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By John R. Spencer

A capillary tube variable volume cell is described, which has operated satisfactorily over a range of 100°F and 3,500 psi to 550°F and 1,500 psi. The cell contents are entirely visible over the length of the capillary with the exception of a space at the top amounting to three per cent of the total volume. Observations on the critical behavior of simple systems have been greatly facilitated by the apparatus, it being possible to establish the critical conditions for a particular mixture in the course of a day's run. INTRODUCTION Many types of apparatus have been designed for obtaining data on the phase relationships of hydrocarbon systems. Such apparatus can in general be subdivided into two classifications; (l), indirect measurement of phase volume, and (2), direct visual observation of phase volume, each of which has outstanding advantages and disadvantages. Indirect measurement of phase volume requires the use of rather elaborate apparatus including internal probes in which are located the device for determining the locus of the interface between phases. Such equipment is by its very nature costly, and is complex from the standpoint of operating technique. Probing techniques can be used, however, over wide ranges of temperature and pressure with a high degree of reproducibility. Apparatus for visual observation of phase behavior obviously has the advantage of enabling the experimenter to see exactly what takes place, but because the material to be tested is contained in a cell constructed of both metal and glass, is limited severely as to the temperature range of operation. Furthermore. the maximum pressure usually is limited by the choice of material used for sealing the glass to the metal, and by the strength of the glass itself. In the interest of increased efficiency of observation, as much of the cell as possible should be visible to the eye. Glass capillary tubes have been used successfully but have always given difficulty at the metal-to-glass seal. An apparatus has been devised to overcome the problems of sealing and resistance to temperature effects that have heretofore been the limiting factor with glass apparatus in the observation of phase volumes at elevated temperature and pressure. APPARATUS The objective which dictated the general arrangement of the apparatus (Figs. 1 and 2) was simplicity of operation. The air bath, A, was constructed of an iron framework to which was attached approximately one inch of glass wool bats which were covered on the outside with "Masonite." A roughly octagonal center piece was installed to provide forced circulation of the air by the fan, B, past the heaters, D, cell, F, and thermoregulator, C, respectively. The entire top of the box is removable to facilitate charging of the cell and to permit easy maintenance. Two windows are provided before and behind the cell to allow the operator to observe the contents against the background fluorescent light, E. The heaters,

Jan 1, 1951

By J. T. Dewan

An experimental setup is described whereby the responses of Neutron logging instruments have been determined opposite formations of different porosities and under various borehole conditions. The results of these tests are presented in several charts which show how the Neutron log is affected by the following factors: hole diameter, casing, cement, salinity and weight of drilling mud, and position of logging tool with respect to the wall of the hole. The responses in the case of empty holes are also shown. A chart is furthermore presented which shows the shapes of the Neutron log, as a function of logging speed and time constant, at the boundaries between two formations with different porosities. These were derived mathematically using as a basis laboratory determination of the shape of the curve under static conditions, i.e. at very low logging speed. Corrections for the readings made opposite thin beds are given by these computations. The correction is found negligible under usual logging conditions for beds thicker than about 4 ft. INTRODUCTION The Neutron log is used in borehole surveys both for the delineation of porous formations and for the quantitative estimation of their porosities.1,2,3,4,5 It is common practice to calibrate the response of the Neutron log in terms of porosity values for each given geological unit by means of empirical comparisons between the deflections of the neutron curve and the porosity values given by the core analysis in a sufficient number of wells. Usually, the plots of the porosity values vs Neutron log deflections show a definite trend. It is therefore possible to trace an average line across the plotted points. This average line constitutes a calibration curve which can be used to evaluate the porosities from the Neutron logs in the other wells drilled in the same region. Futhermore, when the porosity values are plotted on a logarithmic scale and the Neutron log deflections on a linear scale, the calibration curve is practically a straight line. Accordingly the calibration curves are often determined by simply tracing a straight line between two points corresponding to two widely different porosities. Different choices are made for these two points, depending on local conditions. For example, one point will be defined by plotting the deflection of the Neutron curve opposite a formation known to be very tight, for which an average porosity value of 1 or 2 per cent is assumed. The other point may correspond to shale sections, to which a porosity of around 40 per cent is ascribed. The information provided by the eletrical logs — in particular the Laterolog, Limestone log or Micro-Latero-log — is also very often a help in the calibration of the Neutron logs. Empirical approaches such as these make possible the derivation of fairly reliable porosity values from the Neutron logs in many cases, at least in open holes and in essentially clean formations. There are, however, several causes of uncertainty which may sometimes entail appreciable errors. On the one hand, the Neutron log readings are influenced by the borehole conditions: hole diameter, presence or absence of casing and cement, presence or absence of drilling mud, characteristics of the mud, and position of the logging instrument with respect to the wall of the hole. The amplitudes of the curves opposite thin beds are furthermore atfected by the bed thickness,

