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By M. E. Wadsworth, J. R. Lewis, J. M. Quets

Samples of snythetic magnetite were reduced in hydrogen at various partial pressures and temperatures. The reaction mas found to be surface controlled and directly proportional to hydrogen partial pressure over the temperature range studied (400° to 1000°C). A transition in the mechanism occurred at approxirnately 590°C. This has been attributed to a change in the slow step of the reduction reaction resulting from the presence of stable wüstite at higher temperatures. Below 590°C the heat of activation for the reduction was found to be 14,700 cal per mole and it was 3,200 cal per mole above 590°C. THE reduction of the oxides of iron has been a subject of study and interest for many years. Edstrom1 has reviewed the work up to 1953 and his findings provide much basic information concerning details of the reduction of hematite (Fe2O3 ) and magnetite (Fe3O4) with both H2 and CO. He concluded that below 600°C the reduction of both hematite and magnetite was essentially identical, since the rate was controlled by a surface reaction at a magnetite gas interface and the iron formed was very porous. The decrease in the reduction rate for both hematite and magnetite immediately above 600°C was attributed to the formation of a stable wüstite phase across which diffusion was very slow. The wide difference in reduction kinetics for hematite and magnetite above 600°C was explained in terms of the character of the wüstite formed. The rate of magnetite reduction increased slowly with temperature beyond the minimum immediately above 600°C and rates equivalent to those observed at 550°C were not obtained until the temperature was increased beyond 850oC. Edstrom and Bitsianes2 studied the solid-state reduction of magnetite, the reaction of which can be written (4x-3)Fe + Fe3O4—4 FexO [1] where x is between 0.83 and 0.95. The rate was found to be controlled by the kinetics of transport of iron ions through the wüstite phase. Bogdandy and Riecke3 studied the kinetics of reduction of small grains of iron oxide in hydrogen and qualitatively attributed the slow step in the reduction process to the diffusion of hydrogen and water vapor through pores. McKewan4 has analysed the data of Joseph,5 Stalhane and Malmburg,6 and Lewis7 and has demonstrated that the kinetics of reduction of both hematite and magnetite are controlled by surface reactions and also that the variation in surface area during reduction must be accounted for. McKewan was able to correlate the reduction data by the equation rodo[1-(1-R)1/3] = Kt [2] where ro is the initial particle radius, do is the density of the iron oxide, R is the fraction reduced at time t, and K is a rate constant. The applicability of Eq. [2] for temperatures above 600°C where a stable wüstite phase is present, indicates the slow step in the over-all kinetics does not result from diffusion unless diffusion occurs laterally along the oxide metal interface or through a wüstite layer of constant thickness. Diffusional control through a layer of wüstite is unlikely, however, in view of the pressure effects demonstrated by Tenenbaum and Joseph,' Diepschlag,9 McKewan,10 and the results of the present study. McKewan has demonstrated a linear rate dependence on the hydrogen partial pressure over the temperature range 400" to 1050°C for the reduction of hematite.

Jan 1, 1961

By H. R. Thresh, A. F. Crawley

THIS paper reports the results of viscosity measurements on cadmium and indium undertaken as part of a continuing program of liquid metals research at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. For several years this work has continued with support from the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. In the literature, existing viscosity data for cadmium are conflicting and for indium are scarce. To achieve reliable viscosity values, further work was deemed desirable. Viscosities were measured using an absolute technique applied to an oscillating closed right cylinder of liquid metal. The apparatus, constructed in this laboratory, and the techniques involved in its use have been described in an earlier paper.' In calculating viscosity coefficients from the experimental data. Roscoe's2 mathematical analysis was used. Because accurate viscosity determinations are dependent on accurate density data, and since the available data in the literature are conflicting, the densities of liquid cadmium and indium were also determined in this laboratory by a pycnometric technique. This increased the control exercised over all the variables contributing to the accuracy of viscosity measurements. For both density and viscosity determinations, cadmium and indium of 99.999 pct purity were used. These materials were obtained from Cominco Ltd. In order to suppress excessive evaporation losses and help prevent oxidation, a technique developed in measuring the viscosity of zinc' was used for cadmium. This involved maintaining an atmosphere of purified hydrogen in the viscosimeter during the rela- tively long periods while the experimental temperature was changed and stabilized between individual determinations of the logarithmic decrement. Then, immediately prior to a decrement measurement. the viscosimeter was rapidly evacuated to a pressure of about 2 X 10-6 torr. On the other hand. with indium. no difficulties arise from vaporization or oxidation. In this case. therefore. the apparatus was held under a constant vacuum of about 2 x 10-6 torr. When all sources of random and systematic error have been evaluated, the technique is considered to yield data accurate within 10.5 pct. The viscosity of cadmium was measured to a maximum temperature of 451.8°C and that of indium to 346.5°C. These temperatures are. respectively. 130° and 190°C above the melting points. Two separate runs were made on indium. The results are given in Table I and, when plotted. yield the smooth curves evident in Figs. 1 and 2. Values of A and C to fit the well-known Andrade1 equation were determined by a regression analysis. The equation is: where n = coefficient of viscosity. i = specific volume. T = temperature in °K Despite its empirical nature. Andrade's equation has been shown by many workers to describe accurately the temperature dependence of viscosity. During the current research program, this equation has been found to fit the data precisely for all the metals and alloys that have been studied.5,6 The A and C' values for cadmium and indium are given in Table 11. Comparing the magnitude of the present data with those of previous workers,7-10 as has been done in Fig. 1, it is evident that the results of Fisher and Phillips10 deviate markedly from the rest. With the exception of one point from Gering and Sauerwald,7 all other data agree within ±2.5 pct. However, the agreement between the present results and the work of Menz and sauerwald9 is especially good over the entire experimental temperature range. Such agreement may be expected since Menz and Sauerwald's

