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By J. S. Blakemore, E. O. Hall

SERRATED yielding, commonly called the Portevin-Le Chatelier effect, is known to occur in a wide range of alloys where the moving dislocations are considered to be locked by the diffusion of solute atoms to them. From the work of Cottrell,1 an approximate relationship between strain rate, E, dislocation density, p , and solute diffusion coefficient, D, giving rise to serrated yielding is: e =Dp

Jan 1, 1969

By S. Dinda

A series of as -quenched 4340 bars were drawn through a carbide die to various reductions. The X-ray diffraction technique of Lopata and Kula was employed to detect preferred orientation in drawn martensitic steel bars with low amounts of deformation, as lord as 0.8 pct The specimen face of each bar examined was cut at a 45-deg angle to the bar axis. The reflecting planes in the 45-deg face were varied by appropriate rotation of the sample using a spectrogonionzeter. TIE X-ray bean of a diffractometer was reflected from the center of the bar and the diffracted intensity was delected with a proportional counter and recorded. Intensity peaks were developed by cold working for 110 planes oriented at 0 and 60 deg to the bar axis. The intensity peaks increased with increasing defortnalion us a preferred orientation with a 110 texture developed parallel to the drawing direction. The intensity peaks for deformed as-quenched specimens remain unchanged after tempering at temperatures as high as 1000°F. The same amount of preferred orienlalion was observed both inferritic (hot-rolled) and martensitic (as-quenched) structures after an equivalent amount of deformation. THE deformation of martensite with medium carbon content. less than 0.5 pct, has been studied by Breyer et a1.1,2 It was reported that changes in properties such as resistivity, carbide precipitation, and the introduction of a yield point phenomenon were produced after cold reduction of as-quenched AISI 4340 steel bars. Later, Breyer and Nachtman3 studied the effect of cold reduction upon X-ray line intensity. They showed that the integrated 110 line intensity increased with increasing deformation when the planes examined were perpendicular to the die drawing direction. The integrated 110 line intensity for planes oriented at 45 deg to the die drawing direction, in contrast, were found to slightly decrease. These changes were proposed to be consistent with the previously proposed model of a stress-induced ordering of carbon atoms in the vicinity of dislocations.1,2 Objections can be raised to the above interpretation of the X-ray results on two grounds: a) Rough structure factor calculations indicate that the intensity changes are too large (50 pct observed vs 2 pct calculated4,5) to be the result of changes in the location of iron atoms produced by the stress-induced ordering of the carbon atoms. b) The results might be explained in terms of preferred orientations, although X-ray evidence of the development of texture has not been reported in the literature for deformations as slight as 1 or 2 pct. The aim of the present work was to determine if preferred orientation was present in such cold-drawn martensitic steel bars. In drawn rod or wire there is generally a certain crystallographic direction which is aligned in the direction of the wire axis, and the crystallographic planes are distributed symmetrically around this "fiber axis".6-8 This type of cylindrical specimen, with the fiber axis located at the center, will show rotational symmetry. Lopata and Kula9 proposed an experimental method utilizing a specimen cut at 45 deg, see Fig. 1. The X-ray beam is diffracted from the center of this bar cross section. The specimen is rotated around an axis perpendicular to the bar axis and lying in the 45-deg cut face. This permits the angle between the normals to the reflecting planes and the bar axis to be varied from 0 to 90 deg.9 With this arrangement the errors due to absorption and irradiated volume compensate each other.' This greatly simplifies analysis of the data and is of considerable advantage for quantitative measurements. If there is preferred orientation in the specimen, more planes are oriented in a particular direction in the bar. When the bar is rotated to the favorable Bragg condition for that particular orientation, the intensity will be higher than that for some other angle. This technique was adopted for the present investigation.

