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By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By A. Kaufman

More than 3 trillion gal of water are used annually by the mineral industry. Of this, approximately 21/2 trillion gal are recirculated, the rest constituting intake water. The major users are natural gas processing plants and phosphate rock, sand and gravel, and iron ore producers. Water was used by the mineral industry for mining (6%), processing (64%), cooling and condensing (27%), and miscellaneous uses such as boiler feed and sanitary purposes (3%). Whereas total water use is dependent on the quantity of material processed and on the particular process requirements of an industry, recirculation is dependent on processing, as well as cooling and condensing requirements, quality of new water intake, and the necessity for treating new and discharged water. Consumed water, on the other hand, is dependent on the quantity of water recirculated, and temperature and humidity in the area. Based on this analysis, an increase in water use by the mineral industry of 21/2 times by 1985 is forecast. Wster intake, however, will only rise 62%, because of a substantial increase in recirculation. In one report of a special series concerning the water resources of the United States, the Senate Select Committee on National Water Resources, 87th Congress, estimated that water demand would double by 1980 and triple by 2000.' In view of the possible water deficiencies that might result from such expanded usage and the need for research guidance, the Bureau of Mines organized and carried out a statistical canvass of water use in the mineral industry for calendar year 1962. The data used in this paper, unless otherwise noted, are derived from that canvass.' The efforts in this paper are devoted toward summarization of the canvass and analysis of the data. SOME DEFINITIONS Intake: Water introduced from an external source for the first time into a given mine or plant regardless of quality. Intake water is also called new water, water withdrawn, or makeup water. Fresh Water: Water suitable for cooking and drinking. Saline Water: Water containing more than 1000 parts per million of dissolved solids. Contaminated Water: Water not suitable for domestic use, but excluding saline water. Recirculated Water: Water reused to conserve intake water. Solutions that are recycled primarily because of fixed metallurgical practices, such as copper leaching solutions containing sulfuric acid, are excluded. Gross Water Used: Recirculated water plus intake water. Also called total water used. Consumed Water: Water that is lost by evaporation, as well as water lost in product. Seepage and transferred water are not considered consumed. The use of either intake or recirculated water may result in consumption. However, because of difficulties in measuring consulmption, consumed water is defined as the residual between intake and water discharged from the mine or plant. Mineral Industry: For the purposes of this paper, mineral industry includes all metal and nonmetal surface and underground mines and their associated processing plants, as well as custom mills, coal washing plants and associated mines, petroleum and natural gas well drillers, natural gas processing plants, and secondary recovery operations. WATER USE IN THE MINERAL INDUSTRY Water used by the mineral industry constitutes a relatively minor fraction of the water withdrawn by all users. Data compiled by the U.S. Geological Survey in 1960 indicate that water withdrawals, exclusive of that used to generate hydropower, approximate 99 trillion gal annually.3 Our data indicate that water withdrawals by the mineral industry comprise only 1% of this total, or 2% of the water withdrawn by industrial users. Use by Industry: Water used by various mineral industries is shown in Table I. The table indicates that close to one-half of the gross water used by the mineral industry in 1962 was used by natural gas processing plants, followed by sand and gravel, phosphate rock, and iron ore producers. The largest aggregate users of water are also the largest users per dollar of product. For example, Fig. 1 shows that the natural gas processing and phosphate rock industries are very large users of water per dollar of product. Their recirculation per

Jan 1, 1968

By W. O. Philbrook, H. E. Burner, F. S. Manning

The equation of continuity for the hydrogen reduction of hematite in a fixed bed of closely-sized particles is solved assuming a flat velocity profile, negligible temperature gradients, md negligible axial diffusion. A kinetic expression from the literature is used which assumes the reduction process is controlled at the oxide-metal interface. The integral fractional conversion is computed, and the importance of particle diameter, flow mte, temperature, bulk axial diffusion, and inter- and intra-particle mass trarnsfer is predicted. Comparison with experimental data suggests one or more additional undefined variable(s) is significant. Equipment modifications are suggested for fidture experimentcll work. WITH the increasing desire to "design" the ore feed of a blast furnace, it has become necessary to define more quantitatively the process variables and to evaluate the extent of their control upon the reduction process. The bulk of the work reported in the literature has centered about the reduction of single particles; however, the blast furnace process more closely resembles reduction of a fixed bed than that of single particles. To simplify this analysis, the isothermal reduction by hydrogen of a natural hematite in a fixed bed of closely-sized particles is examined. With appropriate modifications in the kinetic and flow rate expressions, the approach employed should be extensible to mixtures of carbon monoxide, hydrogen, and inert nitrogen, and to adi-abatic conditions, thus approaching the blast furnace process more closely. The fixed bed variables which are investigated in this study are particle diameter, flow rate, temperature, and bulk axial diffusion, as well as inter-and intra-particle mass transfer. Of particular interest is the effect of particle size upon fractional conversion for a bed operating under constant pressure drop. The constant pressure drop concept bears a close resemblance to the blast furnace process, where regions of larger particles may provide a greater permeability to divert most of the reducing gas flow from the regions of smaller ore particles. Under such conditions one would expect qualitatively that, for sufficiently small particle sizes where the flow rate is small and the total surface area is large, the reduction rate would be limited by the gas flow rate. Initially the gas entering the bed reacts very rapidly and the composition approaches the equilibrium conversion value a short distance from the reactor inlet. This concentration "wave-front" then moves up the bed as the flow of reducing gas is continued, leaving in its wake an ever increasing layer of reduced particles. Providing that the reducing gas leaves the bed at equilibrium concentrations, conversion is expected to increase with an increase in flow rate, and hence with an increase in particle diemater. Conversely, for sufficiently large particles the flow rate will be high but the surface area available for reaction will limit the reduction rate. Since the total surface area decreases with an increase in particle size, conversion, in this case, is expected to decrease as the particle diameter is increased. It is clear then that between these two extremes an optimum particle diameter must exist. THEORETICAL DEVELOPMENT Above the temperature where wiistite is stable (about 560°C) the reduction of hematite proceeds through the series Fe2O3/Fe3O4/FeO/Fe. On the basis of microstructural studies and earlier work, Edström1 has postulated a mechanism for the reduction of an ideal hematite lattice: 1) Iron phase formation at the boundary between wiistite, iron, and gas (for sufficiently porous iron). 2) Diffusion of iron across a wustite layer. 3) Phase boundary reaction of Fe3O4 to FeO. 4) Diffusion across a dense magnetite layer. 5) Phase-boundary reaction of Fe2O3 to Fe3O4. According to the mechanism postulated, gaseous reaction product has to be removed only at the boundaries between wüstite and iron or gas, the only possible exception being enveloped Fe3O4 specks. On this basis McKewan2,3 has proposed that one may consider the hematite reduction process as a simple two-phase system of oxide/metal. If, for FeO and Fe3O4 layers of negligible thickness, the hypothesis is made that the rate of formation of a