Jan 1, 1970

By Charles R. Cavanaugh, John F. Elliott

The activity of nickel in liquid Pb-iVi alloys which are rich in lead was measured in the temperature region of 700° to 1100°C by means of the galvanic cell: The electrolyte used was stabilized zirconia. Tlze data were correlated using the a function, and a plot of the temperature coefficient aE/aT All subsequent calculations of the thermodynamic properties are based on these two functions. The activity, activity coefficient, and molar properties of mixing of nickel are reported. Nicke1 shows extreme positive deviations frorn ideality while lead shows a very slight positive deviation in the composition range studied The study of the activity of nickel in liquid Pb-Ni alloys reported herein was undertaken to explore the use of stabilized zirconia, an oxygen-ion electrolyte, with liquid-metal electrodes, and to obtain further information on the thermodynamic properties of the liquid binary Pb-Ni system. The cell The reversible electromotive force of the cell results from the difference in the chemical potential of the oxygen at the two electrodes: po, (left) - p~ (right) = -4E5 [I] The chemical potential of oxygen on the right is fixed by the activity of nickel in the solution and pure solid nickel oxide. That on the left is set by pure solid nickel in equilibrium with pure solid NiO. By definition: Since the chemical potential of nickel is related to the chemical potential of oxygen through the equilibrium constant for the formation of NiO from nickel and oxygen gas, the electromotive force of the cell is also expressed In this case, n is 2, E is the reversible potential of the cell, and 5 is Faraday's constant. The work of Kuikkola and wagnerl and Schmalz-reid2 has shown that the stabilized zirconia electrolyte is essentially an ionic conductor at the oxygen levels encountered in the experimental arrangement of the work, i .e., PG > 10-l7 atm. THE EXPERIMENTS The advantage of this type of reversible cell over those using a liquid electrolyte is the simplicity arising because the electrolyte also functions as one of the containing crucibles. A further simplification was the choice of the Ni (sat.)-NiO electrode as the standard. This permitted a ready check on the behavior of the electrolyte, as the potential of the cell must become zero when the right electrode becomes saturated with nickel, either because of a change of temperature or because of the addition of nickel to the electrode. It also permitted the potentials being measured to lie in the most satisfactory experimental range of 0 to 100 mv. Although it was not theoretically necessary, lead was included in the standard electrode as it assured good contact between the electrode and electrolyte. Cell Design. The general arrangement of the experimental cell assembly is shown in Fig. l(a) and the details of the cell itself are contained in Fig. l(b). The anode lead wire on the interior of the cell was connected to a coil of perforated sheet nickel. Within this coil were nickel oxide pellets which were held beneath the surface of the liquid Pb-Ni alloy. A disc of nickel oxide was held at the bottom of the external crucible (alumina) by means of the thermocouple protection tube. The nickel oxide disc and pellets were compressed dry at 10,000 psi and sintered at approximately 1000°C for an hour in air. A major experimental difficulty of reversible electromotive force cells with liquid electrodes is the selection of suitable materials for connecting