Jan 1, 1969

By D. C. Seidel, M. C. Fuerstenau, R. J. Roman

The existence of a surface charge on the alkali halide salts is shown, and a flotation mechanism involving surface charge and collector solubility is developed. Data suggest that KC1 is positively charged and that NaCl is negatively charged in saturated brines, and that the neutral molecule RNH,Cl is the collector in the amine-KC1 system, RSO, is the collector in the sulfonate-KC1 system, and RCOONa) is the collector in the fatty acid-NaCl system. A number of hypotheses have been advanced to explain the mechanism of soluble salt flotation; one of these involves exchange between collector ions and surface cations. With this mechanism Gaudin1 suggested that the differences in flotability of halite and sylvite with primary amines are due to the ionic size of the RNH;, Kt, and Na t ions. Fuerstenau and Fuerstenau expanded this hypothesis to include many other alkali halide salts. Several exceptions to this hypothesis are known. That is, this model does not explain why salts containing the same cation, or why salts of different degrees of hydration, respond differently to flotation. For example, why NaI is floated with an amine whereas NaI .2H,O is not. Further, no correlation between ionic size and flotation response can be made with sulfonate or car-boxylate as collectors. In addition, this hypothesis does not explain the effect of magnesium or lead activation, nor does it offer any explanation of the role of temperature in salt flotation. Rogers and Schulman3 realized some of the inadequacies of the ion exchange mechanism and proposed another mechanism based on the heat of solution of the salts. They concluded that weakly hydrated salts can be floated with alkyl amines and sulfonates, that strongly hydrated salts can be floated with fatty acids, and that excessively hydrated salts cannot be floated at all. Their work was not limited to the al-

Jan 1, 1969

By N. G. W. Cook

The conventional cyclic system of deep-level mining by drilling and blasting gives rise to an inadequate degree of stope sorting when mining thin reefs. This results in poor utilization of the capital facilities of a mine in the form of shafts, haulages, airways and associated equipment. Continuous and controlled removal of the thin gold-bearing portion of the reefs would permit better stope sorting and hence greater utilization of capital facilities. Results of experiments to develop hard rock cutting machines for mining are reported and the benefits which could be derived from their use are discussed.

Jan 1, 1969

By Norman F. Schulz

The technical excellence of separation achieved in a mineral concentration process, or any other process where two constituents of any kind are physically separated from each other, is expressed uniquely and quantitatively by the Separation Efficiency: ES = (R ? Rg) where R is the percentage of the valuable constituent and Rg the percentage of the waste appearing in the concentrate. The Separation Efficiency meets all the usual requirements of a true efficiency and is independent of the nature of the process used. It can be visualized as the percentage of the feed material that, in effect, actually undergoes complete separation while the rest of the feed is distributed randomly and unchanged into the two separation products.

Jan 1, 1969

The Bulli and Wongawilli Seams, the two principal sources of coking coal for the Port Kembla steelworks of Australian Iron & Steel Pty. Ltd., vary in rank and in type over the Southern and South Western Coalfields.The Bulli Seam, ranging widely in type, produces coke varying from weak to strong. The Wongawilli Seam, more consistent in type, produces coke of more consistent strength, but considerably less strong than that from the best Bulli Seam coal.Plans of seam variation show the regional trends in rank and type for each seam.The strongest coke is derived from coal containing between 45 and 55 per cent vitrinite, m.m.f. This is obtainable from the Bulli Seam in a zone embracing Bulli and Appin collieries.A satisfactory correlation is achieved between vitrinite content and coke stability and hardness, enabling prediction of coke strength for Southern Coalfield coals.The use of vitrinite reflectance, as an indicator of rank, in addition to type to predict coke strengths is at present hampered by lack of data, particularly in the South Western Coalfield. Nevertheless, data available at present allow the use of both variables and give better correlations with coke strengths than type alone.A spread of comprehensive data across both coalfields will enable advance assessment of cokes produced from coals having known rank and type. Blending to a ranktype specification for optimum coke strengths would allow the best use of the coal reserves of the coalfields.

