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By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By R. H. Doremus, E. F. Koch

The first carbide phase that precipitates at 120°C from a iron containing about 0.02 wt pct, C was studied with the electron microscope. In both strained and unstrained material the carbide particles appeared to form on the dislocations in the iron, in agreement with the results of the kinetic study in part II. The structure of the carbide was tentatively identified as an expanded a-iron lattice (body-centered tetragonal) with about 0.7 wt pct C. This phase appeared to be metastable and apparently transformed into cementite or epsilon carbide when the iron was over-aged. WhEN a iron containing less than about 0.025 wt pct C is quenched from 700°C to room temperature the carbon is retained in solid solution and precipitates out slowly with time. The morphology and structure of the precipitating phase are still in doubt, two different carbide phases, epsilon carbide and cementite, have been identified, but there is considerable disagreement about the time and temperature at which they appear.1-4 Epsilon carbide seems to form at lower temperatures than cementite, although one group of investigators4 found only the latter phase over a wide range of aging temperatures. Usually these two phases have been identified after aging times much longer than needed to drain the carbon from supersaturated solution, at least for aging temperatures below 200oC. The precipitated carbides have been observed with the electron microscope,'-5 but again most results have come from samples aged much longer than necessary to reduce the carbon concentration in solution to a low value. In this study the carbide phases were observed in earlier stages of precipitation with the electron microscope, in order to learn more about the shape, size, and distribution of the carbide particles. Samples strained small amounts before aging, as well as unstrained samples, were studied, and the structure of the carbide phase was tentatively identified. EXPERIMENTAL "Ferrovac E" vacuum-melted iron, from which the wires for kinetic studies were also made (Refs. 6 and 7 and the following paper) was used for this work. An analysis of this material is given in Table I; it agrees well with the manufacturer's values. The number of inclusions in the iron was very small, as can be seen in the optical micrograph in the following paper. Pieces of iron about 1 mm thick and 5 to 10 mm in diam were used for all the studies except for those in which the sample was strained before aging; then the specimen was a rod 3 to 6 mm in diam and 20 cm long. The samples were held at about 700°C in wet hydrogen for at least an hour to remove residual carbon and nitrogen, after which they were heated to 950" (in the y region) and cooled to room temperature in the furnace. This treatment gave an average grain diam of more than 1 mm, so that the effect of grain boundaries on the precipitation process was negligible. The samples were carburized at 710°C for about 2 hr in hydrogen that had passed over toluene held at -30°C; then they were rapidly quenched into water. From chemical analysis this treatment gave a carbon concentration of from 0.012 to 0.016 wt pct, which is less than the solubility of carbon at this temperature. After quenching, the samples were aged at 120 "C in an oil bath for vari-