Jan 1, 1964

By W. A. Rachinger, C. Graeme-Barber, R. L. Bell, R. C. Gifkins, T. G. Langdon

R. L. Bell. C. Graeme-Barber, and T. G. Langdon (Imperial College. London)— The internal-marker technique developed by Ishida, Mullendore, and Grant has enabled them to make some interesting observations on the role of grain boundary sliding in creep. Certain of their conclusions are supported by our own similar experiments on Magnox AL80 (Mg-0.8 pct Al) specimens containing several markers, full details of which will be published shortly. In particular, we would agree that: 1) Using the internal-marker method, there is little difference between Egb, the contribution made by grain boundary sliding to the total strain, measured at the surface and in the interior of a specimen. 2) The measurement of the change in grain shape during creep leads to an underestimation of the grain strain, and hence an overestimate of Egb.. However, the discrepancies between the values obtained by this method and those obtained using markers are not as great as Tables IV and V of Ishida, Mullendore, and Grant would suggest; see below. The authors' Eq. [I] which is used to compute Egb from the transverse displacement ITt of longitudinal marker lines is not given in the reference quoted,'' where in fact only relations for Egb in terms of the longitudinal displacements of markers were developed. As first pointed out by Gifkins and Gittins,12 a problem arises in the use of longitudinal markers. and we will show that Eq. [1] underestimates Egb in the interior by a factor of 2. In Fig. 12, two grains X and Y have become displaced by the vector AC which lies in the plane of the grain boundary ABCD separating them. A longitudinal marker has been split by this displacement into the two parts LA and CAW. If these were surface grains the transverse displacement, Ut. could be obtained by viewing normal to the "top" surface. If interior, a section through CD parallel to the top surface would show the same result, provided the longitudinal internal markers delineated planes normal to the top surface. (This is an essential feature of the markers not pointed out in the paper.) The important point is that the quantity Ut tan B (=BE=DF) only gives the elongation due to the one component AB of the sliding. The elongation V/tan 8 (=GD) due to the component AD must be added to produce the total elongation resulting from the boundary displacement AC. If the grain boundaries in a poly crystalline specimen are randomly oriented with respect to the stress axis it follows that In the interior of a specimen the two sums depend for any difference simply on the definitions "top'' and "side". On the surface it is possible that the two sums could differ somewhat. In either event it is clear that the authors' Eq. [I] underestimates Egb, and in the interior, and perhaps at the surface also, the appropriate formula is given by The suggested modification probably makes little difference to the comparison between surface and interior values of Egb where both were obtained from marker measurements. For the estimation of the correction becomes extremely important where the boundary contribution is large. In our own work on magnox, for example, we have obtained values of as large as 70 to 80 pct, under conditions of high temperature and low strain rate. The use of planar markers transverse to the stress axis would simplify the comparison between surface and interior behavior, because measurement of the longitudinal offsets Us of these markers could be summed to give the total elongation di-

Jan 1, 1965

By G. Ansell, J. Weertman

G. Ansell and J. Weertman (Rensselaer Polytechnic Institute and Northwestern University, respectively) —The great increase in creep strength that you found in your indium-glass composites is quite striking. You ruled out a decrease in the dislocation source density as an explanation of the reduced creep rates. Could you tell in greater detail why you feel this is an inadequate explanation of the phenomenon. It appears to us that it is a reasonable one. Consider the spacing between the glass spheres in your composites. It is of the order of 10-3 cm. The spacing between dislocations in a (single-phase) annealed metal with a dislocation density of the order of 106 to 107 cm per cm3 also is of the order of 10-3 cm. Therefore it is not reasonable to expect that the arrangement of the dislocation lines is the same in the composite material as it is in pure indium. If the dislocation arrangements are different the density of the dislocation sources likewise will be different. Another way of saying the same thing is the following. The presence of the glass spheres reduces one of the dimensions of the metal phase to 10-3 cm. Thus the metal phase, in effect, is equivalent to a metal whisker or a thin metal film. These are strong because they have so few dislocation sources within them. T. D. Gulden and J. C. Shyne (authors' reply)—It is to be expected that the arrangement of dislocations in the indium-glass composites would be quite different than that observed in annealed pure metals. The dislocations probably exist primarily as segments connecting the dispersed particles. These segments and discontinuities at the very large area of particle-metal interface could act as dislocation sources. For this reason it was considered unlikely that the very high observed creep strengths were due to a low density of dislocation sources. A more likely explanation is that the distance a dislocation can glide is limited by the interparticle spacing. The particles averaged about twenty in diam and were less than 10 µ apart in the 40 pet composite. It seems reasonable to assume that a dislocation loop in a volume of metal surrounded by these relatively large particles would not bow out around them but would be restricted to the region between particles. A general expression for creep rate is given by the product of the dislocation source density, the average rate at which loops are generated from a source, and the average area swept out by a loop times the Burgers vector magnitude. Assuming that the area swept out is limited by the interparticle spacing and the rate of generation of loops is controlled by the rate of climb of loops over second-phase particles, as suggested by Ansel and Weert-men,9 a calculation of the dislocation source density may be made from the experimentally observed creep rates. The result comes out 10" to 10" per cm3 which seems reasonable in view of the assumptions involved. Thus it is concluded that the anomalously low creep rates that were observed were due not to a low dislocation source density but rather to a limitation on the area swept out by each dislocation loop.

