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By W. A. Wood, W. H. Reimann, K. R. Sargant

A study is made of the microstructural changes produced in armco and pure iron subjected to alternating torsion at amplitudes above and below the knee of the S/N curve. The aim was to identify the basic mechanisms of fatigue and to find why they should give rise to a sharp S/N knee in contrast to the type of S/N curve shown by fcc metals. It is found that the basic structural change above the knee in the iron is a pronounced cell formation in the grains, which determines irregular micro-cracks, and below the knee a dispersion of fine slip that determines a dispersed pore formation in the grains. Comparison of these changes with those in fcc metals similarly tested shows that they do not include an intermediate structural change, a concentrating of slip in narrow bands with associated slip-band cracking, that characterizes the fcc metals and accounts for their different type of S/N curve. RECENT conferences on basic mechanisms of fatigue emphasize that fatigue damage takes many forms: for example, cracking in slip bands (Thompson1), at grain boundaries and inclusions (Hempel'), at precipitation zones in alloys (Han-stock, Forsythe), or at surface notch-peak effects, both hypothetical (Mott, cottrel16) and observed (Wood). Evidently it is not easy to see in this diversity a basic mechanism. At the same time the contributions suggest that some reconciliation may be possible if distinctions are drawn between three phases of the fatigue process: initiation of damage at nuclei, distribution of these nuclei, and the final macroscopic crack system. In initiation, the relevant features appear to be that nuclei may appear early, at least by 1/100th to 1/1000th of the life of a test specimen; that they may do so at many independent centers, appearing according to some observationsa as pores or voids; and that they are not necessarily self-propagating, damage spreading rather by their multiplication. In distribution, the relevant feature appears to be that they form preferentially in zones where the microstructure becomes abnormally strained (as defined more closely below). Now in these two phases the basic fatigue process should be systematic. But, at the same time, the "abnormal strains" in particular set the stage for considerable diversity in the final phase of macroscopic cracking, for where zones of abnormal strain develop will depend on what kind of fatigue deformation is applied and what kind of prior processing the test material has had. On this view it seems desirable to know what in

Jan 1, 1964

By W. F. Hergert, L. H. Banning

Experimental production of Al-Si alloys, containing from 33 to 55 pct Al, by direct reduction of aluminum silicates in a three-phase arc furnace is described. Advantages of a smelting technique utilizing hogged wood waste as part of the reductant and for temperature control are discussed. WORK on the problem of producing aluminum by smelting has been in progress since the middle of the eighteenth century. Early work met with little success and in 1782 Lavoisier, an eminent French chemist, expressed the belief that alumina could not be reduced by carbon. It was almost a century later when the Cowles brothers developed a process for the production of aluminum alloys by reducing alumina coincident with the reduction of other metal oxides. In practice, the other metal oxide was usually copper. In 1907 it was first shown that alumina alone could be reduced by carbon at a temperature of 2200°C. The metal produced was volatilized and lost or recombined with the oxides of carbon formed in the reaction.' For a number of years after the Cowles brothers abandoned production of Cu-A1 alloys because their product was not commercially competitive with the aluminum produced by the Hall process, there was little interest in thermal reduction processes. After World War I interest in such processes was renewed and a number of patents were issued on processes for the production of A1-Si alloys.' , "he function of the silicon in these processes was the same as the function of the copper in the Cowles brothers process, namely, to prevent the reduced aluminum from recombining with the oxides of carbon and to promote absorption of the aluminum vapors set free at the high temperature required for the reduction reaction. The advantage of using silicon in place of copper for this function is that silicon has a higher boiling point (2600"C) than copper (2310"C) and its oxides, combined with aluminum oxides, occur in nature in almost unlimited quantities. No A1-Si alloys have been produced commercially in the United States, as far as is known. However, considerable experimental smelting of aluminum silicate materials has been done by the TVA at Wilson Dam, Ala.' The most extensive development and commercialization of the electrothermal production of A1-Si alloys took place in Germany before and during World War II.V he furnaces used in the

Jan 1, 1956

By C. C. Wright, T. S. Spicer

A characteristic property of bituminous coal is that upon being heated the coal becomes plastic, evolves volatile gases, and finally solidifies into coke. This fundamental characteristic is of utmost importance and is utilized in the production of the high-temperature coke upon which the steel industry is so dependent; but from the standpoint of operation in the domestic underfeed stoker this coking tendency seriously interferes with efficient combustion. When the coke formed has too strong a structure, certain difficulties result, such as low rate of burning, slow response to heat demand, and, in extreme cases, extinction of fire. The plastic mass prevents uniform distribution of air through the fuel bed and, with strongly coking coals, large dense pieces of coke are produced which have much less reacting surface than was possessed by the original coal. In both ignition and combustion of solid fuels, the extent of the reacting surface is an accelerating factor. Poor combustion permits a surplus of fuel to accumulate in the furnace because the rate of feed and the rate of combustion are not in equilibrium, and this produces an unbalanced condition detrimental to continued automatic service. In order to bum strongly coking coals satisfactorily in a conventional stoker during the three requisite types of operation—continuous, intermittent and hold-fire, frequent attention is necessary. Domestic stokers are defined by the industry as residential stoker heaters that burn 60 lb. of coal or less per hour. With a few exceptions, these units employ the underfeed principle of combustion in which both air and coal move in the same direction up and through the fuel bed. Domestic combustion equipment has difficulty in meeting the problems presented by the several variations in ash and volatile matter, in ash-clinkering tendencies, in coking properties, and in the particle size of bituminous coals. The work of Bituminous Coal Research Inc. at Battelle Memorial Institute has shown that, of these, coking characteristics and the clinkering tendencies have the greatest effect upon the operation of the conventional clinkering type of stoker. Typical coke formations in a clinkering type of underfeed domestic stoker are illustratcd in Fig. I, which shows (A) the ideal fuel bed obtained with a noncoking or free-burning coal; (B) the type of fuel bed formed with a coal that produces a weak coke; and (C) the type of fuel bed obtained with a strongly coking coal. C is characteristic of the fuel bed developed when the average Pennsylvania bituminous coal is burned in an underfeed stoker of conventional type. It is apparent from these pictures that the formation of coke trees will seriously interfere with the efficient automatic combustion of Pennsylvania bituminous coals.

