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By L. A. Panek

Research on roof bolting has developed significant information with respect to the functions that can be performed by properly installed bolts and the methods that can be used to ensure that effective installation has been achieved. The present paper brings together results that are pertinent to the design of a bolting system for reinforcing horizontally stratified mine roof with vertical bolts. The design approach is based on the use of bolts to decrease the maximum bending stress within an arbitrary sequence of roof strata (see Fig. 2) in which the only loads are the weights of the individual beds. The use of rock bolts to achieve other objectives, such as to stabilize a fractured rock mass on the periphery of a mine opening,3 is excluded from consideration herein. Reinforcing effect of bolts consists of a friction effect and a suspension effect in combination. "Friction effect" refers to reduction of bending in a stratified roof due to clamping action of tensioned bolts, which compress the strata, thereby creating frictional resistance to displacement along planes of stratification. (The flexure of a sequence of strata is necessarily accompanied by horizontal displacement of each bed with respect to its neighbor, along mutual surfaces of contact.) Although the sliding of the beds tends to exert a shearing effect on the bolts, tests show that this has negligible influence on the bending stresses, probably because the bolts are so far apart. "Suspension effect" refers to the transfer of part of the weight of the weaker or thinner strata to one or more thick strata, which occurs when strata with differing tendencies to deflect are constrained to have equal deflection. The term "suspension" is used irrespective of whether the thin strata are above or below the thick strata, because tests show that the supporting effect of the flexurally more rigid roof strata is for practical purposes independent of their position in a bolted sequence of strata. An earlier paper4 dealt with a bolted unit in which all strata had equal flexural rigidity; bolting could develop a friction effect but no suspension effect. The present paper deals primarily with a bolted unit in which all strata do not have equal flexural rigidity, so that bolting can develop both a friction effect and a suspension effect. The reinforcing effect of the bolts was determined by a combination of experimental and theoretical stress analysis.4'6'7 The experimental method consisted of loading a model by rotating it in a centrifuge to simulate the gravity forces exerted about an underground excavation. Models were made from two different limestones, although the results are independent of the material because the elastic constants were taken into account in the data analysis. Electric resistance strain gages were bonded to the highest and lowest members of the bolted unit to determine the outer-fiber bending strains at the center and at the supports. The quantitative results presented herein are based on tests of 56 different models, which included a range of values for the structural parameters. Each model was tested several times, with different combinations of spacing and tension of the bolts. DESIGN EQUATIONS The effects of friction and suspension on the flexure of a bolted stratified roof can be expressed by the following equations, which give the maximum bending stress, the deflection, the friction effect, the suspension effect and the transferred load for any (the i-th) member of the bolted unit in terms of the structural parameters:

Jan 1, 1964

By A. G. Weber, H. J. Welge

A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. INTRODUCTION The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature.1-3 When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well's limit of drainage. Calculations can be made for the producing history both before and after cone breakthrough. A typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). Vertically, the blocks are bounded by horizontal planes located at different depths through the

Jan 1, 1965

By Carlos E. Roggero

The influence of high temperatures on the zinc roasting practice has been investigated by full-scale tests in fluid bed reactors operating at temperatures from 950° to 1150°C. It was definitely shown that, throughout the range, an increase in tem perature resulted in a 2 to 3 pct increase in zinc solubility because of decreased content of zinc fer-rite and lowered sulfide sulfur. The former is attributed to thermal decomposition of ZnFe,O,, and the latter to increased oxidation rates, ad longer retention times. Data on the gveatly increased volatilization of lead, cadmium, and silver above 1000°C, are presented. A considerable fraction of the iron present in the feed was also transferred at high temperatures from the coarse roaster discharge to the flue dusts. AS part of its metallurgical complex1-3 situated in a 12,000 it Andean valley at La Oroya, Peru, Cerro de Pasco Corp. (a wholly owned subsidiary of Cerro carp.) operates a 150 short ton per day electrolytic zinc refinery. Electrolysis is carried out at a cathode current density of 65 amp per sq ft with an electrolyte content of 55 g per liter of Zn and 150 g per liter of su lf uric acid. Due to the high iron content of the marmatitic concentrate used, a large fraction—about 15 pct—of the zinc reports in the leach residues. To minimize such losses, efforts have been exerted toward improving calcine solubility. One method, as noted in the literatre,, is to retard zinc ferrite formation by decreasing the roasting temperature. Unfortunately, such a procedure tends either to reduce the roaster throughput or increase the sulfide sulfur in the calcine. Consequently, this approach was discarded in favor of experimental work in the opposite direction, i.e., high temperature roasting. Full- scale tests were promising and resulted in the granting of a patent to Cerro de Pasco carp.' After a brief account of plant equipment and operating procedure, this paper describes the tests made and attempts to assess the results obtained. GENERAL PLANT LAYOUT AND OPERATION The Roasting Plant, see Fig. 1, comprises an agglomerating plant feeding three fluid bed roasters with a combined capacity of 10,000 tons per month. The Peruvian patent rights on this process were purchased from the New Jersey Zinc Co. The concentrate, assaying: is pelletized to a -3 +14 mesh product and fed to the fluid bed roasters. The roaster exhaust gases pass through a waste heat boiler, cyclones, a fan, and an electrostatic precipitator. Approximately half of the dust collected in the cyclones returns to the pellet-izing plant as one of the binding ingredients, the remainder joins the cooled bed discharge ('overflow') and is conveyed to the grinding plant. The -35 mesh product obtained, together with the dust collected in the electrostatic precipitator constitute the feed to the leaching plant. Batch leaches are made in vessels with mechanical and air agitation, the residues are separated and washed in Burt Filters, and pumped to storage ponds. THE FLUID BED ROASTERS Two reactors are as shown in Fig. 2, and the third,' of about the same configuration, is approximately 40 pct smaller. The total grate and freeboard (just below the gas outlet) areas measure 170 and 426 sq ft respectively. The feed, continuously weighed and controlled by Merrick Weighto-meters fitted with variable speed motors, enters the reactors at the top of the expanded bed level. The coarse calcine overflows through the opposite end by