Jan 1, 1963

By H. C. Casey, M. B. Panish

The roles of the phase diagram and the diffusion and solubility analyses in the selection of sources for the diffusion of zinc into GaAs are discussed. Isothermal sections of- the phase diagram are described at 1000°, 775°, 744°, and 700°. Below 744° the three solid phases, Zn3As2, GaAs, and ZnAsz, may be in equilibrium. In the composition regions where the three solid phases are in equilibrium, the partial pressures of the components do not vary with composition and there is no liquid phase. A diffusion source composition within that region containing 5, 50, and 45 at. pct Ga, As, and Zn was selected to yield reproducible diffusion profiles without surface damage. The 5/50/45 ternary source Provides a significant improvement in the reproducibility and planarity of- the zinc diffusion as compared with other zinc diffusion sources that result from starting with elemental zinc, dilute solutions of zinc in gallium, or various combinations of zinc and arsenic. Several experimental diffision profiles for the 5/50/45 diffusion source have been determined. The profiles are very steep in the region of the junction and produce devices that exhibit step junction behavior. The junction depth varies as the square root of time. Diffusion at 700°C for 4 hr gives a 5-µ junction depth and a surface concentration of 2.4 x1020 cm-3. The surface concentration is enhanced by a factor of three and the junction depth decreased by a factor of ten as compared with diffusion with a starting source 01- elemental zinc. The differences in dijyusion behavior with these two sources are due primarily to the approximately 10' greater equilibrium As4 partial pressure for the 5/50/45 source. ThE most common technique for the preparation of GaAs p-n junctions for diverse applications ranging from switching diodes to injection lasers has been to diffuse zinc into the solid from the vapor phase. The zinc impurity has generally been provided by introducing into a diffusion ampoule elemental zinc, dilute solutions of zinc in gallium, or various combinations of zinc and arsenic. For the purpose of eliminating surface deterioration, zinc has been diffused into GaAs through SiO2 films1 and from zinc-doped SiO2 films.2 During a study of the injection and recombination mechanisms in GaAs junctions, we found that these diffusion techniques either resulted in nonreproducible diffusion profiles and nonplanar junction interfaces or were extremely inconvenient to use. An unpublished report by Allen and pearson3 emphasized that an understanding of diffusion requires relating the diffusion conditions and system compositions to the ternary phase diagram. Recent studies have made it possible to relate the effect of starting source composition on the GaAs sample surface and diffusion profile reproducibility and, in addition, to estimate the expected surface concentration and zinc diffusivity. These studies include the Ga-As-Zn phase diagram,415 the determination of the incorporation reaction for zinc as a substitutional impurity,6 and the analysis of the concentration dependence of the diffusion coefficient.' In this paper the role of the phase diagram in the selection of the starting diffusion source composition is illustrated, and an application of the diffusion and solubility analyses is used to demonstrate their utility in the estimation of surface concentration and diffusivity for various starting source compositions. Consideration of the isothermal sections of the ternary phase diagram shows that below about 744° C a composition region exists where the three solid phases Zn3As2, GaAs, and ZnAs2 are in equilibrium without a liquid phase. In this region the partial pressures of the components do not vary with composition, and thus the surface concentration and diffusivity depend only on temperature. A diffusion source composition within that region containing 5, 50, and 45 at. pct Ga, As, and Zn was selected. As will be described in detail, this diffusion source yields reproducible diffusion profiles without surface damage, planar junction interfaces, and steep profiles that result in devices with step junction behavior. Only closed diffusion systems are considered. Open or flowing vapor systems require the maintaining of constant vapor pressures in the flowing gas and represent control problems outside the scope of this discussion.

Jan 1, 1969

By J. Downie, H. A. Kendall, G. H. F. Gardner

Some cases of the motion of two miscible fluids in uniform linear models are discussed. There is no bulk flow through the models, and the convection currents are caused solely by density gradients. Horizontal, vertical and inclined positions of the models are treated separately. Analytical formulas for the motion of a narrow transition zone between the fluids are obtained and compared with measurements, and the limitations are discussed. Observations of the ultimate stabilizing effect of diffusion on the motion me compared with the theory. It is shown that fluid motion in an inclined model with a constant rate of bulk flow can be directly deduced from the cases discussed, provided the viscosity ratio is small. INTRODUCTION In some reservoirs, convection currents caused by variations in the fluid densities may be significant. For practical purposes it may be desirable either to minimize the effect, particularly in miscible displacement, or to maximize the effect as in some schemes for the production of heavy crude oils by combustion. Experiments by Craig, et al,l have shown the effectiveness of gravity in reducing the efficiency of a miscible displacement when the mixed zone between the displacing and displaced fluids is narrow compared with the height of the system. The presence of a board transition zone from one fluid to the other has been shown by Perkins, et al,2 to nullify considerably the influence of a difference in density. Indeed, the theoretical discussion given by Perrine3 has shown that when the transition zone exceeds a certain critical length the efficiency approaches 100 per cent. Many additional results 495 have been published on miscible and immiscible displacements which show the importance of density difference and also mobility ratio. The aim of the present paper is to discuss some cases of gravity segregation of miscible fluids in linear models such as are often used in the laboratory to evaluate recovery processes, and to supply additional experimental evidence in support of the conclusions. An attempt is made to calculate simply the magnitude of the fluid motion caused by density pdients and mobility ratios, and to quantify the modifications in the fluid motion produced by the combined effect of molecular and convective dispersion. However, it should be pointed out that the uniform permeability of the models and the use of only a single pair of fluids (whereas several pairs of fluids may be employed in a recovery scheme) severely restricts direct conclusions about natural reservoirs. For conciseness, the motion generated by density gradients is emphasized for the case of no bulk flow through the models. This is not a drastic limitation because, as shown in Appendix A, a fluid motion with a constant bulk flow through any linear model is equivalent to a fluid motion with no bulk flow in the same model inclined at a different angle to the horizontal, provided only that the density is a linear function of the viscosity of the fluid mixture. HORIZONTAL MODEL In this case the model is assumed to have a rectangular cross-section with a horizontal breadth b, vertical height and a great length L. Throughout.the paper it will be assumed that x-axis points along the length, the y-axis along the width and the z-axis along the height. Thus, in the present case the x, y plane is horizontal. Initially, the transition zone between the fluids is assumed to be thin and parallel to the y, z plane. An example of this situation in a practical problem arises in a scheme for using air for cushion gas in the storage of fuel gas in aquifers. 6 With the passage of time the denser fluid sinks and spreads along the bottom of the model while the lighter fluid rises. The interface extends from the top plane of the model to the bottom. Experiments have shown that for practical purposes this interface may be treated as a plane surface at all times. The surface is significantly curved, however, for viscosity ratios greater than about 10. Other complications arise with large viscosity ratios because of the nonlinear dependence of the viscosity on the composition of the mixture, so that the simple results given here are restricted to fairly low viscosity ratios.

