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By Y. Wang, M. M. Singh, H. L. Hartman

Knowledge of the state of stress at the bottom of a drillhole is of practical importance in rock drilling, since the induced stresses must exceed the strength of the rock in order to cause fracture. This note reports on a numerical method to determine the stress distribution at the bottom of a borehole induced by a static bit load and overburden and fluid pressures. The procedure adopted is similar to that for the plane-strain, discrete model employed by Harper and Ang.1,2 The rock medium is considered to be homogeneous, isotropic, and elastic-perfectly-plastic. METHOD OF ANALYSIS AND PROGRAMMING The discrete model adopted consists of two types of points: mass points and stress points. The configuration and numbering notation are depicted in

Jan 1, 1967

By J. G. Bouwkamp

This paper presents three general approaches towards the solution of the stress distribution and the behavior of tubular connections as used in offshore well drilling structures. First, the possibilities of using plastic models and photoelasticity techniques in evaluating the stress distribution in gusset plate connections are analyzed. The results of photoelastic studies on the stress distribution in the in-plane gusset plate of two-dimensional joints are presented. The influence of the configuration of the gusset plate (with and without cut-outs) is discussed. Second, the paper deals with recent developments and applications of computer programs to analyze connections with directly inter-welded tubes and with gusset plates. The possibilities and limitations of these programs are discussed. Stress patterns analyzed with these programs are presented for different joint configurations. Finally, the basic test procedures and results of a test on a tubular joint under static and alternating loads are discussed. INTRODUCTION The effective design of tubular connections as encountered in offshore well drilling towers or floating platforms has been complicated basically by the radial flexibility of the tube walls. This flexibility is a source of severe stress concentrations which can initiate an early failure of these joints. In an attempt to reduce the influence of the wall flexibility of the column tube, certain joints are presently designed by inter-welding the incoming branch members. In those designs, the force acting normal to the chord tube can be reduced considerably. A second group of joints incorporate gusset plates or stiffening rings to stiffen the column wall and to distribute the incoming branch member forces over a larger part of this wall. A third approach to improve the stress distribution in a tubular joint is to increase the wall thickness of the column member. This can be achieved by simply applying a thicker wall section in the vicinity of the joint. A fourth possibility to restrain the radial flexibility of the tube wall is to fill the column member with concrete. Also, a single, cast steel seat welded to the column tube can be used to improve the stress distribution in this wall. Although all these designs improve, in general, the state of stress in the column wall, the altered stiffness often causes the development of critically stressed areas in the web members. At the same time the actual design in most instances is decisively influenced by the site which governs the depth and controls the forces produced by waves, earthquakes and ice flow. Also, the towing, erection and foundation requirements of offshore structures can affect the actual design selection. Because of the complexity of the structural configuration of tubular joints, the stress analysis of these connections has necessarily been based on simplified and often crude assumptions. For the earlier and smaller type of connections with about 4-ft diameter column sections, the primary problem was to evaluate the relative stiffness of the column wall section and the load transfer between joint members. Due to the recent developments of offshore drilling structures with increasingly larger connections (e.g., column diameter. 32 ft; web members, 8.5 ft) this problem has become even more critical. One design philosophy for such large joints follows a member-to-member connection with radially heavy reinforced column sections. This radial stiffness can be attained by closely spaced and intensively stiffened horizontal diaphrams together with vertical stiffeners. A second solution incorporates a concrete-filled section between the outer and inner walls of the column tube. Another philosophy considers large gusset-plated joints. The problem in these joints is to develop an effective load transfer between the branch tubes and the gusset plate and to minimize the stress concentrations in the member walls as effectively as possible. Several concepts are followed to achieve this gradual transfer between web-member walls and gusset plates. Because the number of joints in these huge platforms is limited compared to the over-all size, a proper design of these joints is even more important than was the case for the many joints in the smaller, but multi-legged towers. A failure of one of those ultra-large joints could well cause the complete collapse of such a structure. Under these circumstances an accurate analysis of the large joints is of the greatest importance, together with information regarding the expected behavior of such joints under critical alternating load conditions. Recent applications of photoelastic model techniques have proved to be quite effective in evaluating the elastic behavior of such joints. Although a complete study of such connections is quite well possible with present-day photoelastic techniques, it might often be feasible and necessary to limit the objectives and to restrict these investigations to the study of a specific aspect of the joint. Another very promising avenue of approach to solve the complex stress pattern in these connections seems to be the recent development of digital computer programs. In this category, cylindrical shell programs and finite element methods for more complex configurations have