Jan 1, 1942

By T. S. Spicer, C. C. Wright

A characteristic property of bituminous coal is that upon being heated the coal becomes plastic, evolves volatile gases, and finally solidifies into coke. This fundamental characteristic is of utmost importance and is utilized in the production of the high-temperature coke upon which the steel industry is so dependent; but from the standpoint of operation in the domestic underfeed stoker this coking tendency seriously interferes with efficient combustion. When the coke formed has too strong a structure, certain difficulties result, such as low rate of burning, slow response to heat demand, and, in extreme cases, extinction of fire. The plastic mass prevents uniform distribution of air through the fuel bed and, with strongly coking coals, large dense pieces of coke are produced which have much less reacting surface than was possessed by the original coal. In both ignition and combustion of solid fuels, the extent of the reacting surface is an accelerating factor. Poor combustion permits a surplus of fuel to accumulate in the furnace because the rate of feed and the rate of combustion are not in equilibrium, and this produces an unbalanced condition detrimental to continued automatic service. In order to bum strongly coking coals satisfactorily in a conventional stoker during the three requisite types of operation—continuous, intermittent and hold-fire, frequent attention is necessary. Domestic stokers are defined by the industry as residential stoker heaters that burn 60 lb. of coal or less per hour. With a few exceptions, these units employ the underfeed principle of combustion in which both air and coal move in the same direction up and through the fuel bed. Domestic combustion equipment has difficulty in meeting the problems presented by the several variations in ash and volatile matter, in ash-clinkering tendencies, in coking properties, and in the particle size of bituminous coals. The work of Bituminous Coal Research Inc. at Battelle Memorial Institute has shown that, of these, coking characteristics and the clinkering tendencies have the greatest effect upon the operation of the conventional clinkering type of stoker. Typical coke formations in a clinkering type of underfeed domestic stoker are illustratcd in Fig. I, which shows (A) the ideal fuel bed obtained with a noncoking or free-burning coal; (B) the type of fuel bed formed with a coal that produces a weak coke; and (C) the type of fuel bed obtained with a strongly coking coal. C is characteristic of the fuel bed developed when the average Pennsylvania bituminous coal is burned in an underfeed stoker of conventional type. It is apparent from these pictures that the formation of coke trees will seriously interfere with the efficient automatic combustion of Pennsylvania bituminous coals.

Jan 1, 1942

By A. E. Back

A method is described in which particulate iron, as distinguished from high purity iron powders used in powder metallurgy, is a precipitant for copper contained in dilute solutions. A new precipitation apparatus utilizes particulate iron precipitants to recover copper more efficiently than is possible in a conventional launder precipitation plant. In the search for lower cost methods of recovering copper from mine water, the use of sponge iron or particulate iron (as distinguished from iron powder used in powder metallurgy) as precipitants in place of tin cans, detinned scrap iron, or scrap iron is an intriguing possibility. The relatively faster copper precipitation rate obtained with particulate iron as compared to scrap iron promises economic and processing advantages when, and if, particulate iron becomes competitive cost-wise with available scrap iron. Kennecott has developed a precipitation cone,' see Fig. 1, utilizing various particulate iron precipitants and has demonstrated the process successfully in a prototype at a flow rate of approximately 1000 gal of solution per min. Essentially complete precipitation of copper is obtained, the cone overflow solution is clear and contains no particulate copper, and the iron factor is more favorable than in a conventional launder plant. Initially, sponge iron produced at the Ray Mines Div. Kennecott Copper Corp. for use in a Leach-Precipitation-Flotation process was used in exploratory tests to develop a suitable apparatus to take advantage of the rapid precipitation rate and efficient iron utilization for the recovery of copper from dilute solutions. Here it was demonstrated that, when sponge iron was added to a launder, the particles of iron collected in the bottom of the launder and tended to cement together. This resulted in incomplete precipitation of the copper and inefficient utilization of the iron. Next, sponge iron was suspended in glass columns to study the dynamics of the precipitation reaction. Again it was observed that the particles tended to cement together at low solution flow rates, while at higher flow rates large amounts of the precipitant overflowed the column, resulting in loss of precipitant and an inefficient process. Next, the precipitant was suspended in an inverted cone in a rising column of solution. Dynamic suspension of the solids was maintained at relatively rapid solution flow rates with instantaneous and complete precipitation of copper and with improved iron utilization. The first tests were conducted on a batch basis and it was determined that a dynamically suspended bed of precipitant was necessary for satisfactory operation. More than 99% of the metallic iron could be converted to metallic copper by careful control of the residence time in the cone and copper precipitation was essentially complete, even when the available iron precipitant was almost depleted. Several cones were built, ranging in capacity from 1 to 200 gal of feed solution per min, and finally, a prototype cone was constructed which was 20-ft high

