions of x, z and t. With this in mind, we turn to Eqs. 8.1 through 8.5 which were derived from Eqs. 4.1 through 4.5 by substituting Eq. 6.0. The significance of this substitution is that the author thereby limits the solutions of Eqs. 4.1 through 4.5 to equations of the form of Eq. 6.0. Eqs. 8.1 through 8.5 represent an infinite linear system with five unknowns: c, u, v, w and p. The coefficients cx, cz, gl, g3 and µ in this system are known at each point and at each instant; the coefficients containing derivatives of f are unknown. If this infinite linear system in c, u, v, w and p is to have a nontrivial solution, then it is indeed necessary (as the author states) that the determinant of the coefficient matrix of Eqs. 8.1 through 8.5, i.e., ( A 1, be equal to zero. This condition, however, is not sufficient. A non-trivial solution exists if, and only if, the rank of the coefficient matrix of the entire infinite system is smaller than five. In other words. all minors of order five must vanish and only if all the coefficients in Eqs. 8.1 through 8.5 are constant is this equivalent to the condition |A| =0. Constant coefficients means that gl, g3 and µ, for instance, are constant; and, since they depend on c it follows that c must be constant. We conclude that the condition I A I = 0, on which the author bases his calculations, is necessary and sufficient for a nontrivial solution only if the concentration c is constant. In other words, the author does not investigate the stability of a miscible displacement but, rather, only the stability of the flow of a homogeneous liquid. Using the initial condition and the fact that the coefficients are constant, we find

By J. E. Owen

A model of a porous body is presented in which the pore space consists of a system of voids and interconnecting tubes. Relationships between porosity and resistivity formation factor are determined partly by calculation, partly by experiment. Con triction effects characteristic of the model are shown to be sufficient to account for high formation factors. It is shown that constriction may be combined with moderate amounts of tortuosity to give model pore systems exhibiting to a first approximation porosity and resistivity properties similiar to those of natural porous bodies. INTRODUCTION The relationship between the electric resistivity of a fluid-filled porous body and the geometry of its pore space is so complex that the calculation of the resistivity of a natural porous rock is a practical impossibility. Both the resistivity of a body and its porosity are measurable quantities, however, and previous successes at relating them have been reached by an empirical approach. Efforts at obtaining theoretically derived formulae relating them have generally been unsatisfactory. One of the reasons for this may lie in the pore geometry that has been assumed. THE TORTUOSITY CONCEPT A Parameter called the formation factor is useful in dis-cussing the resistivity of a fluid-filled porous body. This parameter is the ratio of the resistivity of a fluid saturated porous body to the resistivity of the saturating fluid. Formation factors are often available from measurements on cores or from electric logs, and many attempts have been made to correlate formation factors and porosities of geological formations. Whenever a successful correlation is found, the engineer working with electrical logs has a useful tool for the determination of porsities of pay section?. One of the more successful formulae applicable to these correlations is the familiar equation empirically obtained by Archie.' which F is the formation factor. $ is the porosity, and rn is an exponent called the cementation factor. When the for- mula applies, the cementation factor usually is found to be between 1.3 and 2.2. The values for formation factors experimentally obtained are often higher than simple pore geometry would lead one to expect. In an effort to account for such high values certain formulae have been derived based on a so-called "tortuosity concept." In deriving these formulae a synthetic porous body is usually assumed in which the solid material is an electrical non-conductor. and in which the pore system consists of three sets of fluid-filled tubes of uniform diameter connecting opposite faces of the body which, for convenience, is considered to be cubical in shape. The three sets of tubes account for the whole of the effective porosity of the body, and usually, it is specified that they do not interconnect. By considering that the pore tubes are not straight but tortuous, their resistance to the flow of electric currents can be made as high as needed to explain high formation factors. Such an explanation has some basis in fact, but it appears that the tortuosity concept is often incorrectly applied when other factors are largely responsible for observed high resistivities. Recently, Wyllie and Spangler have recognized that tortuosity as calculated by conventional formulae has little if any physical significance.' RESISTIVITY AND THE CONSTRICTION CONCEPT Any explanation of high formation factors which depends solely on tortuosity of uniform pore paths necessarily ignores the effect that variations in the cross-sectional area of the conducting paths have on the resistivity of a body. Although, as previously pointed out, the calculation of such paths for an actual body is impossible, it will he shown that a synthetic pore network can be devised which will yield to analysis, and lead to results in agreement with the experimental data represented by Equation (1). The porous body to be considered is assumed to be homogeneous and isotropic or, for present purposes, identical in its characteristics in the three directions parallel to its coordinate axes. It will he assumed to be built of identical unit cubes, each of which contains a single pore network connecting all faces of the unit cube. A unit of such a pore network is shown

