Search Documents

By L. D. Jaffe, F. W. Cotter, E. Cordon

The hardenability of titanium-base alloys was studied by metallographic examination and hardness survey of Jominy specimens end-quenched from the B range. Analyses of the data led to the equation log J = -0.57 + 0.25 @ct Fe + pct Mn + pct Mo) + 0.19 @ct Cr) +0.16 @ct V) + 0.03 @ct Zr). Here J is the distance, in sixteenths of an inch, from the quenched end of a Jominy hardenability specimen in the position of peak hardness, for material quenched from the B range. This equation fitted the experimental data with a standard deviation of approximately 0.29. The effects of the elements Al, Sn, W, Cu, Ni, B, C, N, 0, and H, and of pain size, were not statistically significant or not practically significant. A check against hardenability measurements in the literature showed agreement within the stated standard deviation. The equation should be useful in estimating hardenability of new or modified titanium alloys. HARDENABILITY in a titanium-base alloy is the ability of the alloy to retain the B structure on quenching. An alloy with high hardenability will retain the /3 structure even when cooled relatively slowly from a temperature at which B or P plus a is stable. A low hardenability material will retain P only if quenched extremely rapidly from the range of p or 0-plus-a stability, or will not retain it at all, at room temperature. High hardenability is desirable in titanium alloys to be heat-treated to high-strength levels. Its value is by no means limited to large section sizes. With high hardenability, a material can be solution-treated and cooled at a variety of rates, either to give high strength directly or, more generally, to give a soft ductile condition from which high strength can be obtained by subsequent aging. With low hardenability, high strength can be obtained, if at all, only by very rapid quenching, and there will generally be little increase in hardness on subsequent aging; an alloy of this type is limited in its applicability. On the other hand, alloys of very low hardenability have some advantages in weldability; essentially, they are always in the annealed condition, after welding as well as before. For commercial alloys, hardenability data are usually available, in the form either of property data after cooling from the solution temperature at various rates, with or without subsequent aging, or of results of a standard hardenability test, such as that originally developed for steels by Jominy and Boegehold.' When modifications of an available alloy are considered, or preparation of new alloy compositions, it would be Very convenient to be able to estimate the hardenability of the new material without having to make and test it. A method of estimating hardenability of titanium alloys from their composition was suggested by one of the authors some time ago, on a preliminary basis, utilizing scattered data found in the literature.' It seemed worthwhile to carry out a systematic experimental study of the effect of composition upon hardenability. EXPERIMENTAL PROCEDURE Approximately fifty heats of various compositions, weighing 8 to 10 Ib apiece, were melted in a small inert-gas tungsten-arc furnace with water-cooled copper walls. The starting material was 110 Brine11 titanium sponge, with high-purity metals added for alloying. Each heat was bottom-poured under vacuum through a molybdenum burnout strip into a cold graphite mold, to form an ingot approximately 4-1/2 by 3-1/2 by 3 in.* From each ingot were cut *The material was melted and cast by Pitman-Dunn Laboratory, Frankford Arsenal, to whom the authors must express their thanks. two pieces 4-1/2 by 1-1/2 by 1-1/2 in. These were forged, at temperatures adjusted to the composition, into 1-1/4-in. rounds, from which standard 1-in.-diam hardenability specimens3 were machined. A number of small samples were also prepared from forged materials of each heat, annealed, quenched from various temperatures, and examined metallographically. The P-transus temperature was determined by observation of the degree of resolution of primary a in these pieces. samples for chemical analyses were also taken from the forgings. One hardenability specimen of each heat was solution-treated for 1 hr approximately 50°F above the measured transus temperature, and the other for 1 hr approximately 250°F above the transus. (An additional hour was allowed for the specimens to reach furnace temperature.) These are not necessarily the temperatures that would be selected for

Jan 1, 1964

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By Richard H. Kennedy, G. A. Swanquist, John W. King, Frank F. McGinley, Dale C. Mathews, Hans H. Adler, E. C. Peterson, Ralph M. Wilde

INTRODUCTION From the first historical records of the discovery of uranium as an element and the attempted classification of its minerals in the early 18th century-through its first uses in pigmentation and the coloring of glasses and ceramic glazes-until 1939 when it was discovered that the isotope U235, was fissionable, uranium oxide in the form of pitchblende ores and concentrates (produced mainly in Bohemia, Canada, and the former Belgian Congo) in recent times was the source of uranium compounds incidental as byproducts to the recovery of radium from this invariable associated source. In 1938 this byproduct production from pitchblende concentrates was about 471 st of U3O8, with over 90% from Canada and the Belgian Congo and only 25.85 st from carnotite ores in the United States.1 Under the impetus of the Atomic Energy Commission's (AEC now part of the Energy Research Development Administration) domestic and foreign production incentives and buying programs, and as an initial assurance of atomic armament capability of the United States and the Free World, the growth of the uranium mining and milling industry burgeoned from 1952 to 1962. After a short period of decline, in the second decade and in large commitments beyond, it has again extended its capacity to meet ever-increasing fuel demands of atomic power generation by the electric utilities industry. In 1961 the peak production in the United States alone was 17,758 st of U3O8. Peak aggregate domestic and foreign deliveries of 34,581 st of U3O8 to the AEC occurred in 1960.z Canada's maximum delivery of 13,506 st of U308 was made in 1959. These peak and continued productions in the Free World are largely from: the Mesozoic (Jurassic) and Tertiary (Eocene) sandstones in the United States; the quartz pebble conglomerates of Canada and the Witwatersrand; pegmatites, Jurassic limestones, and Precambrian complexes, with less but significant production; the phosphoria, where byproduct production is minor. This uranium production in the form of precipitated concentrates has come from the milling of ores from these sources, both directly and by retreatment of gold cyanidation tailings on the Witwatersrand. Milling of crude ore has followed these processes: conventional crushing and size preparation, ore drying when required, salt roasting for high vanadium ores and byproduct vanadium recovery, carbonate or acid-leaching processes, classification sand-dine separations or countercurrent decantation (CCD) circuits and complete liquid-solids separations, resin-in-pulp (RIP) or liquid-liquid (solvent) ion-ex- change extractions, clarification of pregnant liquors, precipitation, filtration and washing, sodium and vanadium removals, and drying or roasting and packaging of the high-grade, high-purity uranium concentrate commonly referred to as "yellowcake." Coupled with the hazards and control of dust generation incident to conventional crushing and milling operations, more stringent control of airborne respirable and ingestible radioactive particulates and the protection of personnel against definitive external radiation are inherent to uranium milling. Impoundment and control of tailings and other effluents of uranium milling are more restrictive than in conventional practice, be- cause long-term disposal and containment of the uranium series of radionuclides, whether in solution or in solid form, are requisite to uranium milling and are made manadatory under regulatory agencies of government. 2. GEOLOGY AND MINERALOGY OF URANIUM Early Uses and Byproduct Production of Uranium Uranium was discovered by Klaproth in 1789 but had little commercial importance until the discovery of uranium fission by Hahn and Strassman at the close of 1938. The well-known uranium ores of Joachimsthal, Czechoslovakia, the Congo, and the Colorado Plateau were early sources of radium. Minor quantities of uranium were used for small-scale technical and industrial applications, particularly in coloring glass and ceramics, but most of the uranium was discarded. The Colorado ores were also mined later, chiefly for vanadium. Impetus of Armament Capability and Fuel Demands for Atomic Power Following the discovery of atomic fission, uranium became critically important for military applications and, more recently, as a nuclear fuel. Prior to 1966 uranium was acquired in the United States almost solely for use in the weapons program of the AEC. By 1970 the AEC had procured approximately 325,000 st of U3O8 from domestic and foreign sources. Current and future marketability is primarily dependent upon commercial demand for reactor fuel. Estimates of