Jan 1, 1961

By M. P. Tixier, M. Gondouin, G. L. Simard

In the quantitative interpretation of the SP logs, the electrochemical component is generally taken equal to — K log Rm /Rw where K has the theoretical value corresponding to solutions of pure sodium chloride. This method may be misleading when relatively large quantities of salts other than NaCl are present in form-rrtion waters—as is generally the case for low salinities —or in gyp-base muds. In such cases recourse is made in the field to changing the K value or to adding a correction term to the equation on the basis of local experience. An investigation has been made in the laboratory of the influence of HCO3, SO4=, Ca++, and Mg++ on the amplitude of the SP deflection, which included in par-ricular determinations of the activity coefficients of Ca++ and Mg++. The theory, the experimental techniques and a tentative method for applying the results are described. So far, applications to actual field cases where chemical analyses of waters were available have provided an excellent confirmation of the proposed method. The case of the SP in very salty brines is also considered and it is shown that the use of activity data for sodium gives satisfactory results. HISTORICAL In early times of electrical logging, the SP curve was used exclusively as a tool for the location of permeable beds and the definition of their boundaries. Later, with the introduction of methods of quantitative analysis, attention was called to the possibility of deriving from the SP log some information on the formation water resistivity, which constitutes one essential element for the computation of water saturation from log data. The first laboratory experiments' in 1932 had shown that, as a result of electrochemical phenomena arising at the contact of the niud and the formation, the amplitude of the deflection of the SP curve was, at least partly, a function of the salt concentration of interstitial water and accordingly of its resistivity. It was indicated that the amplitude of the electrochemical component of the SP should be equal to K log R1/R2, R1 and R2 being the resistivities of the mud and of the formation water respectively. However, the exact value of the K coefficient was not determined at that time because the surface clay used for a laboratory model was far from an ideal shale membrane. Consequently, the way was not yet open towards quantitative interpretation. In the early forties, Tixier reported2, on the basis of field log observations, the following equation for the case of NaCl solutions, SP = -71 log f1c1/f2c2, c1 and c2 being the concentrations and f1, f2 the mean activity coefficients. The local variations observed in the empirical values of K, chiefly in the Rocky Mountains, led him to advance the opinion that, besides the relative amounts, the nature of the salts present in the solutions had a bearing on the magnitude of the SP. At about the same time Mounce and Rust- ad published laboratory results which emphasized the part played by the shale in the generation of the SP. On the basis of laboratory tests and theoretical considerations, Wyllie in 1948' published the following equation of the electrochemical SP for the case of NaCl solutions, SP= - 71 log (a1)m/(a2)m

Jan 1, 1958

By Clark L. Corey, Bogdan Lisowsky

Electrical resistivity, X-ray line positions, degree of order, and microstructures have been investigated for Ni-A1 alloys near the Ni3Al composition. The results indicate that Ni3Al undergoes disordering between 1250oC and the mp; also supersaturated y, produced in y + y' alloys by gas quenching, is extensively ordered prior to y' (Ni3Al) phase separation. The latter reaction, if not both, must follow the cooperative phenomena model. Shifts in line position as a function of quench-indulced super satulration are shown. Lattice pavarneters of equilibriunz and nonequilibrium phases are given. THE objective of this investigation was to determine the mechanism and kinetics of the reactions which occur in Ni3A1 and hypostoichiometric Ni3A1 alloys. The results are of particular significance relative to pre-precipitation phenomena. Early work on Ni-A1 binary compositions near the Ni3A1 composition (13.6 wt pct Al) has been adequately reviewed by Hanssen,1 whose phase diagram is presented in Fig. 1. williams2 verified the suggestion made by Taylor and Floyd3 and others4 that y', Ni3A1, may precipitate coherently on (100) planes of the y phase (see Fig. 1 for phase nomenclature); he further suggested a two-step precipitation mechanism consisting initially of probably short-range ordering followed by actual precipitation of y'. The precipitation stage in low-aluminum hypo-eutectic compositions has been studied by a number of investigators;*"7 short-range order or "zone" formation have been suggested as explanations for various diffuse X-ray scattering effects. The ordering reaction in Ni3A1 alloys is characterized by a) a very rapid rate of ordering in nonstoi-chiometric compositions, b) absence of a disordered phase region for the stoichiometric compound, y', or Ni3A1, c) precipitation phenomena as a dominant aspect in hypoeutectic alloys, and d) an increase in elec-trical resistivity on ordering.' The latter two factors were found by Newkirk to characterize ordering in Co-Pt, for which an extensive and detailed analysis was made.' An electrical-resistivity increase on ordering has also been reported for cuAu3.10 PROCEDURE Ni-A1 alloys in the form of 1300-g chill-cast ingots were prepared by vacuum melting electrolytic nickel and high-purity (99.99 pct) aluminum. Very small heats prepared from high-purity carbonyl nickel, supplied through the courtesy of Dr. Goff of the Naval Research Laboratory, were used for comparison with the larger ingots and no differences were noted. The cast material was homogenized in purified argon for a minimum of 72 hr at 1200°C and water-quenched from 1350°C. Compositions studied are given in Table I. The 10 pct A1 alloy was both hot- and cold-rolled. X-ray superlattice line intensities and peak positions were obtained from -270 mesh filings, using CuK, radiation with a LiF crystal monochromat adjusted to receive both 01 and a2. One-degree slits and a 1/8 deg per min scan rate were used to record line traces. A standard tungsten powder, obtained through the courtesy of G.E. Research Laboratory, was used to calibrate line positions.