Jan 1, 1969

By E. T. Turkdogan, W. L. Worrell

The rate of reaction of hydrogen sulfide with ferrous sulfide was studied by measuring the initial rates of sulfidation of iron strips in hydrogen sulfide-hydrogen-argon mixtures at 670°, 800°, and 900" C. The time-dependent surface sulfur activity is derived from the instantaneous rate of sulfidation with the assumption that diffusion in the sulfide layer is in a pseudo-steady state with the gas-sulfide chemical reaction. The rate of sulfur transfer from hydrogen sulfide to the surface of iron sulfide is proportional to the partial pressure of hydrogen sulfide and inversely proportional to the activity of sulfur at the surface of the sulfide layer. The derived rate equation is based on the assumption that most of the surface sites on the chemisorbed layer of iron sulfide are occupied by sulfur atoms and that the slow rate-controlling reaction is the dissociation of hydrogen sulfide on the chemisorbed layer. The experimental results are in reasonable accord with this reaction model. 1 HE slow approach to parabolic growth rate in the sulfidation of iron in hydrogen sulfide-hydrogen mixtures is a manifestation of slow approach to surface equilibrium between the gas and the surface of the sulfide layer. For example, at 800°C and Fig. 7 in Part I, the parabolic growth rate begins after approximately 1 day of sulfidation time. With decreasing temperature and decreasing partial pressure of hydrogen sulfide, the time necessary to reach gas-sulfide surface equilibrium is much longer. These observations are similar to those reported previously by Turkdogan et al.' on the oxidation of iron to wustite in hydrogen-water vapor mixtures. The slow approach to gas-sulfide equilibrium is well-demonstrated by the results in Fig. 1 where the square of the weight gain per unit area, ( g S per sq cmI2, is plotted against time for gas mixtures having PH g//>H = 1.0 with 0, 25, 50, and 67 pct Ar at 800°C. The value of 1.5 X lo-' (g S per sq cm)' corresponds to almost complete sulfidation of the iron strip (- 0.05 cm thick) to iron sulfide. The points fall on S-shaped curves. If the inflection parts of the curves are considered to be linear, thus indicating parabolic growth rate and the establishment of gas-sulfide equilibrium, their slopes would have to be the same for a fixed ratio in the gas mixture. Such is not the case, and the slopes for the "linear" parts of the S-shaped curves are lower than the value when gas-sulfide surface equilibrium is established. The subject matter of this paper is the kinetics of the surface reaction of hydrogen sulfide with iron sulfide during the early stages of sulfidation of an iron strip. EXPERIMENTAL RESULTS The apparatus and materials used were the same as those discussed in Part I. In the present experiments of relatively short duration, a purified iron strip, 5 by 2 by 0.05 cm, which was suspended in the uniform hot zone of a vertical zircon tube, reacted with a flowing gas mixture of hydrogen sulfide-hydrogen-argon. The sample was suspended from a gold chain attached to a calibrated silica spring. The amount of sulfur picked up by the iron, which formed a layer of iron sulfide, was determined by measuring the displacement of a reference point on the silica spring, using a cathetom-eter. In all cases, the degreased sample was first annealed in a stream of oxygen-free dry hydrogen for several hours to remove any impurities such as oxygen, nitrogen, or carbon which might have been present on the surface of the sample.' The rate measurements were carried out at 670°, 800°, and 900° C in hydrogen sulfide-hydrogen-argon mixtures with pH2 s/Ph2 ratios from 4 to 0.1. In a few experiments of short duration no sulfur deposition was observed in gas mixtures with (comments concerning sulfur deposition at high pH s/ph ratios were made in Part I.) Typical examples of the results obtained are shown in Fig. 2 for two temperatures and two gas compositions. With the present experimental technique, reproducible rate data could be obtained only after a uniform