Jan 1, 1985

By S. S. Marsden, S. A. Khan

Externally generated foam was injected continuously into short porous media. Both flow rate and pressure drop were measured. Liquid saturation was determined by electrical conductivity. Foam yuality I, expressed as the ratio of gas volume to total volume, was varied from 0.70 to 0.96. As measured with a modified fann VG Meter, apparent viscosity of this foam µa decreases with increasing shear rate but usually falls within the range of 50 to 500 cp. At a given shear rate, µa increases almost linearly with I-. When measured with a Bendix Ultraviscoson, kinematic pa is independent of V but absolute pa increases with T from about 3 to 8 cp. The effective permeability -apparent viscosity ratio ke/µa decreases almost linearly with V for porous media of high permeability, but the rate of decrease becomes less for tighter ones. The relative permeability-apparent viscosity ratio kr/µa us V data does not fall on a single line. The kr/µa ratio increases with liquid saturation in the porous medium and with surfactant concentration. Estimates of pa for foam in porous media vary from 30 to 100 cp. INTRODUCTION Although research on the development of a foam-drive, oil recovery process has been going on for almost a decade, most of the significant publications have appeared within the last several years. This illustrates well the rate at which interest in this process is accelerating. Bond and Holbrook 1 were the first to describe the use of foam to improve oil recovery in their patent of 1958. They proposed that an aqueous foaming agent slug be injected into the formation and that this be followed by gas to produce a foam in situ. Fried 2 studied the injection of foam into porous media which had already been subjected to conventional gas or water drives and found that gas could be used to drive a foam bank which would, in turn, displace additional oil in the form of an oil bank. He attributed the increased oil recovery to the high effective viscosity of foam flowing in porous media. His microscopic observations showed the importance of foam generation and regeneration within the porous medium. By injecting both air and aqueous surfactant solution, Bernard3 generated foams within the porous medium in which oil displacement was being studied. In a separate empirical test, he also measured the dynamic foaming characteristics of the same surfactants in water and/or oil. With some exceptions and for the seyen surfactants studied, there seems to be a qualitative relationship between the efficiency of liquid rlisplacrment and the dynamic foaming testtsed. This relationship was not consistent enough to eliminate the necessity of actual foam flood tests in porous media for surfactant selection. In a study basic to gas storage in aquifers, Bennett4 described the displacement of brine by foam in consolidated porous media. Among other things, he stated that the ability of a surfactant solution to foam is more important than the stability of its foam. The presence of a foam bank between the displacing air and the displaced brine improved both breakthrough and ultimate recovery. In a continuation of this work Kolb5 attributed the great reduction in surfactant solution production rate as displacement by air progressed to a decrease in relative permeability to gas. These several effects reported by both Bennett and Kolb can all be attributed to the high apparent viscosity of foam which was obviously flowing in the porous media. Bernard and Holm6 observed that gas permeability in the presence of foam was much less than in the absence of foam when both were measured at the same gas saturations. This reduction in permeability was proportionately greater for more permeable sands and sandstones than for the less permeable. Viscosities of the surfactant solution and air were used for their calculations rather than apparent foam viscosities. The foam stability increased with decreasing permeability, which was probably due to the natural regenerative properties of porous media, and the permeability reduction increased

Jan 1, 1967

By B. Chalmers, L. Bäckerud

The growth temperature of dendrite tips has been measured in a binary alloy system, Al-Cu, as a function of rate of formation of solid phase. Metallographic examination has rerealed the dendritic structure dereloped during different stages of the freezing process and factors influencing the undercooling, such as solute buildup, surface tension, and kinetic effects, have been estimated. Practical implications of the results are discussed. THE development of a dendritic growth pattern during the solidification of metals and alloys has an influence at least equal to that of grain size on the properties of the casting or ingot being produced. and consequently much interest has been devoted to the study of this phenomenon. A review of the knowledge gathered up to 1964 has been given by Chalmers.' Among recent publications in the area the works of Jackson et al 2 and Flemings and his coworkers3,4 are of special interest. This work is an experimental study of the factors which influence the development of a dendritic pattern during the solidification of a typical binary alloy system, A1-Cu, when there is no heat source in the liquid. This means that the temperature and the temperature gradient are controlled by the heat extraction from and latent heat evolved by the growing crystals. EXPERIMENTAL PROCEDURE Samples were prepared from a master alloy made up of aluminum, 99.995 pct, and copper. 99.99 pct, of the concentrations given below and of sufficient size to fill cylindrical graphite molds of 35 mm ID and 35 mm height. Bottom. wall. and lid of the graphite molds were all of 6 mm thickness, Fig. 1. Thin ceramic thermocouple shields could be introduced at different positions in the sample through holes in the lid. The assembly was heated in a small vertical resistance furnace to a suitable temperature. 700° to 720°C. which is well above the melting point of the sample. It was thereafter taken out of the furnace and chilled at selected rates, and the temperature changes in the sample were recorded. For high sensitivity in the temperature recordings, a reference thermocouple was held in a solidifying pure aluminum melt. which was very well insulated and therefore was at a constant temperature. 660°C, for nearly half an hour. The thermocouples were connected so that the difference voltage was fed into the recorder of which the most sensitive range was 1 mV. Temperature variations could be read to within 0.l°C. The thermocouples used were of the Chromel-Alumel type (28- or 38-gage wires) and the recorder a two-pen Moseley strip chart recorder. The different rates of chilling were obtained in the following way. a) The graphite crucible was wrapped in one or two layers of an insulating. feltlike material (Fiberfrax paper from the Carborundum Co.). The drop in temperature per unit time after complete solidification could thereby be varied from 8" to 18°C per min. This corresponds to a rate of heat extraction in the given samples from 0.08 to 0.17 cal cm-' sec-I. 6) The bare graphite mold was placed free on a piece of firebrick. The measured temperature drop was around 50°C per min (-0.5 cal cm-" ' sec- I). c) By blowing compressed air through a tube with many holes surrounding the mold in a ring shape. the rate of heat transfer could be raised to 150' to 200°C per min (-1.7 cal cm-3 sec- I). d) Cooling rates around 1000 C per mill (-9.4 cal cm-3 sec-l) were obtained by substituting the air in the device used in c by water. The range of cooling rates used in these experiments correspond to technical casting processes from slow solidification as obtained in sand molds to very rapid freezing which occurs in some continuous casting and welding processes. EXPERIMENTAL RESULTS The A1-Cu system was chosen for the experiments: the relevant part of the phase diagram is reproduced in Fig. 2. Observation of the Center Temperature. When a thermocouple is inserted in the center of the melt. the type of cooling curves obtained at slow solidification rates differs little from numerous published curves from similar systems. and the solidification pattern

Jan 1, 1970

By N. L. Wesis

General History The first jaw crusher in the US was patented about 1830, but the Blake crusher that has maintained a substantial advantage over other types was invented in 1858 by Eli Whitney Blake. For going on 150 years the jaw crusher has been an invaluable machine; even today, when gyratory crushers have assumed most of the burden of crushing large tonnages of large rock and ore, the jaw crusher has a firm place in the mining industry. It is interesting that soon after the invention of the Philetius Gates gyratory crusher in 1881, a contest between the first No. 2 Gates and Blake jaw crushers of equal gape showed the gyratory to be 3.2 times as fast. This foretold a day not far in the future when the jaw crusher would not be adequate on the largest jobs. In his Textbook of Ore Dressing (1909) R. H. Richards recom¬mended that the word breaker be used for all machines breaking to relatively large sizes (say to 5 in. or greater), and crusher be used for finer work. Even in the 1968 US Bureau of Mines dictionary of mining terms the work breaker is defined by Richards in this context. However, in modern US usage it is nearly limited to coal breaking. Over the years the jaw crusher has been developed in a variety of forms but it appears today in these three general forms: (I) Blake type, (2) Dodge type, and (3) single toggle (or overhead eccentric) type. All of these crushers have a fixed jaw and a moving jaw, between which the coarse rock fragments are intermittently caught and crushed. The three types are differentiated by the manner in which the movable jaw is moved in relation to the fixed. Types The Blake-type crusher is shown in cross section in Fig. 1. The simplicity and strength that have made it first among jaw crushers are evident. The movable jaw is suspended from a cross-shaft at its upper end, this shaft being carried in bearings on the sides of the frame. The actuating mechanism consists of an eccentric shaft, also supported in frame-mounted bearings, which imparts through a pit¬ man and a pair of toggles a reciprocating motion to the bottom of the swing jaw, the return movement being effected by several spring¬loaded rods. The whole is built into a box frame with the crushing chamber at one end. As in all jaw crushers, the eccentric shaft is equipped with a heavy flywheel that maintains an even speed through¬out each stroke. The Dodge-type crusher illustrated in Fig. 2 is simple, mechani¬cally. Its movable jaw, being pivoted below the discharge opening, has minimum movement at crusher discharge and maximum at crusher feed. Because the choke point coincides with the point of least motion, these crushers are of relatively low capacity, and the rapid action in the feed area gives the machine the advantages of large reduction ratio and closely sized product. Thus, it fits well into low-capacity operations like sample reduction. Besides low capacity, its principal disadvantages are tendency to pack and make fines. The single-toggle or overhead-eccentric type of jaw crusher (see Fig. 3) has gained in usage, starting as a modification of the Dodge idea in that the greatest movement of the movable jaw occurs at the top, and being gradually improved and strengthened to its position today where it covers just as wide a field of application as the Blake type from the standpoint of feed opening. The motion of the movable jaw is the result of the circular motion of the eccentric shaft at the top of the swing jaw combined with the rocking action imparted to the bottom by the inclined toggle plate. Because of light weight and mechanical simplicity, it is economical in small mills and portable plants where the rock is not as tough and abrasive as to punish the machine with excessive impact from shocks, or excessive wear result¬ing from the pronounced vertical component of motion.