Jan 1, 1968

By N. J. Grant, B. C. Giessen, R. Koch

The system Nh-Ir was investigated over the complete concentration range by metallography and X-my techniques, using forty one alloys. The solubility limits of terminal and intermediate phases and the solidus temperatures were determined. Five intermediate phases were found: a Nb3Ir, cubic, Cr3O type; tetragonal, ofecr thorhomhic, isostruc-turn1 with (ta-Rh); and a Nhlr3. cubic, AuCu, type. a Nb3lr and a Nbfr3 melt congruently; three eutectic and three pentectic reactions occur. The phase diagram of the Nb-Ir system had not been fully treated in the literature; only surveys of intermediate phases were found.1"5 In this study, the details of the phase boundaries were investigated as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS The experimental procedures such as arc melting of powder compacts, heat treatments, solidus measurements, X-ray, and metallographic observation were identical with those used in the work on the Nb-Rh phase diagram.&apos; They will therefore not be repeated here except where the conditions differed. The purity of the niobium powder was as stated in Ref. 6; the iridium powder of 99.9+ pct purity from J. Bishop and Co., Malvern, Penn., did not contain impurities exceeding 100 ppm, except rhodium (200 ppm). The melting points and vapor pressures of both elements are very similar. This fact contributed to a very small weight loss on melting and facilitated preparation of homogeneous alloys. As shown in Ref. 6 for Nb-Rh, no oxygen pick-up exceeding 200 ppm had to be considered; this was regarded as valid also for Nb-Ir. A total of forty one alloys were used in the determination of the phase diagram; their concentrations are shown in Fig. l, which presents the phase diagram. The concentration limits as determined by the weight-loss method averaged <0.2 at. pct, and never exceeded 0.5 at. pct. Heat treatments were carried out as described in Ref. 6. Depending on the concentration, only tantalum, tungsten, or iridium containers were employed, avoiding oxide crucibles altogether. Alloys from 0 to 25 and from 65 to 100 at. pct Ir were homogenized at 2095°C for 15 hr, intermediate compositions from 25 to 65 at. pct Ir for 65 hr at 1780°C. A typical annealing-time schedule is presented in Table I. Solidus points were measured as described in Ref. 6 with the modification that samples rich in niobium were held between pieces of tantalum foil and samples of high iridium concentrations were held between rhenium platelets or in iridium wire. After each run it was ascertained metallographically that no reaction with the holder had occurred. Rhenium was selected as holder material after it had been shown in separate tests that the melting points of Re-Ir alloys rise continuously from 2440°C. Metallographic examination was carried out as described in Ref. 6, and the same procedure and etchants were used successfully. While metallographic discrimination between a Nb3lr and o was easily possible, X-ray diffraction was necessary to separate al and ct2. X-ray powder patterns were taken and evaluated as for Nb-Rh6 yielding the error limits indicated in Table 111, to be introduced later. For the determination of the invariant reactions and phase boundaries, the same techniques as for Nb-Rh6 applied. The general accuracy of invariant concentrations is regarded as somewhat higher than for Nb-Rh due to the small slope of most solvus lines.