Jan 1, 1967

By J. A. Lund, A. M. Lawson

THE structures of quenched eutectoid and hypereu-tectoid Fe-Cu alloys have been examined by X-ray diffraction and by optical and electron microscopy. The relevant portion of the Fe-Cu phase diagram is given in Fig. 1. Several values have been reported for the solubility of copper in a Fe at the eutectoid temperature, including 1.4 wt pct by orton' and 2.13 wt pct by Wreidt and Darken.2 Alloys containing 4.8 and 7.5 wt pct Cu have been prepared from two batches of Ferrovac E iron (0.005C and 0.013C) and electrolytic tough pitch copper (99.90 Cu). Specimens of dimensions 0.8 by 0.8 by 0.1 in. were cut from hot-rolled material, austenitized, and quenched into brine at 25°C. Similar specimens were also cooled in the furnace, after a short soaking treatment at 1100°C, at a rate estimated to be 10°C per min in the temperature range of 900" to 500°C. X-ray diffractometry was performed on quenched and on furnace-cooled bulk specimens using iron radiation. Only a bcc phase could be detected in all samples. Lattice parameters were calculated from measurements on four lines, made up of two resolved high-angle doublets. Comparisons were made against a silicon standard. Results are shown in Table I. Based on X-ray diffraction studies of a series of alloys of lower copper concentrations, orton' estimated that the tattice constant of a Fe at 25°C increases 0.0014A per wt pct Cu in solution. Extrapolating Norton's data, it may be concluded that all copper was retained in solution in the brine-quenched 4.8 pct Cu alloy, and that approximately 5 pct Cu was also held in solution on quenching the 7.5 pct Cu alloy. Typical microstructures of brine-quenched specimens, as observed by optical microscopy, are shown in Figs. 2 and 3. Precipitation of the E phase (copper-rich) occurred along the y grain boundaries on quenching the 7.5 pct Cu alloy, rendering them readily detectable in the microstructure, Fig. 3. The original boundaries in the 4.8 pct Cu specimens were gener- ally not discernible, however. This indicates that the z phase which was seen in the higher-copper alloy was probably of proeutectoid origin. Thin foils for transmission electron microscopy were obtained from bulk specimens by spark machining to 0.006 in. thickness, followed by electrolytic polishing. Typical transmission electron micrographs

Jan 1, 1967

By L. A. Neumeier

A refinement of the tungsten-cobalt phase diagram is presented for compositions to 85 at. pct cobalt and for temperatures to the solidus. Preparation of alloys by powder metallurgy methods is described, and the results of studies made by a combination of techniques involving microscopy, X-ray diffraction, thermal analysis, and dilatometry are discussed. The existence of u-W6Co7 is confirmed (rhombohedral D85 structure). The W6Co7 phase forms periectically at 1,685'115° C by reaction of liquid with primary W; the peritectic melt is at 71 at. pct cobalt. The homogeneity range of u-W6Co7 extends to both sides of the ideal stoichiometric ratio, through a compositional range of about 5 at. pct. The compositional limits for u-W6Co7 vary slightly below 1,471°±5° C, the temperature of the eutectic reaction forming u-W6Co7 plus a. The eutectic composition is at 79 at, pct cobalt. The existence of WCo3 is confirmed (hexagonal D019 structure). WCo3 forms peritectoidally at 1,093°±5° C by reaction between a and u-W6Co7 and exists over a narrow homogeneity range of 0.5 to 0.6 at. pct. The solid solubility of cobalt in tungsten is low (maximum 0,9 at, pct cobalt) and results in contraction of the tungsten lattice. Tungsten is extensively soluble in a-Co at higher temperatures; the a-Co lattice is expanded by the presence of tungsten in solid solution. There was no indication of the formation of a o-phase nor of any intermediate phases other than WeCo7 and WCo3. The WeCo7 and WCo3 phases are compared with similar phases in other systems.