By J. G. Savins

Certain types of macromolecules added to water and salt solutions flowing in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these materials. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89-in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a I-in. water line yields a throughput capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion. INTRODUCTION This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe f1ow.I Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required* to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd,3 Agoston et al., Bundrant and Matthews, Robertson and Mason,6 Ousterhout and Hall,7 Daily and Bugliarello~ Lummus, Anderson, and Fox. 9 That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels,l0 Dever, Harbour, and Seifert.11 One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver12 and Dodge.13 However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction-. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabulal5 and Granville.16 Along somewhat different lines are the drag reduction studies of Kramer.17118 He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne,19 Cess and Sparrow,20'21 Sparrow, Jonsson, and Eckert.22 Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merri11,23 Dodge and Metzner, Clapp,25 and Thomas.26

Jan 1, 1965

By J. L. Huitt, J. L. Pekarek, D. K. Lowe

In a theoretical study of hydraulic jetting, the velocity of the abrasive material relative to the velocity of the fluid in the jet stream is analyzed as the jet stream moves through the convergent and straight sections of the nozzle and the region between the nozzle exit and target. The results revealed that the abrasive material exits from the jet nozzle at a lower velocity than the fluid. The exit pmticle velocity can be increased by increasing either the density of the fluid or the length of the nozzle, and/ or decreasing either the particle density or particle diameter. In the divergent jet stream, there exists a point after which the particle velocity exceeds that of the fluid. The relative velocities were considered in the derivation of an equation to predict cutting rate of a circumferential notch and maximum notch depth. Data of a general nature and data which substantiate the theoretical results were obtained experimentally. INTRODUCTION The use of a fluid containing an abrasive material has been an established technique for cleaning and cutting for many years. In the petroleum industry, the early effort to use this technique1 to perforate and/or to overcome wellbore damage met with only limited acceptance because of the short life of the jet nozzle. With the introduction of improved perforating techniques, and later, hydraulic fracturing, the use of hydraulic jetting as a well completion technique became even less appreciated. It was only in recent years that interest in hydraulic jetting was revived. Once this interest was revived, the results of surface tests stimulated the interest of the industry even more than the state of the technology probably warranted because many of the tests were not appropriate for down-hole conditions. However, because of the stimulated interest, the development of the jet nozzle progressed very rapidly to the point where the nozzle life was no longer a prob- lem. With this accomplished, the use of hydraulic jetting in well completion became an accepted practice in a short time. The purpose of this paper is to present a theoretical analysis of the hydraulic jet stream as it passes through the nozzle and travels to its target. With a better understanding of the jet stream and the effects of various parameters, the performance of the process can be predicted more accurately. Equations are presented for cutting rate as applied to circumferential wellbore notching that relate the jet stream make-up, notch configuration and formation material. Also, experimental data are presented on some factors pertinent to hydraulic notching that are not theoretically analyzed. RELATED STUDIES Most of the studiesl-5 reported in the recent literature have pertained to the more practical aspects of hydraulic jetting; i.e., the effects of certain parameters as interpreted from experimental results, and the application of hydraulic jetting in well completion. In reviewing the effects of various parameters, it is interesting to note the reported depths of penetration obtained under various imposed conditions. In general, the depths vary from a few inches to several feet; however, a depth of penetration of less than 6 in., as reported by Thompson,4 seems more realistic for the usual field practice of hydraulic jetting with sand in water for a period of 20 to 30 minutes. In addition to the practical aspects, the study of Brown and Loper5 included a theoretical approach to hydraulic jetting. Their study resulted in the development of a theoretical expression for the maximum depth of penetration if jetting were continued for an infinite time. An analysis of the equations presented reveals that the initial cutting rate is infinite. The equation expressing centerline velocity is that of Forstall and Gaylord,6 which is applicable for a jet stream exiting in a large stationary medium. Since practically all of the fluid pumped into a perforation (or cut) must flow back through the perforation prior to re-entering the wellbore, a description of the medium as finite and non-stationary seems more reasonable. Thus, in this

By H. Carroll Weed

By caving a block into the workings of its open pit and using the block as an ore transfer, the lnspiration Consolidated Copper Co. has solved a transportation and sizing problem, making possible a great expansion of open-pit methods as applied to Inspiration ore-bodies. FROM 1915 to 1948 the entire production of Inspiration Consolidated Copper Co. was supplied from underground mining. The sole method used was block caving. Underground haulage and hoisting facilities were designed and geared to large-scale production. Beginning in 1948 open-pit mining was substituted for block caving in a portion of Inspiration's Live Oak orebody. The idea proved so attractive that before the Live Oak pit had come into production, another pit on the Colorado orebody (now the Thornton pit) had been laid out and stripping started. It should be noted that these orebodies were not new and the entire program was one of changed methods of mining. Since part of these orebodies had already been mined by block caving methods, it must be recognized that haulage levels had been established under the area or adjacent to it. The orebodies lay on the south side of Inspiration Ridge, while the shafts, crushers, and treatment plants are all on the north side of this ridge. The existing main crushing plant was designed to take a maximum of 12-in. material, and all ore was sized to this dimension by passing through grizzlies in the stopes. In the original planning for open-pit work much thought was given to the transfer of ore to existing underground levels for haulage and hoisting from the regular shafts. If this could be done the necessity of crossing the ridge could be eliminated. Final decision called for cutting a road through the ridge, installation of a primary crusher at an elevation of 3968 ft on the north side of the ridge, and railroad haulage with existing facilities to the main coarse crusher. This decision was brought about by the difficulties of properly sizing and transferring to underground haulage large tonnages of coarse breaking oxide which lay on the upper benches of the proposed pit. Trucking over the ridge on a 7 pct grade would give a cheaper and more flexible operation in handling this material. The benches in the pits are laid out at 50-ft inter-vals and designated according to elevation above sea level. The lowest bench in the original pit was laid out at 3500-ft elvation. All haulage roads are on a 7 pct grade and a vertical lift of 468 ft was considered about the maximum economically possible from a cost standpoint. After 2 years' operation the advantages of pit mining, both from the standpoint of costs and flexibility of operation, became more and more apparent. Studies were then started to develop the extension of open-pit mining to more of the ore reserve than had been planned originally. The idea of transfer raises was again explored. Obviously, as elevation of the pit was lowered, shorter transfer raises would be needed to reach the main haulage levels. Transportation from the lower elevations to the rim of the pit by belt conveyor or skip hoisting was also considered. However, it was recognized that sizing would be required both for conveying and regulation of feed size to the main crusher plant. This would necessitate a fixed or portable crusher located somewhere in the pit. It was known that the sulphide ore at the lower elevations was softer and easier to break than the overlying oxide of the upper benches. This sulphide ore is very suitable for grizzly sizing. Calculations indicated that for ore mined on 3650 elevation, costs for trucking to the primary crusher, crushing, and delivery by railroad to the coarse crusher would equal costs for dropping the same material to the 600 level, hauling underground, and hoisting directly to the coarse crusher bins, provided a suitable method of sizing and transferring could be developed. Above 3650 elevation costs would favor surface haulage; below they would favor underground haulage. The idea of caving an underground block from the 600 haulage level directly into the bottom of the pit