Jan 1, 1957

By Thomas D. Henderson, Donald E. Crowell

INTRODUCTION This paper presents a "case history" of the steps taken to estimate capital and operating costs for a typical porphyry copper concentrator of ±9,070 metric tons (10,000 short tons) per day capacity. The concentrator described herein is hypothetical, but is based on experience and is, in effect, a composite of several actual projects. The numbers used are illustrative only and do not represent actual costs at any particular concentrator. These numbers are, however, representative of typical milling costs at one point in time, and. are sufficiently accurate to illustrate the cost estimating procedures described in this paper. It is not possible to publish actual, current milling costs and, in any event, actual cost figures quickly become meaningless in today's economic situation with various costs all rising at different rates. The paper is divided into three parts: (1) order-of-magnitude estimate, (2) feasibility study estimate, and (3) discussion of differences between estimated and actual costs.

Jan 1, 1978

By P. Barnes

The object of this paper is to make a brief comparison of the outlines of several forms of ports for steel-melting turnaces, in reference chiefly to the proper mixture; of the gas and air, and to the direction in which the flame is thrown down into the interior of the furnace. In the illustrations on the accompanying plate, Fig. 1 shows a form of port designed by M, Pernot, of St Chamond, France. This is used with the dome roof preferred by him fur the revolving bottom that bears his name. From No. 1 has been derived No. 2. This is shown on the plans of Mr. A. L. Holley, and from them three large furnaces have been built and put into operation by the Springfield Iron Company. Fig. 3 shows an outline proposed by Messrs. Richmond & Potts for the Pernot furnace. In this the ports are brought in under an arched roof of nearly the ordinary form, instead of over the top of the roof, as with the dome of M Pernot, Fig. 4 shows a furnace as built by Krupp of Essen, Prussia, for fluid refining, or " washing "-—to use the briefer French term. in this the gas and air come into contact in broad sheets one above the other, Fig. 5 shows the form used by Messrs. Richmond & Potts