Jan 1, 1952

By R. E. Cook

This work presents the development and application of equations of the form developed by Martin1 to describe gravity segregation performance during natural depletion. One-dimensional depletion analyses are applied to several hypothetical reservoirs. Considerable attention is given to the changes in saturation distribution in the dip direction resulting from depletion at various rates. Vertical gas saturation distribution within a sand having vertical permeability is studied to illustrate conditions which provide For low gus-oil ratio production from wells selectively completed away from sand tops, as observed from well performance. Results of performance calculations are shown graphically and illustrate the rate sensitivity of the gravity segregation mechanism and the influence of reservoir geometry and withdrawal distribution. It is shown that for sufficiently high depletion rates gas saturation distribution in the dip direction is characterized by the formation of two discontinuities, or saturation "fronts"; the updip front being the gas-oil contact of the secondary gas cap and the downdip front occurring at a position dependent upon the reservoir depletion rate, withdrawal distribution and reservoir geometry. The gas saturation in the region between fronts is shown to continually increase with time, while that downdip from the lower front remains very low and relatively stable. The effect of increased depletion rate is to reduce the region of stable gas saturation and thus enlarge the portion of the reservoir producing with continually increasing gas saturation. Special attention is given to the performance of reservoirs having sufficient vertical permeability to permit liberated gas to segregate vertically within the sand section before proceeding in the updip direction. It is shown that reservoirs of this type are far less sensitive to depletion rate due to the mechanical control of producing gas-oil ratios afforded by selective well completions away from sand tops. It is shown that gravity segregation performance is adversely af- fected by decreasing reservoir cross-section area in the updip direction. It is also shown that down-dip withdrawal concentrations can restrict gas segregation rates in the dip direction. INTRODUCTION The natural depletion performance of several large producing reservoirs in Western Venezuela has unmistakably shown the significant role that gravity forces play in governing the gas-oil ratio behavior of individual wells and the over - all pressure-production performance of the reservoirs. Analysis and prediction of the natural depletion performance of these reservoirs is of great importance in determining the economics of pressure maintenance operations. In 1957, a method for the analysis of pressure maintenance performance was presented by Martin1 which, in the original and more general form of the equations involved, provides a physically sound basis for the analysis of one-dimensional gravity segregation performance during natural depletion. The work reported herein is an application and extension of Martin's outstanding developments to a series of hypothetical reservoirs in an attempt to explain the general behavior of the gravity segregation mechanism and the influence of such parameters as depletion rate, reservoir geometry and withdrawal distribution. The study considers two types of flow: "distributed flow", where vertical permeability in the reservoir is zero and fluids flow only in the dip direction while uniformly distributed over the sand thickness; and "segregated flow", where vertical permeability is sufficient to permit gas to segregate against the sand top before proceeding updip. This latter type of flow has been recognized as an important mechanism active in the massive sand reservoirs of Western Venezuela. ANALYSIS OF ONE-DIMENSIONAL DISTRIBUTED FLOW SYSTEMS For an inclined reservoir having zero vertical permeability, the velocities of oil and gas flow at any point in the reservoir can be derived from Darcy's equations as