Jan 1, 1954

By G. Gutierrez, D. A. Elgillani, M. C. Fuerstenau

The zero-points-of-charge of apatite, calcite, and fluorite are pH 6.4, 10.8, and 10.0, respectively. Scheelite is negatively charged above at least pH 3. In this article, the flotation responses of these minerals in the presence of potassium oleate and sodium silicate are described and compared with electrokinetic data. Colloidal silica appears to be the species principally responsible for calcite depression, while silicate anion is the species responsible for fluorite depression. Additions as high as 1 x 10-3 mole/liter silicate have no effect on the flotation responses of apatite and scheelite. Selective flotation of nonmetallic minerals is difficult to achieve with fatty acids or soaps by themselves. As a result, specific reagents are added to aid these separations, and one of the reagents commonly employed for this purpose is sodium silicate. Flotation separations of various calcium-bearing minerals such as fluorite from calcite1-3 and scheelite from calcite2,4 and apatite,2,5 for example, almost always involve the use of sodium silicate. The mechanisms by which sodium silicate functions as a depressant are still not understood, probably for a number of reasons. For one thing, the dissolution process of sodium silicate is complex, giving rise to a number of ionic and colloidal species.' Moreover, the type and concentration of these species depend on the ratio of Na2O to SiO2, the concentration of sodium silicate, and the pH of the system.' At the present time, it is not known which species, colloidal silica or silicate anion, is responsible for depression. If colloidal silica is the species that is adsorbing, then adsorption must occur by electrostatic attraction between the colloid and the mineral surface. Silicate anion, on the other hand, may adsorb either physically or chemically. The objective of this paper is to determine first the active species of sodium silicate and then the conditions under which this species will adsorb and function as a depressant. EXPERIMENTAL MATERIALS AND METHODS Pure samples of apatite (Durango), calcite (Iceland-spar), fluorite, and scheelite were used in this investigation. Pure potassium oleate was used as collector, while reagent-grade HC1 and KOH were employed for pH adjustment. The sodium silicates used were samples obtained from the Philadelphia Quartz Co. In one series of experiments, various sodium silicates containing different ratios of SiO2 to Na2O were added to calcite systems. These sodium silicates contained SiO2-to-Na2O ratios of 3.75 to 1, 3.22 to 1, 2.40 to 1, and 1.60 to 1. All other experiments were conducted with the sodium silicate containing the ratio of 3.22 to 1, which is the one that is normally used in industry. Flotation experiments were conducted with 21/2-g charges of 48 x 150-mesh material in conductivity water with an apparatus and technique described previously. Electrokinetic experiments were conducted with both a Zeta Meter and streaming potential apparatus. Particle size was 48 x 65 mesh for the streaming potential experiments. EXPERIMENTAL RESULTS The first series of experiments involved flotation of scheelite in the absence and presence of sodium silicate. As shown in Fig. 1, flotation response was not affected with even the relatively high addition of 1 x 10-3 mole per liter sodium silicate. Interestingly though, no flotation was effected below pH 6 with this collector addition. The responses of apatite to flotation under these same conditions are given in Fig. 2. Similarly, no depression was obtained in basic media under these conditions. Similar experiments were conducted with fluorite, and in this case, depression was noted above about pH 11 with 1 x 10-3 mole per liter sodium silicate (Fig. 3). When calcite was floated with these same levels of addition of sodium silicate, essentially no flotation was possible above pH 7 (Fig. 4). The effect of collector addition with a constant addition of sodium

Jan 1, 1969

By R. Schuhmann

Available thermodynamic data applicable to copper smelting systems are collected and tabulated, and the important gaps are pointed out. A few examples are given of estimations which can be made from the available data. An experimental research program is proposed to supply the thermodynamic data that appear most essential to better quantitative understanding of the chemistry of copper smelting. The proposed program is designed also to shed specific light on the practical problems of slag losses and magnetite behavior. OPPER smelting, from flotation concentrates to V-/ blister copper, is conspicuous among the large scale chemical processes which are conducted with only relatively incomplete knowledge of the physical chemistry involved. For example, no common metallurgy text explains adequately why copper enters the matte phase while iron enters only to the extent that sulphur is left over after satisfying the copper. Explaining this important phenomenon as a manifestation of the greater affinity of sulphur for copper than for iron is unsound because the affinities of copper and iron for sulphur are about the same at smelting temperatures. As will be shown, other affinities are really decisive in the relatively clear-cut separation of copper in the matte. In contrast, thermodynamic studies have contributed much to our understanding of copper refining, zinc oxide reduction, magnesium production, steelmaking, etc. For each of these processes, the important reactions are clearly recognized, and fair to good quantitative values of the free-energy changes and equilibrium constants are available. Such data have proved to be of constantly increasing practical value in process development and improvement. Work in other fields has furnished much thermodynamic data applicable to copper smelting systems. In fact, several promising starts have been made in applying such data to specific smelting problems. Kelleyl made an appraisal of the possibilities of recovering elementary sulphur from low grade matte. His calculations and compilations of thermodynamic data have represented the starting point for much of the work in this field, including the present survey. Huang and Hayward2 nd Aksoy3 used thermodynamic methods in the study of copper losses in reverberatory slags. Peretti4 used thermodynamic data in explaining the chemistry of converting. The recent publications of Darken and Gurry"." and of Darken,' dealing with the iron-oxygen and iron-silicon-oxygen systems, respectively, present equilibrium data that are applicable to copper smelting systems. Also additional data were reported recently on the affinity of sulphur for copper, manganese, and iron8 and on the sulphur pressures of iron-sulphur melts." The survey presented in this paper was made as the basis for planning an experimental program on the thermodynamics of copper smelting. Few researches on the chemistry of copper smelting have been reported in recent years, so that a reappraisal and coordination of old and new data are essential if further work is to take the directions of maximum value. The experimental program is now in progress, and the plan of attack is outlined at the end of this paper. Progressive Oxidation and Desulphurization of Copper-bearing Liquid Phases: The chemical activities of sulphur and oxygen are two of the most important thermodynamic yardsticks to be applied to copper smelting processes. Virtually the entire smelting and refining sequence involves a series of systems characterized by decreasing sulphur activity and increasing oxygen activity. In this section, therefore, an attempt is made to define and explain these activities in terms of equilibrium partial pressures of SO2, s2, and O,. Also, estimates of these quantities are presented, the estimates being based largely on calculations presented in a later section of this paper. The sequence of steps from raw flotation concentrate to fully oxidized copper ready for poling involves progressive and controlled oxidation. Iron is oxidized and enters the slag. Sulphur is oxidized and leaves in the gas. Table I summarizes several important features of this oxidation and desulphurization sequence, starting at the beginning of the matte blow in the converter. The top line gives in order the principal smelting and refining stages up to fully oxidized copper, plus the additional step, not used commercially, of oxidizing all the way to Cu,O. In the second line are shown the principal copper-bearing liquid phases which characterize the process. Through most of the sequence the copper