Jan 1, 1969

By C. Y. Cheng

THE purpose of this note is to show that the dislocation mechanism controlling the creep of Fe-4 pet Si alloy1 may equally account for the behavior of a-Fe2 over the same temperature range. A recent study of the creep behavior of a-Fe has been made by Ishida et al.2 Their results were in agreement with the mechanism of nonconservative motion of jogged screw dislocations over the entire range of temperatures investigated, from 480° to 1045°K. However, the observed creep rate was much higher than that which could be accounted for by the above model unless the authors assumed that pipe diffusion became significant below 775°K. More recently, Cheng et al.1 inves-gated the creep of Fe-4 pet Si alloy over about the same temperature range and found that the results could be correlated fairly well with a dislocation climb mechanism as represented by Eq. [l]. Proceeding as shown previously,1 if creep is controlled by a single climb mechanism, at intermediate stresses, the shear creep rate, y, can be represented by where n and K are material constants {K is independent of the temperature but dependent on the structure, that is, K decreases during the primary stage and reaches a steady-state value over the secondary stage of creep), t is the applied shear stress, G is the shear modulus, gc is the free energy of activation for creep (usually equal to that for self-diffusion, gd), and RT has the usual meaning. By solving for y, the apparent activation energy for creep, Q which can be determined experimentally, is given by where hc is the enthalpy of activation for creep which usually is also equal to that for self-diffusion, h^. By using Eq. [2], the data in Fig. 2 of Ref. 2 can be re-plotted as shown in Fig. 1. By comparing the two figures, it is seen that the slight increase in the apparent activation for creep over Region II, as noted in Fig. 2 of Ref. 2, is due to the influence of temperature on the shear modulus rather than of the stress on the

Jan 1, 1969

By J. K. Abraham

In recent years there has been interest displayed in the precipitation phenomena occurring in austenitic alloys based on the binary Fe-Ni system.1'2 Previous communications have been extended covering the kinetics of clustering in the Fe-Ni-Ti system and the effect of cluster size on subsequent mechanical properties.3'4 To a great extent the question of coherency, which has a dominant role in determining the mechanical properties, is dictated by the degree of misfit between the precipitate and matrix. Thus, the change in lattice parameter of the matrix with composition is an important variable that should be examined. The lattice parameter, ao, of austenite was determined for Fe-29.75 Ni-1 to 6 Ti and Fe-27 Ni-1 to 10 Ti alloys in this study. The alloys used in this investigation were melted in a vacuum induction furnace from a starting stock of plast iron (99.95), electrolytic nickel (99.9), and ti- tanium sheet (99.5) in a MgO crucible. The alloy compositions in atomic percent are given in Table I and their relative position in the Fe-Ni-Ti ternary is indicated in Fig. 1. The chemical analyses were taken from the homogenized bulk materials treated in a manner related earlier.3 A diamond file was used to obtain powder from the bulk. To remove the stresses induced by filing, the powders were austenitized at 1875°F for

Jan 1, 1969

By G. H. Keith

Oxygen and nitrogen cause strain aging in electrorefined vanadium, as evidenced by maxima in yield and tensile strengths and by Snoek internal friction peaks. Alloys containing up to 0.22 percent oxygen and 0.11 percent nitrogen were investigated. Tensile strengths of oxygen-and nitrogen-containing alloys were 66,000 and 68,000 psi at 300° to 400° C, compared with 53,000 and 62,000 psi, respectively, at room temperature. Total elongation decreases to about 7 percent at the temperature of maximum strength. At 600° C, strain aging is not evident. Based on interstitial contents calculated from internal friction measurement, the increases in strength caused by nitrogen and oxygen were 440,000 psi per weight-percent nitrogen and 260,000 psi per weight-percent oxygen. Application of the Schoeck and Seeger treatment to the Snoek effect in these systems results in a calculated lattice distortion of 0.24 and 0.15 caused by the presence of an interstitial nitrogen or oxygen atom, respectively. Alloys containing boron or carbon were also investigated. Both elements refine the grain size but have no other effect because of their low solubility in vanadium.

