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

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

Jan 1, 1969

By J. C. Martin

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

Jan 1, 1969

By R. R. Joseph, K. A. Gschneidner

The solid solubility of magnesium in the close-packed modifications of lanthanum, cerium, praseodymium, neodymium, gadolinium, dysprosium, and lutetium was determined from approximately 250°C to the eutectoid temperature by the X-ray parametric technique. The maximum solubility at the eutectoid temperature was found to be 9.4 at. pet in La, 8.2 in Ce, 9.2 in Pr, 8.2 in Nd, 14.1 in Gd, 13.5 in Dy, and 11.5 in Lu. The solubility when compared at a homologous temperature was found to increase in a smooth manner with decreasing size factor from lanthanum to lutetium. It was found that the apparent atomic radius of magnesium when dissolved in the lanthanide solvent was constant and could be accounted for by consideration of several models dealing with departures from Vegard's law. The eutectoid temperatures for the lanthanide-rich La-Mg, Ce-Mg, and Nd-Mg systems were found to be 544", 505°, and 551°c, respectively. A study of the solid solubility of magnesium in the lanthanide metals was initiated because the valency and electron egativity difference are essentially constant and favorable for solid-solution formation, and thus one could examine the effect of size on terminal solid solutions. The size factors based on metal radii range from 14.6 pet for lanthanum to 7.5 pet for lutetium. Since the electronegativity difference is small, 0.06 unit or less, application of the Hume-~othery' and Darken and Gurry2 criteria for solid-solution formation indicates that the solubility of magnesium would be expected to be small for lanthanum (between 5 and 10 at. pet) and to increase as we proceed along the lanthanide series. A search of the literature revealed no data on the solubility of magnesium in the lanthanide metals except for the solubility of magnesium in cerium at 450oCA typical phase diagram for the lanthanide-rich end of the lanthanide-magnesium phase diagram is shown in Fig. 1. EXPERIMENTAL PROCEDURES Preparation of Alloys. The lanthanide metals used in the preparation of alloys for this investigation were prepared from the corresponding fluoride by metallothermic reduction techniques previously described by Daane.4 The chemical analyses of the metals used are listed in Table I.

Jan 1, 1965

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

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

Jan 10, 1963

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

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

Jan 1, 1970

By John T. Norton

N order to attempt to arrive at a better under-Jl standing of the whole basic problem of sintering, these remarks will serve as an introduction for discussion that is included and will, perhaps, help to isolate specific questions which need to be answered or to suggest some definite avenues of investigation which should be followed. To bring some sort of logical order into the presentation, I will consider the various types of interaction between the metal to be sintered and the atmosphere which surrounds it, depending upon whether the phenomena are essentially chemical or physical in nature. For example, when the only necessary criterion for the satisfactory sintering of a certain powder is the removal of an oxide skin, then the problem of choosing a suitable atmosphere is primarily chemical; however, if a special surface condition as a consequence of the oxide skin removal is necessary for particularly effective sintering, then the problem becomes a physical one. Of course, the two aspects overlap considerably, but it may be possible to make a distinction in principle if not in practice. The chemical characteristics of the phenomena will be emphasized, since these are the better known. Metal-gas reactions involved in sintering are controlled primarily by the thermodynamics of the processes involved. In which direction will a reaction go and how far before it stops? The answer is to be found in the magnitude of the free energy change associated with the reaction. If a constituent is to be removed from the specimen as completely as possible or if a constituent is to be formed in the specimen as completely as possible, then one chooses conditions which are far from equilibrium so that the reaction is driven toward completion. On the other hand, if the composition is to be maintained at a desired value, then conditions are adjusted as closely as possible to the equilibrium point. This aspect of the problem is susceptible to quite precise analysis, provided, of course, that the significant reactions can be recognized and the required thermodynamic data are available. Conversely, if one asks how fast the reaction goes or how far it proceeds in a given time, the answer is frequently much more difficult to answer in quantitative terms. Yet the rate-con trolling factors of the reactions may be of primary importance in the success of a particular operation, especially where competing processes are at work. Both equilibrium and rate factors must be understood if a clear picture is to be obtained. For instance, in a process for carburizing titanium dioxide, is the difficulty of obtaining a stoichiometric Tic due to a true limitation of the equilibrium or simply to a very slow rate of reaction? An example of this appears in the work of Kalish and Mazza.' They showed that the oxygen content of sintered iron compacts was lower when sintered in pure hydrogen than in the case where the hydrogen was diluted with either argon or nitrogen. The equilibrium oxygen content of the iron would be the same in the two cases, since it is determined by the ratio of the partial pressures of water vapor and hydrogen and this pressure ratio is unchanged by dilution. The rate of oxygen removal, however, under the conditions of a constantly replaced furnace atmosphere, depends upon diffusion and thus upon the concentration of hydrogen in the furnace atmosphere. Possibly the clearest way to illustrate the interplay of these two factors is to consider in more detail some of the typical metal-gas reactions. Adsorbed Gases It is common experience that fine metal powders with their very large surface areas often contain large quantities of gas. This gas, which results from exposure to air or perhaps from some step in the