Jan 1, 1968

By H. D. Outmans

Present first-order theory for frontal stability and viscous fingering of immiscible liquids is improved by including the nonlinear terms in the equations describing conditions at the interface of the liquids. This leads to the revision of several conclusions which were based on first-order theory. They concern the growth rate and changing shape of a sinusoidal disturbance, particularly in relation to the wave number of this disturbance. Nonlinear aspects of effective interfacial tension are discussed and it is shown that this tension is not simply a positive proportionality constant in a linear relation between pressure difference and curvature at the interface. Scaling requirements are determined from the dimensionless groups which govern fingering. Gravity and interfacial tension invalidate a previously formulated conclusion that the shape of a finger after a given displacement is independent of the displacement velocity. Also, similarity of fingering (and, hence, of sweep efficiency in case of an unstable front) requires geometrical similarity of the initial disturbance in the model and the reservoir with a scale factor which is the same as the one for scaling down the dimensions of the reservoir. INTRODUCTION The critical velocity at which the transition zone in the vertical displacement of immiscible liquids becomes unstable was calculated by ill. More recently, the same was done for nonvertical displacements and it was also shown that the stability is affected by an effective interfacial tension between the liquids. 2-4 Although in the oil reservoir a stable front is always desirable from a recovery point of view, the necessary velocity may have to be so low that the corresponding production rate is not economical. In that case, a knowledge of the fingering unstable front is necessary for predicting recovery at break- through. Studies in this direction have not gone beyond the very moment at which fingering first occurs.5,6 Conclusions about stability and fingering in these references are all based on linear theory. In this theory the nonlinear terms in the equations describing conditions at the front are neglected. The usual justification for this lack of mathematical rigor is that the nonlinear terms can be made small relative to the linear terms and, supposedly, small causes produce only small effects. It has been recognized, however, that this is not necessarily true in the nonlinear problems of hydrodynamics.7 The hydro-dynamic stability and fingering of the front between two liquids, accelerated in a direction normal to the front, for instance, is strongly influenced by the nonlinearity of the boundary conditions.8-10 Since these boundary conditions are not unlike those arising in the problem of stability and fingering of the front during a slow immiscible displacement in porous media, it was thought that there, too, the nonlinear terms should be taken into consideration. A summary of the results obtained in linear theory and a comparison with experimental data precede the nonlinear theory developed in this paper. This summary serves to introduce some quantities which will be used in the further develop ment. It should also be pointed out that the method of higher-order approximation by which the nonlinear stability problem is solved has application in other reservoir studies.11 SUMMARY OF LINEAR THEORY 1. A plane interface remains stable if its velocity is smaller than a critical velocity. vc = (p2-p1)gn/(l/A2- l/A1 .........(1.1) This equation is derived for uniform flow in a thin layer inclined to the horizontal plane. The displacement takes place in a direction normal to the intersection of this layer and the horizontal plane. The undisturbed (line) interface is normal to the velocity. Fluid 1, the upper fluid (gas), is displacing Fluid 2 (oil). (VcQS would be the injection rate in cc/