Jan 1, 1951

By I. A. Goddard

INTRODUCTION This paper deals with the development of the sublevel open stoping (SLOS) method in lead orebodies at the Isa Mine of Mount Isa Mines Limited, during the last ten years. Open stoping in different forms has been used at the Isa Mine for many years. Prior to the period under review, stopes were small, pillars were not always recovered, and scrapers extracted the ore. By the end of the sixties, the use of load-haul-dump units was becoming more widespread. Wagner ST5's were the mucking units for the lead cut and fill stopes. Some of the open stopes in 5 orebody above 13 level had 100 kW slushers, but the more southerly stopes were the sites for the introduction of diesel front-end loaders for extraction. In the early seventies, new methods were used in the block of six stopes in 2 and 5 orebodies between 8 level and 13 level and a trial stoping project was undertaken in 7 orebody between 11 level and 13 level to determine possible stope dimensions for the extraction of the Racecourse orebodies below 13 level. By the mid-19701s, stoping was well underway in 5, 7 and 8 orebodies between 13 level and 15 level, using the 'triplet' system, incorporating cemented hydraulic fill to allow greater pillar recovery. As the eighties were entered, development of the Racecourse orebodies below 15 level commenced, as did preparations for 1 orebody in the upper levels of the north end of the mine. In both cases, the pillar recovery method has been changed to reduce the amount of cemented fill required for pillar recovery. GEOLOGY Most of the lead orebodies at Isa Mine lie chiefly to the north of the central shaft complex. They are bedded sulphide deposits in a host rock called Urquhart Shale, which dips at roughly 650 to the west. The main minerals are galena and sphalerite, with the silver mineral, freibergite, being contained in the galena. To the hangingwall of the sequence are the Black Star orebodies (1, 2 and 5) which are relatively wide, pyritic and with low to above average grade lead. The Racecourse orebodies (6 to 16) lie to the footwall, and have a large variation in width, low to high grade lead, and gradation in the lead to zinc ratio from north to south. Stope outlines are often determined by economic or engineering considerations rather than geological. The published extraction reserves are 56 million tonnes of primary ore, containing 150 grams of silver per tonne, 6.4% lead and 6.5% zinc. Traditionally, it has been regarded as lead ore, although the dominant revenue earner varies from time to time. In the Black Star orebodies, the ore and hangingwalls are more competent and open stoping has long been used. The major Racecourse orebodies which have been open stoped are 7 and 8 orebodies. This has been where the orebodies are wider (to the south) and where hangingwall conditions allow. This latter aspect has been greatly influenced by the presence of 'silica dolomite1. This tough, relatively homogeneous, non-bedded rock is, in fact, the host rock for the copper mineralisation at Mount Isa, and provides a competent hangingwall for some of the lead stopes. While the shale's bedding and jointing has a major influence on the ground conditions, there is a major fault system which causes local problems. The principal virgin stress direction is perpendicular to the bedding, but the local stress situation is complicated because of shielding by filled stopes in the hangingwall copper orebodies and because of the interaction between orebodies being extracted to the footwall. Most development on strike is mined with a 'shanty-back’, with the back being as close to normal to the bedding as possible. This is near parallel to most jointing and the principal stress direction. Figure 1 is a plan view of 14 level north, which provides a representative horizontal section through the orebodies. A typical cross section is shown in Figure 2. The narrow, parallel footwall orebodies can be seen to differ from the wider hangingwall orebodies.

Jan 1, 1981

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-

By D. A. Elgillani, M. C. Fuerstenau

In this paper, oxidation potentials measured in the presence of various concentrations of cyanide, ferro-cyanide, and ferricyanide and ethyl xanthate at various values of pH are related to flotation response. Eh-pH diagrams are presented to show that the formation of surface ferric ferrocyanide is probably responsible for depression when cyanide is added. The influence of cyanide on the depression of pyrite with xanthates as collector has been the subject of a number of investigations,'-6 and several theories on the mechanism of depression have evolved from these studies. Wark and Cox7 and Gaudin8 have suggested that the depressing effect is due to a competition of cyanide ion with xanthate ion for the surface. Cook and his colleagues9-11 have explained this phenomenon in terms of competition between hydrocyanic acid and xanthic acid. Sutherland 12 has shown that although both of these theories accurately describe the relation between pH value and cyanide addition at constant collector addition, they fail to describe the relation between pH value and the amount of collector required to cause flotation. Taggart 13 suggested that depression in these systems is due to the formation of a reaction product between ferric ion at the pyrite surface and ferrocyanide ion derived from solution. Majumdar4,6 has attempted to prove this hypothesis by measuring the contact angles of pyrite in the presence of 25 mg per liter ethyl xanthate and different concentrations of potassium ferrocyanide and ferricyanide. In all cases the contact angles were quite high up to pH 10. These results indicate that pyrite should not be depressed by either potassium ferrocyanide or ferricyanide. In view of these facts, Majumdar has assumed that the compound Fe(CN)2 forms at the surface. Gründer and Bornl4 have stated that depression may be due to the formation of the compound K2Fe(II)Fe(CN)6 at the pyrite-solution interface. This compound is thought to be an interaction product between the K2Fe(CN)6-2 ion from solution and the Fe++ ion at the pyrite surface and, accordingly, K4Fe(CN)6 should depress pyrite at least as effectively as KCN. This was proven experimentally, but there was no simple relation between the depression of pyrite and the concentration of either KCN or K4Fe(CN)6 in solution. In view of the many mechanisms that have been proposed for pyrite depression by cyanide, it is apparent that a clear understanding of the phenomena occurring in these systems is lacking. One reason for this may be the fact that the species responsible for pyrite flotation in the presence of xanthate is not the xan-thate ion but rather dixanthogen.15 Since the oxidation of xanthate to dixanthogen is dependent on the oxidation potential of the solution, it would seem that knowledge of these potentials would be a requisite to understanding the pyrite-xanthate-cyanide system. It is the object of this paper to measure both the oxidation potential and pH of the pyrite systems in the presence of various concentrations of cyanide, ferrocyanide, and ferricyanide and xanthate and to relate these values to flotation response. EXPERIMENTAL MATERIALS AND 'TECHNIQUES In the experiments discussed here, pure potassium ethyl xanthate was used as collector, and reagent grade potassium cyanide, potassium ferrocyanide, and potassium ferricyanide were used as depressants. Reagent grade HC1 and KOH were added for pH adjustment. Conductivity water, made by passing distilled water through an ion exchange column, was used in all experimental work. Two natural samples of pyrite were used in the investigation. Sample preparation for flotation included dry grinding with a mortar and pestle and sizing the product to 100 x 200 mesh. Prior to flotation, a 0.75-gm sample of pyrite was added to a solution containing a known amount of depressant at the desired pH value, and the system was conditioned for 4 min. Following this, a known amount of collector was added and the system was conditioned for another 4 min. The pH — termed flotation pH - was measured; the pulp was transferred to a Hallimond cell, and flo-