Jan 1, 1963

By H. K. Najarian

This paper describes recent development work on the Wheaton-Najarian Vacuum Condenser for Zinc at Josephtown Zinc Smelter, wherein, to dissipate the heat of condensation, the "airlift" action of gases bubbling through the molten zinc in the condenser is utilized to circulate the zinc through an outside "cooling well" and cooling it continuously. AN earlier paper1 gave an account of initial development of the Wheaton-Najarian Vacuum Zinc Condenser at the Josephtown Zinc Smelter of the author's company. This paper is a progress report of further development work over the years directed toward improving the efficiency and increasing the capacity of the condenser. In this type of zinc condenser, zinc vapor with accompanying noncondensable gases from electro-thermic zinc smelting furnaces is passed upwardly through a mass of molten zinc confined in a refractory-lined U-tube. The zinc vapor condenses in the molten zinc and the noncondensable gases are drawn out of the condenser by suction applied over the surface of the molten zinc. The heat of condensation of zinc, amounting roughly to 1000 Btu per lb of zinc condensed, is absorbed by the molten zinc and, in turn, is dissipated continuously to keep the temperature of molten zinc in a range to permit effective condensation. At the time of publication of our first paper, we had at Josephtown Smelter five units of 69-in.-bore metal furnaces and one larger metal furnace having 96-in. bore. Each 69-in. metal furnace had a condenser with 22-ft overall length. The 96-in.-bore furnace had a condenser with overall length of 31 ft. Condensers were of circular cross section, with corrugated steel outer shell and carborundum lining. Diameter of these condensers was 32 in. inside the refractory lining. Molten metal in the con- denser was kept cool by spraying cold water on the outside of the condenser shell. Under good operating conditions, 22-ft condensers produced some 12 tons of metal per day; and the 31-ft condenser, about 22 tons. When the furnaces produced zinc vapor at higher rates, invariably the condenser temperature would rise to levels where excessive blue powder would form and accumulation of accretions in the condenser would be accelerated. We found that, with the system of cooling in use, we had to provide heat-exchange surface of some 150 sq ft to condense 1000 lb of metal per hr with reasonable efficiency. The wall of the condensers was made up of 5/8-in.-thick corrugated-steel shell having next to it several layers of mica and inner refractory lining of special carborundum shapes to fit the corrugation in the steel shell, and having a minimum thickness of about 2 in. Relatively low rate of heat transfer through the thick condenser wall and slow internal circulation of the molten zinc limited the rate of heat exchange between hot metal within the condenser and the cold water flowing over the outer steel shell. The thickness of the condenser wall was about minimum that we considered suitable for continuous operation. As we learned to operate the electrothermic furnaces with higher power input, producing zinc vapor at higher rates, it became apparent that we needed condensers having larger heat-exchange surfaces. Our 96-in.-bore furnace had 6 single-phase power circuits with transformers rated at 500 kva each and normally good for power input of 3000 kw.