Jan 1, 1967

By P. G. Shewmon, H. E. Collins

A study has been made to determine the sites at which sulfur adsorption occurs on copper surfaces. measurements were made of the relative torques, Ys, at the intersection of twin boundaries with surfaces near the three low-index orientations, i.e., (100), @lo), and 011), over a range of H2S/H2 ratios. HZS concerztvations j'ro~n 3 to 1500pp)n between 830" and 1050°C were used. It is concluded that sulfur adsorption occurved preferentially though not exclusively at edge sites near the (100) and (110) surfaces in the HzS range — 700 Ppm giving rise to negative torques near these orientations. Beyond this HzS range, adsorption occurred at all sites. Near the (111) surface, 7/y little with HzS concentration up to approxiwzately 75pptn. Above this range, the results indicate adsorption is occurring OH both terrace and edge sites. SCIENTIFIC interest in surfaces and their interactions with a gaseous environment dates back to the beginning of the 19th century. The scientific luminaries of that period—Faraday, Maxwell, Rayleigh, Dewar, and Gibbs—were already concerned about such processes. However, it has only been within the past several decades that adsorption on metal surfaces has been actively studied. This increased interest in adsorption has been brought about by the advent of new and improved experimental techniques and apparatus, e.g., ultrahigh vacuum, and field-emission and ion microscopes. However, most of the work done using these techniques has been carried out at low temperatures. When adsorption studies have been made at either low or high temperatures, they usually gave no indication of the particular surface orientations or type of sites on which adsorption was occurring. In the last few years, there have been a series of studies in which the surface tension, y,, and/or its derivative with respect to orientation, 7, have been studied as a function of orientation and atmosphere.'-7 Nearly all of the work on the relative torque,* ~/y, silver annealed in hydrogen and air.6 Recently Winterbottom and Gjostein" have used a modified and more accurate Mykurian method to determine the y plot of gold in hydrogen The only work in which T/~, has been measured over a range of chemical potentials for a given solute, p2, is that of Robertson and shewmon7 on the Cu-0 system. They measured T/Y, vs Po, (10"" to 10- l3 atm) at 1000°C in various mixtures of Hz0 and HZ. From this work they estimated the value of p2 at which one half of the surface sites are occupied with oxygen, pg, as being in the range 10- l6 to 10- l5 atm of oxygen. They also found that increasing Pa increased the magnitude of ~/y, near the (111) and (100) orientations. This indicates that oxygen is not adsorbed preferentially at step edges, but uniformly over all surface sites. In addition, they did one experiment on sulfur adsorption on copper surfaces, which indicated that sulfur adsorption decreases ~/y, near the (100) orientation, while not affecting ~/y, near the (111). This could be interpreted as indicating that sulfur adsorbs preferentially at step edges near the (100). In this paper the primary objective of the work has been to carry out a study of sulfur adsorption on copper surfaces over a range of temperatures and p,. In conjunction with this work, thermal grooving at grain boundaries has been examined as a method of determining the effect of sulfur adsorption on y,. METHODS Ideally, one would like to have information on the quantity of solute adsorbed on a surface and the types of sites at which it is absorbed as a function of p2. The total quantity adsorbed or the surface excess is given by the thermodynamic equation Thus data on the variation of y, with pz indicates the value of p2 at which adsorption becomes appreciable and the quantity adsorbed. The type of adsorption site is more difficult to deduce but information on this can be obtained from the variation of rz with 8, the angular deviation of the surface orientation. This is obtained from the thermodynamic equationlg Data on t and ys as functions of p2 have been obtained by the following methods. 1) Twin Boundary Grooving—By determining the effect of adsorption on the torque, 7, where T is the variation of surface energy, y,, with orientation, it is possible to obtain some indication as to the preferred sites of adsorption. Experimentally, the torque value measured is the relative torque, 7/ys The twin boundary grooving technique suggested by Mykura'' was used in this study to determine near the three low-index orientations— (loo), (110), and (111). Mykura's equation relates 7 /yS to measurements of the di-

Jan 1, 1967

By R. S. Shepard

The closing remarks of a paper which I presented at the annual AIME meeting at Dallas, Texas during February of 1963; contained a forecast of increased activity in trackless underground ore mining which finalized that presentation. At that time, HAD I been peering through my brightest rose colored glasses, I could not have foreseen the unprecedented rapidity of acceleration of underground ore mining methods which has since ensued. From Death Valley, California diagonally to St. Johns, New Foundland; from Australia to Africa to Sweden to France and Germany; from South America to Southern Mexico to Northern Saskatchewan and Northern Manitoba the expansion of trackless underground ore mining methods has probably progressed at a faster rate than any other revolutionary' change in the history of underground ore mining.

Jan 1, 1967

By Robert M. Becker

The evaluation of existing rock stresses from measurements of the change in diameter of a borehole that is stress relieved by overcoring has become a common practice, The stress evaluation has been generally based ,on isotropic relations whereas rock in varying degrees is anisotropic. A plane elasticity solution for a circular hole along one axis of an orthotropic medium is adapted for evaluation of in situ stress from borehole deformation measurements. A consistent triaxial testing approach for determining elastic properties of the overcore is also outlined. Comparison of isotropic with anisotropic interpretations of the state of stress show that large errors in evaluation may occur if the anisotropic character of the rock is neglected.