Jan 1, 1969

By J. L. Walter

Extra-low carbon iron sheet, when deformed and annealed, undergoes exaggerated or abnormal grain growth in the critically deformed regions of the sheet. This exaggerated pmth occurs, for low strains (3 to 6 pct), only in sheet which has a fine dispersion of precipitates in the subsurface region of the sheet and fewer and coarser precipitates in the sheet interior. These particles have been identified as manganese sulfides. Wing the anneal, grains near the surface are gvowth-inhibited by the fine particles but the grains in the interior are free to grow normally. With the additional driving force provided by the strain energy, the interior grains first grow into the small subsurface pains. Eventually, these growing grains grow completely through the sheet. Calculations of limiting grain sizes at various values of strain indicate that a volume fraction of precipitates in excess of 10-' would be required to eliminate exaggerated growth in material strained to 10 pct. OPEN-COIL annealing has made decarburization of sheet steel both efficient and economically practical. Use of such material for porcelain-enameling stock is one of many possible applications of low-carbon iron since carbon in steel is deleterious to porcelain-enameling properties.' However, the extra-low carbon iron presently available presents another problem, that of exaggerated grain growth in regions where the sheet has been deformed as by bending or stretching. In exaggerated grain growth a few grains start to absorb their neighbors and these may become very much larger than the average grains of the sheet. Other names for exaggerated grain growth are coarsening, critical grain growth, secondary recrystallization, abnormal grain growth, or discontinuous grain growth. While this grain growth does not affect the enameling qualities of the low-carbon iron sheet, their presence results in a marked reduction of tensile-yield strength in the region of the sheet containing the large grains. The loss of tensile yield strength may render the material unsuitable for many applications . This report describes the results of a study undertaken to determine the cause of the exaggerated grab growth in extra-1ow carbon iron and, if possi- ble, to prescribe practical procedures for its prevention. GENERAL THEORY The driving force for exaggerated grain growth is the grain boundary free energy. This driving force is proportional to (l/rl + l/r2) where rl and r2 are the mutually perpendicular radii of curvature of the boundary between the growing grain and the grain being consumed. Thus, the greater the difference in size between the growing grain and the matrix grains, the higher the driving force for grain growth. If, however, the matrix grains are free to grow simultaneously, the driving force for exaggerated growth will be diminished. Stability toward growth of the matrix grains may be caused by a) a strong single orientation texture (texture inhibition),' b) a dispersed second phase,3"5 c) the thickness effect,' or d) intergranular segregation.7"9 As exaggerated growth occurs when growth of the matrix grains has been slowed by the stabilizing processes mentioned above, there must be an additional factor acting to promote growth of a few of the grains to the point where they are enough larger than the matrix grains that boundary energy driving forces are sufficient to cause continued growth. For instance, at the annealing temperature, growth-inhibiting inclusions may slowly dissolve and coalesce. Eventually, a grain boundary becomes unlocked and migration occurs at the expense of neighboring grains. Or, an additional driving force may be supplied to some of the grains if the material is strained. Then, since some grains will be strained less than others, the difference in strain energy between adjacent grains may be sufficient to overcome boundary locking and allow growth of the grains with lower strain energies. In the present study, therefore, such factors as the presence or absence of dispersed phases, the nature of the exaggerated growth, and the effect of strain have been considered. EXPERIMENTAL PROCEDURE I) Material and Processing. Three types of low-carbon iron were used in this study; types A and B were commercial grades, each from a different supplier.* The precise details of the processing of