Jan 1, 1964

By P. Schwarzkopf, J. H. Brophy

A modification of the Mendenhall wedge blackbody1 has been used to determine solidus temperatures and to anneal alloys in the tantalum-rhenium binary system. The technique has proven to be simple and accurate with modest power requirements. For temperatures up to 2800° C a piece of 10-mil tantalum sheet was folded double and formed as shown in Fig. 1. The middle of the resulting ribbon filament was a cylindrical-shaped crucible with less than a 1/8-in. opening. After inserting a specimen in the cavity, the filament was clamped between molybdenum electrodes in a high vacuum chamber. A representative filament 2 in. long and % in. deep was heated to 2800°C with a current of 700 amp at 4 v. The specimen temperature was determined by sighting into the cavity with a Leeds and Northrup optical pyrometer. The twisted filament shape was necessary to avoid serious geometric changes during thermal expansion. For temperatures between 2800" and 3000°C a 4-mil tungsten filament was employed. To facilitate fabrication it was warm-folded, and a twisted segment of 10-mil tantalum was used to support one end to absorb thermal expansion. This element assembly required about 700 amp at 10 v to reach 3000°C. Two geometric modifications of the filament were helpful for solidus temperature determinations. A shallow chamber, with depth to opening ratio of 3 to 1, permitted direct observation of the specimen through the optical pyrometer. The fact that the specimen was visible permitted the melting point to be determined when sharp features on the specimen surface became rounded; it also indicated that blackbody conditions did not prevail. By standardizing against the melting point of molybdenum, the observed melting temperature was corrected by the following form of Wien's Law: in which T is the true temperature, To is the observed temperature, and K is a constant characteristic of the filament geometry and determined experimentally for the molybdenum standard. The resulting corrected melting point for each alloy served as a reference temperature for the second more precise filament geometry. With a 6 to 1 depth to opening ratio, the specimen was indistinguishable from the filament interior, indicating good blackbody conditions. Using this technique, a series of specimens was isothermally treated at temperatures above and below the corrected direct reading. Incipient melting was detected by visual or micrographic examination of the specimen after cooling. This procedure was checked with specimens of pure chromium, molybdenum, and tantalum. Table I represents the values obtained, together with the solidus temperatures in the tantalum-rhenium binary system determined by the same technique. The alloy specimens were approximately 1/8 in. in diam. They were pieces of 10-g buttons melted four times in a nonconsumable tungsten electrode arc furnace on a water cooled copper hearth in 2/3 atmos of titanium gettered helium. Several sources of error are possible in such temperature measurements. Within the accuracy of the pyrometer no gradients were detectable near the specimen, and element distortion was virtually eliminated by twisting the tantalum. Compensation was made for the 1/8-in. sight glass by inserting several identical thicknesses and extrapolating to zero thickness. As a result an additional 10°C correction was added to all observations in the temperature range of 2500" to 3000°C. The principal source of error was then in the operation of the

Jan 1, 1961

By Richard R. Bains

"When l hear - I normally remember 10 percent When I hear and see - I can remember 15 to 25 percent When I hear, see, and do - I usually remember up to 50 percent" While this is not a truism in relation to each and every individual; on the average, this is the case. If we use this as a premise in training operator and maintenance personnel, then it must be obvious that we can't rely on a mere presentation, even one which includes the needed classroom participation and/or hands on work, to do a thorough job and to make this personnel totally proficient - 100 percent proficient. We have to have some other device some other means to make this a continuing process, a process wherein the people can grow in knowledge while performing their normal duties. We have to feel that the words "normal duties" are the key to the whole program. If you would ask a crusher operator what his duty is, he might say "To run this crusher so that we produce 250 tons per hour of a minus 13mm (minus 1/2 ") product." A maintenance man could say "To fix the unit when there is a problem." Both of these answers are legitimate but, they are only a part of the total picture. In order for each of these individuals to do the best job, he must know not just the specifics about the machine he works with or on - he must know the interrelation of all the machinery in the crushing circuit - how the efficiency of each machine affects the others - why a minor problem on one piece of equipment can generate a major problem for another unit which follows it or precedes it. In short, you cannot separate machine operation and maintenance from the application of the equipment in the crushing circuit - and obtaining this knowledge must be a part of the normal duty of crushing plant personnel. As an example a crusher - any crusher - is designed to crush oversize material. It is not designed to accept feed which is already at or less than the required product size. If sized material goes to the crusher, increase wear results by using the crusher as a chute or the crushing chamber can be clogged up with the fines. This latter point is particularly true with cone crushers, especially in the third (Short Head) stage of crushing. When a Gyradisc is used (fourth stage crushing) it is even more critical that the product be removed before the material goes to the crusher. The crusher cannot control this - the screen ahead of the crusher does. The screen must be of adequate size and be functioning properly to allow the crusher to work at optimum. Screening is both an art and a science. Since there are so many variables which affect the output of the screen, it is always best to have a screen which is larger than the sizing calculations dictate. The screens are the most important elements in the circuit. Without screens, specification materials cannot be made and the size of the screen will ultimately aid or hinder your ability to get the most production possible out of the plant. There is a formula available from all screen manufacturers which is designed to calculate the proper screen size. It takes into consideration the