By William H. Breeding

The remarks that follow are based substantially on experience covering 45 years, 80% of which has been in placer work, rather than on a review of available literature. Most commercial placers have been deposited by the action of water. The richer and more- difficult-to-mine placers are those in the headwater areas where gradients are steepest. The most lucrative placers are generally in inter- mediate areas where volumes are greater, fewer boulders are present, and gradients are from 3% to 1-1/2%. The higher volume, lower grade placers are in the lower reaches of river systems where gradients are lower. Where gold-bearing rivers have discharged into the sea, wave action can concentrate values on beaches, past and present. Most of the rich, readily accessible placers were mined by our forefathers. Current opportunities exist: (1) in remote areas where infrastructure has been absent in the past, or development has been prohibited by adverse ownership - political or commercial; (2) in deposits that could not be mined by equipment available to our forefathers; (3) in deposits unidentified by our forefathers; (4) where the-price-of-product/cost ratio is substantially better than in earlier years; or (5) a combination of those factors. When I entered the placer business in the late 1930s, and subsequently, a prevailing opinion believed that glacial deposits should be avoided as irregular in mineral content and composition, and unrewarding to explore and develop; yet an operator has been mining a fluvio-glacial deposit profitably for the past 17 years. Rich buried placer channels, of ten called paleo-channels were worked in the last century, generally by hand methods, and under conditions that would be unacceptable today. Exploration and mining equipment now available make some of these channels attractive targets. Well-known examples are in California and Australia. The formation of a commercial placer requires a source of valuable minerals. Above primary deposits, there may be eluvial deposits formed by the erosion of gangue minerals and the concentration "in situ" of valuable minerals. Down slope from these deposits are the hillside or colluvial deposits, and below them are the alluvial deposits of redeposited material. Most of the great placer fields of the world are the result of several generations of erosion and deposition. Well-known examples are in California and Colombia. Gold is a very resistant and malleable material, and gold placers may extend for 64 or 80 km (40 or 50 miles) along a river system. Platinum is less malleable, but is very resistant to disintegration. Diamonds are extremely hard, and (especially gem diamonds) may be found over great lengths of a river system. Cassiterite is less resistant to disintegration, and tin placers seldom extend over two miles without resupply from an additional source or sources of mineralizaton. Tungsten minerals are generally more friable, and within a few hundred yards of the source disintegrate to the point that they are uneconomical to recover. Rutile, ilmenite and zircon placers generally result from the weathering of massive deposits, and may be encountered over extensive areas; most are fine grained and durable. What does a geologist or mining engineer look for in placer exploration? The old adage to look for a mine near an existing mine is still valid. You need a source of valuable mineral. Then you require conditions for concentration, which means a satisfactory gradient and/or other conditions that will permit heavy minerals to settle. Nicely riffled gravel, often called a shingling of the bars, is conducive to placer formation. Coarser gravel is logically associated with coarser gold. Excessive clay and/or high stream velocities in narrow channels can carry gold far downstream and distribute it uncommercially over a large area. When material is extremely fine, in situ weathering and concentration become more important. Placers frequently occur distant from lode mines, and one must remember that in a larger watershed the exceptional floods that occur once in a hundred or a thousand years can move great quantities of material long distances. The carrying power of water is said to vary with the fifth or sixth power of its velocity. I am not ready to disagree with Waldemar Lindgren and accept that many commercial placers are substantially enriched by the chemical deposition of gold from solutions; however, I have seen crystalline gold in clayey material quite distant from known sources of primary gold that is dif-

Jan 1, 1985

By A. W. Schlechten, R. P. Abendroth

Equilibrium H2S/4 ratios were determined as functions of temperatunz and composition in a hydrogen recirculation apparatus. A high-temperature solid solution exists in the range two-phase regionfrom TiS 1.96, to TiS1.30, Various thermodynamic quantities were calculated from the data. COMPOUNDS in the titanium -sulfur system have not receiyed much attention in the past, probably because they do not occur naturally in the earth's crust. However, titanium-sulfur compounds have been used in various metallurgical processes. The U.S. Bureau of klines' studied the formation of ti- tanium-sulfide mattes from charges composed of rutile, pyrite, and carbon, with the resulting sulfide matte being chlorinated to form titanium tetrachlo-ride. Fishel, Roe, and Ellis' investigated the de-sulfurizing action of titanium in steels, and Schwarz and Koster studied the preparation of metallic titanium from the sulfide using aluminum and magnesium reduction. The thermodynamic properties of some of the compounds present in the titanium-sulfur system may prove to be of some use in the consideration of future processes using these sulfides, and would