Jan 1, 1963

By S. K. Tarby, A. E. Rathke

A series of 0.21 pci carbon steel melts was processed under conditions which sinzulated industrial vacuum degassing practices. The results indicated that the efliciency of carbon deoxidation was not significantly increased by vacuunz degassing at chamber pressures below 100 torr. The two common phenomena of vacuu?rz carbon deoxidation, i.e.,an unaccountable carbon loss and nonequilibrium deoxidation, were observed in this study. Oxygen from adsorbed and chenzically combined water of certain refractory structures was probably responsible for the unaccourttable carbon drop. The nonequzlibrium deoxida-tion phenomenon was adequalely correlated by a bubble nucleation )mechanism. Although the major limiting factor in oxygen removal from these melts contained in alumina crucibles could not be eslablished with certainty, there was some evidence that melt-refractory interactions were not the most imp-portant limiting factor. CONSIDERABLE attention has been given to the use of carbon in conjunction with vacuum degassing* as a deoxidation technique. An advantage of utilizing the reaction: for deoxidation purposes is that the reaction product is gaseous and hence can be effectively removed from the melt. The pressure dependency of Eq. [I] is illustrated by the expression for the thermodynamic equilibrium constant, K: where pco is the partial pressure of carbon monoxide, and hc and ho are, respectively, the Henrian activities of carbon and oxygen in molten steel. The thermodynamic aspects of the C-0 reaction in molten Fe-C-0 alloys have been investigated extensively. Theoretical predictions based on Eq. [2] indicate that, at the chamber pressures reached in most vacuum degassing units, carbon is the most effective deoxidizer that can be obtained. ~ornak' has compared industrial values of carbon and oxygen contents with values calculated from theory, and has shown that on a commercial basis vacuum carbon deoxidation has not achieved the degree of success that is predicted from theoretical considerations of the C-0 reaction. The use of industrial units to determine the reason for this deviation is limited by economics and the difficulty in controlling critical process variables. Therefore laboratory-sized experiments in this area should yield valuable information. Investigations on vacuum carbon deoxidation have been made in experiments conducted under vacuum induction melting conditions where pressures in the low micron range, long treatment times, exposure to highly dynamic vacuum conditions, and relatively quiescent bath conditions have been maintained. Inve~ti~ators~~~ utilizing vacuum induction melting for the production of high-purity iron by carbon deoxidation have concluded that, under high vacuum conditions, melt-refractory interactions constantly supply oxygen to the melt. Thus, it has been suggested that refractory dissociation rather than the C-0 reaction establishes the lowest possible oxygen content of a melt. Thomas and Moreau4 and Bennett, Protheroe, and ward5 have studied carbon deoxidation of Fe-C alloys melted in magnesia crucibles under reduced pressures. The results of both studies differed considerably from those predicted by theory, and the limiting factor for lower oxygen contents was attributed to melt-refractory interactions. Because the refractory material used in both investigations was magnesia, no quantitative measure of crucible reaction could be made and the amount of carbon consumed during treatment was utilized as an indirect indication of the extent of crucible reaction. Studies concerned with the determination of the minimum oxygen content attainable in pure iron and Fe-C alloy material vacuum-induction-melted in various crucible materials have also been conducted."' The suitability of a crucible refractory for use under vacuum conditions appears to depend upon the major refractory constituent, the amount and type of impurity oxides, and the composition of the melt. Meadowcroft and Elliott9 have presented a theoretical review of the type and extent of various refractory reactions which should be considered in vacuum refining. ~eadowcroft'~ considered the vacuum degassing process to be dependent upon the "carbon boil" and has proposed that a part of the difference between the experimental and theoretical results for vacuum carbon deoxidation may be explained by the fact that the pco term in Eq. [2] is not the chamber pressure. Instead, the pressure necessary for carbon monoxide

Jan 1, 1970

By C. Wert, G. Mah

A relaxation peak thought to be due to the presence of C-C pairs in cobalt has been observed. It exists both above 420"C, where cobalt has the fcc structure, and below 420"C, where cobalt has the hcp structure at equilibrium. The effect is thought, however, to be caused by motion of C-C pairs in the fcc phase in both instances; enough retained fcc phase was deduced to be present at temperatures below 420°C to make the phenomenon possible. Measurements of the aniso-tropy of the effect in single crystals of various orientations of fcc phase showed the effect to have a maximum value in longitudinal strain for a [loo] crystal and a minimum value for a [Ill] crystal. This observation seems to rule out the possibility of (110) nn pairs being responsible for the effect. From measurements of the strength of the relaxation in the alloys, we reach the conclusion that both the binding energy of the pairs and the specific relaxation per pair are smaller than corresponding quantities for interstitial pairs in bcc metals. DETERMINATION of the details of atom placement of small atoms such as carbon, nitrogen, oxygen, and hydrogen in metals has been a difficult problem. In certain alloys such as martensite extensive departure from random placement of the interstitials can be deduced from X-ray diffraction off the atoms of the host metal, but such diffraction techniques are of small help for small departures from randomness. A technique which does offer promise in the latter instance is the anelasticity of these interstitial alloys. Most previous investigations using this property have utilized alloys in which the solvent is one of the bcc metals, alloys such as These studies have been interpreted to show that an interaction exists between interstitials which causes them to form clusters in more than random numbers; the binding energy of interstitials in such clusters has been deduced to be about 0.1 ev per atom (for small clusters of size two to four atoms). Similar investigations have been carried out on close-packed solvent metals, Ni-C by and Diamond and Ag-O by Papazian.8- In both of these svstems. no relaxation of the singly dissolved interstitial is expected, so an-elastic behavior of the interstitials must be caused by their association in some cluster or complex of non-cubic symmetry. Since relaxations in these alloys were observed to have a strength which varied about as the square of the interstitial concentration, the effect was deduced to be caused predominately by motion of i-i pairs in the crystal. A striking difference is observed in relaxation strength of interstitial alloys between the bcc and fcc systems. The specific effect per interstitial atom is much larger for the alloys in the bcc crystals than for those in fcc crystals. Comparing clusters of size two in the Nb-O system4 and the Ni-C system,7 one finds the magnitude of the anelastic effect per interstitial atom in the former to be some 100 times greater than that in the latter. Such a difference in relaxation strength might be caused by a difference in concentration of the pairs (this means a higher binding energy in the bcc crystals). It might also be caused by a large difference in shape factor of the elastic strain field about the pairs between the two cases (a much more noncubic shape factor would be required for the bcc crystals). This investigation was undertaken to examine the possibility of C-C pair formation in alloys of cobalt and carbon using anelastic effects. Since cobalt has both fcc and hep phases, it seemed to offer the chance that measurements over a range of frequency might permit comparison of properties of pairs in the two crystal types. Although this goal was not reached, several significant facts were deduced from the observations. 1) An anelastic phenomenon believed to be associated with the presence of C-C pairs in cobalt exists. It has many features in common with that observed in nickel. 2) The effect is thought to be caused by pair motion in the fcc phase. 3) Calculations of the relaxation strength A, which includes as a parameter the product of the pair concentration, C, and the square of the shape factor ', show that this parameter is much smaller in the CO-C alloy system than in the interstitial alloys in the bcc systems. 4) From this finding, we reach the conclusion that both the binding energy of C-C pairs in cobalt and the specific relaxation strength per pair are small compared to corresponding values for such pairs in the bcc systems. 5) The crystalline anisotropy of the effect permits the identification of reasonable geometrical models of close C-C pairs. I) EXPERIMENTAL PROCEDURE A) Method of Measurement. The anelastic measurements-—all of which were constant frequency measurements of internal friction—were designed to study the expected phenomenon in both the hcp and fcc structures in cobalt. Knowledge of similar measurements in Ni-C alloys led us to believe that the damping peak should occur below the transformation temperature for frequencies near 1 cps and above for frequencies near 100 kcps. This surmise was correct. The low-frequency measurements were made on wire specimens using a vacuum torsion pendulum; the damping peak was found at about 2'70°C at a frequency of 1 cps. Because of large superimposed damping of magnetic origin at this temperature, a longitudinal magnetic field of about 1500 oe was applied to the