Jan 1, 1959

By W. R. Foster, J. M. McMillen, A. S. Odeh

The complete equations of average linear momentum balance for a single-phase fluid in an incompreisible, homogeneous, porous medium are derived. The derivation begins with Euler's equation of motion for a continuum and uses an integral transform recently developed by Slattery. 7 For steady flow of a compressible, Newtonian fluid, the usual equations of motion result. For transient flow, the space-time description of the pressure is determined in the lowest approximation by the telegrapher's equation. From the analysis a new phenomenological coefficient results which connects the viscous traction to the deriv ative of the linear momentum density. The magnitude of this coefficient determines the velocity of sound through the pore structure in this approximation to the pressure field. INTRODUCTION The modification of Darcy's law of momentum balance for steady, single-phase flow through porous media has been discussed for many years. The first modification was suggested by Forcheimerl who added terms of higher order in the velocity. These can be expected to appear because the underlying microscopic equations of momentum balance are themselves nonlinear in the point velocity field. The Reynolds tensor pvv, which represents the convective flux of momentum density, appears in the momentum balance equation. Only in rectilinear flow (parallel stream lines) does the divergence of this tensor vanish. Since the steady flow stream lines in most porous media are not parallel, nonlinear dependence of the pressure gradient on the velocity should naturally appear. This nonlinearity has nothing to do with turbulence in the ordinary sense of random fluctuations in the pressure and velocity fields. It arises simply because the stream lines converge and diverge, even for steady flows. Klinkenberg2 demonstrated that the permeability coefficient in Darcy's law depends on the absolute pressure or, alternatively, on the density field. However, because he neglected inertial terms of the Forcheimer type, his correction coefficient could not be represented by a constant but tended toward a constant as the velocity decreased. Forcheimer's and Klinkenberg's modifications can be combined in a rigorous way to account for both inertia and slip during steady flow. This will be shown in a future paper. The transient change of pressure in porous media has been described by the diffusion equation.3 This form results from eliminating the velocity and density fields from a combination of the equations of motion in the form of Darcy's law, the continuity equation and an equation of state. Fatt4 suggested that the cause of deviations from the prediction of the diffusion equation for pressure transients lies not in the choice of Darcy's law as the equation of motion but on the existence of dead-end pores which might invalidate the averaged equation of continuity. On the other hand, Oroveanu and Pascal5 noted chat the time derivative of the momentum density must be included in the equations of motion since this measures the local rate of change of momentum density. Their differential equation for pressure is the telegrapher's equation (neglecting gravity). However, their form of this equation predicts that the speed of pressure propagation through the pore structure is the same as that through the bulk fluid. M. K. Hubbert6 attempted a derivation of Darcy's law by volume averaging the Navier-Stokes equations. Since these equations represent momentum balance at a point within an open set of points containing the fluid itself, Hubbert's volume averaging cannot lead to tenns involving transfer of momentum between the fluid and the walls of the pores. Once these viscous tractions are lost by choosing a control volume containing only fluid, they cannot

By M. J. Spendlove, H. W. St. Clair

An automatic surface-follower mechanism was used to measure the surface temperature and the rate of evaporation of molten zinc while undergoing distillation at low pressure. At pressures of 50 to 100 microns Hg, the rate of evaporation may be 60 to 80 pct of the theoretical maximum corresponding to the measured temperature. The rate decreases rapidly at pressures above 100 microns Hg, to only 7 pct of the theoretical maximum at 2000 microns Hg. Measured temperature gradients at the surface are in agreement with theoretical gradients calculated from the heat of vaporization, rate of evaporation, and thermal conductivity of molten zinc. THIS paper covers a series of careful measurements of the rate of evaporation of molten zinc at low pressures, undertaken as a part of a general investigation on the separation of metals by distillation.' Preliminary results on the rate of evaporation of zinc were described in a previous publication.' The results of the preliminary study are as follows: 1—The observed rates of evaporation of zinc were as high as 0.60 g per sq cm per min, corresponding to 75 pct of the maximum rate as determined by the temperature of the metal. 2—The evaporation rate was decreased from 0.30 g per sq cm per min at a pressure of 25 microns to only 0.09 g per sq cm per min when the pressure was increased to 5 mm. 3—The temperature of the surface during rapid evaporation may be 35" to 100°C less than the main mass of metal. Observed temperature gradients at the surface are consistent with those calculated from the heat of vaporization and the thermal conductivity of liquid zinc. In the preliminary experiments, the rate of evaporation was determined from the loss in weight of the metal in the crucible during the test. This was compared with the weight of the condensate. Obviously, this method was subject to error because of some uncertainty as to the period of evaporation that should correspond to the loss in weight. Furthermore, this method did not permit taking into account probable variations in the rate of evaporation during the test. A more serious shortcoming was that the temperature at the evaporating surface was not known, so the maximum theoretical rate of evaporation could not be calculated accurately. To improve the precision of rate measurements and to allow accurate measurements of the surface temperature, a refined experimental technique was developed whereby the temperature and position of the surface could be measured accurately. This was done by an automatic surface-follower mechanism that gave a continuous record of the surface temperature and the amount of zinc evaporated. These data permitted an instantaneous determination of the actual rate of evaporation and the surface temperature throughout the test. Pure zinc (99.99 pct Zn) was used in all experiments. Description of Distillation Furnace The details of construction of the distillation furnace are shown in Fig. l. The furnace is enclosed in a large quartz tube open at one end. The open end of the quartz tube is sealed by means of a water-cooled head. The entire enclosure is vacuum tight. The connection between the water-cooled head and the quartz tube is sealed by means of a rubber gasket which fits tightly against the smooth end of the tube. The metal is heated by induced current set up in the molten zinc and the walls of the graphite crucible by means of a water-cooled induction coil outside the quartz tube. High frequency current is passed through the induction coil from a 6 kw mer-