By L. W. Emery

Undergrorlnd combustion operations were initiated in a 60-acre Bartlesville sand "shoe-string" reservoir in Allen Connty, Kans., in 1956. Tests in separate patterns were conducted using various co~nbinations of air and recycle gas to propagate combustion fronts from the injection toward the producing wells. These patterns were made up of 6 injection and 20 prodrrcing wells Gas and liquid prorluctiorz from each pattern was measured on an individual-well basis, and comparisons were made between the three patterns to ascertain the relative effects of injected gas composition on production behavior. Breakthrough of the combustion front at a well was characterized by an increase in water production from the well followed by an increase in bottomhole temperatrrre to approximately 250" F. After burning fronts had broken through at five producing wells, operations were terminated in 1960. From the total project approximately 79,000 bbl of oil were produced during thermal operations at a cumulative produced GOR of 23 Mcf/bbl. No appreciable change in the character of the produced crude was observed. Combustion in the reservoir was maintained with injected gas compositions ranging fronz 6 per cent oxygen in recycle gas to 100 per cent air. lnjectiotz of large quantities of recycle gas resulted in higher producing GOR's from offset wells than were measured from a pattern into ~vhich straight air ~vas injected. The air required to move the combustion front through I acre-ft of reservoir was computed to be 20 MMscf. This valrre was found to be relatively independent of the quantities of recycle gas injected. The recovery efficiency from the swept area was esti~izated to be about 59 per cent. Areas swept were similar in shape to tlzose obtained with a laboratory potentiometric model. Samples of sund taken from behind the burning front by coring indicated almost total oil removal from the sand. Petrographic analysis of the core samples indicated that the sand had been heated to peuk temperature of rlbout 1,200" F. No rignificant difference in peak temperature was forrnd in two areas where compositions of injected gas were quite different. Compression costs for thermal recovery were estimated to be $1,20/bhl of produced oil. INTRODUCTION The use of the "forward combustion" process as an oil recovery method has received a great deal of attention. This method involves ignition of the formation in an injection well, followed by propagation of a combustion front through the reservoir. Combustion is maintained by the injection of an oxygen-containing gas to react with reservoir hydrocarbons. As the flame front progresses through the reservoir, oil and formation water are vaporized, driven forward in the gaseous phase and recondensed in the cooler part of the formation. In turn, the condensed fluids push oil into the producing wellbores. Completed field tests of the process were first reported by Kuhn and Koch,' and by Grant and Szasz.' Results from other tests have since been reported by Walter,3 by Moss, White and McNeil,' and by Gates and Ramey." ach of these tests essentially utilized a single injection well surrounded by four or more producing wells. Sinclair Research, Inc., elected to do field experimental work using a number of test patterns in a single field in order that comparisons between various operating schemes could be made. The site selected and purchased in 1955 for this experimental work was a 60-acre Bartlesville sand reservoir located in Allen County, Kans. Combustion operations were initiated in mid-1956. Between that time and termination of the project in mid-1960, combustion fronts were propagated from injection wells to producers in three separate well patterns, using different mixtures of air and recycle gas. The test was terminated before sweep of the three patterns was complete so that information about the effect of combustion on the swept areas could be obtained by coring. Results from the test in the form of injection and producing well performance have been carefully recorded, and these form the general basis for this paper. DESCRIPTION OF RESERVOIR The reservoir in which the combustion tests were conducted is a Bartlesville sand "shoe-string", typical of a number of small reservoirs in Southeastern Kansas. Average reservoir characteristics are shown in Table 1. Fig. 1 is an isopachous map of the producing sand showing the reservoir to be approximately 400-ft wide and 2,500-ft long. Maximum net productive sand thickness is 21 ft. Fig. 2 shows a typical core analysis obtained by coring with water-base mud. The reservoir has no appreciable dip and is closed on the sides by degradation of sand into shale. The main body of sand is heavily laminated with shale stringers, which are not continuous between wells. The main reservoir is overlain by 30 to 40 ft of laminated low-permeability sand and shale streaks. No information is available on the original properties of

By R. W. Balluffi, R. Resnick

NUMEROUS investigations of chemical diffusion in a brass have been made and the results are collected in several places.1-3 This work has been mainly concerned with the determination of the chemical diffusivity as a function of composition and temperature. In 1947 Smigelskas and Kirken-dall&apos; showed that zinc and copper diffuse at different rates in face-centered-cubic brass, and since then, a number of efforts have been made to determine the intrinsic diffusivities of zinc and copper in this alloy.1, 5-9 Horne and Mehl8 in particular have recently determined the intrinsic diffusivities as functions of temperature and composition using sandwich-type couples and inert markers. Inman et al." also have determined the intrinsic diffusivities in homogeneous alloys using tracer techniques. When the present work was started, no information of this type was available. Consequently, measurements of the intrinsic diffusivities were made as a function of temperature at a constant composition of 28 atomic pct Zn with vapor-solid diffusion couples where the zinc was diffused into the diffusion couple from the vapor phase. The application of these couples to the study of diffusion in a: brass has been described previously.0,7 The temperature dependence of the intrinsic diffusivities was found to follow the relation D, = A, exp(-Hi/RT) and the values of Hzn, and Hcu, were found to be closely the same. It is emphasized, however, that the chemical dif-fusivity (D = N1D2 + N2D1) is a composite diffusivity and does not necessarily follow this exponential form. It is usually found to do so within experimental error for substitutional alloys because the heats of activation of the intrinsic diffusivities generally are not greatly different.&apos;" Also, at the onset of this work, there was no information available concerning possible unequal diffusion rates of individual components and the existence of a Kirkendall effect in alloys with other than face-centered-cubic structures. Since then, two reports indicating a Kirkendall effect in body-centered-cubic ß brass have appeared. Landergren and Mehl" have published a note describing Kirkendall diffusion experiments with sandwich-type couples. Inman et a1.9 also find a Kirkendall effect in this alloy using the tracer technique. In the present work, several aspects of the Kirkendall effect in ß brass were further investigated using vapor-solid couples. Two different couples were used, one in which the zinc was diffused into the specimen from the vapor phase and the other in which the zinc was diffused out of the specimen into the vapor phase. Briefly, the existence of a Kirkendall effect is confirmed and it is found that Dzn/Dcu = 3 at about the 46 atomic pct composition in this alloy at 600°, 700°, and 800°C. As a result of the unequal diffusion rates of zinc and copper, volume changes occur and subgrain formation is observed in the diffusion zone. In addition, significant porosity is produced by the precipitation of supersaturated vacancies. Diffusion in this alloy is therefore outwardly similar to diffusion in a brass where these effects are also observed, a Brass Experimental Methods—The use of vapor-solid couples in studying diffusion in a brass has been described in previous articles.6,7 The method briefly consists of sealing a copper specimen with Kirkendall markers initially placed on its surface in an evacuated quartz capsule along with a large zinc source of fine a brass chips and then diffusing the zinc into the specimen through the vapor phase. The zinc concentration at the specimen surface rises rapidly enough to a value near that of the a brass source so that the surface concentration may be regarded as constant during diffusion. Under these boundary conditions, values of the chemical diffu-sivity may be obtained by applying the Boltzmann-Matano analysis to the concentration penetration curve, and the intrinsic diffusivities may be obtained from Darken&apos;s5 equations when the velocity of marker movement is known. The diffusion specimens were made from OFHC copper in the form of disks 3.2 cm diam and 0.5 cm thick with faces surface-ground parallel to within +0.001 cm. Markers in the form of fine alumina particles <0.0002 cm diam were placed on the specimen surface. These specimens were then sealed in quartz capsules along with enough a brass chips of a 30.0 atomic pct Zn composition to keep the source concentration from decreasing by more than 0.3 atomic pct Zn as a result of the loss of zinc to the specimen during diffusion. The quartz capsules which were initially evacuated to a pressure of