Jan 1, 1969

By C. C. Harris

An analytical solution of the integro-differential equation of batch grinding is proposed as a first appoximation to the xYt surface. The size distribution equation (xY plane) is a three parameter equation previously suggested. Possible refinements are outlined. Comminution kinetics research is presently following several related courses. Some are equivalent, in that they represent different ways of viewing the same facet of the problem, though the entire endeavor cannot be described as being completely integrated. The purpose of this note is to propose and discuss a framework into which the various approaches might be fitted. This must clearly be founded upon an analysis of the xYt surface.' (See also Fig. 1 of Reference 26.) The investigations referred to above comprise mainly researches into the following: (1) The kinetics of the creation of the finer sizes during relatively small grinding times. This is the Fahrenwald-Arbiter-Bhrany 2-3 approach which leads to equations equivalent to a special case of the charles4 relationship. It emerges that initial production of fines follow essentially zero order* kinetics. (2) Disappearance kinetics of the coarser fractions. This appears to be a first order relationship.5-6 (3) Prediction of the xYt surface via the selection and breakage functions utilizing computer-programmed or approximate solutions of the integro-differential equation of batch grinding.5,8-17 A recent discussion by Mika et al.5 references the relevant literature up to about 1966. In addition to these main-stream researches there is some work on the minor topic of extremely long grinding time considered as a limiting case.18-19 The field is supported by investigations into the size distribution of fragments produced by breakage processes, some of this work being most valuably statistical-mechanical in nature.20-25 Better fitting equations, however, are obtained by statistical and curve-fitting methods.26 This

Jan 1, 1969

By A. Rosenzweig, M. M. Karnowsky

The generalized binary diagram of the Au-Sn-Pb system is presented. The chief characteristic is the pseudobinary between lead and AuSn. On the high-gold side of the pseudobinary, four reaction isotherms were found at 363°, 274°, 225°, and 204°C. On the low-gold side of the pseudobinary, three reaction isotherms at 277°, 205°, and 176°C were found. A vertical section from the eutectic solder composition to gold was developed from the isothermal sections generated. METALLURGICAL problems arising from the intentional or accidental formation of Au-Sn-Pb alloys in soldering applications have indicated a need for information on the phase equilibria in this ternary system. The literature indicates that a complete diagram presenting this information has not been prepared. Even the recent excellent work by prince' entitled "The Au-Pb-Sn Ternary System" actually extends only to the AuSn or 50 at. pct Au range. There are more events in the 50 to 100 at. pct Au than in the less than 50 at. pct range. This article by Prince furnished much guidance in preparing this report. Initial efforts with the isopleth from the eutectic solder composition 61.9 wt pct Sn-38.1 wt pct Pb and 0 to 90 wt pct Au indicated that extensions of the work to the whole of the diagram (even if in less detail) were necessary to understand this system. In undertaking the construction of such a diagram, this study used differential thermal analyses (DTA) and metallography with verification and identification of phases by electron microprobe analyses. EXPERIMENTAL PROCEDURE The procedure began with the development of a cell which would be unreactive with lead, tin, and gold, retain its strength to 1100°C, exclude oxygen, and also furnish a suitable well for insertion and protection of a thermocouple to monitor temperature changes in the material. Such a cell would make it possible to reuse the sample should a repetition of determination be desired. Fig. 1 is a photograph of two such quartz cells as finally developed. The specimens have been run many times. The cell is made up of an inner sample bucket and an outer capsule with a thermocouple well which the sample surrounds. The DTA unit was an assembly devised from available instrumentation. The sample holder was a 3-in.-long cylinder of nickel, 2 1/2 in. in diam, fitted securely in a vertical tube furnace. Two holes 7/8 in. in diam were symmetrically located to receive the quartz cells. A dummy cell with nickel powder was used as the reference. The absolute temperature was recorded with a Pt/Pt 10-pct Rh thermocouple with an automatic Kaye ice bath compensator. (Calibration indicated the compensator to be accurate to better than ±0.5° over the 100° to 1000°C range.) The absolute temperature was measured in the sample and recorded on an L&N mul-tirange recorder with a full-scale display of 1 mv and automatic ranging of 99 mv. The differential signal between the sample temperature and the reference temperature was amplified with an L&N microvolt amplifier and recorded on an L&N Speedomax G recorder. Since two charts were obtained, the chart speeds were equalized and each event was noted on the differential chart, and the temperature at that time was obtained from the temperature record.