Jan 1, 1967

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967

By Charles L. Mantell, George Ferment

This investigation determined the jeasibility of current-potential curves as an analytical tool for monitoving manganese electroicinning solutions for metallic impurities. Nine metallic impurities were studied: trickel, cobalt, silver, copper, zinc, molybdenum, catlmiun magnesium, and sodium. The individual effect of each metallic irzplrl,iLy on the standard point-izatiorr was determined for a range of &apos;concentration. Not all of Ihe impurities affected the polarization curve; correlation between transition current and cotrcetztration of impurity. Molybdenum had an uncorrelated effect on the polarization curie. The effects of binary mixtures of impurities were studied to see if the transition current of the mixture could be predicted. Interactions occurred between impurities which prei&apos;etzted the pvecliction the transition current of tile rrlisLitr.e by additive laws. The polarization curve was shown to be sensitive to metallic impurities which affect the current efficiency of a manganese cell. THE application of current-potential curves in manganese electrowinning is not new but played an important part in the conversion of an inoperative large-scale pilot plant into a continuous comnercial operation.1"" The effects of trace metallic impurities in manganese electrowinning solutions on cathode current-potential curves,5-19 specifically nine impurities (nickel, cobalt, silver, copper, zinc, molybdenum, cadmium, magnesium, and sodium) were studied for a range of concentrations. Cadmium, magnesium, and sodium had no effect. Nickel, cobalt, silver, copper, and zinc yielded a correlation between transition current and concentration of impurity: molybdenum had an uncorrelated effect. Binary mixtures of impurities were studied to de-termine if the transition current could be predicted from the values for the individual constituents. Interactions between impurities prevented the prediction of the transition current of the mixtures by an additive law. The polarization curve was shown to be sensitive to metallic impurities which affected the rurrent efficiency of a manganese cell. The electrowinning of manganese relies upon maintaining a high-purity electrolyte. Purification schemes were developed to remove all of the heavy metals, the magnesium and calcium. Concentration limits have been established for single impurities. With high-purity electrolytes, favorable cell efficiencies are consistently obtained; but with impure solutions there is a reduction in efficiency. With the rapid rise to commercial prominence of electrochemical processes, there has been a lag in developing rapid methods for determining whether an electrolyte is sufficiently pure for efficient electrolysis. The most sensitive test for impurities is the behavior of the electrochemical cell. Impure electrolytes will cause a serious reduction in cell efficiency, and in many cases metal deposition will be prevented or reversed. The effects of impurities are not usually evident until after long periods of electrolysis, resulting in a disruption of the process. A method which could predict the behavior of an electrolyte in terms of cell efficiency prior to reaching the commercial cell is needed. Van Arsdale and Maier," Allmand and Campbell,a1&apos;22 and others attempted to develop an electrochemical process for manganese,"3"29 but all met with some degree of difficulty. Jacobs et a studied the effects of metallic impurities in manganese electrowinning. Plant methods were based on a 2-hr plating in a small electrolytic cell. The final method was based on a 24-hr plating run, performed in a relatively large test cell. Here, current efficiencies were calculated with and without impurities in the electrolyte, and the critical concentration was established as the maximum amount of impurity that the electrolyte could tolerate before there was a serious loss in efficiency. The amount of impurity that could be tolerated decreased as the plating time increased, indicating deposition of the impurity. This test duplicated the conditions of commercial practire, and was sensitive to impurities. Small amounts of impurities significantly affect the hydrogen overvoltage at a metal surface, increasing or decreasing it depending upon the nature of the impurity. ockris established the limit for the onset of poisoning at 10-l moles per liter. The effects of impurities were studied by potential-time curves at a constant current density. The technique did not lend itself to rapid analysis in that several hours were needed to establish stable potential-time curves. Serfass and coworkers3&apos; developed calorimetric and spectrophotometric techniques for analyzing for trace impurities. Our method4&apos;" is based on current-cathode potential curves produced by continuously changing the cell voltage at a programmed rate. Starting with a clean stainless-steel cathode, the cell voltage was initially adjusted to yield zero current: the program was then started and the current was plotted as a function of the cathode potential. Fig. 1 is a typical current-potential curve. In initial region A the hydrogen-evolution reaction predominates and the polarization curve