Jan 1, 1952

By F. E. Jaumot, A. Sawatzky

IT as long been recognized that there is a need for accurate systematic data on diffusion in solids. Originally, such data were needed to check existing theories but, more recently, it would appear that it could be used most advantageously as a guide to, or a check for, much needed extensions of the theory of diffusion. The awareness of the conditions which are important to experimental accuracy, the availability of the materials for accurate experiments, and the techniques have improved to the extent that it would now seem to an experimentalist that, unless extensions of the theory are made which take into account the fundamental parameters of the atoms, the electrons, and the lattice in some detail, the field of diffusion will rapidly become an empirical or semi-empirical field. The present series of experiments was designed to provide accurate data on the diffusion of the elements of the IB and IIB subgroups in silver; that is, to provide data on the diffusion in silver of three face-centered-cubic elements with roughly similar chemical properties, but with different atomic or ionic sizes and, similarly, for three noncubic elements. The elements of these two subgroups have different valences, so that the data will not give any significant information on differences due to the crystal structure of the solute. The present paper reports data on the diffusion of copper and mercury in single crystals of silver; the data for the other elements of the IB and IIB subgroups were reported previously by the authors1'2 and by Tomizuka and Slifkin.8 Experiment The general technique used was identical to that previously described1,2 and will not be repeated here. In all cases, the sectioning technique and high specific activity isotopes" were used. The short half-life of Cu64 made decay corrections more important than for the other isotopes, and necessitated around the clock shifts while data were being taken. Each section was counted at least twice (as was true for all longer half-life isotopes) and a monitor was counted along with each sample. Data for the diffusion of mercury in silver are presented at a greater number of temperatures than for the other solutes. This is a result of two circumstances. First, six (of 30) samples had to be discarded because of pitting or recrystallization which occurred during the diffusion runs, even though the samples had sustained high temperature prediffusion anneals. Either of these was a very rare phenomenon in the other experiments, and their occurrence in this case is considered in more detail below. Second, the curves of the logarithm of the activity of the sections vs the square of the penetration deptht were, in general, quite good, but frequently seemed to show one point to have high activity and the next point to have slightly low activity in terms of the best straight line. When this occurred, there was remarkable regularity of the high-low sequence. In any event, the results, as far as diffusion coefficients are concerned, were not affected by this amalgam effect. In fact, the mercury data had the highest internal consistency of any of the data. Results Diffusion of Copper in Silver—-Diffusion runs were made at eight temperatures In the temperature range from 700° to 950°C, for times ranging from 5 to 45 hr. A linear curve of the logarithm or the activity vs the square of the penetration depth was obtained for all samples. Table I summarizes the results for individual samples and Fig. 1 gives a plot 02 the logarithm of the diffusion coefficients as

Jan 1, 1958

By Sam N. Dewitt, Albert S. Trube

This paper presents a discussion of the pressure maintenance operations which were begun in the New Hope Field. Franklin County. Texas. in 1944. The project has required the injection of extraneous waters at depths from 7.300 to 8.000 ft with intake well-head pressures up to 4.000 psi in three different reservoirs — the Bacon. Hill. and Pittsburg. Records of oil and water production. water injection and the GOR have been kept for each reservoir and reservoir pressures were taken at regular intervals. These data indicate that the Bacon Reservoir had no apparent water encroachment up to the time of water injection. However. the Pittsburg and Hill reservoirs had some natural water influx hut not sufficient to prevent pressures from declining below the bubble point. The Bacon and Hill reservoirs responded almost immediately to water injection. while the Pittsburg which is the least permeable. has shown good pressure response only since .August, 1948. The principle objective of the project has been to increase ultimate recovery. Success of the project to date also has resulted in reduced lifting costs. Esti- mates based on the initial water breakthrough patterns indicate that the primary objective of substantial additional recovery will he accomplished, and there is a possibility that the original estimates elf oil recovery with pres-sure maintenance will he exceeded. INTRODUCTION This pressure maintenance project was one of the earliest primary pressure maintenance programs to he attempted on a multiple zone field. There are three producing reservoirs into which water is being injected for the purpose of maintaining pressure and increasing the ultimate recovery- from each. This paper is limited in scope to al1 account of the development of the project. the pressure production relationship prior to the injection of water and the effect of water injection on the producing reservoirs. Also discussed are the nature of the injection system and the indicated results on initial water break-through in the Bacon Reservoir. FIELD CONDITIONS The New Hope Field, which is located about 12 miles northeast of Winusboro, Franklin County, Texas, is an elongated symmetrical anticline containing four known oil reservoirs. The reservoirs are of the Trinity group of the Comanchean or Lower Cretaceous period and are found in Table I. The oil productive portion of each reservoir is not present in all of the producing wells because their areas and positions vary with respect to one another. Fig. 1 shows the relative position of the four reservoirs and illusIrate? how some wells could penetrate all four, while others are restricted to three. two. or perhaps one. depending on structural location. The first three reservoirs contain undersaturated oil. The deepest. the Elledge, has a primary gas cap. Although this reservoir covers a considerable area of the field. it has a very thin section and a low order of permeability. Elledge producing wells have generally been characterized by an early increase in GOR, making it necessary to recomplete them in other reservoirs. (At present. one well is completed in the Elledge. which is still producing.) Because of the difficulties en-countered in producing oil from this reservoir. and the small quantity of oil actually present. future attempts at producing it will probably be on a salvage basis during the later life of the program. For this reason, the remainder of this report will be confined to a discussion of the Bacon, Hill and pius-burg reservoirs.