Jan 1, 1956

By B. H. Bergstrom, Will Mitchell, T. G. Kirkland, C. L. Sollenberger

In a previous article&apos; the authors outlined a study I of the variables in rod milling and also reported data from a series of open circuit grinding tests on a massive limestone in a 30-in. x 4-ft end peripheral discharge rod mill. As a second part of the experimental program, an analysis is now presented for the 30-in. x 4-ft overflow rod mill grinding under identical conditions, except that discharge ports on the periphery of the mill shell have been sealed so that the products from the present series overflowed through a 9-in. diam opening in the center of the end plate. A variance analysis has been made of the combined data for the two experiments, and performances of the two mills are compared here. Included in the first report were descriptions of feed preparation, rod mill circuit, instrumentation and controls, and techniques used to evaluate data. Dependent and independent variables were defined, and variance analyses were made to test the relative significance of variables and to establish magnitude of error for the experiment. Significant data were plotted in various combinations, and conclusions were drawn from the graphs. The procedure and analysis in this series of tests follows the first tests and is not repeated.

Oct 1, 1955

By F. M. Lewis, Johnson. E. C.

BY now application of the liquid-solid cyclone to various classification problems in the chemical and metallurgical fields is more or less familiar. A less publicized application receiving wider consideration as time goes on is its use as a classifier in closed-circuit grinding operations. This paper presents the costs involved and the experience gained from operating a unit of this kind. In May 1951 the Tennessee Copper Co. installed in its London mill at Copperhill, Tenn., a liquid- solid cyclone in closed circuit with a 6x12-ft ball mill. The circuit in which this cyclone is used is the regrind or secondary grinding circuit of a copper flotation plant. Originally it consisted of a 7x1-ft conical ball mill in closed circuit with a bowl classifier. Changes made in the primary grinding circuit of the mill necessitated a regrind circuit of greater capacity. The bulk concentrate to be ground was raised from 900 or 1000 tpd to 1200 or 1300 tpd, and to accommodate this increase a 6x12-ft ball mill which had been in the primary grinding circuit was moved into the regrind circuit. When this was done it was found that the classifier was too small to give efficient operation. Space in the plant was at a premium, and since use of the cyclone offered considerable economy the installation shown in Figs. 1-3 was made.

Jan 6, 1954

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well&apos;s production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. &apos;The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm&apos; A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using

By J. B. Newkirk

IN 1939 Bitter and Kaufmann1 suggested that iron, precipitating from a copper-rich, Cu-Fe solid solution, appears initially as coherent particles of r-Fe which transform to the body-centered-cubic form of iron when the alloy is cold worked. Since then there has been considerable discussion, supported only by indirect evidence, regarding the validity of the concept. For example, Reekie, Hutchison, and Hether-ington2 interpreted the changes in electrical resistance accompanying the aging of Cu-Fe specimens in terms of a coherent 7-Fe precipitate which transformed to the incoherent a-phase during long aging or cold working. Greninger- ound that Cu-Fe alloys which had been water quenched from 1050" and then held at 650°C for 3 hr changed from weakly to strongly ferromagnetic as the aged wire was subsequently cold worked. He also found diffraction lines corresponding to body-centered-cubic iron in Debye-Scherrer patterns given by aged and worked specimens but lines corresponding to only one face-centered-cubic phase in specimens which had been aged but not worked. Knoppwost,&apos; and later Cech and Turnbull,5 found that aged Cu-Fe specimens showed a slight increase in ferromagnet-ism after they had be? cooled in liquid nitrogen. Very recently Denney6 followed the kinetics of the precipitation reaction as indicated by the saturation magnetization, hardness, and diffuse X-ray effects. The experimental results reported by all of the authors mentioned above are readily explained in terms of the Bitter and Kaufmann concept. However, most of the evidence is indirect when used to define the structural changes involved. It was the aim of the present investigation to determine the mechanism of precipitation of iron from a Cu-Fe solid solution in the light of available published information and with additional new and more direct experimental data. Experimental Method At 1060°C copper will contain up to 3 atomic pct Fe in equilibrium solid solution.7 The solvus slopes rapidly toward lower iron concentration, so that at 600°C only about 0.5 pct Fe remains in solution at equilibrium. Below the eutectoid temperature (850°C), the iron-rich phase in equilibrium with the copper-rich solid solution consists of body-centered-cubic a-Fe. Above 850 °C the equilibrium iron-rich phase is face-centered-cubic r-Fe. The alloy to be studied was made by melting electrolytic iron and OFHC copper by induction under vacuum in an Alundum-lined crucible. The metal was held molten for about 5 min, after which time the power was turned off and the crucible was tipped about 70" to promote directional solidification. The resulting ingot, containing 2.5 wt pct Fe by analysis, was clean, large grained, and free of gross segregation. Slices % in. thick were cut from the ingot, rolled to 1/8 in. in thickness, homogenized in hydrogen at 1060°C for 24 hr and, finally, quenched in cold water. Specimens for all subsequent tests were made from these slices. Squares measuring about 1 cm on a side were cut from the slices to make specimens for studying hardness and microstructure. Wires (0.020 in.) for the Debye-Scherrer survey were drawn from 1/8 in. sq rods which had been cut from the homogenized slices. Large crystals for observing diffuse X-ray diffraction effects were prepared by mechanically