Jan 1, 1969

By Avis W. Effinger

In conjunction with pilot steamflood tests in the Venango sands of Warren and Venango Counties, Pa., the Marx and Langenheim (4)3 calculations were adapted and programed for digital computer solution to predict test performance. The Monte Carlo technique was incorporated in the calculations to provide values of several variables which could not be adequately defined from available information. The computation methods are explained and the FORTRAN IV program listing is presented. Data and results of the prediction calculations for Venango oil sands are also shown.

Jan 1, 1969

By S. J. Aresco

The Bureau of Mines has been active in promoting the purchase of coal for Government use under specifications that define the requirements in terms of heating value of the coal, expressed in British thermal units, and the composition as shown by proximate analyses. To these, when required, are added the ash-softening temperature, the free-swelling index, and the Hardgrove grindability index. Under most of these specification contracts the bidders guarantee the quality of the coal, and that guaranteed by the successful bidder becomes the standard of his contract. The deliveries are sampled in accordance with instruction3 issued by the Bureau of Mines; the samples are analyzed in the Bureau laboratory to determine whether the coal is of the quality guaranteed by the contractor; if it is not, a price adjustment is made. Analyses of the delivered coal and tipple samples (samples collected at mine tipples as coal is being loaded into railroad cars or trucks) provide valuable data for use in evaluating future bids. In addition, the continuous sampling of coal as delivered is a check on the practical results obtained in burning the coal.

Jan 1, 1969

The ultraviolet spectrum of isopropyl ethylthionocarbamate (the principal constituent of Dow flotation collector Z-200) in water and of Z-200 itself in water was found to have an absorption peak at 242 nanometers(nm). The height of this peak was found to be directly proportional to isopropyl ethylthionocarbamate concentrations up to 15 p.p.m. Z-200 contains about 90 per cent isopropyl ethylthionocarbamate and the heightof the peak was proportionately lower, but obeyed the straight line relationship up to 15 p.p.m. This showed the potential value of spectrophotometric measurements for the determination of Z-200 residuals in flotation liquors.Methyl ethyldithiocarbamate (an impurity in Z-200) increased the peak height slightly, but other impurities in Z-200, xanthates, and most inorganic salts present in flotation liquors do not interfere. However nitrate ion and thiosulphate ion have absorption peaks which overlap the isopropyl ethylthionocarbamate peak.The simplest general method to overcome this effect is to extract the isopropyl ethylthionocarbamate into cyclohexane and to measure the absorbance of the extract.The maximum absorbance of the cydohexane extract was at 247 nm and the peak height at this wavelength was found to be directly proportional to the isopropyl ethylthionocarbamate or Z-200 concentration in the original aqueous solution. An alternative method is to measure the spectrum of the original aqueous solution using the aqueous raffinate from extraction as a reference solution. This gives the spectrum due to isopropyl ethylthionocarbamate alone and measurement of the absorbance at 242 nm gives the concentration in the original aqueous solution. Both methods give the same value for the concentration of isopropyl ethylthionocarbamate in the original solution.

Jan 1, 1969

By J. M. Singer

The Bureau of Mines investigated the threshold of dispersal of monolayers and piles of rock dust, anthracite, and Pittsburgh seam coal dust in a small wind tunnel that simulated a coal mine gallery, with the objective of preventing or limiting the formation of flammable dust clouds. The effect of selected variables on entrainment velocity was examined. Mode of entrainment and flow processes in the wake region of dust configurations were investigated by means of high-speed motion pictures. Significant results were as follows: 1. Local minimum air velocities required for dispersal were only slightly higher for shallow dust ridges than for dust particles. 2. Minimum velocities for entrainment of dust particles from smooth glass and coal surfaces increased in the order rock dust, anthracite, Pittsburgh seam coal. 3. The mechanism for dispersal of dust poles depended significantly on dust pile geometry, cohesiveness of dust, bulk density and compaction of dust, adhesive surface, and vibrations perturbing the supporting surface.