Jan 1, 1950

By K. Torssell, U. Lindborg

The kinetics of precipitation deoxidation is considered from a theoretical point of view. The size distribution and the total content of deoxidation products are estimated statistically as a function of time, taking into account Stokes and gradient collisions between the particles and separation at the top surface of the bath. The assumption is made that two particles coalesce into one larger particle as a result of a collision. General expressions are derived and calculations are carried out numerically for the case of silica particles in liquid iron. The analysis predicts a three-stage behavior for the removal of oxygen, an incubation stage, a stage of rapid separation, and a slow final stage where the content approaches the equilibrium value. The agreement with experimentally determined size distributions and deoxidation times is considered to be good. A quantitative estimation of such growth mechanisms as diffusion from the melt and redistribution of oxygen from small particles to large ones shows that these latter mechanisms cannot explain the experimentally observed gvowth of inclusions. This also indicates that collisions provide the important growth mechanism. OXIDE inclusions precipitate when a deoxidizer like silicon or aluminum is added to a steel bath. The inclusions grow and the large particles tend to separate from the bath. For each type of oxide the growth determines the sizes of the final inclusions as well as the total inclusion content of the steel. The mechanism of growth is controversial, however. It has been suggested that an inclusion grows principally by diffusion of atoms through the melt to the inclusion particle or principally by collisions and coalescence with other inclusions. Diffusion growth is always present to some extent but recent experiments and calculations by Torssell,' Kniippel et 'a1.,2 Sano et al. and Miya-shita4 indicate that collisions may be more important than previously realized. A detailed analysis has so far been lacking. The present paper is a quantitative, statistical analysis of the growth and separation of inclusions and is based on a collision theory. Nuclea-tion is not considered. The numerical estimates are based on the experimental conditions of Torssell's' investigation and comparisons are made with his observations. Torssell' studied the growth and separation of silica particles in liquid iron. Samples were taken from a 0.6 kg iron bath at various times after the addition of silicon. By a particle-counting technique developed by Bergh and Lindber~the size distribution of the inclu- sions was determined. The number of particles at the first sampling, 10 sec after silicon addition, was of the order of 3 x lo7 to 10' per cu cm, the largest particles having a radius of 2 to 4 pm. The volume fraction was 0.001 to 0.004; i.e., the dispersion was very dilute. During subsequent holding the largest particles increased their radius by a factor of 10 after about a minute, and the whole size distribution was displaced toward larger values. These results were obtained with allowance for precipitation of the equilibrium concentration of oxygen during solidification. The bath contained less than 0.01 pct of C. Figs. 1 and 2 show the typical appearance of the inclusions. Most particles are very closely spherical and appear to have been liquid or semiliquid in the melt. The observed number of inclusions, about 5x 10' per cu cm, is of the same order of magnitude as found by ~er~h.' This is a large value. It follows that the diffusion distances are very short and that the precipitation

Jan 1, 1969

By N. T. Cotman, C. H. Pickering, P. B. Crawford

A beat-conduction model has been developed to study the flow of fluids in a stratified oil reservoir which is being subjected to unsteady-state depletion. To simulate stratification, plates of different metals were joined together so that cross flow could occur between strata. A description of the model, plate construction and necessary instruments is included. The data indicate that stratified oil reservoirs experiencing cross flow may be treated as a single, homogeneous, producing sand having properties intermediate between those of the layers making up the system. A technique for averaging core-analysis data to arrive at the proper average value of rock permeability and porosity is presented INTRODUCTION Although oil has been produced from reservoirs for 100 years and reservoir injection processes have been undertaken for 40 years, the industry is still inadequately informed on the problem of reservoir inhomogeneities. Stratification is perhaps the best-known type of reservoir heterogeneity. Urenl discussed the possible significance of this nonuniformity in his 1927 paper on the theoretical aspects of water flooding. Since this time the problem of vertical permeability variations has been the subject of much discussion and numerous papers. Levorsen2 simply describes the origin of layered beds in his Geology of Petroleum. Some beds are field-wide and may be traced from well to well, while others apparently pinch-out and become discontinuous. In addition, the physical characteristics of a layer may vary from place to place. For these reasons, a stratified system is not easily defined. In calculations involving oil reservoirs in which permeabi1ities vary, methods presently used contain many simplifying assumptions. The reservoir frequently is considered as consisting of permeable layers, each of uniform vertical and lateral permeability and each behaving as if separated from adjacent layers by thin impermeable layers. Other assumptions frequently made in reservoir calculations are steady-state flow conditions, unit mobility ratio, linear geometry, average or homogeneous porosity, and negligible capillary-pressure and gravity effects. Muskat3 has. developed solutions to the stratification problem for mobility ratios other than unity for both linear and exponential permeability distributions. He assumes lateral uniformity and continuity of all productive strata and does not consider porosity. This study will take into account transient effects, cross flow and varying porosity, as well as the variations in permeability, by means of a heat analogy. Muskat5 has shown the similarity of the equations which describe the flow of fluids in a porous medium to the flow of heat through a solid. Landrum, et al,6 made an analogy between the flow of fluid in an unsymmetrical reservoir and the conduction of heat in a similarly shaped metal plate. This analogy is summarized briefly as follows. If fluid is produced from an oil reservoir above the bubble point, the resulting pressure distribution will be identical to the temperature which would result in a metal or heat-conducting plate if heat were similarly removed. This means that a study of heat flow in stratified thermal models will behave like fluid flow in stratified oil reservoirs. For mathematical correspondencies, set- Ref. 6. The fluid mobility k/p is proportional to the thermal conductivity, and the porosity-times-compressibility product is proportional to the density times specific heat of the thermal plate. EXPERIMENTAL EQUIPMENT AND PROCEDURE The stratified reservoir model used in this study is illustrated schematically in Fig. 1. A Leeds and Northrup Speedomax Type G temperature recorder