Jan 1, 1957

By W. H. Boyer, J. W. Gabelman

The concept of metal zoning has long been recognized (Spurr, 1907, 1923; Emmons, 1924, 1926; Lindgren, 1933; Rateman, 1950), although it has been considered indistinct for most epithermal districts. The geometric relation of barren zones of hydrother-mally altered rock to ore deposits was emphasized in the work of Lovering (1941, 1949, 1950), Sales and Meyer (1948, 1949, 19501, Burbank (1941, 1950), Schwartz (1939, 1950), and Kerr (1947). Lovering (op. cit.) and Sales and Meyer (op. cit.) emphasized the consistent presence of barren alteration envelopes enclosing individual ore bodies, particularly of the vein type. Schwartz (1950) noted a difference between the distribution of alteration zones described by Lovering and by Sales and Meyer, as compared with those associated with the porphyry copper deposits of the Southwest. The disseminated deposits of the Southwest usually occur within large bodies of altered rock whereas most veins do not. In the following discussion the mineralization process is conceived of consisting of two distinct phases: pre-ore nonmetallic alteration and metallization. In the present investigation the position, size, and shape of all known hydro thermally altered areas and the position, size, and metal type of all known ore deposits were plotted on base maps of southwestern and west-central Colorado (Figure 1). The maps indicate a generally consistent geometric relation between altered and metallized areas. The addition of alteration to the pattern of metal deposits establishes a temperature zoning pattern of much greater clarity than that formed by the epithermal metal deposits alone, and allows a more precise definition of mineral belts. The center of strongest mineralization is indicated to be the area of greatest barren alteration, and metal deposits are grouped about it both under structural control and crudely in response to temperature zoning. The combination of an area of strong alteration and associated marginal clusters of metal deposits is defined as a mineral district. The strong similarity in individual deposits, in groups of different types of deposits, and in the alteration-metallization relation in districts throughout the region implies that a single metallogenic province is represented in southwestern and west-central Colorado. The occurrence of deposits in Tertiary voi-canics indicates a late Tertiary metallogenic epoci., although an early Tertiary epoch is known locally as at Ouray. Patterns formed by mineral districts can be

Jan 1, 1961

By Alfred E. Hunt

By the death of Joseph Dame Weeks, past-President of this Institute, which occurred December 26, 1896, the world has lost an earnest and unwearied philanthropist; the Christian church, a zealous, active and consistent representative; the United States and the State of Penusylvania, a patriotic, pub-

Jan 1, 1898

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

Jan 1, 1936

By W. Hurst

The authors of this paper, in substituting values in a material balance equation associated with a gas reserve and a water drive, cannot find sustainment of what the gas in place should be; therefore, their conclusion is that this type of problem dealing with gas reservoirs is insoluble. They have introduced the word, "cybernetics," based on the work of Norbert Wiener, that further extends this line of reasoning, namely, to the effect that the system is a "black box", and that the gas reservoir and aquifer can take on infinite aspects 'based upon their past performance, to quote the authors. The inference is that this black box is an unknown. which permits in computer programming to subscribe as many variables as possible to observe by adjustment of one to another those combinations of conditions that fit field behavior. This may satisfy those in this discipline whose dedication is to programming, but to the others this is a comparison to the rationalization of the combinational results of the throwing of dice—a probability procedure. In reservoir engineering we are more direct. We learn from the examination of individual we'll and field data exactly what is in this black box. I now come to the impasse that has confronted these authors in their machine calculations. In this I have reproduced from their own production data (Tables 1 and 2 of their paper) pressure vs cumulative gas produced. shown as Figs. D-1 through D-5. A perusal of any of these five plots, for the corresponding fields in the Po Valley, shows the straight-line relation of pressure vs gas produced, evidencing pressure depletion. The point I make is that in their fundamental production data, there is no variance from a straight line that can support a water drive.

By Richards J. W.