Jan 1, 1982

By Carlos G. Valenzuela

The value generally accepted for stacking-fault energy, of copper has been approximately 40 ergs per sq cm based on Fullman's2 value for the coherent twin-boundary energy and the assumption that is twice the twin boundary energy However, Thornton and coworkers8 determined that the lower limit of for copper is approximately 60 ergs per sq cm, based on measurements of dislocation-node radii. They suggested that the assumption of = 2t is invalid. It is the purpose of this note to present results which indicate that the values of obtained by measurement of twin-grain boundary intersections and the values obtained by measurement of dislocation-node radii are actually compatible. The most reliable values for of the a brasses, based on electron-microscope observation of dislocation nodes, are probably those values reported by Smallman and Green6 who applied the Siems correction (1961) to data obtained by Howie and Swann.3 These values shown in Fig. 1 give an extrapolated value of approximately 70 ergs per sq cm for pure copper. In the present work, Fullman's method for determining the stacking-fault energy of copper was extended to the a brasses. High-purity copper (99.999 pet) and high-purity zinc (99.999 pet) were mixed in proportioned amounts and melted in sealed and evacuated quartz tubes. The alloys were homogenized for a week at 750°C and chemically analyzed by means of X-ray fluorescence. These alloys, along with a specimen of pure copper, were rolled to 98 pet reduction and a thickness of 0.009 in., resealed, and annealed for 40 hr at 715°C. Values for the ratio of twin-boundary energy to the grain-boundary energy, it gb, were obtained from measurements of dihedral angles formed at the intersections of twin boundaries and grain boundaries by using Fullman's2 mechanical analogy of surface tensions acting at the intersection of an annealing twin and a grain boundary. The angles between the twin traces and the grain boundaries were measured for a large number of twin-grain boundary intersections at a magnification of X500 using a rotating mechanical stage on a Reichert metallograph. The rotary stage has a calibrated angle scale with vernier so that measurements can be made to 0.1 deg. The mean twin-grain boundary energy and standard deviation were calculated for copper and each of the brasses by the use of an IBM 7072 computer. It was found that the mean value of gb stabilized after approximately 100 twin-angle measurements. This was determined by plotting the mean against the number of angles measured. Since the measured angles deviate from true dihedral angles, a correction factor for grain orientation, discussed below, was applied. The stacking-fault energy was then calculated from these values and the values of grain-boundary energy derived by Taylor.7 The data obtained are tabulated in Table I. Values for stacking-fault energy are plotted in Fig. 1. The value of gb for the specimen of 1.03 pet Zn is close to the value obtained by Fullman2 for OFHC (99.98 pet) copper, 0.045. It is believed that the purity of the copper affects gb significantly. The 99.999 pet purity Cu used in this investigation yielded a value of yt/ygb, 0.76, which is much higher than that obtained by Fullman. Additional evidence suggesting that the purity of

Jan 1, 1965

By C. R. Criss, R. J. McCormick

ThiS paper .summarizes the development and perform. ance of the Coldwater Oil field, Isabella County, Mich. Production is obtained at a depth of 3750 ft from a dolomite reservoir, which is probably both Rogers City and Dundee. There appears to be no persistent barrier to vertical fluid movement between the Rogers City and Dundee, and both formations are believed to have a common original oil-water contact. No we1ls are open to production at the level of the Dundee. The discovery of the field in 1944 was followed by the drilling of 81 producing wells and nine dry holes. By the end of 1952, the field had produced 12,763,000 bbl of oil, at which time 69 active wells were producing 3600 B/D oil and 21,000 B/D water. The reservoir has an effective natural water drive, and bottom-hole pressure has declined 75 psi from an original pressure of 1453 psi. Oil is undersaturated at reservoir conditions with a solution GOR of 512 cu ft/bbl and a saturation pressure of 1190 psi. INTRODUCTION Although the Coldwater Field is now in its ninth year of production, it ranks seventh in cumulative recovery, and second in current daily oil production in the State. Following complete development of the field in 1946, it has consistently contributed approximately 11 per cent of Michigan's daily production. Coldwater appears to have a greater pay thickness than most fields producing from the Rogers City forma- tion in the west central part of the Michigan basin. Except as influenced by the extent of closure and the thickness of the oil column, reservoir performance is believed to be representative of Rogers City fields in this part of the basin. For this reason, it is felt that the following presentation of factual data for the field will be of general interest. HISTORY AND DEVELOPMENT Discovery of the Coldwater field during Aug., 1944, followed favorable subsurface geological correlations and core tests drilled to a shallow stratigraphic marker horizon. The field is located in the west central part of the Michigan Basin in Coldwater Township (T16N-R6W), Isabella County. It is 60 miles west-northwest of Bay City, and near the geographic center of the southern peninsula of Michigan. The discovery well flowed 200 bbl of oil the first 24 hours from the Rogers City dolomite at a depth of approximately 3750 ft. Field production is principally from the Rogers City with a minor amount assumed to come from the underlying Dundee dolomite, although none of the wells are open to production at the level of the Dundee. Both the Rogers City and Dundee formations belong to the Devonian system (See Geologic Column-Fig. I.) In addition to Rogers City-Dundee oil production, sweet gas is produced from the Michigan Stray sand of the Mississippian system at a depth of 1400 ft. The gas reservoir has approximately the same areal extent as the underlying oil reservoir. Although gas production is an important feature of the Coldwater field, this report is concerned only with the oil reservoir. The productive area is approximately 3200 acres. The pool is developed on a 40 acre spacing pattern with wells drilled in the center of the north half of 40 acre tracts, except for a few off-pattern wells drilled along