Jan 1, 1969

By George B. Griswold

The two most stringent parameters for in place fracturing of rock are the lack of any initial void space in the rock which to expand into and the ability to gain access only through drill holes. These two restrictions have proven so severe that as of today the only proven techniques for efficient fracturing are the contained nuclear detonation and hydrofracing. Both of these methods have highly developed technologies for their application. Hydrofracing has been a standard oil field practice for two decades, and the experience gained from a couple hundred underground nuclear detonations has resulted in a thorough understanding of the phenomenology of cavity and chimney formation. What is still lacking is a practical method to create a suit- able degree of fracturing for those ore bodies which do not meet the application criteria for either the nuclear explosion or hydrofracing. Nuclear applications must be restricted to thick ore deposits so as to take advantage of chimney collapse height--preferable in excess of 200 feet thick. Other requirements such as ground shock, containment, and radioactive contamination further reduce the number of sites that prudently can be selected.

Jan 1, 1969

By M. M. Tilman

In a Bureau of Mines investigation to develop lead alloys with improved tensile strength and creep resistance, lead-base alloys containing cadmium and antimony in nominal 1-to-1 atomic ratios were melted in air, cast, and rolled into sheet to 90 percent reduction at temperatures varying from room temperature to 175° C. Tensile testing at room temperature and stress-rupture testing at 900±3° F were conducted on the as-rolled alloys. The best tensile properties were observed in an alloy of Pb-4.2 wt pct Cd-4.5 wt pct Sb which exhibited an average tensile strength of 7,270 psi with 36 percent elongation in 2 inches. An alloy of Pb-5.5 wt pct Cd-6.0 wt pct Sb had 100-hour stress-rupture values of approximately 2,100 psi and 1,000-hour values of approximately 1,700 psi.

Jan 1, 1969

By B. H. Caudle, B. M. Hickman, I. H. Silberberg

Secondary recovery projects often are not started in oil reservoirs until dictated by rising GOR's or declining oil production. Such circumstances require a well dispersed injection pattern to prevent the oil bank from bypassing the production wells. Many times this purpose is served by using the five-spot or line-drive patterns, in which half of the wells are made injection wells. A regular injection pattern is proposed that is based on the same well spacing as the five-spot but in which only a third of the wells need be converted to injection wells. Fluid flow model studies on this proposed pattern show that production histories will be as good as those for a five-spot pattern at mobility ratios of three and above. The model data are presented in a form that may be used to predict recoveries from both homogeneous and stratified formations. Introduction The injection of fluid into a petroleum reservoir usually is prompted by an actual, or predicted, loss in the productivity of the reservoir. Often, an oil reservoir is produced by pressure depletion until high GOR's dictate a change in policy. Fluid injection also causes increased ultimate recovery, but this usually is of less importance to the operator than is the maintenance of the production rate. It is a fact that the ultimate recovery in any particular fluid injection project is relatively independent of the number and spacing of the injection wells as long as the reservoir voidage through the production wells is balanced by the total injection rate. However, the response of a production well is directly affected by the distance it lies from an injection well. In places where the well productivities are declining, the injection wells should be spaced as evenly as possible among the producing wells ("dispersed" injection pattern). More particularly, if the production response depends upon the formation (and subsequent production) of an oil bank, each production well should be surrounded by injection wells. Otherwise, the oil productivity will increase very little as the oil bank moves past the well.'.' An evenly spaced injection pattern has the best chance of generating an oil kick in the production wells. If reservoir voidage and injection rates are to be equal, the ratio of injection wells to production wells must be equal to the ratio of the average injectivity to the average productivity (in reservoir volumes). This ratio is in strumental in choosing the injection pattern. Table 1 shows the production well to injection well ratio for the dispersed injection patterns that have been described in the literature.'-' All of these patterns will have comparable recoveries and response times (for the same basic distance between wells). The choice of pattern there fore depends upon the relative injectivity and productivity of the wells and upon the type of drilling pattern employed. Another important factor may be the ability of the proposed production wells to make up the lost productivity from those wells converted to injectors. These factors become more pronounced at the higher oil viscosities (low gravity oils). All other things being equal, the probable ratio of single well injectivity to single well productivity will be equal to the water-oil mobility ratio of the proposed flood. Thus, high mobility ratios (due to low gravity oil) should call for fewer injection wells — as long as these injection wells are "dispersed" to obtain more even pro duction response for the remaining wells. Secondary re covery projects in oil reservoirs seldom, if ever, will have mobility ratios requiring more injection wells than production wells. Thus, only the last five of the patterns listed in Table 1 will be of significant interest in oil recovery. Almost every development drilling program calls for the wells to be drilled along equally spaced rows and