By B. H. Caudle, A. B. Dyes

In a recent publication' it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n '. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/q, = 1/(1 + y) y and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The resrilts obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce all infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of diflerent permeabilitv and thicktress or two lnyers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when wing only data over early years 01 decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index INTRODUCTION As a result of both experimental work with models and theoretical deductions, it was recently concluded' that wells having a free surface in a homogeneous reservoir producing by pure gravity drainage should have a hyperbolic decline with n = 2. The present report details efforts to extend this work on ideal homogeneous reservoirs to actual field cases. It should be remembered that both the previous work and the present extension are based on the assumption that the reservoir is at very low pressure, and hence, nearly all the potential available for driving fluid to the well is the gravity head. Attempts to apply conclusions of this study to reservoirs which have considerable pressures supplementing the gravity drive may lead to difficulty. WELLS WITH NO FREE SURFACE In a dipping gravity-drainage reservoir such as that shown in Fig. 1, some of the down-dip wells have no free surface. The previous study' showed that the up-dip wells, which have a free surface, should follow Eq. 1. The following approximate analysis, of a type which was justified experimentally for up-dip wells in the work just mentioned, leads to results for the down-dip wells.

By Alexander R. Troiano, Eugene P. Klier

SINCE the very early work on quenched structures, where the products of the martensite transformation had been recognized, this transformation has provoked much interest and study. Theoretically it was desirable to account for the extreme changes in physical properties resulting from the formation of martensite, as that information might lead to results of practical importance. Desirable information, therefore, was on the kinetics of transformation from austenite to martensite as well as on the physical constitution of the martensite. It has been known for years that certain steels quenched to room temperature will contain persistent austenite as well as martensite. Other important and now well- established features of the martensite reaction are the progress of the reaction on cooling only and the independence of Ar" with cooling velocities exceeding the critical velocity. These facts have been experimentally determined by various methods and investigators. Notable among the early investigators were Tammann and Scheill and Wever and Engel.2 Unfortunately, all investigators did not fully interpret their results, which, coupled with several investigations that yielded conficting results, caused a state of confusion that was not clarified until quite recently. X-ray investigations of martensite in steels3-6 indicate it to be a supersaturated solid solution of carbon in alpha iron. This supersaturation is evident from the appearance of a body-centered tetragonal structure with the addition of sufficient carbon. The dimensions of this tetragonal structure are alinear function of the carbon content within the limits of accuracy of the determinations. Slight tempering of tetragonal martensite leads to the destruction of the tetragonal structure, which is converted to a body-centered cubic structure. This phenomenon has precipitated a controversy concerning the nature and mechanism of the tempering of martensite. The facts in the case have been outlined by Epstein7 and more recently by Antia, Fletcher, and Cohen.8 The significance of Ar" on theoretical grounds is not clear, however, although considerable study has been devoted to its determination. The precise position of Ar" as a function of carbon content was first stated by Greninger and Troianos for steels covering a range of approximately 0.7 to 1.8 per cent carbon. The effect of alloying elements on Ar" has recently been the subject matter of investigation by various methods.