Jan 1, 1967

By D. T. Peterson, F. A. Schmidt, J. D. Verhoeven

The velocity of mig-ration of these solutes in thorium metal due to a high amperage dc current was measured at several temperatures. All three solutes migrated in the same direction as the electron flow. Diffusion coefficients were combined with the migration velocities to predict the steady-state concentration profile. Electrotransport was shown to be an effective method of removing carbon, oxygen, and nitrogen from thorium and resistance ratios several times larger than for crystal bar thorium were achieved. However, the maxirnum attained purification was well below the predicted values, apparently due to some form of contamination. THE migration of solutes in metals when a high current density dc current is passed has been known for many years. This phenomenon has been the subject of a number of reviews published in recent years.l~* Many of the earlier investigators of electromigration of interstitial solutes interpreted the direction and velocity of migration on the basis of a charge on the solute particle. This interpretation is unclear because, in a given experiment, one cannot separate the contributions to the force moving the solute which arise from the charge on the solute in an electric field gradient and the momentum transfer from the scattering of the electrons or holes. There have been only a few quantitative measurements of interstitial migration velocities and some of these have been characterized by poor accuracy or by errors in the analysis of the experiment. The electrotransport mobilities of carbon, nitrogen, and oxygen in thorium were determined by observing the rate of movement of a discontinuity in the concentration profile. This method was used by Carlson el a~.~ to determine the mobilities of interstitial solutes in yttrium and its advantages are discussed in that paper. The specimen is essentially a pair of semi-infinite, bar-type diffusion couples. The electro-transport velocity was measured by observing the displacement of the mean concentration point in a measured length of time. The diffusion coefficients were calculated by the Grube method from the concentration profile. The transport mobilities and diffusion coefficients can be used to predict the concentration profile in an electrotransport experiment of a given time, current density, and specimen length. At long times a steady state will be reached such that the natural logarithm of the concentration of each solute varies linearly along the bar with a slope which is equal to the velocity of the migrating solute divided by its diffusion coefficient. The estimation of the purification potential of electrotransport is discussed by ~erhoeven.&apos; A comparison of the concentration profile and the purification which should be expected from known solute velocities and diffusion coefficients with that which is obtained in an experiment can be very useful in indicating whether the maximum possible purification has been achieved. EXPERIMENTAL METHOD The apparatus used in this study consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a high-vacuum system capable of obtaining pressure of 2 x lo-? Torr. The chamber was made of stainless steel and was 4 in. in diam and 6 in. long. The seal between the electrodes and the chamber was made with "0" rings and compression bushings. The thorium specimens were threaded and screwed into tantalum "U"-shaped adapters attached to the ends of the electrodes. This arrangement is shown in Fig. 1

Jan 1, 1967

By J. W. Town

The Bureau of Mines made continuous-circuit beneficiation studies to determine the optimum conditions for concentrating phosphate minerals from the intermediate-and marginal-grade ores of the Phosphoria Formation in southeast Idaho. Intermediate-grade ore was represented by a sample from Georgetown Canyon and marginal-grade ore from the Gay mine near Fort Hall. Two flow-sheets were developed: The first involved roasting, attrition scrubbing, sizing to remove a concentrate, grinding of the oversize, des liming, and flotation; in the other flowsheet roasting was eliminated. Controlled attrition scrubbing was used to remove clay and silt-size quartz particles imbedded in the phosphate pellets without breaking the pellets. The minus 35-plus 200-mesh fraction was removed by sizing as a finished acid-grade concentrate. The plus 35-mesh material was ground in a rodmill to minus 35 mesh and recycled to the attrition scrubber. The minus 200-mesh fraction was des limed at about 800 mesh to remove clay slimes and floated with 3 to 4 pounds of emulsion per ton of feed. The aqueous fatty-acid oil emulsion consisted by weight of 3 parts No.2 diesel oil, 3 parts crude tall oil, and 0.5 part water-soluble petroleum sulfonate.