Jan 1, 1964

By T. E. Scott, R. P. Zerwekh

The charactevistics of the deformatiotz of fcc thorium were examined between 78 and 473 K. Activation energy, actiuation volume, and the temperature dependence of the flow stress were determined and conlpared uith several theories for the rate-controlling mechnnistn of the tempemture-dependent component of the flou~ stress. It was established that the Cottrell-Stokes law does not hold, even approximately, for thorium. Through consideration of the above factors and other parameters, it was concluded that the vandom solute barrier theory proposed by Friedel demonstrates the best agreement with experimental observations of the deformation of thorium below ambient temperature. THORIUM, the first metal in the actinide series of rare-earth elements, is interesting and important from two points of view. In the more practical vein, it is a potential reactor fuel. As such, it is important to know its properties. Of specific interest here are the mechanical properties of thorium. Second, no detailed information concerning the deformation characteristics of the actinide elements has been gathered to date. In view of the interesting physical and chemical properties of these metals, their mechanical behavior might reveal characteristics which could improve our understanding of the mechanisms controlling deformation of the more common metals. For example, it has been shown1 that thorium exhibits a yield point which is greatly enhanced by interstitial solute elements such as carbon. This is not a normal occurrence in fcc metals. The goal of this investigation, therefore, was to characterize the deformation of polycrystalline thorium. MATERIAL AND PROCEDURES Thorium, made by the magnesium intermediate alloy process described by Peterson et al.,2 was rolled and swaged to 0.065-in.-diam wire. The metal analysis is given in Table I. After preparation, the oxygen and nitrogen contents had risen to 308 and 60 ppm, respectively. The 0.065-in.-diam wires were cut into 2-in. lengths and annealed in a vacuum of lo-&apos; Torr at 750°C for 1 hr, producing a grain size of 2735 grains per sq mm. The ends of the 2-in. sections were masked off so that a 1-in. gage length could be electropolished. Specimens were polished at 35 v in a solution of 6 pct perchloric acid in methanol which was maintained at 0°C . The gage diameters after polishing were about 0.0625 in. The tests were run on a screw-driven tensile machine at a constant crosshead speed corresponding to a strain rate of 0.005 min-&apos;. The strain rate was changed rapidly after each 0.01-in. extension between 0.005 min-&apos; and one of three higher strain rates which were selected in order to achieve strain-rate ratios of 5, 10, and 20. Tests were run at several temperatures from 78" to 473°K; most were tested at 423", 300°, 215", and 78°K. EXPERIMENTAL RESULTS Flow Stress vs Strain and Temperature. Typical true stress-true strain curves for thorium are shown in Fig. 1 for several temperatures over the range 473" to 78°K. The curves for 78", 215", 300") and 423°K were obtained from strain-rate change tests using the lower (0.005 min-&apos;) or base strain-rate values of stress. Additional tests, using the same base strain rate at different strain-rate ratios, gave curves which virtually superposed on those shown, indicating that strain-rate changes did not materially influence the work-hardening characteristics at the base strain rate. The curves for 273") 373") and 473°K were standard tensile tests at 0.005 min-&apos;. The behavior of the flow stress with temperature is

Jan 1, 1968

By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967

Draftsman and transitman for coal mine work in Middle West. Salary $125 per month. No. 277. Mechanical draftsman familiar with mill and machinery design for metallurgical and chemical plants. Advise experience, salary expected, and references. No. 289. Two cyanide shift bosses, one cyanide mill supt, and one assayer, for work in South America. Expenses clown and return if two year contract is made. No. 290. In assay laboratory of University in the Middle West, man to take charge of ore-dressing and. help in assay laboratory work. Willing to give right man assistant professorship. No. 291. Experienced appraisers familiar either with field or office methods, capable of field survey of the physical properties and able to check up their survey on the books of the company, which require a very intimate knowledge of accountancy. Salary $2000 to $2700. No. 292. Young man trained in chemistry and engineering to conduct experimental work on storage of coal. No. 293.