Jan 1, 1955

[A session of the Institute of Metals held during the February, 1926, meeting of the Institute, was devoted to a symposium on ''gas" in copper. S. Skowronski, Perth Amboy, N. J., was chairman. On the program were papers by T. S. Fuller; W. H. Bassett and J. C. Bradley; Susan B. Leiter, and W. H. Bassett and H. A. Redworth. These papers follow the chairman's introductory discussion.] S. Skowronski, Perth Amboy, N. J.—There are today two groups of metallurgists, one group who believe in oxygen-free copper and another group who believe that oxygen is absolutely essential in copper; not that the two groups disagree, but that a certain grade of work calls for oxygen-free copper, while another grade of work does not. I can sum up the problem by reading the abstract of an article by Frederick Johnson of Great Britain in The Metal Industry of Sept. 4, 1925. Few, who have watched the trend of things during the last two decades, can have failed to notice the steady growth of opposition to the prevalent use of copper in the "tough-pitch" condition, which for many ages enjoyed an unchallenged supremacy. Broadly speaking, there are two schools of thought in the metallurgical world, one holding the view that copper containing a small proportion of oxygen is an eminently suitable material for users, the other expressing its preference, in no hesitating or uncertain manner, for copper from which oxygen has been removed by means of a deoxidizer. In the old days, before the advent of the converter and the electrolytic refining process, the copper of commerce was so impure that the presence of oxygen was imperative in order to neutralize the influence of impurities which militated against the hot-working properties of the metal. For electrical purposes, oxygen must be present, because sound bars and billets cannot be produced without it, except at the expense of electrical conductivity. For most engineering purposes, however, electro-deposited copper may be used either by itself or with the addition of alloying elements, e. g., arsenic and nickel, which experience has proved to be beneficial, such copper being freed from oxygen by the aid of a deoxidizer, e. g., phosphorus. Such material has positive advantages over "tough-pitch" copper as at present produced from refinery furnaces. It has greater toughness and malleability, and is immune from the action of reducing gases at high temperatures, the destructive action of which, in the case of "tough-pitch" copper, is well known. The reasons why there has been no wholesale replacement of "tough-pitch" copper by deoxidized copper are commercial in nature; copper can be more economically melted in large-capacity furnaces which lend themselves to the poling process and are not so suitable for control of uniformity of action of deoxidizers as the smaller electric or crucible furnaces, whilst they are also more convenient for the production of very large castings. Moreover, the equipment of most large copper manufacturing plants is designed for casting "tough-pitch " copper in open moulds, e. g., wire bars and cakes, and these could not be used for deoxidized copper, which must be cast in vertical moulds as in brass-shop practice. Further, there are still certain impure brands and

Jan 1, 1926

By C. F. Weinaug

In recent years, several methods have been proposed for correlation of physical properties and behavior of hydrocarbon systems. These correlations were found to be unsatis. factory for predicting differential gas liberation and shrinkage data now obtained experimentally. To achieve the desired accuracy, methods were developed to adjust the correlations with two experimental pieces of data. The required data are the saturation pressure at reservoir temperature and the specific volume or density at these conditions. The saturation pressure is used to adjust the vapor-liquid equilibrium-ratio correlations. The density measurement is used to determine the apparent density of liquid methane. With these adjustments, differential gas liberation and shrinkage are predicted within the experimental error. EQUILIBRIUM RATIOS Equilibrium ratios published by the National Gas Assn. of America' were used as a basis for the calculation. The convergence pressure for the sample was determined by using a hypothetical binary system, with methane as one component and the remainder of the system lumped together to form the other component. For the critical temperature of the heavy constituent, the weight average of the critical temperatures of the ethane and heavier components was used. The correlation of pseudo-critical temperature, density and molecular weight of Matthews, Roland and Katzl was used in this calculation for the hexane and heavier fractions. Points for the critical properties of methane and the hypothetical heavy constituent were placed on a chart of the critical loci of hydrocarbon systems. A critical loci for the hypothetical binary system was drawn, and the critical pressure of this system was determined at the reservoir temperature. This critical pressure became the convergence pressure for which equilibrium ratios were read from the NGAA4 charts. The NGAA equilibrium constants for C, through C, were used for the C,; through C, fractions since they were separated on the bases of normal paraffin boiling points. The correlation of Hoffman, Crump and Hocott5 as used to estimate the equilibrium constant for the C fraction. The NGAA eauilibrium-ratio charts are based primarily on paraffin systems and have to be corrected for the presence of naphthenes and aromatics. The correlations in the literature proved too unsatisfactory for determining these corrections. EXperimental data, the saturation pressure, is used with the correlation of Soloman2 to make this adjustment. The correction factors of Soloman were cross-plotted so that the factors for ethane and heavier components were made a function of the factor for methane. a2 = 0.7927 at + 0.1646 .........(1) where a, = correction coefficient for for methane NGAA equilibrium ratio, and a2t = correction coefficient for ethane and heavier NGAA equilibrium ratios. This equation and the equation for the bubble point are solved simultaneously for the correction coefficients. The bubble-point equation is anKnXn = 1.0 . . . . (2) The equilibrium constant for the saturation pressure at reservoir temperature is used. This procedure not only corrects for the relative volatility between components, but also assures that the results will be directly related to the experimental saturation pressure. METHANE DENSITY After determining a set of equilibrium ratios, the apparent density of condensed methane at 60°F and 14.7 psia was estimated. This was found to be necessary because the correlations of Standing3 ere found to be unsatisfactory. The law of additive volumes was employed to make this calculation.