Jan 1, 1881

By R. W. Bartlett

Hydrometallurgical processes for copper flotation concentrates avoid the SO2 emission problems associated with smelting, but they require oxidation of copper to obtain solubilization during leaching. The resulting copper ions must be reduced to metal, which normally requires large amounts of energy or energy equivalent reagents such as hydrogen or iron. The conventional reduction method is electrowinning which is labor intensive and involves 35 to 40% of both the entire operating and capital cost of the better hydrometallurgical processes. There is considerable incentive to reduce the cost and energy required for producing copper ions from solution. Furthermore, it is thermodynamically possible to do this using sulfur contained in the concentrate itself. In fact, the thermodynamic potential of oxidizing sulfur from S+4 to the S+6 state is greater than required to reduce cupric ion to metallic copper.1 Realization of this potential in a practical process would significantly reduce the cost of hydrometallurgical processing of sulfide concentrates because sulfur would become a cost-free reducing agent. An apparently practical method is to use SO: and HSO3 ions, obtained by ammonia scrubbing of SO2 from a concentrate roaster gas, to reduce leached copper to metal in an autoclave. This reduction step is the Jumau 1907 A series of steps, including sulfite reduction, constituting a crude flowsheet was suggested by Parker in 1976.3 The present paper describes a detailed complete. sulfite process flowsheet based on materials and energy balances, discusses the chemistry, and discusses further work that is required to develop this process. Process materials, utilities costs, and energy requirements are projected to be unusually low because of the utilization of sulfur from the concentrate. Process Description The sulfite reduction process requires a copper concentrate containing approximately as much sulfur on a weight basis as copper. For those few concentrates that are deficient in sulfur, additional sulfur can generally be obtained by allowing more pyrite to float in the concentration process. The process steps, shown in [Fig. 1], are (1) a fluid bed roast of the concentrate, (2) a leach of the roaster calcine using recycled barren liquor from the reduction autoclave, (3) scrubbing of the SO2 gas with ammonium sulfite liquor to produce ammonium bisulfite, (4) reduction and precipitation of copper in an autoclave by combining part of the SO2 scrubber effluent (SO5

Jan 1, 1980

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'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. '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' 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 N. W. Sager, H. W. Mossman

The arrangement and general dimensions of the reverberatory furnaces and waste-heat boilers for the Nos. 2 and 3 smelting units at the McGill plant of the Nevada Consolidated Copper Corporation are shown in Fig. 1. Each of the two reverberatory furnaces has its own set of waste-heat boilers, and before February, 1932, each furnace, when it was in operation, delivered waste-heat gases to its own boilers only. In January, 1933, the idea was suggested of using some of the waste-heat boilers as economizers to operate in conjunction with the waste-heat boilers that were generating steam. The execution of this idea gave rise to the gas-flow scheme depicted in Fig. 1, the advantages of which were obvious, particularly so in view of the fact that for some months prior to the adoption of this scheme the smelting had been confined to No. 2 furnace, with No. 3 furnace and its boilers idle. The waste-heat gases from No. 2 furnace pass through the boilers serving this furnace as steam-generating units, thence through the original exit duct to a point where a bulkhead diverts the gases in a reverse direction through two of the boilers of No. 3 furnace. After the gases have traversed these two boilers, another bulkhead placed in the duct between No. 3 furnace and its boilers causes them to traverse still one more boiler, from which the gas path leads to the stack. In this scheme the last three boilers traversed by the gases, i.e., the boilers behind No. 3 furnace, function as economizers and preheat the feed water for the two steam-generating units directly serving No. 2 furnace. This discussion will give consideration to the results obtained in waste-heat recovery by the scheme shown in Fig. 1, and, further, will compare these results with those obtained before the boilers of No. 3 furnace were set up to act as economizers, but before going into the detail of heat generation, distribution and recovery, will present some additional details of the equipment. All boilers in this waste-heat plant are of the Stirling type. The two behind No. 2 furnace, acting as steam-generating units, of class 13, are 40 tubes wide and rated at 1112 boiler hp., while the three boilers behind No. 3 furnace, acting as economizers, are also of class 13, but 28 tubes