J.W. RICHARDS, South Bethlehem, Pa. (communication to the Secretary?).-Mr. Howland's paper, data and conclusions have interested me intensely, and have led me to study carefully the record-of his 26 furnaces therein given. Mr. Howland is undoubtedly right in his conclusion that when expressing the amount of carbon burned at the tuyères in percentage of the total

Jan 1, 1917

CONTENTS PAGE MERRISS, M. H.-Direct Electrolysis of Black-copper Anodes of High Nickel-lead Content. Discussed by C. S. Witherell, C. P. Linville, G. E. Dalbey, M. H. Merriss 1 GRISWOLD, GEORGE G.-Calculating the Zinc for Desilverizing Lead Bullion by the Parkes Process. Discussed by C. S. Witherell, George G. Griswold, Milo W. Krejci, Lawrence Addicks, W. F. Gross, H. H. Alexander, A. F. Beasley, C. P. Linville 3 ALEXANDER, H. H. and STACK, J. R.-The Reduction and Refining of Tin in the United States. Discussed by Edward F. Kern, J. R.' Stack, R. L. Hallett, C. R. Hayward, William H. Bassett, R. C. Canby, H. G. S. Anderson 20 GREENAWALT, WILLIAM E.-Greenawalt Electrolytic Copper Extraction Process. Discussed by Stuart Croasdale, Colin G. Fink, Arthur L. Walker, Edward F. Kern, Henry A. Tobelmann, Oliver C. Ralston 26 BENEDICT, C. H. and KENNY, H. C.-Ammonia Leaching of Calumet and Hecla Tailings. Discussed by G. E. Dalbey, C. H. Benedict 34 RALSTON, OLIVER C.-Hydrometallurgy of Lead. Discussed by F. L. Bosqui, Jr., George D. Van Arsdale 34 TAINTON, U. C. and LEYSON, L. T.-Electrolytic Zinc from Complex Ores. Dis¬cussed by W. G. Woolf, C. A. Hansen 39 Direct Electrolysis of Black-copper Anodes of High Nickel-lead Content Discussion of the paper of M. H. MERRISS, presented; at the New York Meeting; February, 1924, and, issued, as Paper No. 1273-M, with MINING AND METALLURGY, September, 1923. C. S. WITHERELL, New- York, N. Y. (written discussion).-This paper is particularly valuable in that it gives the results of operations -carried out under conditions differing from standard practice. In the electrolytic refining of copper, as in other kinds of metal refining, it is occasionally necessary to treat extraordinary foul or complex material, in which cases 'it is valuable to know what other metallurgists have accomplished under similar conditions. As tapping the slimes-covered anodes brought the tank-voltage down to 0.45 to 0.50 volt, the counter electromotive force was, probably not more than 0.1 or 0.2 volt; hence the so-called polarization was, mainly,

Jan 6, 1924

By J. Douglas, W. T. Ford, G. E. Henderson, I. F. Roebuck

An implicit numerical method is presented for simulating the differential and algebraic relations governing one-dimensional three-phase flow in porous media. The method is based upon compositional representation of the hydrocarbon system. Variable physical properties and water-oil capillary forces are included in the formulation; however, the effect of gravity is ignored. The effects of changing composition and mass transfer are considered through the use of known phase behavior concepts and correlations. The differential and algebraic equations and the numeric approximations to these equations are presented, and the computing algorithm is discussed in detail. This method is used to simulate a single-phase, two hydrocarbon-component gas displacement laboratory experiment. The method is also applied in simulating a solution gas drive and a gas injection problem using a reservoir oil represented as a nine-component mixture. For comparative purposes, the latter two problems also are examined with a one-dimensional volumetric model. The results of the simulation of the laboratory experiment demonstrate the relevance of this method to problems wherein the effects of mass transfer significantly enter the displacement process. The comparison of the results of the volumetric and compositional methods applied to a reservoir system illustrates not only the advantages and benefits derived from examining the hydrocarbon system composition, but also the necessity of this approach in application to a general reservoir problem. INTRODUCTION The advent of large memory, high-speed digital computers enabled reservoir engineers and mathematicians to pool their knowledge in the development of sophisticated techniques for the prediction of oil and gas reservoir performance. These techniques have progressed from volumetric and trend analysis calculations to the development of "mathematical models", or reservoir simulators. These latter models, in general, utilize finite difference approximations to the rather complex partial differential equations that mathematically describe the physics and thermodynamics of fluid flow in porous media. Many forms of this "model" type are available today, and much of the recent literature has been devoted to either improving known methods or developing new techniques for use in these prediction methods. The more advanced techniques in use at this time consist of the solution of differential and algebraic relations that describe a reservoir geometry in one, two or three dimensions and that incorporate reservoir hydrocarbon and water fluid systems that obey specified physical laws, having properties that might easily be measured in the laboratory. This type of model utilizes formation volume factors and other volumetric data, expressed directly as functions of pressure, to represent the reservoir fluid system. Experience gained with this type of simulator, commonly known as a "beta-factor model", has indicated that the approach has many outstanding defects, most of them due to the assumption that those properties measured in the laboratory completely describe the behavior of the fluid system throughout the life of the project under study. The effects of varying hydrocarbon composition and mass transfer between the phases of this hydrocarbon system must, by definition, be ignored. These defects, which may often be ignored in