Jan 1, 1958

By D. T. Peters

To better understand the Co-Mo interaction in maraging steels, the precipitate reversion behavior of two alloys closely related to the 18 Ni-250 grade has been studied. The reversion experiment is carried out by aging at a low temperature, T1 (preaging temperature), for some period of time and then aging at a higher temperature, T2, called the reversion tetnperature. Aging and reversion tmzperatures used were in the range 679 to 1050°F. Reversion is marked by an increase in resistivity and a decrease in hardness. It teas found that some reversion took place at all cornbinations of T1 and T2 but that pronounced rei3ersion resulfed for an Fe-18 pct Ni-5 pct Mo-8 pcl Co alloy exposed to preagz&apos;ng&apos; temperatures at or below 850°F. A similar alloy not containing cobalt exhibited no such discontinuity in reversion behazior with TI. The results are interpreted in terms of two types of molybdenum-rich precipitates, one nucleated at dislocations and the other in the matrix. The increased supersaturation resulting from the presence oj- cobalt evidently provides sufficient energy to nucleate the matrix phase. Anotnalies in the temperature dependence of the resistivity decrease and peak hurdness in the Fe-18 pct Ni-5 pct Mo-8 pct Co alloy as a junction of aging temperature noted in an earlier study are explained on this basis. SEVERAL investigatorsl-9 have studied the details of the precipitation-hardening reaction of the maraging steels. The great majority of conclusions have been drawn from transmission electron microscopy. Although much has been learned by this method, alternate techniques which will give information earlier in the aging process are needed for a more complete understanding of the series of precipitation steps probably involved in the aging reaction. Peters and cupp&apos;&apos; have recently shown, by measurements of the kinetics of precipitation, that an 18 pct Ni-Co-Mo maraging steel shows a distinct change in precipitation behavior at aging temperatures below 850°F. The results were interpreted in terms of the existence of two types of precipitates at low aging temperatures. Only one precipitate type is present at higher aging temperatures. The low-temperature precipitate was found to be a particularly effective strengthener. No evidence for the additional low-temperature precipitate was found in the 18 pct Ni-5 pct Mo ternary alloy. The object of this investigation was to study further the characteristics of the two types of precipitates and the interaction between cobalt and molybdenum characterizing this system. Some preliminary experiments indicated a difference in reversion behavior in specimens aged above and below 850°F. This suggested that knowledge of the reversion behavior might shed some light on these two questions. Hardy and Heal11 have defined reversion as the loss of hardness, electrical conductivity, or other properties caused by heating for a very short time at temperatures above the aging temperature. The precipitate reversion referred to in this paper is entirely distinct from "austenite reversion" often referred to in maraging steel literature. This latter phenomenon could more accurately be called the diffusion-controlled formation of austenite. Much has been written about reversion in several of the aluminum-base binary and ternary alloys.&apos;2-16 Two explanations for reversion have been advanced. Based on the classical nucleation theory of Volmer-Weber-Becker-Doring,17 Konobeevski18 suggested that reversion was due to the size of the precipitate particles

Jan 1, 1968

By J. Gordon Parr, D. H. Polonis

High purity alloys of titanium and iron, made by a technique of levitation melting, have been investigated with particular reference to martensite formation and decomposition in the hypoeutectoid range. A preliminary study has been made of the occurrence of the phase corresponding to the structure Ti2Fe. MANY of the previous investigations of Fe-Ti alloys have been made using Kroll sponge as a source of titanium; and the subsequent heat treatments to which alloys have been subjected has, on occasion, led to further contamination. Worrier,&apos;,&apos; who suggested a part of the equilibrium diagram for the binary system, and Wallbaum and coworkers,3-5 who worked largely with iron-rich alloys, all used Kroll sponge. Van Thyne, Kessler, and Hansen,6 in their determination of the equilibrium diagram, used iodide titanium for alloys up to 30 pct Fe. Duwez,7 who measured the M. temperature of titanium binary alloys with many solute elements, used iodide titanium in all cases except in his work on Ti-Fe alloys for which he used Kroll sponge. The investigation of the supposed phase Ti2Fe by Rostoker8 nvolved the use of iodide titanium. A section of the constitutional diagram, after Van Thyne et al., is reproduced in Fig. 1. Frequently too much stress is placed on the effect of contaminants in equilibrium and nonequilibrium systems, but there is no doubt that titanium alloys are extremely susceptible to interstitial atoms. Consequently, the main purpose of the work to be described was to determine those features of phase transformations in pure Ti-Fe alloys that were considered of importance in commercial heat treatments. For, although commercial alloys may not be of high purity, the investigation of a system uncomplicated by traces of impurity is a desirable starting point. Another incidental feature, the occurrence of Ti2Fe, was also investigated. The entire study was carried out using powders obtained from alloy ingots, for diffusion reactions are often more rapid in small particles than in bulk specimens. The frequently adopted practice of ascertaining phase constitutions by X-ray analysis of powders, and relating these to the microstructures and mechanical properties of bulk specimens, is considered by the authors to be open to criticism. In the martensite reactions in the Fe-Mn system, for example, it has been shown- hat similar phase distributions in solid and powder may result in different hardness values and appearance under the microscope; and it is possible that similar anomalies might occur in the Ti-Fe system. Consequently, in order to