Jan 1, 1967

By M. R. Tek, F. F. Craig, J. O. Wilkes, C. S. Goddin

The waterflood performance of a water-wet, stratified system with crossflow is computed by a finite difference procedure. The effects of five dimensionless parameters on tile oil displacement efficiency, water saturation con-tour.7 and crossflow rates are evaluated in the absence of gravity forces. Crossflow due to viscous and capillary forces is shown to exert a significant effect on oil recovery in a field-scale model of a two-layered. water-wet sandstone reservoir. The crossflow is at a maximum in the vicinity of the front advancing in the more permeable layer. Under favorable mobility ratio conditions, the comparted oil recovery with crossflow always is interrnerliate between that predicted for a uniform reservoir and that for a layered reservoir with no crossflow. INTRODUCTION The important erects of reservoir heterogeneity on waterflood performance are commanding increased attention in the technical literature. Much of this attention is centered on two categories of layered reservoirs: those in which layers are non-communicating and those in which crossflow of fluids occurs between the layers. In the first category, the reservoir is assumed to consist of discrete layers, each uniform within itself and differing from the others only in such properties as thickness, porosity and absolute permeability. The performance within each layer is calculated by one-dimensional flow theory, and the performance of the total reservoir is obtained by summing individual layer performances. Capillary and gravity effects usually are not considered. Representative publications dealing with thi5 type of reservoir are those of Stiles,&apos; Dykstra and Parsons,&apos; Hiatt,3 Warren and Cosgrove&apos; and Higgins and Leighton." Prediction of performance for reservoirs in the second category is considerably more difficult since viscous, capillary and gravitational forces all play important roles in causing crossflow between layers. A number of authors have investigated the simpler problem of two-dimensional displacement flow in a stratified system with a mobility ratio of unity and negligible capillary and gravity effects.&apos;; Others have considered two-dimensional, non-steady-state flow of a single, slightly compressible fluid in a stratified reservoir. A limited number of laboratory oil displacement tests in layered models with crossflow have been reported. Miscible floods (with resultant zero capillary forces) in layered five-spot models were conducted by Dyes and Braun," who studied the effect of mobility ratio with zero gravity forces, and by Craig et al. 12 who studied the effect of gravity forces at constant mobility ratio. Waterfloods in layered five-spot models (with cross-tlow due to capillary, viscous and gravity forces) were conducted by Gaucher and Lindley,"&apos; who showed the effect of gravity forces in causing underrunning of the injected water and by Carpenter, Bail and Bobek, 14 who demonstrated the reliability of Rapoport&apos;s" dimension-less parameters for scaling layered systems. Waterfloods in rectangular layered models were conducted by Richardson and Perkins."&apos; who investigated the effect of velocity at constant mobility ratio and with zero gravity forces, and by Hutchinson," who studied the effects of varying mobility, layer permeability and layer thickness ratios. The differential equations which rigorously describe waterflooding in a heterogenous porous medium are non-linear and do not facilitate analytical solution. By using finite difference approximations it is possible to obtain a solution to any desired degree of accuracy. Such a solution, using an alternating direction implicit procedure (ADJP), is described by Douglas, Peaceman and Rachford.18 In the present study, a computer program using ADJP explores systematically the effects of important parameters on waterflood performance of a two-dimensional, two-layered, field-scale model of a water-wet sandstone system. Particular attention is given to evaluation of the water saturation contours and crossflow rates at the interface between layers to gain improved understanding of the crossflow mechanism. PROCEDURE BASIC: FLOW EQUATIONS The basic flow equations for two-dimensional, two-phase, immiscible, incon~pressible flow in a porous medium are:

Jan 1, 1967

By R. E. Lindstrom

The mineral bastnasite is utilized to describe alternate processes for the extraction and separation of the rare-earth elements by solvent extraction. The rare earths can be acid-leached directly or fused with NaOH before acid leaching. Cerium, the major constituent, can be recovered by fractional precipitation, fractional leaching, or solvent extraction with tri-nbutyl phosphate. The latter process is capable of producing 99.5-percent pure CeO2 at 98+ percent recovery. Lanthanum is subsequently recovered by fractional precipitation or solvent extraction with a nitrogen-based extractant. A 20-stage mixer-settler operation with a primary amine extractant results in a 95-percent pure La203 fraction at 96 percent recovery. Europium is amenable to extraction from most of the remaining rare earths with an organophosphate extractant. Selective stripping of the europium, followed by reductive precipitation, produces high-purity Eu203. Another possibility for europium purification involves the differential extraction of europium with an amine followed by a sub- sequent reducing strip. Separation of the remaining elements is more difficult but can be accomplished with amine or quaternary ammonium extracts. Typical separation factors achieved are 3. 8 for praseodymium-neodymium and 10. 5 for neodymium-samarium.

Jan 1, 1967

By James A. West

The South Asian countries of India, Pakistan, Afghanistan, Ceylon, Nepal, Bhutan, and Sikkim arc to varying-degrees just beginning to achieve significant economic and industrial development. These countries are richly endowed with certain mineral resources, and development of these resources is being accelerated. In 1965, the mineral industry remained a relatively small sector of the region&apos;s economy, accounting for only about 1 percent of its estimated gross national product of $62,528 million. Nevertheless, the estimated $630 million total value of minerals produced in South Asia during 1965 represented an increase of nearly 15 percent t over that of 1964. India continued as the dominant mineral producer of the region, accounting for 85 percent of the total value of all minerals produced ill 1965. India increased its output of iron ore, manganese, mica, coal, and petroleum. Pakistan accounted for 13 percent of the value of the region&apos;s output and recorded increased output of iron ore, chromite, coal, natural gas, and most other minerals. The small mineral industry of Ceylon attained remarkable growth in the production of ilmenite, graphite, and gem stones. The mineral industry of Afghanistan remained relatively insignificant, although development of large known resources of natural gas was continued, Nepal, Bhutan, and Sikkim produced no commercially significant quantities of minerals in 1965.