Jan 1, 1985

By F. A. Schaufelberger

Early work on chemical precipitation of metals from metal salt solutions is reviewed. The chemistry and thermodynamics of precipitating copper, nickel, cobalt, and cadmium metals by reaction with hydrogen are discussed. Mechanisms of metal precipitation, nu-cleation, growth, and agglomeration are reviewed, as well as some solubility phenomena of cleation,gases and solids at elevated temperatures. Experimental data presented deal mainly with the reaction of copper sulfate solution with Hz. METAL can be recovered from a leach solution either indirectly by precipitation as a compound that is later reduced or directly by electrolysis, cementation, or chemical reduction, for example, with hydrogen. The widely used electrowinning processes suffer from the inefficiency of converting fuel to low voltage dc and from low current efficiency when complete recovery is attempted. With the batch hydrogen reduction methods outlined here, a unit of fuel converted to hydrogen in modern gas reform plants will make two to three times as much metal as can be obtained with electrolysis. With continuous hydrogen reduction, four to six times as much metal is obtained. Precipitation by reducing a metal salt solution with H, has been known for almost 100 years.' Commercial use of the process, however, awaited the research and development program initiated by Chemical Construction Corp. Within the last few years this program has brought about construction of commercial plants, listed on p. 701. Ideal hydrogen reduction will precipitate a pure metal from a solution obtained by commercial leaching methods at a rapid rate without excessive temperatures and pressures. The metal precipitate will be of desired size and density, less than a percent left in the vessel being deposited on the wetted parts. The present discussion will outline Chemical Construction Corp.'s early development program and will discuss the chemistry and mechanics of reducing copper, nickel, cobalt, and cadmium from solution by H2. Work on selective reduction of nickel from cobalt has been described earlier.2 The article is not concerned with precipitation of copper by disproportionation of cuprous solutions where yield is limited" to 50 pet.* It does not discuss use of gaseous reducing agents other than hydrogen, such as SCV which may lead to contamination with sulfur, or CO," which is considerably more expensive than hydrogen and produces a gaseous reaction product, CO2.† The article does not include use of other nongaseous reducing agents: which are far more expensive than CO. Also, notes on the history, engineering design, and performance of commercial plants have been given elsewhere." It will be shown that a pure metal can be precipitated by reduction with hydrogen from solutions obtained by commercial leaching methods when the solution cohposition is controlled and proper acidity, proper metal ion concentration through controlled complex formation and hydrolysis, and adequate agitation for suspension of metal and for transfer of reducing gas are maintained. Reasonable temperatures and pressures are used which are less excessive than those used by previous workers, although they are maintained at above equilibrium values because of process kinetics.' It has also been found necessary to induce nuclea-tion and to control growth and agglomeration in order to get a powder product of suitable physical properties. Review of the Literature Muller, Schlecht, and Schubardt of I. G. Farbenm claimed a successive reduction of silver, copper, nickel, cobalt, and zinc from ammoniacal solution by applying progressively higher temperatures and hydrogen pressures. Metals produced by this technique were not pure, since no attempt was made to adjust the solution composition between the different reductions. It is doubtful that the zinc product contained any metallic zinc. The major contribution to the literature" was made by the Ipatiews,12 who prepared platinum, iridium, copper, nickel, cobalt, lead, tin, arsenic. antimony, and bismuth at often extreme conditions, up to the critical temperature of water (373"C), at 1500 to 7500 psi, for as long as several days. Even cadmium and zinc were claimed to have been observed in trace quantities precipitated together with basic salts. In the early experiments solutions were not stirred. Extensive formation of oxides and basic salts occurred. probably long before sufficient hydrogen could be supplied in the unstirred liquid to decrease the metal concentration in solution by reduction. The importance of hydrogen pressure was

Jan 1, 1957

By Robin Phinney

Certain statements in this presentation may constitute "forward-looking" statements which involve known and unknown risks, uncertainties and other factors which may cause the actual results, pe1formance or achievements of the Corporation, or industry results, to be materially different from any future results, performance or achievements expressed or implied by such forward-looking statements. When used in this presentation, such statements use such words as "may", "would", "could", "will", "intend", "expect", "believe", "plan", "anticipate", "estimate" and other similar terminology. These statements reflect the Corporation's current expectations regarding future events and operating performance and speak only as of the date of this presentation. Forward-looking statements involve significant risks and uncertainties, should not be read as guarantees of future performance or results, and will not necessa1ily be accurate indications of whether or not such results will be achieved. A number of factors could cause actual results to differ materially from the results discussed in the forward looking statements including, but not limited to, the factors discussed in the Corporation's annual information form filed on March 9, 2011. Actual results could differ materially from those currently anticipated due to a number of factors and risks. These include, but are not limited to, the failure to obtain necessary regulatory approvals, including environmental approval, the failure to secure full project financing, the failure to implement the recommendations set out in the Technical Report, the failure to raise financing to implement the recommendations in the Technical Report, risks associated with the mining industry in general (e.g., operational risks in development, exploration and production; delays or changes in plans with respect to exploration or development projects or capital expenditures; the uncertainty of estimates and projections relating to production, reserves and resources, costs and expenses; and health, safety and environmental risks), decrease in potash prices and exchange rate fluctuations. Although the forward-looking statements contained in this presentation are based upon what management of the Corporation believes are reasonable assumptions, the Corporation cannot assure shareholders that actual results will be consistent with these fonvard-looking statements. These fon\?ard-looking statements are made as of the date of this presentation and are expressly qualified in their entirety by this cautionary statement. Subject to applicable securities laws, the Corporation assumes no obligation to update or revise them to reflect new events or circumstances. This presentation is a market update based on the Corporation's public disclosure and does not form a part of any offer of securities, or constitute a solicitation of any offer to purchase or subscribe for securities. Any purchase of securities in the company should be made solely on the basis of information contained in the Corporation's public record which is available on www.sedar.com .

May 1, 2013

By M. R. J. Wyllie

The relationship between the electromotive force (E.M.F.) across a shale barrier and the concentrations of sodium chloride solutions on either side has been investigated. It is shown that the action of a shale barrier is analogous to a glass membrane separating two acid solutions of different hydrogen ion concentrations. The shale behaves as a sodium electrode and is responsive to the activities of the sodium ions in the two solutions in such a way that the potential can be calculated by means of the Nernst equation. This conclusion is confirmed by laboratory experiments. In a borehole the total E.M.F. of a shale cell is the algebraic sum of the ~otential across the shale and a boundary potential. The relationship between total E.M.F. and the resistivity ratio of two sodium chloride solutions is indicated for a number of formation temperatures. The E.M.F. thus predicted is then compared with the .elf potential read from an electric log and good agreement is demonstrated. Based on both the self potential and resistivity curves of the electrical log. a method is given for calculating connate water content in a bed having in-tergranular porosity and containing both connate water and hydrocarbons. INTRODUCTION The first paper on electrical well logging by C. and M. Schlumberger and E. G. Leonardon in 1934' attributed the self potential curve principally to streaming potentials, i.e. to electroki-netic effects. Almost immediately great difficulties were encountered in reconciling many of the curves they obtained with this interpretation. and a ~econd paper' by the same authors soon appeared. In this second paper self potentials were attributed to the combined effects of streaming potentials and electrochemical potentials, the electrochemical potential being considered the result mainly of the interaction of fluids of differing salt concentrations, i.e. a boundary potential, and partly of potentials set up at the faces of impermeable materials. Some experiments involving a gray clay for the impermeable material were quated. The Schlumbergers and Leonardon deduced from the equation for a simple boundary ~otential that the electrochemical potential, as opposed to the electrokinetic potential, could be expressed in the form E=Klog- .......1 pe where K is a constant, pm the mud resistivity. p, the resistivity of the connate water in a porous bed. However, no general expression for the constant K was obtained. Although the literature between 1934 and 1943 contains a number of quotations of their results, the valuable work of the Schlumbergers and Leonardon was not extended so that the electrochemical potential has been generally attributed wholly to boundary potentials between the mud in the borehole and the connate waters in porous formations. Unfortunately, however, the fundamental premise of all these papers, that a boundary potential can give rise to current flow in a borehole, is thermodynamically untenable. As will be shown. the fact that the electrochemical potential can be fairly accurately express as E = K log pm/pc, a form in which a boundary potential may also be written, is partly fortuitous. The boundary potential is indeed an integral part of the expression for the electrochemical potential in a horehole, but in magnitude it represents only about 20% of the total potential. In 1943 an important step in the elucidation of electrochemical potentials was made by Mounce and Rust3 who showed that if a wall of shale separated two compartments which contained saline solutions of different concentrations, and if the two solutions were themselves brought into contact in the pores of a porous inert membrane (such as unglazed porcelain) a current flowed through the shale and saline solutions. The direction of positive current was from the shale into the more dilute solution. The paper of Mounce and Rust, while repeating some of the observations of the Schlumbergers and Leonardon, seems to be the first to show that the shale was the seat of a genuine electrochemical effect capable of causing current flow. In the same paper Mounce and Rust pointed out the similarity between the fundamental conditions of their experiment and the conditions which existed when a bed of shale in the ground was simultaneously in contact with a porous sand containing saline connate water and mud fluid of salinity different from that of the water in the sand. Since it is now generally recognized that the S.P. curve measures ohmic potential changes in the mud fluid in the well bore resulting from changes in current flow, it is apparent that currents having their origin in the electrochemical interaction of mud filtrate and connate waters with shale beds are a very important portion of the total S.P. The work of Mounce and Rusta and others appears to indicate that, in general, the electrochemical portion of a particular kick on a S.P. curve far exceeds any electrokinetic potentials resulting either from streaming potentials or Dorn effects. The Dorn effect, or sedimentation potential. arises when small particles are allowed to fall through certain fluids under the influence of gravity. a difference of potential being observe? between two electrodes placed at different levels in the stream of falling particles. The Dorn effect is unlikely to affect seriously the S.P. curve as now measured. A successful analysis of the electrochemical aspects of the S.P. log should