By Kenneth A. Moon

Kenneth A. Moon (U.S. Army Materials Research Agency)—The authors are to be congratulated for a very interesting and valuable paper. Their discussion of the structural implications of the results shown in their Fig. 5, however, requires a small correction. The model of Speiser and Spretnak with 0 = 1 and z' = 2 is perfectly reasonable for the Ti-O a phase, but Eq. [3] is valid only for solutions sufficiently dilute that the number of empty sites excluded by more than one filled site is negligible. The composition at which intrinsic saturation occurs therefore cannot be deduced from Eq. [3], but but must be decided by consideration of the structural details of the phase in question. In this case, intrinsic saturation is expected not at the composition Ti3O but at Ti2O, because Ti2O has the anti-Cd structurel4 for which each filled octahedral site has two nearby empty sites, one in the hexagonal plane immediately above it, and one in the similar plane below it. The other two models, with ?=1/3 and 1/2, imply a distinction between octahedral sites in pure titanium which is not easy to justify. The problem of extending Speiser's and Spretnak's treatment in a general way to more concentrated solutions will be the subject of a forthcoming publication by the writer. M. T. Hepworth and R. Schuhmann, Jr. (authors' reply)—The authors wish to thank Dr. Moon for calling to their attention the paper by Holmberg which presents the results of X-ray studies of Ti-O solutions ranging from 0 to 33 at. pct 0 and quenched from various annealing temperatures between 400" and 1800°C. Within these ranges, Holmberg found three types of phases: 1) At high oxygen contents (above 25 at. pct) and low annealing temperatures, he found the anti-Cd(OH)2 structure referred to by Dr. Moon. In this structure each titanium atom is in contact with 3 oxygens and each oxygen is in contact with 6 titaniums, the "available" oxygen sites corresponding to every other layer of octahedral sites in the titanium matrix. The limiting composition is Ti2O. However, this anti-Cd(OH)2 structure was not observed for samples containing 25 at. pct 0 or less. 2) For the specimen containing 25 at. pct 0 annealed at 400°C an ordered Ti3O structure was observed. This structure is related to the anti-Cd(OH)2 structure but differs from it by providing only two oxygens adjacent to each titanium atom and thus is consistent with the model represented by Eq. [5] in our paper, with 6 = 1/3, z' = 0. 3) For dilute solutions and for more concentrated solutions annealed at higher temperatures, the structure corresponds to that of the metal with random distribution of oxygens among all the octahedral sites. Thus, it is interesting to observe that the thermo-dynamic indications of ordering in the vicinity of Ti3O can now be supported qualitatively at least by Holmberg's X-ray evidence of the existence of an ordered phase of the composition Ti3O. That is, for solutions with oxygen contents close to that of Ti3O, both the thermodynamic data and the X-ray data are more consistent with models based on the ordered structure of Ti3O than they are with the model which Dr. Moon suggests corresponding to "intrinsic saturation" at Ti2O.