Jan 4, 1918

Paralleling recent experiments in the U. S., the Mines Branch of the Department of Mines and Technical Surveys in Ottawa has developed a laboratory process for recovering cell-grade alumina from aluminiferous shale. Mines Branch Research Report R45 (1959) entitled The Alum-Amine Process For The Recovery of Alumina From Shale by G. Thomas and T. R. Ingraham states " . . . With the recent resurgence in Canada, and in the United States, of attempts to recover cell-grade alumina from clays and shales, the Mines Branch undertook to review certain processes that had been tried with marginal success . . . In particular, it seemed quite possible that some recent developments in organic chemistry, relating to uranium technology, might be utilized for the removal of the last traces of iron from intermediate products to permit the attainment of a satisfactory grade of alumina." This introductory paragraph explains the authors&apos; approach toward development of an alumina recovery process from shale. The following is an abstract of their successful laboratory experiments.

Jan 3, 1960

The paper by Professors Sun and Mitchell illustrates the value of ultrasonics as a tool for the mineral engineer. In particular, it opens up a number of possibilities to those interested in the field of comminution. The provision of desliming technique, which is thorough as well as rapid, is a distinct contribution, but the data of the paper suggest applications beyond desliming, in that the same treatments may be useful for size determination purposes. Fig. 1 shows that a marked dependence exists between particle size and the height to which it can be elevated by ultrasonic vibrations. While the curves are only extended down to a size of about 100 p, the fact that they appear to be increasing in slope in this range suggests that the separation may be even more marked here. This, we feel, is very strong evidence that a method for fine sizing could be developed to use ultra- sonic waves as the separating force.

Jan 1, 1957

By Henry M. Howe

I NOW call your attention to two directions in which very important progress may be confidently hoped for—pyrometry and the heat-treatment of steel. We already find in the market more than one pyrometer which, in spite of serious defects, may lie used advantageously for determining and controlling the temperature of many of our metallurgical processes. It is to be hoped, and with much confidence, that by the rapid extension of the use of such instruments, the economy and efficiency of these processes may undergo an increase which, in the aggregate, will be of the greatest importance. In this connection, the lucid paper of Prof. Roberts-Austen," and the learned bulletin of Mr. Barus, are most welcome. But much remains to be done in the way of devising pyrometers suitable for manufacturing purposes. While some of the present pyrometers are most convenient and accurate in the laboratory, serious difficulties attend the use, in factories, of those which I have

Jan 1, 1895

By P. Barnes

In a paper recently read before the Institute by Mr. W. A. Goodyear, a useful presentation was made of the subject of the production of&apos; water-gas on a large scale, by the use of a regenerative form of apparatus. By way of supplement to that paper, a brief statement of the details of a plan which was carried out at the works of the Elgin National Watch Company at Elgin, Ill., may be of interest, &apos;although the ultimate result of the working of the producer was not successful or satisfactory. This company had decided to build a gas-works for the supply of illuminating gas to their factory, on a much larger scale than that of the petroleum-works which had very successfully supplied the smaller buildings for many years, and in March, 1882, the material for a gas-making cupola furnace was purchased. A few weeks later it was decided to make the attempt to bnrn the gas under the steam-

Jan 1, 1884

Mr. Joseph P. GAZZAM,Germiston, Transvaal, So. Africa (communication to the Secretary*) :—About fourteen years ago, in southeastern Missouri,I used a method for the wet determination of lead which closely resembles the modified sulphate-chromate method described by Mr.. Guess. The principal difference, however, is, that after dissolving the lead chromate in hydrochloric acid, the chromic acid is determined by means of a standard solution of ferrous sulphate. The method, which I believe is still in use in southeastern Missouri, was found to be convenient and accurate for the determination of lead in the ores and various products of the mills and furnaces in that district, but it was never used for complex ores. A number of determinations of lead in mill-tailings were made in the year 1891; a few of these results are given in Table I. Table I.—Determinations of Lead in MilL-Tailings by Wet Assay.