Jan 1, 1955

By W. E. Rice

The ceramic industry has to do with forming or molding articles of clay, and imparting to them their characteristic properties of permanence, strength and color by subjecting them to heat treatment in kilns. This heat treatment is commonly known as "firing" or "burning." The art of firing clay ware antedates the industrial use of coal; hence wood was the fuel first used, and the earliest kilns were built to burn wood. The majority of the clay ware produced today is fired in periodic kilns that are essentially enlarged structures similar to the earliest enclosed kilns; a kiln consists of a large chamber 16 to 32 ft. dia. (or rectangular) in which the ware is charged and fired either in direct contact with flame or hot gases from the fuel, or in saggers which shield the ware from direct contact with the gases. The fuel is burned in a number of small furnaces built in the thick wall that encloses the chamber; these furnaces are from 16 to 36 in. wide and from 3 to 5 ft. long; some of them have horizontal or sloping grates, but many have no grates; the last are called "dead-bottom" furnaces. The temperature necessary to mature the charge in the kiln varies for different clays; for some it is as low as 1800°, and for others as high as 2700" F. Wood was an ideal fuel for the low temperatures that were used in early kilns; it burns freely and produces a long, clean flame, which promotes uniform distribution of the heat in the kiln; it does not coke and so restrict the passage of air through the fuel bed; the ash does not melt in the fuel bed to form clinker; and the ash that is carried into the chamber and deposited on the charge does not contain iron and sulfur to discolor the clay. The extent of the ceramic industry now precludes the general use of wood in kilns, so that today this industry is one of the large users of bituminous coal, burning more than eight million tons annually in kilns. Manufacturing plants usually are at or near the source of clay, with deposits of coal suitable for kilns occurring near the clay. The cost of coal is the largest single item of expense in the manufacture of clay ware, and, because all coals are not equally suitable for the process, the careful selection of coal is important. In this selection the desidera-

Jan 1, 1932

By W. H. Ashby, R. W. Cassingham, C. R. Blomberg, J. B. Justins

The Brookhaven field is one of several Basal Tuscaloosa reservoirs located in south-central Mississippi. It is a standstone reservoir, of erratic deposition and with several faults, having an approximate subsea depth of 9,800 ft. A large variation in permeability exists with a weighted average being 256 md. Estimated average interstitial water saturation is 45 per cent. The undersaturated reservoir fluid exhibits marked differences in physical properties with measured saturation pressures ranging from 733 to 2,255 psi. Early rapid decline in reservoir pressure caused the operating interests to unitize the field and initiate a program of pressure maintenance by gas injection. At the time gas injection was commenced, the reservoir pressure had fallen to nearly half of the original pressure with only 4.5 Per cent of the original oil in place produced. The reservoir pressure has since been maintained at approximately 2,750 psig, and cumulative production to date is 17 per cent of original oil in place. An analysis of field performance during gas injection is presented in detail. The program of pressure maintenance by gas injection is considered to be a success, since the expected ultimate recovery has been increased and the current production rate is in excess of 2 per cent of original oil in place per year. Performance has been better, anticipated ultimate recovery is larger, and total production costs are lower than for a similar Basal Tuscaloosa reservoir nearby, even though that field appears to have a more effective natural water drive. INTRODUCTION The history of the Brookhaven Unit is a testimonial for unitization and for the application of engineering techniques in the operation of an oil field. The operating and royalty interests in this field have mutually benefited from their early recognition of the need for unitization and pressure maintenance and from the forthright manner in which these were accomplished. The tangible benefits accruing to the participants in the Unit are: (1) income from gasoline plant products, (2) reduced lifting and operating costs from those of competitive operation, (3) maintenance of high levels of current income by mitigation of the inevitable decline in production rates inherent to natural depletion, (4) an increase in ultimate recovery of about 40 per cent over natural depletion operations. This paper should properly be considered a progress report; however, the performance of the field after five years of pressure maintenance clearly indicates that the ultimate success of the project is assured. LOCATION AND GEOLOGY The Brookhaven field is located in south-central Mississippi, about six miles from the town of Brookhaven. Production at Brookhaven