Jan 1, 1934

By d&apos, C. Antonio, S. H. Reichman

In the course of our studies of the annealing behavior of vapor-deposited silver films we have determined the electrical resistivity as a function of annealing temperature for films in the thickness range of 630 to 3240A. Fig. 1 shows the resistivity of the silver films vs film thickness in as-deposited and annealed conditions. The films were prepared by depositing 99.999 pct pure silver from molybdenum boats onto Vycor substrates. Deposition was conducted at a residual pressure of 5 x 10"6 Torr at rates of 20 to 408, sec-'. Thicknesses were determined using a multiple-beam interferometer. During annealing, resistance was measured using the four-probe method. Measurements were made every 5°C during two consecutive anneals to 300°C under a continuous vacuum of 2 x X6 Torr. The heating and cooling rates during annealing were approximately l° and 2°C min-', respectively. Typical resistivity vs temperature curves are shown in Figs. 2 through 4. There is an inflection point evident at 120°C on Fig. 2, the first anneal of a 3240A film. This inflection point was found on all films above approximately 1!00A on both first and second anneals. Below 1400A the inflection occurred at approximately 180°C. Figs; 3 and 4 show the first and second anneals of a 1370A film. The inflection point occurs at 180°C on the first anneal and approximately 120°C on the second. Our interpretation of this phenomenon is based on oxygen liberation from the film surface. It is well-documented that the presence of oxygen on silver surfaces causes a reversible increase in resistivity.1"3 The liberation of this oxygen, for example during vacuum annealing, would therefore cause a decrease in resistivity as observed on Figs. 2, 3, and 4 as a change in slope. This is accounted for by the decomposition of Ag20 on the film surface. The free energy of AgzO becomes positive between 125" and 225°C.4 The thickness dependence of the inflection points can be explained as an orientation effect. The films used in this study were preferentially oriented with their (111) planes parallel to the Substrate.''~ In addition it has been sten that the thinner films, below approximately 1500A, possess a decided "hill and valley"

Jan 1, 1969

By Gerard Matthes

ONLY in recent years has any practical headway been made in the application of aerial photography to geological problems, and up to the present time its principal value to the geologist and mining engineer has been in "areal geology;" i. e., the study of formations as revealed at the surface. The object of this paper is to set forth briefly the principal advantages that may be derived from aerial photographic data in geological work and to serve in a measure as a guide to those who may be con-templating its use. Geophysical prospecting has for object the locating of mineral under the surface. Inasmuch as the geologist's chief complaint in life is a dual one-inability to see under the surface and inability to visualize comprehensively what he does see on top of the ground-geophysical prospecting coupled with aerial photography should do much to lessen his burdens. To what extent aerial photography can be made a useful adjunct to geophysical prospecting remains to be proved, but the inference drawn here is that it holds many alluring possibilities. To avoid disappointments, it should be stated at the outset that to the :geologist or mining engineer an aerial photograph or mosaic is only a tool, the effecient use of which he must set out to master. Upon his skill and ingenuity in applying it to particular problems will depend largely the value of the results that he will obtain. Under the most favorable conditions an aerial mosaic or even a few loose photographs, because of the exceptionally comprehensive oversight which they afford of field data, such as dips and strike observations at isolated outcrops, local indications of faulting, mineral and fossil finds, greatly facilitate study and correlation, save much tedious foot work, and may repay their cost many times. Even so, types of country may be found where the most, skillful use of the best of pictures will produce results so meager as to render the cost of aerial photography entirely unwarranted.

Jan 1, 1928

By D. J. Wynnemer, G. W. Preckshot

Precise electromotive force measurements have been made on the zinc-cadmium system over the temperature range 700° to 900°C. Activity coefficients, partial free energies, enthalpies, and entropies have been determined .for the entire composition range. The integral heat of mixing is positive and compares favorably with calorimetrically determined values. Vapor-liquid equilibrium compositions were determined .for a total pressure of 1 atm and these agree well with previous values determined in other ways. The use of electromotive force measurements to obtain thermodynamic data for liquid metal systems is a simple and well-known method. Several reviews of the various experimental methods and results have been published.2,3,11 However, most of the past work using this technique was carried out at temperatures slightly above the melting point of the alloy system where alloy composition changes due to vapor transport and increased metal solubility in the electrolyte are not important factors. One advantage of extending the electromotive force measurements up to and including the normal boiling point of the alloy is that it is then possible to evaluate the vapor-liquid equilibrium of the alloy at various pressure levels up to 1 atm. A detailed discussion of the thermodynamics of reversible electromotive force cells can be found in most advanced physical chemistry or chemical thermodynamic textbooks. The expression stating the inter-relation of the electromotive force and the thermodynamic functions is the Gibbs-Helmholtz equation.