Jan 1, 1945

By James K. Stanley

WHEN a plastically deformed metal is heated to a certain temperature, it undergoes a complete change in microstructure, the consequence of which is a marked alteration of mechanical properties such as hardness, strength and ductility. This change in microstructure occurs by recrystallization and is a process involving the formation and growth of strain-free nuclei in the deformed matrix. These nuclei continue to form with time and grow until a new grain structure replaces the cold-worked structure. The formation of the nuclei in the deformed sheet of 1 per cent silicon ferrite is illustrated in Fig. 1. If a recrystallization is conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time leads to an isothermal recrystallization curve, first established in 1942.1 Such recrystallization curves are shown in Fig. 4. These curves show that the recrystallization of a cold-worked metal is best considered as a rate process rather than a time independent process such as is suggested by the improperly named and misleading recrystallization diagrams involving deformation, temperature, and grain size. 2-5 Any study of the rate of recrystallization resolves itself into a study of the component rates of nucleation and growth. The previous paper' provided an account of the determination of the rates of nucleation; N, the number of nuclei formed per unit time per unit of unrecrystallized area, and growth, G, the radial growth in unit time, in the recrystallization of silicon ferrite (1 per cent Si). A method was developed to furnish experimental data for evaluating the effect of the recrystallization variables on N and G. The mathematical analysis for the derivation of the isothermal recrystallization curve was developed for a two-dimensional case (in thin sheets where the diameter of the recrystallized grain is greater than the sheet thickness). The present paper is a continuation of the study of recrystallization of 1 per cent silicon ferrite begun in 1942.1 In this work the effect of the factors deformation, temperature, grain size, composition, and recovery is studied with respect to the rates of nucleation and growth. At the same time it is shown how the cooperation of N and G affects the isothermal recrystallization curve. The study of these variables on N and G has a definite bearing on the mechanism of recrystallization and should lay a foundation for a rational theory on the subject. PROCEDURE The procedure used in these experiments was essentially the same as that described previously but in certain details some changes were made in the interests of speed. With few exceptions, the procedure is the same for the study of all the variables. Where the procedure is different from standard manipulations attention is called to this fact.

Jan 1, 1945

By Richard L. Ash, J. H. Kelley, W. H. McCracken, William Bellano, J. D. Morgan, D. R. Mitchell

Rubber-tired shuttle cars are finding increased use as gathering units in under-ground mines. As the name implies, they shuttle back and forth between the loading machine and the section transportation system. In many mines their use has in-creased the efficiency of the loading and gathering operations, resulting in increased output per man employed and decreased costs per ton. A car motivated by cable reel is shown in Fig I, and a car with battery power in Fig 2. A brief chronological account of the development of rubber-tired haulage equip-ment follows: 1936. J. H. Fletcher1 installed his first unit for the Blue Bird Coal Co., Carrier Mills, Illinois. This unit consisted of a battery-powered industrial tractor and a trailer with drop-bottom doors. The coal was transported for short distances to a hopper for discharge into mine cars. 1938. A battery-powered self-contained shut-tle car with rubber-tired wheels was built by the Joy Manufacturing Co. Two units were installed for the Katherine Coal Co., Lumberport, West Virginia. The shuttle car consisted of a materials-receiving body with a conveyor in the bottom to move the coal forward during loading and to unload the coal at the discharge station. 1938. A cable-powered shuttle car with four-wheel drive and four-wheel steer was developed by A. L. Lee. Special wheels mounted on king pins on the car permitted all four wheels to be steered. The cable reel was driven by a torque motor to give the cable proper tension during the payout and uniform tension when rewound on the reel. 1940. A Joy shuttle car equipped with trolley poles and a cable reel was developed to operate on a double trolley-wire system.2 This unit was installed at a potash mine of the International Minerals and Chemicals Corporation at Carlsbad, New Mexico. It is believed to have been the first installation of its kind, and the first of shuttle cars for handling material other than coal. 1941. Truck haulage3 was introduced in the Tri State District by the Eagle-Picher Mining and Smelting Company. Storage battery electric trucks were rebuilt to handle a bottom-dump trailer. 1941—Joy shuttle cars were installed in a mine of the United States Gypsum Company, Oakfield, New York. 1943—Joy shuttle cars were installed in several bauxite mines.4,5 1945—Joy shuttle cars installed in a lime-stone mine. Because of the nature of bituminous coal beds trackless equipment has had its greatest application in bituminous coal mining. Usually a shuttle car is filled by a continuous type of loader. In Fig 3 is shown a continuous machine loading coal into a battery-powered shuttle car, 48-in. coal. However, intermittent types of load-

Jan 1, 1949

By D. J. McAdam

Results of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station have been presented by the author in four papers.1, 2, 3, 4 In those papers references were given to the work of Haigh in 1917.5 The investigation at Annapolis included a variety of ferrous and non-ferrous alloys. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at stresses far below the ordinary endurance limit. The experiments also showed that, for most metals, severe stressless corrosion prior to fatigue is much less damaging than even slight corrosion simultaneous with fatigue. The term "corrosion-fatigue" was restricted to mean the simultaneous action of corrosion and fatigue. The combined effect of corrosion followed by fatigue was called "prior-corrosion fatigue." A stress-cycle graph representing corrosion-fatigue is a curve approaching a horizontal asymptote, the ordinate of which may be called a "corrosion-fatigue limit." To avoid confusion in later discussion, the term "endurance limit" will be restricted to mean the fatigue limit obtained by tests in air with specimens as free as possible from stress concentration and from corrosion. The cndursnce limit as thus obtained presumably represents an inherent property of the metal.