Jan 1, 1905

By H. Krueger, H. N. Hersh

USE of autoradiography in diffusion studies offers the advantage that no repeated sectioning is necessary and that the analyses are performed in a simple manner over the continuous range of penetration depths. As part of a program of solid-state physics, it was desired to develop the autoradio-graphic method&apos; quantitatively for use in diffusion studies. Results are reported here for the self-diffusion of silver. Silver was chosen because the existing data are good enough to evaluate the technique." The silver used in this investigation was obtained in the form of ¼ in. diam rods of polycrystalline material, 99.99 pct purity. The radioactive silver, Ag110 (ß, y), was obtained as the nitrate and converted to the chloride for use in a standard cyanide plating bath. The diffusion specimens were 1/2 in. lengths of the rod. They were mounted in bake-lite and the exposed circular face carefully ground and polished. Prior to electrodepositing radioactive

Jan 1, 1956

By S. H. Ash

With statistics still incomplete, it appears that the safety record of the mineral industry for 1955 will do well to hold its own in comparison with 1954. On the one hand, metal mining shows an improvement in its record, due in part to intensive campaigns for preventing ground fall accidents. Coal mining, on the other hand, is showing a poorer record in 1955 than for the preceding year. While no major disasters occurred during the year, increased fatalities resulted from ground fall, haulage, and machinery accidents. It seems probable that increased job training may serve to improve the situation. Health: Utilization of diesel equipment continues to increase in noncoal mines, in spite of existing prejudice. In 1955 two types of diesel-driven tractors and one shuttle car were approved by the USBM. Where diesel engines are used controlled ventilation is mandatory in order to keep the CO content under 20 ppm, but such ventilation is not difficult to achieve with normal equipment.

Feb 1, 1956

By G. C. Mudd, E. J. Myers

Within the last 15 years David Brown Gear Industries has manufactured approximately 200 large mill gears over 6m diam., 58 of them over 9 m and up to 12 m diam. The experience has not been without problems, due to a lack of clear understanding of the loads and stresses imposed on large gear wheels. American Gear Manufacturers Association (AGMA) practices suggest that a service factor be used for mill gears. But what is meant by "service factor"? The layman might be forgiven for believing that the term is synonymous with "safety factor," but this is certainly not true. The service factor is an aggregate of the following in some proportion: -An application factor, i.e., an allowance for the fact that systems do not run smoothly with uniform torque. -An ignorance factor covering the imperfections in the basic gear calculation. -Possibly a safety factor. In the following sections some of the ways in which the limits of applicability can be overstepped are discussed.

Jan 1, 1983

By Charles Locke

IT will soon become apparent that the Conference Committee&apos;s choice of the title for this presentation is a fortunate one for the speaker; since if it had read "Review of Known Facts Controlling Slag Volume" he would best step down right now. There is a dearth of facts in a quantitative sense on this subject, especially in regard to the effects of slag volume on the acid electric practice for steelmaking, as borne out by a library search involving some 175 references from 1915 to date. Even the opinions in these references on any phase of slag volume are meager. This, then, leads to a report that is candidly based on private observations, on readings and on conjectures gleaned from gossiping with fellow practitioners. Perhaps the subsequent papers, which, as I understand it, are substantiated by actual measurements, of slag volume versus specific contributing factors, will be able to acclaim or disclaim my remarks.

Jan 1, 1947

By Donald N. H. Chi, Henry E. Perlee

Accident cost data bases for all mining sectors covering the period 1975 through 1980 have been created on the PDP-11/70 and VAX-11/780 computers at the Bureau of Mines Pittsburgh Research Center. The total expected costs of the following tangible elements are computed: (a) loss in personal income; (b) compensation of wages from State, Federal, and union funds for disabling injuries; (c) benefits for injuries resulting in death or permanent disability; (d) medical treatment and hospital care; (e) investigation of a fatal accident; and (f) production loss due to accidents involving fatalities or amputation injuries. Each cost record computed contains a reference to the original record in the Health and Safety Analysis Center (HSAC) accident files to permit concurrent analysis. The intended applications include examinations of annual trends in mine accident statistics on the basis of economic loss. This provides an additional perspective on mine accidents. Various examples of the use of these data bases are presented.

Jan 1, 1983