Jan 1, 1960

By Carl Swartz

FOR many years kettles used in the melting and refining of lead and other nonferrous metals and alloys have been made of cast iron. The logic of this probably lies in the fact that cast iron has been known as a material of construction for vessels of this type much longer than steel, and satisfactory fabrication from it has been more easily accomplished and better understood. As the capacity of lead refineries has increased, it has been only natural to increase the size of kettles. Today kettles of 150 to 250 tons are not uncommon. As the size of the kettles increased and better shapes were designed, the uniformity of material of construction became more important. Records kept over comparatively long periods of time have shown that the length of service of kettles has not been uniform. Many causes contribute to this and the importance of each has not yet been evaluated. Kettle design, kettle setting, method of firing and material of construction have been changed from time to time to obtain better service, but the variation in length of service is still great. A kettle may fail during the first few heats or may last through more than one thousand heats. The purpose of this article is not to present the conclusions of a finished piece of research on kettle manufacture and use, but to present a series of observations made over considerable time in the hope that others will publish data and that all may be correlated into a logical scheme which will result in better service and longer kettle life.

Jan 1, 1931

By Arthur F. Taggart

MR. CHAIRMAN: Congratulations! Your four-ring milling show this year was a dandy. It cleared our minds, for a few hours at least, of what Hitler, Hirohito, the New Deal, and the tribe in the Treasury are trying to do to strangle American enterprise. We mustn't forget this, but it's a relief to get our thoughts away from it occasionally. GRINDING-There was a further contribution to the excellent work that the Allis-Chalmers laboratory staff has been doing for the grinding fraternity in compiling-and publishing-a carefully quantitative list of comparative resistances of ores and other materials to comminution (T.P. 1579, Bond-Maxson). A diagnostic accuracy of ± 10 per cent was claimed for estimates based on these figures. Are they really that good? How about some of you men in the field writing M&M about it?

Jan 1, 1943

STANDING COMMITTEES. Executive. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANEWAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library. JAMES F. KEMP, Chairman. JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALEX. C. HUMPHREYS,4 BRADLEY STOUGHTON.

Jan 9, 1913

MINING METHODS W. J. COULTER, Chairman P. B. BUCKY, Vice-Chairman CLYDE E. WEED, Vice-Chairman ROBERT S. PALMER, Secretary Alluvial Mining CLINTON BERNARD O. B. PERRY NORMAN CLEAVELAND C. M. ROMANOWITZ R. B. EARLING J. B. STAPLER BENERE H. GRANTCHARLES THURMAN Open-Cut Mining Iron. A. D. CHISHOLM EARL E. RUNNER G. E. DIEHL G. E. LEVEQUE P. G. HARRISON SIMPSON RICHEY W. A. STERLING

Jan 1, 1943

By Roy A. Koski

INTRODUCTION Cleveland-Cliffs Iron Company, and its subsidiary companies, operate and manage mining, beneficiation, and pelletizing operations in the Upper Peninsula of Michigan, the province of Ontario, Canada, and the State of Western Australia, Australia. The concentrates and natural ores vary mineralogically, physically and chemically. This paper describes the techniques employed in pelletizing the various concentrates and ore fines. The plant operations described are the Republic, Humboldt, Tilden, Empire and Pioneer in Michigan, the Adams and Sherman in Ontario, and the Robe River in Western Australia. Table 1 contains further details regarding design and operating capacities, commissioning dates, and participant ownerships. Allis-Chalmers grate-kiln systems are utilized in Michigan and Ontario, and Dravo straight-grate systems in Western Australia. Currently, the Empire and Tilden operations are being expanded. At Empire the additional pelletizing unit, identified as Unit IV, will have a design capacity of 8 996 metric tonne/d and is scheduled for startup May 1, 1979. The Tilden operation is being doubled with the additional pelletizing unit, identified as Unit 11, having a de- sign capacity of 12 599 metric tonne/d. Startup is scheduled for January 1, 1980. MINERALOGY OF CONCENTRATES AND NATURAL ORES In the Upper Peninsula of Michigan, the operations process ores from the Negaunee iron formation of the Marquette Range. The