Jan 1, 1955

By F. C. Miller

The metallurgical fuel of Colorado, Utah, and New Mexico has been a Veiny tardy member in the caravan of western industrial progress. The history of western coke has naturally been closely related to the development of the metallurgy of iron and steel and the precious metals, in the State of Colorado. It was at Leadville, with a population of 300 in 1877, that the Sentinel was published by Richard S. Allen. The Sentinel gave very full accounts of the various mineral discoveries at the new town of Leadville, which found their way to the more widely circulated journals of the East, and attracted the attention of many people. At the close of 1878, a census slowed a total of 5040 persons. The first smelter was established in 1877, at Malta, two miles from Leadville, by A. R. Meyer, but was not successful. It was succeeded by the Harrison Reduction Works, in 1878. The La Plata began with one furnace in June, 1878, and in 1879 had four furnaces in active operation. These furnaces used charcoal for fuel, and, because of hot tops, suffered a tremendous loss in lead and silver. This difficulty was overcome by the erection of 50 single-bank 10-ft. beehive ovens at Crested Butte, Colo., in 1880. The slack coal sent to these ovens was very pure, and yielded a coke carrying as little as 4.5 per cent. ash. Among the pioneers in the Leadville district were Grant, Eddy, James, Billings, Eiler, and Dickson. To these men the West owes the present expansion of its mining industry, and the erection of metallurgical processes for the treatment of precious metals. On Mar. 1, 1876, Pueblo was connected to the Atchison, Topeka & Sank Fe by the Pueblo & Arkansas Valley branch. The first smelter was erected in Pueblo by Mather and Geist. This modest plant grew into the immense Pueblo Smelting and Refining Co., now a part of the American Smelting and Refining Co. Coke for these small furnaces was made from unwashed Engleville coal, in 186 single-bank 12-ft. ovens at El Moro, in the Trinidad district, and it was not uncommon for the percentage of ash to exceed the percentage of fixed carbon in the coke. On Jan. 23, 1880, the Colorado Improvement Co. consolidated

Jan 1, 1920

By J. Blodget Britton

IN the Journal of the Franklin Institute for May, 1870, there is published a description of a Colorimeter, together with a modification of the method proposed by Professor Eggertz, for determining combined carbon in iron and steel. An instrument of the kind there described, but of a little higher range, though in other respects not differing materially from the one originally made and used in the Iron-Masters7 Laboratory, I now submit to your inspection ; and I propose, also, to make some determinations minations with it for the purpose of showing how quickly they may be made, and enabling you to form some judgment of what reliance can be placed in the results. Professor Eggertz proposed only a single standard, and the solution to be tested should be diluted to exactly correspond in color with that of the standard, and the per cent. of carbon calculated after carefully noting and making allowance for the measures of water used in diluting. In practice, difficulty was found in bringing the color of the normal solution down to the exact shade of the standard; also other difficulties were met with in conducting the process, causing delay and interfering with the accuracy of the results. To materially overcome these, and after numerous attempts, an instrument such as is now before you suggested itself to me; and also I concluded to use a larger quantity of metal than directed by Eggertz, and, in addition, to filter the solution from its insoluble matter before making the comparison; and, more recently, to use an acid of just such strength as would completely dissolve the metal without the application of heat. Experimenting with these changes from the original method I obtained reasonably good results. The instrument, you will observe, consists of a series of tubes, sixteen in number, two and a half inches long, and about half an inch in diameter, standing upright, and securely fastened in a light, portable, walnut-wood frame, but separated one from the other so as to allow just sufficient space between to place for comparison the . tube containing the solution to be tested. The tubes are filled with

HENRY TRAPHAGEN, * Toledo, Ohio (written discussion t).-The occurrence of flakes in steel is a perplexing problem, if we consider this condition as a disease rather than a symptom. But if considered as an exaggerated phase of a common disease, flakes will be recognized as old and well-known enemies. I have frequently found flakes in open-hearth steel, converter steel, and even electric steel; and not only in the so-called alloy steels but in dead soft 12-point carbon castings. In fact, I have some twenty flaky test bars that came from a foundry that manufactures converter steel castings. The physical characteristics of such material are striking in their constancy, for the yield point and elastic limit are always high, the elongation is variable, and the reduction of area is nearly always negligible. Soft steels of this kind can easily be bent to an angle of 150° and the only bad symptom is the appearance of incipient cracks on the surface; when the carbon exceeds 30 points, the bending qualities are seriously affected; and when the carbon reaches the neighborhood of 50 points, the bars are generally pulled short. The elongation is peculiar in that it seems to take place along the whole length of the bar, giving a crinkly appearance such as is found in cast brass and monel metal. Of course, this elongation only takes place in the softer varieties of steel. I have stated that flakes in steel represent exaggerated symptoms of a common disease, and that disease is the presence of higher oxides of iron. In every instance that has come to my attention, this condition is coexistent with the presence of oxides in some form. In open-hearth practice when this condition occurs, almost invariably it will be found that the metal has been loaded with ore or that tons of rusty turnings were being melted. In converter practice, one of three conditions is nearly always present: bad cupola practice, the use of oxygenated pig iron, or faulty tuyeres. With the electric furnace, my experience is quite limited, but the few examples of flaky electric steel that have come to my notice were made from a charge of turnings and low-grade light scrap.

Jan 6, 1919