Jan 1, 1949

By B. B. Sandiford

It has been known for many years that the efficiency of a water flood can be improved by lowering the water-oil mobility ratio in the system. Such a change leads to better sweep efficiency and also to more efficient oil displacement in the swept zone. Data from our laboratory water-flood tests of both small cores and long sand packs are presented which show that water mobility can be reduced and oil recovery increased by the addition of certain polymer solutions to flood water. The reduction in mobility, in many cases, is greater than would be expected from conventional viscosity measurements. These solutions, however, do not cause significant reductions in oil mobility. The over-all effect of these mobility changes is increased waterflood oil recovery. Encouraged by results of our laboratory work, we expanded our study to include pilot field tests of floods with such solutions. One such test, made in the West Cat Canyon field, Santa Barbara County, Calif., is described in detail in this paper. Three other field tests are also discussed. INTRODUCTION Oil production from most reservoirs following primary depletion and/or water flooding is often less than 50 per cent of the original oil in place. Heavy oil reservoirs seldom yield over 15 per cent of their original oil. With new reservoirs becoming harder to find, the improvement of oil recovery efficiency is one of our very important problems. We describe here some of our attempts to increase the efficiency of oil displacement by adding a water-soluble polymer, partially hydrolyzed polyacrylamide, to flood water. This technique will be termed "polymer solution flooding". The concept of using high-viscosity water to increase the efficiency of water flooding is not new. In 1944 Detling (Shell Development Co.) obtained a patent covering the use of several additives for viscous water flooding.' His objective was to improve water-oil mobility ratios by increasing the viscosity of the flood water. Other patents2-27 have been granted covering specific water-SO~LIble polymers or specific conditions of viscous water flooding. Barnes'" described his laboratory model study of the injection of a viscous water slug into a reservoir which had been partially invaded by bottom water. He concluded that, for this type of reservoir, "the cost of viscous water should not exceed a few cents per barrel for viscous water slug injection to be economically feasible" Our studies have led us to a somewhat different conclusion in a number of cases where hydrolyzed polyacrylamide solutions have been injected into reservoir models or actual reservoirs. Possible reasons for this difference are discussed in this paper. Our studies have shown that polymer solutions may lead to an increase in oil recovery over that from an ordinary water flood by (1) improving sweep efficiency, (2) improving microscopic displacement efficiency, or (3) a combination of these mechanisms. In the work of Barnes, only the benefit of improved sweep efficiency was considered. Also, our work has shown that there are marked differences in the effectiveness of different water-soluble polymers as flood water additives. Partially hydrolyzed polyacrylamide is better than many other water-soluble polymers we have tested because, even in very low concentrations, it can lead to increased oil recovery. This is an important advantage when either a dilute polymer solution is injected continuously or a relatively concentrated slug is injected followed by water. In the latter case! portions of the slug become diluted and function in the formation as very dilute solutions. As dilution takes place the effective slug size will increase which, in turn, will reduce the cost per barrel of the effective flooding medium. The reason that partially hydrolyzed polyacrylamide solutions are more efficient at low concentrations than certain other polymer solutions of equivalent viscosity (when measured in conventional viscometers) is not fully understood. We do know that the shapes and sizes of macro-molecules dissolved or suspended in liquids influence the flow properties of their solutions or suspensions. Solutions of partially hydrolyzed polyacrylamide cause greater reductions in water mobility than would be expected from conventional viscosity measurements. LABORATORY STUDIES Laboratory water floods were run in linear and radial systems with different water-soluble polymers and under varying conditions of flow. including reservoir conditions of temperature, pressure and fluid composition. Some of these runs are considered in this section. OIL DISPLACEMENT IN LINEAR MODELS In this group of runs the sweep efficiency approached 100 per cent because the linear sand packs used were as nearly uniform as possible. Results reflect primarily the micro-scopic displacement efficiencies. The laboratory models were unconsolidat-ed sand packs the lengths of which varied from about 4 in, to 40 ft. Further information on the flow models used is listed in Table 1. Using conventional procedures, water floods were run on sand packs containing either refined or crude oil at restored state. Frequently, a repeat run, similar to the first, was made as a check. Then a third run was made on the restored-state model using either polymer solution or a combination of polymer solution (slug) and water. Details of these runs are also reported in Table 1. In Figs. 1 and 2 results of two different groups of runs are shown in which the oil used was a 62-cp refined oil and the flooding medium

Jan 1, 1965

By Y. C. Liu, G. A. Alers

The effect of rolling reduction on the textures of Cu-A1 alloys has been investigated both by pole figure and by modulus methods. In alloys which exhibit complete copper or brass types of rolling texture, the rolling reduction has little effect on the texture except to increase the degree of preferred orientation. In alloys which exhibit a transition texture, however, increased rolling reduction increases the amount of brass-type texture at the expense of the copper-type texture. The present experimental results show that there is no one-to-one correspondence between the SFE and the rolling texture of fcc metals. Additional data taken from the literature for fcc metals also support this conclusion. On the other hand, the present and previous experimental results are shown to be in good agreement with the suggestion that the texture transition occurs at a critical value for the separation distance between two partial dislocations—a consequence of the "dislocation interaction" hypothesis for texture. formation. This critical separation occurs when the parameter .r/ub is 3.75 x 10'3. From this, a value for the SFE of 39 ergs per sq cm may be deduced for a Cu-2.85 at. pct A1 alloy. ThE correlation between the rolling texture of fcc metals and the stacking fault energy, SFE, was one of the first attempts to relate atomistic properties with the type of rolling texture.' This correlation gives a qualitative explanation for the experimental observation that the addition of alloying elements, which generally lower the SFE, changes the copper-type texture to a brass-type texture. The simplicity of this correlation had led to its general acceptance and even its quantitative use.' However, it is only a correlation and is largely based on descriptive features of pole figures, and on the poorly known SFE values in dilute alloys. Quantitative verification of this phenomenologi-cal correlation is, in fact, completely lacking. One purpose of the present study is to test this correlation. Another atomistic description for the formation of rolling texture is the "dislocation interaction" hypothesis of texture formation.3 In this hypothesis, the factor controlling the type of rolling texture depends on whether or not the separation distance between two partial dislocations exceeds a critical value. Materials having a separation of less than the critical value are supposed to exhibit a copper-type texture while those with a separation above the critical value are supposed to have a brass-type texture. At the critical value, it is expected that the material should show equal amounts of copper- arid brass-type orientations in their textures, i.e., a 50 pct transition texture. The SFE appears in this hypothesis as only one of several factors which determine the separation distance between partial dislocations. It is possible to test the validity of these two concepts by studying the rolling texture as a function of rolling reduction. Since the SFE per se is an intrinsic property of the metal, it should not, by definition, be influenced by local irregularities, such as variable stress conditions. Thus, no change in texture-type is expected to occur with changes in rolling reduction. On the other hand, according to the "dislocation interaction" hypothesis, any factor that effectively influences the separation distance of partial dislocations would be expected to change the rolling texture. Since the separation distance between partial dislocations is known to depend upon local stresses,4-6 it is anticipated that there would be an effect of the degree of reduction on the texture-type. Also, since applied stresses are more likely to increase, rather than to decrease, the separation between partials,4'5 the overall effect would be to increase the amount of material in the brass-type orientations as rolling reduction is increased. Furthermore, this reduction dependence would be most prominent in alloys exhibiting the transition texture since the distance between partials in those alloys is thought to be close to the critical value. Experimental data in the literature is insufficient to distinguish between these two alternatives. Haessner studied the effect of rolling reduction on textures in a series of Ni-Co alloys by means of the X-ray intensity-ratio technique,' and found that while one texture parameter indicated no reduction dependence the other indicated a slight dependence of the rolling texture on reduction in the range of 96 to 99 pct. As has been noticed previously, the intensity-ratio technique is a convenient but controversial method7 because there is no a priori reason to suggest which intensity-ratio would describe the texture most meaningfully. A more quantitative method of describing textures is found in terms of the orientation dependence of Young's modulus. Here, the type of modulus aniso-tropy associated with the copper-type texture is sufficiently different from that observed for the brass-type texture to allow the two types to be easily distinguishable and a quantitative measure of the amount of each can be deduced from the numerical results. This ability to provide quantitative data is particularly valuable when the two textures occur simultaneously in one alloy as is the case for the transition textures. In this paper the modulus method, supplemented by pole figure data, is used to look for an effect of roll: ing reduction the texture. Also by combining the texture measurements with recent determinations of the SFE in Cu-A1 alloys'0'" it should be possible to test for a relationship between the SFE and textures.