Jan 1, 1969

By C. F. Allen, G. B. Walker

K. F. TROMP*—In dealing with the question of the most suitable kind of solid media for heavy density suspension processes Walker and Allen point out that the particle size of the solid media should not be taken too fine, as the viscosity increases with the area of the solid media and a low viscosity is essential lor high tonnage and accurate separation. A coarser particle size of the solid media will, in their opinion, of necessity give rise to a differential density in the bath (higher gravity at the bottom of the bath than at the top) but they advocate acceptance of the differential density rather than a higher viscosity. Though I fully agree with the choice the authors have made, I cannot subscribe to their view that only by accepting a differential density in the bath a coarse particle size of the solid media can be used. There certainly is another alternative: stronger agitation. Applying sufficiently strong vertical currents, a uniform gravity can be obtained quite well in a suspension of a coarse solid media. Of course, this is not a very attractive solution, for it means a degradation of the true gravity separation and a step backwards to hydraulic classification, which makes the washing dependent on size and shape of the particles. However, to a greater or lesser extent, this is what actually takes place in all the heavy density suspension processes relying on a uniform gravity in the bath. The so-called "stable" suspension processes make no exception. They all "stabilize" their suspensions by introducing or creating vertical currents, be it upwards or downwards or both, be it by hydraulic or by mechanical means. In fact, there is no such thing as a "stable" suspension in gravity separation, as the very reason for the use of suspensions in this field is the property that the solid media is able to settle and so facilitate the recovery. I have been enlarging on this point because the characteristics of the various processes can only be well understood and viewed from the same angle (from Bar-voys up to Chance) when the fact is recognized that mechanical or hydraulic agitation is a condition sine qua non for obtaining a uniform density from top to bottom in a suspension. Is a Cone-slraped Vessel Essenlial? Of the two alternatives for getting a low viscosity Walker and Allen have preferred correctly the sacrifice of uniform gravity in the bath instead of increasing further their vertical current arid agitation. The resulting differential density of the bath brings the problem of bow to prevent accumulation of intermediate gravity products in the bath, an accumulation which, if not prevented, would ultimately plug their cone. According to the authors an open-top cone combined with a downdraft current of the bath liquid would he the only suitable way to cope with such suspensions and they assume as a fact that "in any vessel other than a cone, such a differential density could not be tolerated." My experience is quilt: different. In my process, which has been in successful operation for more than a decade, differ-ential density of the suspension is applied ranging from values below 0.1 up to differentials above 0.5, according to the prevailing requirements of the individual plant. In this process, which is charac-terized by the use of horizontal currents in a suspension of differential density, the form of the vessel is of secondary importance and different types are in operation. It so happens that none of these are in the, form of a cone. The fact that 24 washboxes on my process have been installed and 12 others are under construction may constitute sufficient proof against the opinion that only a cone-shaped separator would be suited for differential density separation. Horizontal Currents in Differentia1 Den-sity Sepparation I myself have some doubts as to the suitability of a cone with downdraft for dealing with differential density (or, for that matter, any other washbox relying on vertical currents for removing the intermediate gravity products). It ap-pears to me that it is restricted to feed of small size only and even then with watch-fulness. If we take, for example, a piece of 2 in., the draft necessary to pull such a piece down to a zone wherein the den-sity of the suspension is, say, 0.03 higher, is quite considerable. For a suspension of, say, 1.6 sp gr the downdraft will have to be in the region of 3 in. per second. Unfortunately. most of the differential in density is in the part immediately below the reach of the top current which transports the floats. Consequently, we need the downdraft where we like it least: in the upper part of the cone. This entails the risk that light float particles are carried away with the downward current. This current of, say again, 3 in. per second would carry particles up to 1.3 sp gr and 3/8 in. size into the 1.6 gravity zone. This is prohibitive. It is also prohibitive because a downdraft of 3 in. per second in the upper part of the cone would require a tremendous circulation of medium. IIalf way up a 20 ft diam cone, a downdraft of 3 in. per second would correspond with 8500 gpm. With the downward current following the way of least resistance, the strength of the downdraft will not be exactly the same at different places of a cross area. If, as I anticipate, the center of the cone is favored, the strength of the downdraft will fall below the critical value near the

Jan 1, 1950

James W. Malcolmson died suddenly on Dec. 26, 1917, at Kansas City, Mo., where he had made his home for the past ten years. He was born at Dover, Kent, England, on Oct. 6, 1866. He graduated from the Royal School of Science, London, England, in 1889, and almost immediately after graduation came to Mexico, accepting a position with the Michoacan Railway and Mining Co., as mining and mechanical engineer. His work in the mining profession was carried on principally in Msxiac and the United States. • In 1888, he married Katherine Haden Krause, of Woolwich, Kent, England, and leaves, besides his wife, five sons and one daughter. During Mr. Malcolmson's long and successful career as a mining engineer, he was connected with the following companies: from 1889 to 1893, with the Michoacan Railway and Mining Co., as mining and mechanical engineer; from 1893 to 1898, in various capacities with the Kansas City Smelting & Refining Co.; after the consolidation of the Kansas City Smelting & Refining Co. with the American Smelting & Refining Co., he remained as manager of the mining department in Mexico of the American Smelting & Refining Co. until 1902. In 1902, he located in El Paso, and took up the practice of his profession as a consulting engineer. While there, he was consulting engineer for the famous and rich Pedrazzini mines at Chispas, in the State of Sonora. He was instrumental in organizing the La Republics mine in Chihuahua, and for a time acted as consulting engineer for the property. He remained in El Paso until 1907 and then moved to Kansas City and became associated with the United States & Mexican Trust Co., as consulting engineer. In 1909, he became connected with The Lucky Tiger Combination Gold Mining Co., as its consulting engineer, and continued in this connection and in the general practice of his profession as consulting engineer until his death.. His general policy in connection with the Lucky Tiger company was always a progressive one and the success of the enterprise can be largely attributed to him and his good judgment. Mr. Malcolmson contributed several articles to the Institute at different times, one of them being on the ore deposits of the Sierra Mojada Mining District, in 1901. Much of his work was in Mexico, and during his long residence in that country he acquired a very thorough knowledge of the Mexican people and their customs. During the revolution, from 1910 to 1916, this knowledge was of great value in connection with his work for the Lucky Tiger company, and often assisted greatly in keeping the property going. Mr. Malcolmson was one of the very widely known men in his profession; he was everywhere held in the very highest regard, and his position among men in the mining profession was an enviable and honorable one. At the time of his death, besides being consulting engineer for the Lucky Tiger company, he was interested in mines in the Miami zinc fields and was acting as consulting engineer for two of the operating properties there. He invested to quite an extent in real estate when he moved to Kansas City in 1907 and his investments in this line proved successful.

Jan 1, 1920