Jan 1, 1970

By George W. Maynard

(Pittsburg Meeting, March, 1910.) AT the Pittsburg meeting of the Institute, May, 1879, I made the first announcement in America of the results obtained by Sidney Gilchrist Thomas and Percy C. Gilchrist, ill their efforts to eliminate phosphorus in the manufacture of steel in the Bessemer converter and the open-hearth furnace.1 The first published statement in an American newspaper was a reprint of the first Thomas-Gilchrist paper, 2 which I sent to J. C. Bayles, at that time the editor. At the suggestion of many friends who were present at the Pittsburg meeting, and others who are cognizant of the beginnings of the process in the United States, and for the information of the younger generation of the iron and steel fraternity, I have thought it eminently proper that the history of the process in detail should be given where I made the first announcement and where the process has had its largest development. During my residence in England, from April, 1873, to February, 1879, and as a member of the Iron and Steel Institute since 1874, I was present at many of its meetings during those years. At nearly -every meeting the burden of discussion was the question of the use of pig-iron containing phosphorus in the. manufacture of steel by the Bessemer or the open-hearth process. In my biographical notice of Thomas;3 read at the New York meeting of, the Institute, February, 1885, I show that the working-out of the process was not a hap-hazard or accidental inspiration, but the culmination of many years of investigation of experiments and theories which had been carried on and advanced by chemists and metallurgists at home and abroad. 1 Trans., viii., .5 (1879-80). 2 The Iron Age, vol. 22, No. 17, p. 3 (Oct. 24, 1878). 3 Trans.. xiii., 785 to 791.

Jul 1, 1910

By H. D. Outmans

A method has been developed for determining the relative water wet-tability (fraction of the surface wet by water) of porous media. This method involves the adsorption of methylene blue dye from an aqueous solution onto the solid surfaces of rock contacted by the injected dye solution. Experiments on Berea snndstone cores have shown that water-wet cores adsorb a large amount of dye from solution. In oil-wet cores, however, the injected aqueous dye solution is prevented from contacting the adsorptive surfuces by a film of oil and virtually no dye is adsorbed. This method was tested by experiments on mixtures of water-wet and oil-wet sand. Using the dye adsorption method, it was possible to determine quantitatively the fraction of water-wet and oil-wet sarzd in such mixtures. The dye adsorption test is readily applied to determinitrg the relative water wettability of fresh oilfield cores. The cores are not extracted before testing. Observed values of the wettability of field cores tested to date have varied from 100 to 6 per cent water wet. INTR OD UCTIO N Recent articles1 ' have emphasized the important role that wettability plays in almost all phases of reservoir rock behavior. It has been shown that wettability has a profound effect on the interstitial water saturation, residual oil saturation, capillary pressure, relative permeability, waterflood behavior, and resistivity index of oilfield cores. A quantitative investiga- tion of the effect of wettability on these core properties is severely handicapped by the lack of a simple technique for measuring the wettability of a porous medium. If such a technique were available, it would provide investigators with a means of gaining insight into the distribution of phases within a core. A number of qualitative methods of estimating wettability are known. These include contact angle measurements, flotation tests and studies of displacement pressure: imbibition7 and relative permeability data.' Using these tests, it is usually possible to classify a core as water-wet, oil-wet, or some intermediate degree of wettability. One recently proposed method involving measurement of nuclear magnetic relaxatione offers promise of determining quantitatively the fractional wettability of cores. The equipment is rather elaborate and necessary treatment of the cores before testing probably alters the natural wettability. This latter point also applies to most of the cited qualitative methods. This paper presents a new technique for determining water wettability of cores; it is based on measurements of the dye adsorption capacity of the core. This method has the advantage of requiring relatively simple equipment and involves minimum handling of the core before testing. It is important to distinguish between the various concepts of wettability referred to in the literature. The term "wetting" is defined by Bartell as that phenomenon which occurs when a solid and liquid phase come in contact in any manner so as to form a solid-liquid interface. A preferentially water-wet solid is defined by Jennings in terms of the advancing contact angle in the solid water-oil systems. Brown and Fatt regard fractional wettability as the fraction of the total surface area that is preferentially oil-wet or water-wet. However, none of these definitions adequately describes the type wettability measured by the dye test. This calls for the introduction of a new term, "relative water wettability", which we define as the fraction of the total surface area of a core contacted by injected water. DESCRIPTION OF METHOD The ability of a porous medium (especially the clays) to adsorb large quantities of surfactants, dyes, etc., is well known. It is reasonable to assume that a substance can be adsorbed from solution onto a solid surface only if the solution contacts the surface. In this connection Shapiro" has shown by experiments on silica gel that completely dry gel will adsorb methyl red dye from a benzene solution. On the other hand, if a film of water more than several molecules thick is present on the silica gel, the adsorption capacity of the gel for the dye is drastically reduced. Thus, a study of the dye adsorption capacity of cores should give some clue as to the fluid distribution on the surface of the core. TEST OF METHOD As a qualitative check on this theory, dye adsorption tests were run on similar Berea sandstone cores (Table 1, Cores 1-5). Cores saturated initially with water and flooded with 0.01 per cent aqueous methylene blue adsorbed 0.58 mg dye/gm of core. Similar cores saturated initially with water, driven to irreducible water with oil, and then flooded with the same dye solution also adsorbed 0.58 mg dye/gm of core. Another core, treated with a 5 per cent Dri-Film solution, dried and saturated with oil (Soltrol) adsorbed no dye when the dye solution was injected. These tests confirm