Jan 1, 1970

By James H. Fletcher

Much data and experience has been accumulated, especially in the last 5 or 6 years, to show that modern roof trusses, both of the Birmingham type and the bolt-and-channel type, perform well to support certain kinds of coal mine roof. For some time now, roof trusses of the Birmingham type have been effective in controlling thick shale roof, which tends to sag and fall over a period of about eight weeks. These falls leave dame-shaped cavities which are reminiscent of the pressure arch theory of roof failure. Lately there has also been significant interest in supporting some longwall panel entries with channel and-bolt systems. These systems utilize two vertical center bolts and two 45 degree end bolts through a heavy gage channel. Both types of truss systems have long bolts, which require 8 to 9 Foot holes on a 45 degree angle, and point anchor resin bolts, which utilize a 2 or 3 foot rebar grouted in a thin annulus of polyester resin. Consequently, many coal mining people have been impressed with the very good anchorage characteristics and tensionability features of these systems. However, the same people have been proportionately dismayed to find that very often the most difficult part of introducing a trussing program to a mine is deciding on the machine specifications which determine the truss installation rate. The purpose of this paper is to indicate aspects of truss bolter design and use which are not shared by roofbolter design and its vertical pattern of bolts. Of the two types of drill units conventionally accepted, arm feed units and mast units, only one 15 judged suitable. While the arm feed unit offers low collapsed height with a long drill feed length, a great attribute for low seam use, it has not lent itself to being rolled over to a 45 degree angle. One reason for this inability is that many items which are conventionally mounted on the arm feed unit cannot be allowed to rotate with the unit. These items include drilling controls, tool Cray, lights, canopy or safety post, panic bar, and stab jack(s). If these items were independent of the arm feed drilling unit, they would have to be out of the way of the boom arms, links, and feed cylinder as the unit moves. To ease this problem, the arm feed unit can be made very short and even mounted across the machine. However, the resulting short feed length is undesirable. Several short drill steel extensions are required to drill a relatively long hole, making this procedure time-consuming as well as increasing the likelihood of drilling a crooked hole. Another reason for abandonment of the arm feed unit is that a very stiff drill guide (or "centralizer") is required to start the hole. Using the mast tilt control, the roof bolter operator will force the bit against the roof and will rotate the bit without feeding to cut sideways into the roof to form a hole face. Omission of this step often results in the skidding of the bit toward the rib. To date, no such sturdy drill guide has been designed for an arm feed drill unit. The mast style unit has been the most successful design for angle drilling. It is easily rolled over to a 45 degree angle or to 90 degrees and, on single head models, often has been made to roll through 180 degrees. The mast style is compact, in plain view and is easily fitted with heavy duty manual or hydraulically operated drill guides. It can be mounted directly on a machine chassis, or onto a swinging boom, or onto a slider arrangement in a broad variety of configurations which will accommodate controls, tool trays, stab and roof support jacks, lights, canopies, and panic bars. The only significant difficulty with mast drilling units occurs in lower mining heights when desirable low mast height is accompanied by undesirable short feed length. While the lead extension in the drill string can be as large as the mining height will allow, a short feed length will permit only the use of shorter middle extensions and drivers, and perhaps will. require the use of two different length wrenches. The associated problem is the relatively short distance from the drillhead to the drillguide. This distance is further shortened when raising the drillhead to get the bit to the roof. One might keep longer lead extensions on the machine; drill a vertical pocket for the bit, starting the angle hole at this pocket; or modify the mast. If the mast is made so that the distance from the drillhead to the drillguide remains constant while the mast extends, after which the drillhead travels up the mast, the shorter mast can be made to start the hole more easily. However, short teed length will still result in longer drilling time. It is obvious from these points that a proper choice of mast is simply the highest one which will be moved easily in the given mining height. This, of course, goes against the grain of most experienced coal mining people who realize that a relatively small decrease in mining height can create a problem correctable only with the purchase and installation of shorter masts. If the mining

Jan 1, 1982

By R. F. Hehemann, S. T. Zegler

The w phase in zirconium alloys containing more than G pct Nb can form in a difjUsionless manner during quenching or with composition change during aging at temperatures below 550°C. The latter treatment establishes a metastable equilibrium between an w phase containing 5 pct Nb and a ß phase containing 45 pct Nb. The superconducting transition temperat~ire of quenched Z?-10 pct Nb and Zr-15 pct Nb alloys is increased by aging at 375°C and both alloys exhibit the same Tc after prolonged aging. The superconducting transition both in the quenched and in the aged alloys is relatively sharp (occurring ovev a temperature range of <0.5°K), and is interpreted in terms of the microstructure that characterizes the ß-w) mixture and proximity effects postulated for thin-film superconductors. At elevated temperatures alloys of the transition elements from groups 4 to 6 in the periodic table exhibit wide ranges of mutual solubility in the bcc structure. Except for compositions that are high in a group 4 element? the bcc structure can be retained at room temperature by quenching and several systematic studies of the influence of composition on superconductivity in bcc alloys have been reported.&apos;&apos;2 The high-temperature bcc form (ß) of the group 4 elements—titanium, zirconium, hafnium—is not retained upon quenching but instead transforms marten-sitically to the hcp structure (a). The Ms temperature can be lowered by alloying the group 4 metals with a solute from a higher group and with a critical amount of solute the martensitic transformation can be suppressed. The 3 phase, however, is not retained without modification. Rather, a metastable phase, w (in particular in titanium- and zirconium-base alloys), occurs over a fairly wide range of compositions above that required for suppression of the martensitic transformation.3,4 As in the formation of a, the transformation of ß to w occurs in a diffusionless manner during quenching and the temperature for its initiation (ws) is lowered by increasing solute content. The ws temperature can be well below room temperature and reversibility of the transformation allows w that forms on cooling to low temperatures to disappear again when the sample is returned to room temperature.5 In Zr-Nb alloys the w phase can also be formed during aging at temperatures below 550°c.5 In this treatment, a metastable equilibrium is established between a niobium-rich ß phase and a zirconium-rich w phase. The present study of Zr-Nb alloys was undertaken to examine the influence of microstructure: as controlled by composition and heat treatment, on the superconducting transition temperature, Tc. MATERIALS AND PROCEDURE The alloys were prepared from zirconium crystal bar that was spectrochemically pure except for 30 ppm of Al, 40 ppm of Cu, 100 ppm of Fe, and 1 ppm of each B and Pb. The niobium used was 99.5+ pct pure containing according to the suppliers&apos; (Stauffer Chemical Co.) analysis a maximum of 50 ppmO, 60 ppm of N, 30 ppm of C, 5 ppm of H, 200 ppm of Ta, 50 ppm of Mo, and 15 ppm each of Fe, Co, and Ni. The alloys were prepared in the form of buttons weighing approximately 4 g by arc melting on a water-cooled copper hearth in an inert-gas atmosphere. All alloys were heat-treated in the ß-phase region for 3 days at 1000°C and water-quenched. For heat treatment, the specimens, 0.5 cm in diam by 1.0 cm long, were wrapped in zirconium foil and sealed in an inert-gas atmosphere inside quartz capsules. Quenching was done by breaking the capsules under water. Subsequent aging treatments of Zr-10 pct Nb and Zr-15 pct Nb alloys were done by placing the specimens in a lead bath at 375°C and quenching in chilled brine. The phases present in the quenched and aged alloys were identified by optical and X-ray metallography. X-ray powder patterns were taken at room temperature with a 114.6-mm-diam Debye-Scherrer camera and CuK-a radiation. Superconducting transition temperatures were determined from magnetic-permeability measurements6 in a 10 oe field. The superconducting transition temperature was determined from a plot of galvanometric deflection as a function of temperature by extrapolation of the linear portion of the curve to zero deflection. In Figs. 1 and 3 the arrows indicate the temperature range of the transitions. RESULTS AND DISCUSSION Superconductivity in Quenched Alloys. In Fig. 1 Tc for alloys quenched from 1000°C is plotted against nominal composition. Indicated also in Fig. 1 are results of metallographic studies. Alloys containing less than 5 pct Nb transform martensitically to a during quenching from 1000°C and Fig. 1 demonstrates that Tc increases significantly as the niobium concentration in a is increased. On the basis of the Bardeen-Cooper-Schreiffer theory of superconductivity7 it seems most likely that this increase in Tc results from an increase in the density of electronic states as zirconium is alloyed with niobium. This increased density of states has been revealed clearly in low-temperature specific-heat measurements.8 The martensitic transformation to a is suppressed when the alloy content exceeds 5 pct Nb. In the range from approximately 6 to 30 pct Nb, quenched alloys consist of a mixture of B and w phases and the amount