Jan 1, 1977

By D. G. Osborne

Transportation cost is a key factor in both the profitability and competitiveness of coal marketing. With coal exportation growing rapidly, moisture control is important. Although in some cases, too much moisture reduction can lead to losses in transportation and pollution problems, there is normally justification for reducing moisture by mechanical means as much as possible. This paper reviews current technology of dewatering coal fines and examines the comparative capabilities of screens, filters, and centrifuges. Financial considerations are stated and implications of capital and operating costs on selection are discussed.

Jan 1, 1985

By J. R. Kyte, R. L. Dalton, V. O. Naumann, R. L. Ridings, R. W. Greene

This paper presents a one-dimensional numerical method for calculating dissolved-gas-drive behavior for a single well or a linear reservoir. Pressure and saturation distributions can be calculated, including the effects of capillary and gravity forces. The analysis has been programmed for solution on the IBM 7090 digital computer. A comparison of experimental and calculated behavior for two linear models demonstrates that the method is suitable for calculating dissolved-gas-drive behavior under reservoir conditions of flow. Dissolved-gas-drive tests were run, at different production rates and with oils of different viscosities, on short (6.ft) and long (173ft) flow models. For tests approximating reservoir pressure gradients and flow rates, there was excellent agreement between experimental and calculated results. A series of calculations of well behavior for thin, horizontal, homogeneous, dissolved-gas-drive reservoirs shows that ultimate recovery is independent of production rate or well spacing in such cases. These calculations also show that Muskat's method and similar material-balance analyses are not applicable under some conditions particularly for high pressure drawdowns. INTRODUCTION The problem of calculating dissolved-gas-drive reservoir performance has received a great deal of attention throughout the oil-producing indusfry for many years. Really significant advances, however, have been made only in recent years. The rapid evolution of high-speed computing equipment and techniques has opened up new approaches to the problem and led to realistic, quantitative analyses free of many of the assumptions and limitations of earlier methods. The one-dimensional numerical method described in this paper includes the effects of both gravity and capillary forces. A number of test calculations, based on different rates, spacings, and rock and fluid properties, have shown that the method is adequate for systems that can be reasonably represented by a one-dimensional model (linear or radial) and in which fluid segregation perpendicular to the direction of flow is not important. Along with the development of mathematical methods, an experimental program was conducted and the data were used to test the validity of the theoretical basis of the mathematical method. Linear models were used and all experiments were run using 1,000-psig bubble-point oils. The use of long, high-pressure models enabled us to more closely approach reservoir gradients and flow rates. MATHEMATICAL FORMULATION DIFFERENTIAL EQUATIONS The differential equations describing dissolved-gas-drive behavior in one dimension dare summarized here. They include Darcy's law for flow of oil and gas (Eqs. 1 and 2) and the equations for conservation of mass for oil and gas (Eqs. 3 and 4). The oil and gas pressures are related by capillary pressure (Eq. 51.

By George S. Rice

GROUND movement from mining, whether it be for coal, metal, industrial minerals, or .oil, will always present many difficult problems. These are especially serious when valuable surface improvements may be badly damaged. The mine itself, if mining methods are not suitable to the formation, is subject to heavy falls of the main roof in the working places; and with certain structural conditions the movements may cause in coal mines disastrous bumps and outbursts of gas, and in deep metal mines rock bursts. In open-cut work rock and earth slides may result. Absolute prevention of ground movement from mining is impossible unless large pillars are left unmined,

Jan 1, 1937