Jan 1, 1967

By Ronald K. Linde

Metastable Ag-Cu solid solutions at two compositions beyond the maximum limits of solubility obtainable by quenching from the solid state were obtained by rapid quenching from the liquid state. The process of transformation of the metastable solid solutions into the equilibrium phases was studied by means of X-ray diffraction intensity measurements and electrical-resistance measurements; metallographic examination was also performed. Results are compared with those for an alloy quenched from the solid state at a composition which exists as a solid solution at elevated temperatures. Activation energies for the trans-formation were computed to be 33,600 * 2500 and 33,100 * 2000 cal per g mole for the 60.1 and 75.0 at. pct Ag;Cu compositions, respectively THE kinetics of precipitation in supersaturated solid solutions obtained by quenching from high temperature has been thoroughly studied in many alloys, and detailed investigations of the early stages of nucleation and subsequent growth of the equilibrium phases have been carried out. All of these studies have been made on alloys quenched from the solid state, however, and it is the purpose of this paper to present some of the results on the kinetics of transformation of metastable solid solutions in Ag-Cu binary alloys whose compositions lie outside of the solid-state limits of solubility. Limits of solubility in the solid state can be increased by rapid quenching from the liquid state. This was first demonstrated by Falkenhagen and Hofmann, who obtained appreciable increases in solubility limits of the elements of the first transition series in aluminum by rapid cooling of liquid alloys through contact with a copper mold maintained at liquid nitrogen temperature.&apos; The same basic idea of cooling a liquid alloy by conduction onto a substrate rather than by convection of a gas or liquid (conventional quenching) has been recently revived and extended to very high rates of cooling by Duwez and his collaborators. The new technique was first applied to Ag-Cu alloys because the existence of a eutectic in this system is not predicted by the Hume-Rothery rules of alloy phase formation. Rapid quenching from the liquid state resulted in metastable solid solutions at all concentrations. The kinetics of decomposition of these metastable solid solutions containing 60.1 at. pct Ag;Cu (eutectic composition) and 75.0 at. pct Ag;Cu is the subject of the present paper. EXPERIMENTAL TECHNIQUES Alloys were made in 10- to 20-g heats using silver of purity 99.99 pet and copper of purity >99.999 pct. Components were weighed accurately to 0.1 mg and melted by induction heating in an alumina crucible under an atmosphere of hydrogen. Weight losses amounted to less than 0.02 ~ct in all cases. Rapid cooling from the liquid state was achieved in an apparatus of the type described by Pietrokowsky. 3 In this technique a freely falling drop of molten alloy is caught between a stationary anvil and a fast moving piston, both anvil and piston being lined with copper. The resulting foils were approximately circular (about 2 cm in diam) and from about 50 to 150 u in thickness, depending on the pressure driving the piston. Metallographic samples were prepared for polishing by edge-mounting foils in Quickmount. The mostef-fective etching procedure was found to be: 10 parts NH4OH (concentrated), 1 part H2O2 (30 pct), 5 parts H2O, swab for 5 to 10 sec. The transformation of the metastable alloys to equilibrium was followed by X-ray diffraction and electrical-resistivity measurements. The peak intensity and the integrated intensity of suitable Bragg reflections of the metastable and stable solid solutions were studied with a Norelco dif-fractometer, using nickel-filtered copper KO radiation. The peaks were step-scanned at intervals of 0.05 deg. Using either a Kelvin bridge or a null circuit with a Leeds and Northrup K-2 potentiometer, the changes in electrical resistance due to phase transformation were measured for specimens cut into strips about 20 mm long and 4 mm wide. All resistivity measurements were carried out at liquid-nitrogen temperature. The isothermal heat treatment was accomplished by sealing the samples in argon-filled aluminum containers with stainless-steel O-rings. Containers were then suspended in wax baths with temperatures in the

Jan 1, 1967

By Leo A. Schrider

A prediction for oil recovery from a pilot waterflood in the Kane oil- field, located in Elk, Forest, and McKean Counties, Pa., was made and compared to actual field performance. Water-injection and production histories, well logs, other field data, and results from laboratory tests of core material were used in this analysis. Performance of the pilot waterflood, initiated in January 1963, was predicted using a modified Craig, Geffen, and Morse calculation technique. Maximum recovery from this low permeable, preferentially oil-wet formation was predicted to be about 22,500 barrels of oil after 300,000 barrels of water had been injected into the pilot waterflood area. After additional field data were collected it became necessary to reevaluate the pilot waterflood area. The gas saturation prior to the waterflood was estimated to have been 20 percent, based on an assumption regarding the required volume of water injected to initiate oil production. In view of the actual field performance, a gas saturation of 13 percent is indicated. When this gas saturation and the method originally proposed by Craig and others are used) the predicted results are more representative. In December 1965, field performance was further analyzed using a hyperbolic-decline curve as presented by Arps. Based upon this evaluation method, the pilot water flood in the Kane sand should produce 37,000 to 42,000 barrels of oil with the injection of 300,000 barrels of water into the pattern. By continuing this secondary-recovery project to a reasonable economic limit, ultimate oil recovery may be as much as 50,000 to 55,000 barrels, or 129 to 142 barrels per acre-foot from 36.5 acres.