By F. W. Clark

At the present time, when lixiviation versus amalgamation is being so thoroughly discussed by practical men, and published information is so meagre, the following tests, made by students in the mining laboratory of the Massachusetts Institute of Technology, may be of interest to others. The ore experimented upon was obtained from the Sombrerete mines near Zacatecas, Mexico. A careful analysis of the dried sample resulted as follows : Per cent. SiO2,............62.79 S.............13.86 Al2O3............4.39 Fe,............11.26 Zn,............1.57 CaO.............2.91 MgO,........... 0.06 Cu,.............0.12 Pb,.............0.40 Sb and As,..........trace CO2,............2.35 Ag,.............0.16 99.87

Jan 1, 1886

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers' knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By Charles De Witt

The ore treated at the reduction plant (called Yangdei) of the Chiksan -Mining Co., Korea, is brought from four of the company mines, and from the small tribute mines. The largest shipments conic from Sajunkohl mule, situated about a mile and a half from the mill (Fig. 1). The ore is quartz of medium hardness. The overage assay value in gold is $6.95 per ton. At the mine the ore is put into bin,, and is Mien trammed over an 8 per cent. grade to the tipple bins above the mill, where the ore is drawn through the hull holes as desired. The capacity of the tipple bins is about 3,500 tons. On, from Moonsukohl, Chung Tarrie, Yang Chun, and the tribute mines is brought in by bulls and bull wagons. The bulls carry from 350 to 800 lb.; the average wagon load is about 1,200 lb. (Fig. 2). One shovelful of ore out of every ten is taken as a sample. Considerable ore

Jan 5, 1915

By G. W. Phelps

The field of industrial minerals is concerned with both sieve size and distribution of sub-sieve particles. A great deal of work has been reported on the techniques designed to provide information of this work. The term sub-sieve is here considered to include particular material that will pass a 325-mesh testing sieve. Plant men require rapid, precise and simple testing techniques that are, if possible, inexpensive with respect to equipment and manpower. A number of particle-size procedures have been developed, based on the Stokes equation for streamline movement of a particle of diam D, moving at velocity V through a liquid of viscosity n. 1 Particles are considered to be rigid, smooth spheres, completely dispersed at low concentration and moving at low velocity through the suspending medium with no slippage between particle and liquid. In particle size determinations the particle moves either from natural gravitational forces or those provided by centrifugal means. The diagram of Fig. 1 shows a spherical particle of density S and diam D moving downward at velocity L/T (or V) through a liquid of density So and viscosity n. The forces of gravity G (natural) or Gc (centrifugal) cause the particle to move through the liquid, thereby creating a viscous drag F or Fc. Within the streamline flow

Jan 1, 1967

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949