Jan 1, 1929

By D. J. McAdam

Results of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station have been presented by the author in four papers.1, 2, 3, 4 In those papers references were given to the work of Haigh in 1917.5 The investigation at Annapolis included a variety of ferrous and non-ferrous alloys. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at stresses far below the ordinary endurance limit. The experiments also showed that, for most metals, severe stressless corrosion prior to fatigue is much less damaging than even slight corrosion simultaneous with fatigue. The term "corrosion-fatigue" was restricted to mean the simultaneous action of corrosion and fatigue. The combined effect of corrosion followed by fatigue was called "prior-corrosion fatigue." A stress-cycle graph representing corrosion-fatigue is a curve approaching a horizontal asymptote, the ordinate of which may be called a "corrosion-fatigue limit." To avoid confusion in later discussion, the term "endurance limit" will be restricted to mean the fatigue limit obtained by tests in air with specimens as free as possible from stress concentration and from corrosion. The cndursnce limit as thus obtained presumably represents an inherent property of the metal.

Jan 1, 1929

By Lennart Wellenius

LAISVALL - ONE OF THE BOLIDEN MINES Until the Aitik Mine (2,000,000 mtpy) started in 1968 the Laisvall Mine (1,200,000 mtpy) was the biggest unit of about 20 producing mines, belonging to the Boliden Company Ltd. As shown in Fig. 1 the mines are spread over a wide area. Most of them are small complex ore mines (50,000 - 300,000 mtpy), for which reason the total mine production does not exceed 5,500,000 mtpy. When our company was invited to present a paper, Laisvall was chosen because it is the biggest European galena-mine in production today. The Laisvall Mine is situated in the county of Norrbotten, Sweden, at the eastern border of the Caledonian mountain-chain. The road distance to Slagnäs, the nearest railway station, is 60 miles. The railway between Slagnäs and BOLIDEN's smelting plant, the Rönnskär Works, is 140 miles long. PRODUCTION STARTED IN 1943 In the Autumn of 1938 a boulder was discovered, consisting of sandstone with galena, on the shore of the Lake Stor-Laisan. The boulder came from an Eocambrian sandstone formation, which is overlain by Cambrian-Silurian rock.

Jan 1, 1970

By N. E. Truitt, D. G. Russell

The transient pressure behavior of a well which produces a single compressible fluid through a singte-plane wrticat fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited mdial extent, and' to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are somewhat inaccurate. As fracture penetration increases radially, kh values calcutated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the catculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimensionless pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells. INTRODUCTION Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al.1 first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells; however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora10 and Dyes, Kemp, and Caudle2 employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott- reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study were (1) to obtain synthetic pressure build-up and flow test

Jan 1, 1965

OF the many categories into which scientific knowledge has been arbitrarily divided, the one that has proved most applicable in our attempts to gain an insight into the details of steelmaking processes is physical chemistry. To the young metallurgist who has only recently survived a college course in this subject, the application of its principles to reactions in liquid steel should not be difficult. The many excellent textbooks of physical chemistry1 provide ample material on the principles of this subject for the student of steelmaking processes; yet with- out exception those texts draw the greater part of their illustrative material from room-temperature data. It is the purpose of this chapter to provide a concise review of the principles of physical chemistry that have proved useful in studies of steelmaking and at the same time to present some of the data that are essential to the application of physical chemistry to reactions at high temperatures. Certain parts of physical chemistry require rather formidable mathematics for their complete development but in the main those applications in which we are here interested can be ex- pressed in fairly simple terms. Many of the equations are logarithmic, and we shall use the symbols In X and log X to represent respectively the natural and the common logarithm of X. The two are related by In X = 2.303 log X. Logarithms may be read from a good slide rule with sufficient accuracy for our purposes. In a few spots a knowledge of the calculus will be, helpfu1. MATTER Innumerable forms of matter may be recognized, and these may be converted by chemical processes into others, as ore, coke, and air are converted into iron, slag, and gas. Whenever such a change occurs there is a corresponding change in

Jan 1, 1951

By Robert J. Ramsey, Robert D. Jeppson

Introduction The Utah Copper Division of Kennecott Copper Corporation will present its contribution to the A. M. Gaudin Flotation Symposium in four parts. The first two segments will discuss briefly the historical development of the Utah Copper Division and describe the ore body. The third segment will review the facilities and operating procedures for the Utah Copper division's newest plant, the Bonneville Concentrator. The fourth segment describes flotation process circuitry, including molybdenite recovery procedures, at the Arthur and Magna concentrators. (The Bonneville concentrator is a crushing and grinding unit and does not have its own flotation plant). I. Historical Development Progress through change has been the key to the successful operation of the Utah Copper Division for more than 70 years. As the original low-grade copper operation, the pressures to remain competitive and profitable have dictated the timing and extent of each change. Much of the change has occurred through technological and economic advancements in the area of ore concentration. The Utah Copper Division of Kennecott Copper Corporation had its origin June 4, 1903, when the Utah Copper Company was organized. The initial mill of 300 tpd (tons per day) capacity was built at Copperton a few miles below the present Bingham Canyon mine site. From 1904 to 1910, the Copperton mill was expanded to a capacity of 1,000 tpd, and all of the known apparatus for gravity concentration were evaluated.

Jan 1, 1976