Jan 1, 1962

By R. A. Pasternak, B. Evans

A dynamic technique for the determination of solubilities of gases in metals has been explored, using the N-Nb system as a test case. An initially clean sample, maintained at constant high temperature, is exposed to the gas at low pressure: the rate of sorp-tion and the corresponding change in sample resistance are measured continuously. A pronounced decrease in the slope of the resistance concentration curve is observed at the terminal solubility. The rate of gas uptake by the sample was determined in an ultrahigh-vacuum flow system equipped with a servo-control which maintains constant pressure in the sample chamber; the system and the technique have been described in detail elsewhere. 1,2 The sample was held at constant temperature during sorption by maintaining approximately constant power input into it; this results in constant temperature, since the emissivity of a metal is independent of moderate concentrations of dissolved gas. The simple electrical circuit used both for heating and for resistance measurement is shown in Fig. 1. The power input into the filament is where R is the filament resistance, RL is an adjustable resistance in series with the filament, and VT is the constant dc potential of the power source. If RL is set equal to R at the beginning of an absorption run, the power input becomes insensitive to subsequent resistance changes; for example, an increase of 20 pct in sample resistance is accompanied by a decrease in power input of less than 0.8 pct; i.e., the

Jan 1, 1967

By S. P. Goplen, M. Henriksen, T. F. Barron

In the past decade, numerous large scale drilling projects have made use of reverse circulation air lift methods. Reverse air lift pumping can be established by injecting gas into a column of liquid; the subsequently decreased density of the gas-liquid mixture allows atmospheric pressure outside the lift conduit to establish flow. The rate of flow can be controlled by varying the gas to liquid ratio. A typical reverse circulation air lift system is depicted in [Fig. 1]. Allen 1 has described a number of reverse air lift drilling projects. Although cited examples are generally related to large diameter holes, the method has seen use in other applications such as sand dredging, chemical pumping, water well pumping. and continuous coring. One particular benefit obtained with enclosed reverse circulation drilling is elimination of lost circulation. The required air/water ratio for pumping at a given submergence and lift has been established experimentally by Gibbs.2 His data, however, do not reflect sensitivity of flow rate to air/water ratio. Further, in Gibbs' work, air apparently is injec-

Jan 1, 1980

The program for the Annual Meeting to be held in New York, Feb.17 to 20, 1919, inclusive, has been nearly completed. Besides the usual meetings for the reading of technical papers, the social features are being given special attention. They will probably embody the following: On Monday evening, a lecture by one of our fighting airplane pilots, to be illustrated by lantern slides and moving pictures. To this entertainment the ladies will be invited, as well as members. On Tuesday evening, a Smoker at which some very startling features are promised for the entertainment of members. On Wednesday evening, the usual banquet, at which it is hoped to have some very interesting speakers. The usual luncheons will be served in the Engineering Building and other features will be offered for the entertainment of the ladies during the day. No definite plans for the Thursday excursion have yet been formulated, though it is probable that something interesting will be offered the members.