Jan 1, 1967

By W. E. Quist, R. Taggart, D. H. Polonis, C. J. van der Wekken

An intermediate compound that has been identified as Niab is observed to form as a decomposition product from supersaturaled Ni-Nb solid solutions during aging at temperatures between approximately 300" and 500°C. On the basis of data from electron microscopy and selected-area diffraction, the structure of this compound has been determined as fct with a = b - 3a0 and c = a, wlzere a,, is the lattice parameter of the parent solid solution. The compound consists of close-packed layers with triangular ordering, where the niobiutrl atoms are separated by two nickel atoms ([long- close?-packed directions. A nine layer stacking sequence is required to describe the proposed structure. STUDIES of the Ni-Nb binary system have been limited primarily to phase diagram determinations,&apos;-4 investigations of high-temperature equilibrium phases,5"1 and the determination of the influence of deformation on the structure of the equilibrium compound.8 The nickel-rich portion of the binary system is reported to be of the simple eutectic type in which the maximum solubility of 12.7 at. pct Nb occurs at 1282"c.&apos; The two-phase field below the eutectic temperature is bounded by the a fcc solid solution and an orthorhombic Ni3Nb compound. No metastable phases have been reported in previous investigations. In transformation studies of certain nickel-base commercial alloys that contain niobium, two ordered metastable compounds containing niobium have been shown to precipitate from the solid solution, both of which have been identified as y&apos; and have the composition NisNb or Ni,Nb. One compound has been reported to have the bct DOz2 type Al3Ti structure" and the other the cubic LI2 type Cu3Au structure.9,11 In the present work on Ni-Nb binary alloys a metastable y&apos; compound has not been detected after conventional quenching and aging treatments. An anomalous behavior was noted in electrical resistivity measurements. in alloys containing between 7 to 12 at. pct Nb when aging treatments were performed below 500°C after fast quenching from 1250°C. Transmission electron microscopy has shown that this behavior is caused by the formation of a low-temperature precipitate of unreported structure type and composition. EXPERIMENTAL METHODS Several Ni-Nb alloys, containing up to 11.5 at. pct Nb. were prepared by either levitation melting and casting in copper molds or by induction melting in alumina crucibles; both techniques employed purified helium gas as a protective atmosphere. The purity of the nickel and niobium used to make the alloys was 99.98 wt pct Ni and 99.9 wt pct Nb. The composition and homogeneity of the alloys were checked by weight measurements and by electron microprobe analysis. The induction-melted alloys were homogenized for 100 hr at 1100°C. The resistivity specimens were prepared from rods swaged to 2.5 mm and the electron microscopy specimens were cut from sheet that was rolled to 0.4 mm and thinned using a modified Bollmann technique." The elevated-temperature solution treatments were carried out in a purified helium atmosphere followed by direct quenching into a 10 pct NaCl solution at 23°C. Additional protection against oxidation of the samples during solution treatment was accomplished by using tantalum foil as a "getter" in the furnace. The specimens were aged at various temperatures in salt baths controlled to +2oC. A Leeds and Northrup K5 potentiometer was used to make electrical resistivity measurements on specimens immersed in liquid nitrogen. Electron microscopy and diffraction studies were carried out with JEM-7 and Philips EM-200 microscopes operating at 100 kv. RESULTS AND DISCUSSION Ni-Nb alloys containing between 7 and 11.5 at. pct Nb that have been solution-treated in the range 1220" to 1280°C and quenched to 23°C undergo a precipitation reaction when aged in the temperature range 300" to 500°C. Precipitation was detected by selected-area electron diffraction after aging a specimen for as little as 30 sec at 350°C) whereas the reaction was well-advanced after aging for 150 hr at 475°C. Electrical resistivity measurements were used to monitor the progress of the precipitation reaction. In the present experiments the nucleation process for precipitation required a high solution temperature and a rapid quench into brine. The presence of aluminum, iron? and carbon in amounts totaling less than 1 wt pct was found by electron diffraction to completely suppress the formation of the low-temperature precipitate that has been detected in the binary alloy. Electron diffraction techniques were used to determine the structure of the precipitates that formed during the decomposition of the Ni-Nb supersaturated solid solutions. Figs. l(a) through l(d) show electron diffraction patterns oriented to the [loo], [110], [lll], and [I031 zone axes of the matrix. Areas of reciprocal space between these sections were investigated by slowly varying the orientations of the crystal under study; this procedure revealed no reflections other than those depicted in Fig. 1. The presence of super-lattice reflections at points coincident with the matrix reflections was confirmed by the examination of an almost completely transformed structure. On the basis of the accumulated diffraction data, the reciprocal lat-

Jan 1, 1970

By F. W. Schremp, V. L. Johnson

This paper discusses the results obtained from high temperature, high pressure filter loss studies in which field samples of clay-water, emulsion, and oil base fluids were used. High temperature, high pressure tests of some premium priced emrilsion and oil base drilling fluids show filter loss peculiarities that are not predicted by standard API tests. It is recommended that high temperature, high pressure filter loss tests be used to evaluate the performance of such fluids. Apparatus is described which proved to be satisfactory for evaluating filter loss behavior over a wide range of temperatures and pressures. INTRODUCTION The petroleum industry spends large sums of money each year on chemical treating agents for lowering filter loss and on premium-priced low filter loss drilling fluids. While it is an accepted fact that low filter loss is advantageous during drilling operations, it is questionable whether the present standard method of determining filter loss gives a reliable indication of the loss to he expected under bottom hole conditions. The purpose of this paper is to show that high temperature. high pressure filter loss tests Should be used to evaluate filter loss behavior of fluids for deep drilling. Concern over possible effects of filter loss on oil well drilling and well productivity dates back to the early 1920&apos;s. During the years 1922 to 1924, filtration studies were reported by Knapp,&apos; Anderson2 and Kirwan." These studies were the first to be reported in the literature on this subject. No further information was published on the subject until 1932 when Rubel&apos; presented a paper in which he discussed the effect of drilling fluids on oil well productivity. In 1935. .Jones and Babson constructed the first laboratory tester designed to study the effects of temperature and pressure on the filter loss behavior of clay-water drilling fluids. In a discussion of their investigations, Jones and Babsons stated, "Performance characteristics of a mud can he evaluated with considerable reliability by a single test at 2,000 psi and 200°F. Exact correlation between the results of performance test5 made under these conditions and the behavior of muds in actual drilling operations is of course impossible." Jones arid Babson apparently were well aware that at best laboratory tests can give only qualitative answers to the question of what is the actual behavior of a drilling fluid when subjected to deep drilling conditions. Jones&apos; presented a paper in 1937 in which he described a static filter loss tester to be used for routine filter loss tests. This instrument subsequently was adopted as the standard APl filter loss tester. In 1938, Larsen7 developed a relationship between filtrate volume and filtrate time that is in general acceptance today. Larsen was cognizant of the danger of estimating bottom hole behavior from filter loss measurements at room temperature. He tried to predict the effect of temperature on filter loss by relating temperature effects through the temperature dependence of filtrate viscosity. This was undoubtedly an over-sirriplification of the temperature dependence of drilling fluid filter loss. In 1940, Byck" published a summary of experimental results of filter loss tests made on six representative California clsy-water drilling fluids. He concluded that "no existing method will permit even an approximate determination of the filtration rate at high temperature from data at room temperature. It is necessary to measure filtration at the temperature actually anticipated in the well, or to make a sufficient number of tests at various lower temperatures so that a small extrapolation of these data to the anticipated well temperature may be applied." Byck&apos;s findings were presuma1)ly well accepted and recognized by drilling Fluid technologists, and yet, they did not lead to wide adoption of high temperature drilling fluid filtration equipment. This is evidenced by the fact that no addition information has appeared in print on the subject since 194). Study of Byck&apos;s data shows that there was a useful consistency in them. The fluids did not show predictable losses at high temperatures, but they did line up at high temperatures in approximately the same order that they lined up at low temperatures. That is, if a fluid appeared to be a good fluid with relatively low loss at low temperatures, it would also be a good fluid with relatively low loss at high temperatures. In the last decade. the above situation has changed. The drilling fluid art is markedly different from what it was. The outstanding change, as far as the present discussion is concerned, has been the adoption of wholly new types of drilling fluids. Oil base and emulsion drilling fluids have come in to wide use. It is, therefore, necessary- to re-examine previously satisfactory generalizations to see if they are still valid. It turns out. as might have been expected. that Byck&apos;s explicit generalization. already quoted, is still true. Filter losses at high temperatures cannot be predicted from filter losses at low temperatures. However, no further generalizations are valid now. Fluids of different chemical types show different general behaviors. No longer do the fluids line up approximately the same at high temperatures as they do at low temperatures. They may line up entirely differently. Special fluids exhibiting very low loss at low temperatures may have losses as high as those of ordinary clay-water fluids at high temperatures. This fact is highly significant, because premium prices are being paid for the special fluids.