Jan 1, 1967

Jan 1, 1967

By Mark J. Klein

The precipitation of nitrogen in quenched and aged CY-35 at. pct Re was followed by internal-friction and electrical-resistivity measurements. It is shown that the precipitation kinetics of nitrogen from solution are many orders of magnitude lower in this alloy than in chromium. The reluctance of nitrogen to precipitate from sol~ction can be attributed to the composilional r-eadjustnzents required in the z.icinity of a chromium nitrade particle for gowth to occur. AS part of an investigation of the mechanism by which rhenium increases the low-temperature ductility of chromium and other Group VI-A metals, it was of interest to compare the concentration of interstitial elements retained in solution in chromium with that of a ductile Cr-Re alloy. The presence of certain interstitial elements in chromium has been shown to decrease its ductility1-5 and, of these interstitials, nitrogen is believed to have the most detrimental effect on mechanical properties. Thus, a comparison of the disposition of nitrogen in chromium with that in a ductile Cr-Re alloy might provide information about the mechanism whereby rhenium enhances the ductility of chromium. In previous internal-friction studies it was shown that the equilibrium solubilities of nitrogen in chromium and Cr-35 at. pct Re did not differ greatly.= However, results indicated that the actual concentration of nitrogen retained in solution at ambient temperatures is likely to be considerably greater in the alloy than in chromium because the precipitation kinetics of nitrogen are greatly retarded by the addition of rhenium. The objective of this investigation was to study the kinetics of nitrogen precipitation in Cr-35 at. pct Re in greater detail and to obtain information concerning the mechanism of nitrogen precipitation in this alloy. The properties studied were internal friction and

Jan 1, 1967

By B. H. Bergstrom

The Gaudin-Meloy1 size distribution equation requires the evaluation of two constants, xo and r. The common log-log representation of a screen analysis as cumulative weight percentage passing versus size, readily yields the required constants as illustrated for curves A and B in Fig. 1. The 100% passing (y = 1.0) size is simply x,. If the straight portion of the curve be extrapolated to the 100% passing (y=1.0) abscissa, the intercept is the Schuhmann size modulus, k. The ratio of xo to the size modulus, k, is r as shown: The Gaudin-Meloy equation requires that the slope, a, of the size distribution approach unity in the finer sizes, as is the case for curves A and B. Often distributions are better characterized by slopes other than unity. The schuhmann2 equation is able to represent these distributions if the upper portions of the curves are ignored. Empirically, the Gaudin-Meloy equation can be modified to yield slopes other than unity by writing it as Here, a is the familiar Schuhmann slope, and xo is the 100% passing size. The value of r is still given by Eq. 2. Eq. 4 with its easily determined constants is more versatile than either the Schuhmann or the Gaudin-Meloy equations, since a wide variety of size distributions can be closely described. It is easier to fit than the Rosin-Rammler3 equation, and has the advantage that the top size, x,, is finite. REFERENCES A. M. Gaudin and T. P. Meloy: Model and a Comminution Distribution Equation for Single Fracture, AIME Transactions, 1962, Vol. 223, pp. 40 to 43. R. Schumann, Jr.: principles of comminution, I., size Distribution and Surface Calculations, AIME Technical Publication No. 1187, 1940. P. Rosin and E. Rammler: The Laws coverning the Fineness of Powdered Coal, J. Inst. Fuel, 1933. Vol. 7, p. 29.

Jan 1, 1967

By L. F. Heising

The Bureau of Mines evaluated 42 composite samples from selected Michigan-Wisconsin iron formations by reductive roasting-magnetic separation and flotation at minus 325 mesh. Samples having poor to marginal response on initial examination by conventional methods were reevaluated by finer grinding, by reagent suite modifications, and by selective flocculation-desliming techniques. Results ranged from excellent on Menominee Range samples to relatively on Gogebic Range ores. Marquette Range samples ranged from responsive to nonresponsive, depending upon grain size and mineral association.

Jan 1, 1967