Jan 12, 1918

By A. J. Miller, G. R. Brophy

THE Grossmann principle1 for the calculation of hardenability of steel from composition is attractive because of its simplicity. It postulates that the hardenability of a steel for any particular grain size may be expressed in terms of an ideal critical diameter, which is the product of an ideal critical diameter for a "pure" iron-carbon base multiplied by a succession of factors for each element of composition contained, including the incidentals. It infers that the multiplying factor for a given quantity of an element is constant for all combinations of composition. Grossmann has stated that in the great majority of cases the experimental values of hardenability are found to be well within 10 per cent of the calculated values. The validity of the scheme has been confirmed in principle by Crafts and Lamont2,3 and by Kramer et al .4 Their results differ from the original in the magnitude of the effect of some elements but, since they accepted the product concept and followed its direction, it is to be expected that similar results would be obtained. Crafts and Lamont, in their second paper, recognized that the factor relations for manganese and nickel were not continuously linear, but beyond certain critical amounts increase sharply. Austin, Van Note and Prater5 demonstrated nonlinear relations between hardenability and alloy contents. Their curves for chromium, silicon, manganese and nickel were all convex upward to show decreasing incremental effects. They concluded that Grossmann's factors underevaluate the hardening effect of low percentage additions of these elements, and overevaluate the larger additions. [ ] More recently W. Steven6 has found that the factor method fails when applied to complex steels containing two or three principal alloying elements other than carbon. Multiplying factors derived from his results bear a complex relation to composition and are not constant for a given amount of an element as the base composition varies. C. A. Liedholm7 found that, using either the Grossmann or the Crafts-Lamont multiplying factor values, not only were

Jan 1, 1945

By William R. Webster

In view of the good results which have followed the wide discussion of the rail-specifications of the American Section of the International Association for Testing Materials, I now offer for discussion its specifications for steel forgings and steel castings. It is not necessary to emphasize the importance of reaching definite conclusions on these subjects. Engineers, consumers and manufacturers are alike interested in securing good, reliable, uniform steel. In this connection, I would call particular attention to the important paper read by Mr. C. H. Ridsdale, last September, before the Iron and Steel Institute, as bearing on them; and, for convenience of reference in the discussion, I append the Table in Section VI. of his paper, on a Manifestations, Classified mider Heads of Faults of Different Types. appearing after Treatment by the User, for Tracing their Probable Source."* The discussion of these specifications will be practically a continuation of our former discussions on "The Physics of Steel." We have passed through a period in which the chemical composition of steel has received the greatest prominence; but failures of steel forgings and castings of the best chemical composition have shown that we could not control the quality of the finished product by the chemical composition alone. It must be admitted that differences in the physical properties of the steel, greater than those due to small variations in composition,are produced by heat-treatment, both in connection with the mechanical work of forging and otherwise. The present result is a strong tendency to deem the heat-treatment more important than the chemical composition. I think the mean course is the safer. We should give them equal importance; for we know that to produce the best results me must start with a good

Jan 1, 1903

By E. G. Woods, A. G. Comer

A mathematical model is presented and solved for determinution of the saturation distribution and pressure in a radial gas-storage reservoir. The model consists basically of two parts: (I) the growing gas-bubble core, and (2) the surrounding aquifer. Since the total pressure at the injection well is a function of the two-phase flow in the gas bubble and the unsteady single-phase flow in the aquifer, the resistance to flow in both zones was taken into consideration. The assumptions involved for both the radial equivalent of the Buckley-Leverett two-phase-flow equation and the injection-pressure equation are as follows: (I) the geometry is radial, (2) the gas bubble is free to expand or contract, (3) compression or expansion of the gas within the bubble may occur at the beginning of a time step, (4) the fluids are immiscible, (5) water is incompressible within the gas-storage region whereas it is compressible outside of this region, (6) a stable gas-water interface exists and (7) gas injection occurs at a constant rate or a series of constant rates. The mathematical model was solved numerically using an IBM 650 computer. A comparison is presented between the predicted results of the model, the results assuming steady-state flow and the actual initial injection-pressure history of an operating reservoir. Using the initial field pressure for a basis, the average deviation between the predicted pressure and the actual field pressure was less than 4.3 per cent. INTRODUCTION Underground storage of natural gas in abandoned oil fields, in abandoned coal mines, in caverns and in aquifers has had varying degrees of success. The lack of these first three facilities in the vicinity of most major gas marketing areas is leading more and more to storage in virgin aquifers. For the most part, this storage in aquifers has led to the study upon which this paper is based. Several excellent papers have been published discussing the problems involved in the underground storage of natural gas; however, to these writers' knowledge, none of them considered the two-phase flow of fluids in the gas bubble and the fact that the gas bubble will grow or shrink in size depending upon the injection and withdrawal history of the reservoir. Not only will both of these factors influence the required injection pressure, but also they will have a definite bearing upon the amount of water production occurring upon withdrawal from the storage area. To solve this problem on an IBM 650 computer, several simplifying assumptions were made. Only the drainage portion of the relative-permeability curve was considered, thereby neglecting any hysteresis effects introduced during an imbibition cycle. The quantity of gas withdrawn during the period of the field study was only a small percentage of the total gas in place; therefore, this assumption is justified. For the problem studied in this case, the combined effects of capillarity and gravity were assumed to be negligible. This assumption becomes less valid as the formation thickness or the average pore diameter increases markedly. The justification of these assumptions should be studied in each case. THEORY This mathematical model for the prediction of saturation distribution and pressure for a radial gas-storage aquifer is based upon the equations for radial two-phase fluid flow'.' and for radial, unsteady-state, single-phase fluid flow.' The two-phase flow is considered to take place in a "core" whose radius is equal to the maximum radius that the gas zone will attain, as indicated in Fig. 1. The injection-withdrawal history is approximated by a series of constant flow rates. Within the "core", gas is assumed to behave as a semi-compressible fluid; that is, the gas is assumed to have a constant density based on the average gas-zone pressure for the flow period. Between each constant-rate time increment, the gas density is allowed to change. This involves an iterative solution of the pressure equation. The liquid phase in this zone is considered to be incompressible, whereas it behaves as a compressible liquid outside of this region. The equations of incompressible flow in the "core" may be written for the gas phase