Jan 1, 1952

By H. Biloni, R. Morando

The surface structure and substructure of Al-Cu alloys solidified as conventional ingots and under particular conditions such as those used by Bower and Flemings are studied. The influence of lampblack coating on the mold walls is especially considered and the results compared with those obtained in copper and graphite molds where no coatings exist. When high heat extraction conditions exist the observations show that mechanism of copious nucleation is responsible for most of the chill zone. When the heat extraction through the mold walls is low, a coarse grain structure with dendritic morphology arises, with a size that depends on the degree of convection present, analogous to that analyzed by Bower and Flemings. In both cases the effect of the convection on the macroscopic and microscopic appearance is discussed. The ingot macrostructure consists of one or more of three zones: "chill zone", "columnar zone", and central "equiaxed zone". The mechanism of the columnar-equiaxed transition has been subject of considerable interest and at present at least three theories exist about the formation of the equiaxed region: 1) the constitutional supercooling theory1 maintains that the equiaxed crystals nucleate after the columnar zone has formed, as a result of the constitutional supercooling of the remaining liquid; 2) chalmers2 pointed out, however, that there were several objections to this proposal, and that consideration should be given to the possibility that all the crystals, equiaxed as well as columnar, originated during the initial chilling of the liquid layer in contact with the mold; 3) Jackson et aL3 and O&apos;Hara and ~iller~ suggested that a remelting mechanism of the dendrite arms is responsible for the formation of the equiaxed region. After the work of Cole and Bolling and other authors6 it became evident that convection (natural, reduced, or forced) plays a very important role in the transition from columnar to equiaxed and on the size of the resultant equiaxed structure. Until recently the accepted explanation of the chill zone was that it occurs as a result of copious nucleation in the liquid layer in contact with the mold walls.798 The columnar region is a subsequent result of the growth of favorably oriented grains and, as a result of a selection mechanism studied by Walton and Chalmers,9 elongated grains with marked texture are formed. Recently, however, Bower and Flemings" using an ingenious laboratory experiment introduced the idea that the "copious nucleation" mechanism is not responsible for the formation of the chill zone and that the presence of convection, introducing some form of "crystal multiplication", plays a decisive role in the formation of the chill zone. Unfortunately, it is important to consider that for their conclusions Bower and Flemings extrapolated the results obtained in their special experiments to the case of conventional ingots, and that these authors only analyzed the macrostructures of the specimens. Let us consider the work by Biloni and chalmers" concerning predendritic solidification. These authors were able to show that a study of the segregation substructure of A1-Cu gives information about the nucleation and growth of crystals formed in contact with a cold surface. A spherical predendritic region characterizes the first part of every grain nucleated in contact with the surface as a result of the chill effect. The aim of this paper is to elucidate through the observation of the segregation substructure the conditions under which (in the Bower and Flemings type of experiments and in conventional ingots) either the nucleation or the multiplication mechanism gives rise to the structure in contact with the mold walls. I) EXPERIMENTAL TECHNIQUES The experiments were performed on two alloys: Al-1 wt pct Cu and A1-5 wt pct Cu. The purity of the aluminum was 99.99 pct and the copper 99.999 pct. The results obtained with both alloys were similar. In the Bower and Flemings type of experiments the apparatus employed to obtain rapid solidification against a surface was similar to that used by those authors. The liquid was drawn by partial vacuum into the thin section mold cavity. Plate casts were 5 cm wide and usually 7.5 cm high. The thicknesses of the cast were 0.1 and 0.3 cm. Two different materials were used for the mold, copper and nuclear-grade graphite. The internal mold surfaces were polished and left uncoated for some experiments. In other experiments, the copper or graphite surface was coated with a thin film of lampblack material. In some of these particular experiments one of the mold walls was left with an uncoated region (usually in the form of a cross). The conventional ingots were cast in graphite or copper molds. In different experiments the mold walls were sometimes uncoated or coated with lampblack material. The results obtained in conventional and Bower and Flemings copper molds were compared with those obtained with copper molds coated with a very thin film of graphite; the results obtained were essentially similar. The size of the conventional ingots was 5 cm diam and 7 cm high in all cases. The cast surfaces produced by the Bower and Flemings type of experiments and conventional methods were observed macroscopically and microscopically without any metallographic preparation. As Biloni and Chalmers showed," the observation of the chill surface can give considerable information about the structure and segregation substructure.

Jan 1, 1969

By O. J. Hassel, W. T. Maidens, J. H. Calbeck

The rotary gas fired reheating furnace used by the American Zinc Oxide Co. at Columbus, Ohio for Therotarygasfiredreheatingfurnacerefining lead-free zinc oxide is described. The outstanding features of this operation are that the color of the zinc oxide is greatly improved, sulphur is eliminated, and cadmium arethatrecovered without densifying the product to an objectionable degree. IN 1919 Leland S. Wemple obtained a patent for a process of reheating zinc oxide wherein the "coarsening of grain due to excessive heating was avoided." He taught in his specification that if solid carbonaceous material, such as lamp black, was added to the zinc oxide in proper amounts prior to reheating, objectionable sulphur compounds could be removed and the color would accordingly be improved and no objectionable densification would occur because of the relatively low temperature required. The situation that made this invention imperative was the newly opened zinc oxide plant of the American Zinc, Lead & Smelting Co. in Hills-boro, Ill. This was one of the early Western Type American Process zinc oxide operations. Characteristic of all of these early Western operations using Tri-State and Western ores was the great difficulty encountered in obtaining a product low enough in sulphur to compete with the Eastern Type American Process zinc oxides which were made from ores containing very low sulphur percentages. Wemple demonstrated that the refining process of his invention produced a superior color and although this was true and a most welcome feature, the primary purpose of the early refining operations at Hillsboro was to reduce substantially the high sulphur content of the crude zinc oxide. Although many and varied attempts had been made for refining zinc oxide none of the processes had a commercial history of any consequence until Wemple&apos;s invention became standard practice for the American Zinc, Lead & Smelting Co. in 1919 and their operations have been unique in that substantially all of their lead-free zinc oxide has been reheated since the first installation at Hillsboro. This process has become known in the industry as refining. The furnace developed by Wemple and continued in use by the company from 1919 until 1943 was unusual and merits some consideration by way of review in this paper. The furnace was essentially a double hearth coal-fired muffle furnace with a mechanical raking system consisting of a central shaft supporting six rabble arms in each muffle. The untreated or "crude" zinc oxide was fed onto the outer rim of the top muffle, moved to the center where it dropped to the lower muffle and progressed to the outer rim where it was discharged into an alloy screw conveyor. The retention in this furnace was extremely short, about 5 min, and the shallow zinc oxide bed on the hearths of the muffles was being continuously turned by the fast moving rabbles. Soft coal was burned on the grates below the lower muffle and the long yellow flame necessary to carry the heat around both muffles resulted in a very inefficient combustion of the fuel. The temperature of the top of the lower muffle seldom exceeded 65 °C although the oxide itself often reached 700°C before discharge. The capacity of this furnace was approximately 1/2 ton per hr. In our plant at Columbus it was necessary to keep four of these furnaces running in parallel to take care of the production because, as mentioned above, every pound of zinc oxide produced during these 24 yr passed through one of these refining furnaces. An essential part of this refining operation was the use of carbonaceous material admixed with the zinc oxide fed to the furnaces. Between 1 and 2 pct of a bran produced in the processing of cotton seed was added to all zinc oxide charged to the furnaces. The bran ignited on the top hearth and was still burning when the charge fell from the top hearth to the bottom hearth making a cascade of sparks. The rapid turning of the zinc oxide caused these particles of bran to flash on the hearths behind each rabble; but the combustion, of necessity, had to be complete by the time the charge reached the outer rim of the bottom hearth, otherwise the finished product would be contaminated with the charred particles of bran which would give the zinc oxide an unsatisfactory color. Although this operation was initiated to reduce objectionable sulphur percentages, as time went on new properties of the product were appreciated which made advisable continuing the refining process long after other methods of sulphur reduction became known in the industry. The particle size and particle size distribution, the absence of colloidal fines and perhaps a unique surface condition gave this product an outstanding performance when used in paints. The Wemple furnaces installed in Columbus in 1919 had to be rebuilt frequently and were extravagant in the use of fuel. The raking mechanism and the muffles required excessive maintenance expense and as the furnaces wore out the problem arose whether to continue along this line or to explore the possibilities of obtaining similar or better results in the simpler and more commonly used rotary furnace. To this end special research was initiated in 1941 on a small laboratory rotary