Jan 1, 1969

By D. S. Rowley, F. C. Appl

Assuming that rock behavior, during cutting with a single diamond, may be approximated by that of a rigid, Coulomb, plastic material, a theory of single diamond cutting action has been developed. Using this theory, the stresses on the diamond cutting surface and the components of the cutting force have been determined. Theoretical results agree reasonably well with available experimental data. The theory of cutting of single diamonds may be used as the basis for subsequent study of the perfonnance of surface set diamond drill bits and other surface set diamond cutting tools. INTRODUCTION For more than twenty years, surface set diamond bits have been used successfully in the mining and petroleum industries to drill and core rock formations that range from medium hard to the hardest known formations. Most extremely hard rock formations cannot be economically drilled or cored by any other means. In view of the growing use and importance of surface set diamond drill bits, it is reasonable to study the way in which these tools cut, and the factors that influence wear of the diamonds. Such knowledge will contribute to better bit design and will improve operating procedures. To analyze the cutting performance of these tools it is appropriate to consider the way in which an individual diamond cuts. Once this is established, the over-all performance of the bits can be determined by considering the total effect of the individual diamonds. In recent years there has been a growing interest in rock mechanics and there now exist several publications dealing with the deformation and failure of rocks. Notable experimental work has been reported by Bredthauer,1 Handin and Hager,2, 3 and Gnirk and Cheatham.4 An extensive collection of data pertaining to rock properties at low confining pressures has been given by Wuerker.5 Cheatham and Gnirk have recently presented an excellent review of the state of knowledge regarding analytical and experimental rock deformation and failure.6 Generally rocks are extremely weak in uniaxial tension, and weak or only moderately strong in uniaxial compression. Both tensile failure and compressive failure are generally brittle in nature. This means that there is little or no deformation or "flow" of the material before shear or tensile fracture occurs. Thus, until fracture occurs, rock behaves very nearly like an elastic material in uniaxial stress. Significant changes in behavior of rock occur under conditions of triaxial compressive stress. There is generally a marked increase in compressive strength and in ductility. It has been demonstrated that the failure becomes plastic (in a macroscopic sense) at sufficiently high values of confining pressure. Sharp wedge chisel indentation studies conducted by Gnirk and Cheatham indicate that many rocks behave in a plastic manner at relatively low triaxial compressive stress states.4 If "failure" under triaxial compressive conditions is considered to be either complete rupture or macroscopic plastic flow, then the general failure characteristics of a rock can be reasonably well represented by the commonly known Mohr envelope. This certainly is not a perfect failure criterion (since the effect of the intermediate principal stress is neglected) but it has been found to be adequate for most engineering purposes. Mohr envelopes usually are constructed graphically using experimental triaxial test data. For purposes of analysis it is convenient to represent the envelope in equation form. Among the several approximate forms appearing in the literature, a parabolic form is suggested by Cheatham,7 and an exponential form is suggested by Paone and Tandanand.8 The exponential form has been adopted for this study, and based on published data, appropriate parameters have been established for 19 rock types. A typical plot of the data compared with the approximate envelope, and a summary of the rock properties and

Jan 1, 1969