By A. Ahmadieh, J. E. Dorn, Jack Mitchell

A detailed investigation of the disloccrtion mechanisms controlling prismatic, slip in a solid solutions of magnesium containing up to 15.9 at. pel Li revealed that low-temperature prismatic slip is controlled by the Peicrl's mechanism for all alloy compositions. At higher temperatures slip in the 7.9 at. pet Li alloy was found to follow the diclates of the cross-slip mechanism from basal to prism planes, while the higlier-lilhium alloys exhibited an athermal dejormation process which might be due COARSE-GRAINED polycrystalline aggregates of distilled magnesium exhibit very limited ductility at low temperatures.' The ductility of polycrystalline magnesium, however, is much improved by solid-solution additions in excess of about 8 at. pct to shot-range ordering. The major effect of lithium additions on the low-temperature Shear] stress. for prismatic slip appears to be due to its efftct in lowering the Peierl's stress whereas (1 increase in the shear stress with increased lithium conlent at higher temperatures might he due to short-range order strengthening. Additions rip to 7.9 (at. pel Li appear to have only minor effects on the slackiug-jaidt energy. Li.2 Although the relative amounts of basal slip and twinning are not materially altered by such alloying, a substantial change takes place in the relative amounts of prismatic slip. Whereas prismatic slip is negligible and limited to regions of high stress concentrations in the vicinity of the grain boundaries in pure magnesium, extensive prismatic slip over entire grains occurs in the higher lithium content alloys. Furthermore, as the lithium content is increased above 8 at. pct, the flow stress for polycrystalline aggregates decreases. Comparison of the single-crystal data on pure magnesium for basal slip by Sheely and Nash3 and those for prismatic slip by Flynn, Mote, and Dorn4 indicates that the critical resolved shear stress for prismatic slip is much above that for basal slip.