Jan 1, 1951

By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.&apos; The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown&apos; to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown&apos; has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler&apos; is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:&apos;

Jan 1, 1970

By E. S. Fisher, L. C. R. Alfred

The elastic anisotropy factors, c4,/c6,, c3,/cll, and c12/cl,, for hcp metal crystals vary significantly among the dgferent unalloyed metals. Significant variations with temperature are also found. The effects of elastic anisotropy on the dislocation in an elastic continuum with hexagonal symmetry have been investigated by computing the elasticity factors for the self-energies of dislocations in fourteen different metals at various temperatures where the elastic moduli have been reported. For most of the metals the effects of the orientation of the Burgers vector, dislocation line, and glide plane are small and isotropic conditions can be assumed without significant error. Significant effects of anisotropy are, however, found in Cd, Zn, Co, Tl, Ti, and Zr. The elasticity factors have been applied in the calculations of dislocation line tensions, the repulsive forces between partial dislocations, and the Peierls-Nabarro dislocation widths. It is predicted that the increase in elastic anisotropy with temperature in titanium and zirconium makes edge dislocations with (a), (a + c), and (c) Burgers vectors unstable in basal, pyramidal, and prism planes, respectively. The probability of stacking faults forming by dissociation of Shockley partials in basal planes also decreases with increasing c4,/c6, ratio, when the stacking fault energy is greater than 50 ergs per sq cm. The widths of screw dislocations with b = (a) in titanium and zirconium increase very significantly in prism planes and decrease in basal planes as c4,/c6, increases. The effects of elastic anisotropy on various dislocation properties in cubic crystals have received considerable attention during the past few years. In the case of cubic symmetry the departure from isotropic elasticity depends entirely on the shear modulus ratio, A = 2c4,/(cl, —c12); i.e., the medium is elastically isotropic when A = 1. Foreman1 showed that an increase in the ratio A produces a systematic lowering of the dislocation self-energy for a given orientation and Poisson&apos;s ratio. ~eutonico~, has shown that large anisotropy can have a marked effect on the formation of stacking faults by the splitting of glissile dislocations in (111) planes of fcc and (112) planes of bcc crystals. ~iteK&apos; made similar calculations for (110) planes of bcc metals. Both studies of bcc metals showed that the large A values encountered in the alkali metals tend to reduce the repulsive forces between Shockley partial dislocations. In fcc metals, however, A does not vary over the large range encountered in bcc metals; consequently, the effect of A on the forces between Shockley partials is masked somewhat by the differences in Poisson&apos;s ratio between metals. The effect of A on the line tension of a bowed out pinned dislocation has also been investigated for cubic crystals, first by dewit and Koehler5 and more recent- ly by Head.6 In both cases the line energy model is applied and the core energy is not taken into account, thus making the conclusions somewhat tenuous with regard to the physical interpretation. Nevertheless, the fact that a large A decreases the effective line tension is clearly evident and the tendency for large A to produce conditions that make a straight dislocation unstable (negative line tensions) also seem evident. Head, in fact, shows visual microscopic evidence that stable V-shaped dislocations occur in 0 brasse6 For hcp metals the definition of elastic anisotropy is more complex and, furthermore, significant deviations from an isotropic continuum are found among a number of real hcp metals, especially at higher temperatures. The present work was carried out to survey the effects of elastic anisotropy on the elasticity factors, K, that enter into the calculations of the stress fields around a dislocation core. Some isolated analytical calculations have previously been carried out for several hcp metals but they are restricted in the dislocation orientations and temperature.8&apos;9 The present computations are based on single-crystal elastic moduli that have appeared in the literature and consider various orientations requiring numerical computations. The results are then applied to survey the effects of temperature on the dislocation line tension and dislocation splitting in hcp metals. PROCEDURE Anisotropy Factors. The degree of elastic anisotropy in hcp crystals cannot be described by a single parameter, such as the A ratio in cubic crystals. The following three ratios must be simultaneously equal to unity in order to have an elastically isotropic hexagonal crystal: The magnitudes of these ratios at several temperatures, as computed from the existing data for the elastic moduli of unalloyed hcp metals, are given in Table I. There are no cases of complete elastic isotropy, but the large anisotropy ratios encountered in the cubic alkali metals are also missing. There are, however, several significant differences among the hcp metals, the most notable being the relatively small A and B ratios in zinc and cadmium and the differences in the magnitudes and temperature dependences of A. It has been noted that the temperature dependence of A has a consistent relationship to the occurrence of the hcp — bcc tran~formation. For cadmium, zinc, magnesium, rhenium, and ruthenium, A is less than unity at 4&apos;~ and, with exception for rhenium, decreases with increasing temperature. In the case of rhenium, A has essentially no temperature dependence between 923&apos; and 1123"~, so that it is clear that A does not approach unity at higher temperatures. Cobalt is similar to the above-mentioned group of metals in that it also does

Jan 1, 1969

By Morris Muskat

A theory is presented for calculating the performance history of complete water-drive systems producing from idealized stratified formations. The general equations are applied to systems where the permeability stratification is either of the exponential or linear type. Calculations were carried through for different degrees of permeability stratification, but with special emphasis on the effect of the mobility ratio between the produced oil and the invading water on the resultant performance. These results are also expressed graphically as curves for the initial water breakthrough recovery, for the different degrees of stratification, as a function of the mobility ratio, and of the composition of the produced fluid stream as a function of the cumulative oil recovery. For several typical cases the latter has also been plotted as a function of the cumulative oil and water throughflow. The general result is that when the mobility of the oil is lower than that of the invading water the channelling tendency resulting from the permeability stratification becomes aggravated as the higher permeability zones become flooded out. Situations of this type would obtain when producing low gravity or highly viscous oils. Conversely, if the mobility of the oil is high compared to that of the invading water, the flooding of the high permeability zones will lead to a retarding and choking effect, and the gross bypassing phenomena will be partially suppressed. These conditions would correspond to those of flooding high gravity or low viscosity oils. A discussion is given of the various basic assumptions made in the analysis, including that of ignoring the stripping phase of the production history as implied by relative permeability concepts. INTRODUCTION The physical ultimate recoveries from oil reservoirs are basically determined and limited by the physical oil displacement processes associated with the reservoir producing mechanism. In practice, however, the economic ultimate recoveries are further limited by the mobility of the reservoir fluids and the uniformity and continuity of the producing formation. In fact, it is the differential depletion between the component parts of the composite reservoir which ultimately determines the total recovery at the time of field abandonment. While this observation applies to both the solution gas drive and gravity drainage mechanisms, in which use is made only of the energy contained within the original oil-bearing reservoir, it is of even more paramount importance under operations wherein the energy associated with extraneous fluids provides the ultimate oil expulsion mechanism. Whether the invading fluid is the water from an edgewater drive, water injected for pressure maintenance, gas injected for pressure maintenance, or gas returned to the formation in a cycling program, it is often the continuity and uniformity of the producing section which will control the economic efficiency of the operations. The importance of the problem of reservoir non-uniformity does not, of course, lessen its complexity or the difficulties of its solution. In fact, these are inherently such that the concept of a "general" solution is virtually meaningless. About all that can be reasonably hoped for is the analysis of specific and well-defined types of non-uniformity which may give some degree of approximation to actual reservoir conditions. Since variations in the nature of the reservoir which depend only on the position along the streamlines will not lead directly to major differential depletion development within the reservoir, the types of non-uniformity considered thus far have involved stratification assumptions. That is, the producing section has been replaced by a multi-layer "sandwich," each uniform areally, and differing from the others only in its basic physical constants as to thickness, porosity and permeability. The fluid motion in the composite system is thus approximated by a parallel superposition of the independent fluid movements in the individual strata. For the specific application to cycling operations the theory of the effect of permeability stratification has been developed for both discontinuous&apos; and continuous types of permeability stratification. Among the latter, treatments have been given of systems in which permeability distributions are governed by exponential, linear&apos; or probability3 functions. In all these studies complete dynamical equivalence was assumed between the injected dry gas and the displaced wet gas. The overall effective permeability of each stratum was therefore considered as constant and independent of the degree of invasion of the injected fluid. In the case of the displacement of oil by water, the assumption of dynamical equivalence between the water and oil will be strictly valid only by accident. Even if the oil viscosity should be the same as that of the water, the effective permeability to the oil in the presence of the connate water will in general be quite different from that of the water behind the water-oil interface flowing past the trapped residual oil. As a result the effective permeability for the stratum as a whole and rate of water invasion will change with time as the intrusion continues. The differential fluid motion in the individual strata will thus also vary with time. Qualitatively, it is easy to predict the resultant effects. If the permeability to viscosity ratio of the invading fluid exceeds that of the fluid displaced, the stratification and bypassing effect of the perme-

Jan 1, 1950