Jan 1, 1965

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

By Raymond S. Weimer

Of the several characteristics of a coal that influence its suitability for use in a given piece of burning equipment, the clinkering and slagging characteristics of the ash of the coal are highly important. They determine the maximum rate at which the coal may be burned on a stoker or in pulverized form without difficulty from damage to metal parts, from erosion of refractory walls, or from stoppage of gas passages by accumulation on the tubes. They also determine the minimum rate at which a slag-tap furnace may be operated without difficulty in removal of the ash in fluid form. Need for a Better Criterion In common with other producers and users of coal, the Northern Illinois Coal Corporation has long used the available methods for the measurement of the clinkering characteristics of coal ash, chemical composition and fusion temperature of the ash, as criteria for the selection of coal that would suit the particular requirements of its customers. These two available criteria have greatly helped in the problem of selection but it is unnecessary to dwell upon the fact that they are not completely adequate for the purpose. The composition of the ash and its clinkering tendency vary widely over the company's mining area. In a certain period, some years ago, an unusual amount of severe clinkering of the ash of coal shipped made extremely acute the need for a better criterion of the clinkering that might be expected. It was also desirable that the criterion result from a reasonably rapid method, so that the clinkering characteristics of the coal would be known before shipment. Complaints on the severe clinkering of the ash came from only a fraction of the output of the mine but the occurrence of the clinkering seemed quite unpredictable. Attempts to relate the chemical composition of the ash and the fusion temperatures to the clinkering were unsuccessful. Coal from the area of the mine in which the fusion temperature of the ash was the lowest gave the least trouble from clinker-ing. Chemical analysis of the ash from that section giving the most trouble showed high contents of iron and low contents of silica, but frequently these were not greatly different from those of coals that gave little trouble from clinker. Aside from the clinkering difficulty, the coal was quite satisfactory. The ash content was normal and high rates of burning could be obtained, but again and again such severe clinkering would occur that the furnace would be shut down because of the accumulation of clinker. Examination of the clinker from the customers' plants showed that the clinkers that adhered to the grates and fouled the fuel beds were hard, flat, dense, and usually dark in color. Coal that was satisfactory gave clinkers that were softer, bulky rather than flat, of low density, and usually lighter in color.

Jan 1, 1944

By Raymond S. Weimer

Of the several characteristics of a coal that influence its suitability for use in a given piece of burning equipment, the clinkering and slagging characteristics of the ash of the coal are highly important. They determine the maximum rate at which the coal may be burned on a stoker or in pulverized form without difficulty from damage to metal parts, from erosion of refractory walls, or from stoppage of gas passages by accumulation on the tubes. They also determine the minimum rate at which a slag-tap furnace may be operated without difficulty in removal of the ash in fluid form. Need for a Better Criterion In common with other producers and users of coal, the Northern Illinois Coal Corporation has long used the available methods for the measurement of the clinkering characteristics of coal ash, chemical composition and fusion temperature of the ash, as criteria for the selection of coal that would suit the particular requirements of its customers. These two available criteria have greatly helped in the problem of selection but it is unnecessary to dwell upon the fact that they are not completely adequate for the purpose. The composition of the ash and its clinkering tendency vary widely over the company's mining area. In a certain period, some years ago, an unusual amount of severe clinkering of the ash of coal shipped made extremely acute the need for a better criterion of the clinkering that might be expected. It was also desirable that the criterion result from a reasonably rapid method, so that the clinkering characteristics of the coal would be known before shipment. Complaints on the severe clinkering of the ash came from only a fraction of the output of the mine but the occurrence of the clinkering seemed quite unpredictable. Attempts to relate the chemical composition of the ash and the fusion temperatures to the clinkering were unsuccessful. Coal from the area of the mine in which the fusion temperature of the ash was the lowest gave the least trouble from clinker-ing. Chemical analysis of the ash from that section giving the most trouble showed high contents of iron and low contents of silica, but frequently these were not greatly different from those of coals that gave little trouble from clinker. Aside from the clinkering difficulty, the coal was quite satisfactory. The ash content was normal and high rates of burning could be obtained, but again and again such severe clinkering would occur that the furnace would be shut down because of the accumulation of clinker. Examination of the clinker from the customers' plants showed that the clinkers that adhered to the grates and fouled the fuel beds were hard, flat, dense, and usually dark in color. Coal that was satisfactory gave clinkers that were softer, bulky rather than flat, of low density, and usually lighter in color.

Jan 1, 1944