Jan 1, 1963

By W. T. Olsen, R. Ulcer

WHEN a liquid alloy freezes, the solid first formed usually differs widely in chemical composition from that last formed, so that there is segregation in the alloy as cast. For example in the copper-nickel system (fig. 1) the first solid formed from a liquid containing 55 atomic pct Cu may contain as little as 38 pct Cu, while the last must contain well over 55 pct. Three factors may act to decrease segregation from the maximum possible. 1. Diffusion in the cooling solid tends to make the phase homogeneous, decreasing segregation. This may be important at slow rates of cooling. 2. Segregation is impossible without diffusion in the liquid. At extremely rapid rates of cooling there may not be enough time to allow maximum segregation. 3. Supercooling delays nucleation to temperatures well below the liquidus thereby decreasing segregation. Hence the first nucleus in the copper-nickel system may contain well over 38 pct Cu. At sufficient supercooling the first nucleus may form below the solidus, in which case there is no reason to expect any segregation whatever. From these considerations, we could predict that at sufficiently low rates of cooling the alloy would be unsegregated because of factor 1 and at sufficiently high rates of cooling there should also be no segregation because of factors 2 and 3. Considerable segregation should occur only at intermediate rates of cooling. We have demonstrated experimentally that segregation can be completely suppressed by rapid rates of cooling. For the alloys studied, however, these rates are too great to be attained in any commercial practice. An alloy of 55 atomic pct Cu, 45 atomic pct Ni was frozen by cooling at varying rates. The degree of segregation in the solid was determined by X-ray diffraction photographs. Slow rates were obtained by slowly cooling the furnace containing the liquid alloy; fast rates by pouring or ejecting droplets of the alloy into water or iced sodium hydroxide solutions. The cooling rate of the droplets can be cal-culated from their dimensions by assuming reason- able values of thermal conductivity.' The experi-ments were repeated with an alloy of 16.5 pct Cu and 83.5 pct Au. A single experiment also showed a 50 atomic pct Bi-Sb alloy had no segregation at the most rapid quench. The position of back-reflection X-ray diffraction lines is a highly sensitive function of the lattice constant, which in turn depends on the chemical composition of the phase. A phase of varying composition will give broad diffraction lines. By measuring the edges of these lines and making suitable corrections for intrinsic line width, it is possible to determine the range of lattice constants represented. These can be converted to chemical compositions from a lattice constant vs. composition curve. Results are shown in table I. In the copper-nickel system the greatest segregation is found at the slowest cooling rates, where the lowest percentage of copper theoretically possible is found. In the copper-gold system, on the other hand, the degree of segregation is decidedly less at the slowest rates of cooling, being greatest at 11,100°C per sec. At no rate is the theoretically lowest percentage of copper (12 pct) found. At the rates of cooling found in sand and die castings the degree of segregation is large and depends little on the rate of cooling. Acknowledgment Most of the material in this paper is abstracted from a thesis presented by William T. Olsen, Jr. in 1948 in partial fulfillment of the requirements for the degree of Master of Science at the University of California.

Jan 1, 1951

By A. E. Dwight, A. F. Berndt

ThE published U-Ru equilibrium diagram indicates the existence of six intermetallic compounds in this system.' The structure of only two of the compounds, u2Ru2,3 and URU3,4 have been identified. This communication reports on the crystal structure and density of Uau3, which is formed by a peritectoid transformation at 1025° ± 5°C: U3Ru4 + U3Ru5 = U2Ru3. An alloy with the stoichiometric formula U2Ru3 was prepared by arc melting electrolytic uranium and ruthenium of 99.9 pct purity on a water-cooled copper hearth under an argon atmosphere. After homo-genization at 1000°C for 3 days, a metallographic examination revealed that the peritectoid transformation was complete and less than 5 pct of a second phase was present. A powdered sample, obtained by crushing the brittle compound, was annealed for 1 hr at 1000°C and air-cooled. Debye-Scherrer patterns were obtained with filtered CrKa, FeKa, CoKa, or CuKa radiation. The X-ray patterns of U2Ru3 weFe indexed as an fcc structure with a. = 12.895 0.00lA. The unit-cell constant and its standard deviation were calculated by a computer program described by Mueller, Heaton, and Miller.5 The density, measured by an immersion method, was 14.45 g cm-3. A calculated density of 14.48 g cm-3 was obtained on the assumption that twenty-four formula units (120 atoms) comprise a unit cell. The space group is either oh7 Fd3m, or the less symmetric, T4h, Fd3, since reflections indexed as hk0 with h + k + 4n are absent. All values of h2 + k2 + 12 permitted by both space groups are listed in Table I together with dc, do, and I. values. The calculated d spacings were obtained by the computer program of Mueller, Meyer, and simonsen.6 The observed d spacings above 0.77A were obtained from X-ray" patterns prepared with CuKa radiation, above 0.90A with CoKa radiaaion, above 0.98A with FeKa radiation, and above 1.16A with CrKa radiation. An attempt was made to identify the crystal structure of U2Ru3 by comparison with published data on other A2B3 compounds. A recent compilation7 of intermetallic compounds lists thirty-two structure types with the A2B3 stoichiometry. Only two of the structure types are fcc and they are Sb2O3(r), senarmontite, with 16 Sb2O3 per unit cell, and In2Te3 for which several structures have been proposed.8 However, the two cases cited do not have twenty-four formula units in the unit cell. We therefore, cannot identify UPRU3 with any of the other known A2B3 compounds. Ternary alloys were made in which 5 at. pct Os, Rh, or A1 were substituted for 5 pct of the Ru in U2Ru3. The osmium substitution increased the unit cell constant to 12.899 * .001A, which is to be expected since the atomic volume of osmium is slightly larger than

Jan 1, 1969

By W. D. Brown

Newell1 has shown that hydrogen is removed from steel in a vacuum at a temperature of 500° to 900° C. within 136 hr. Holm and Thompson2 also state that, especially when the hydrogen is high, the results obtained by extraction at 800°C. agree with those obtained by vacuum fusion. In this laboratory, an apparatus was designed (Oct. 1940) and used wherein the piece of steel was heated at 100°F. in a Torricellian vacuum (Fig. I). This vacuum was produced by raising and lowering a "leveling bottle or bulb" containing mercury. Extensive tests were made with this apparatus. The weakness of the procedure was the possibility of leakage of air into the tube around the rubber stopper at the bottom. The present plan is to raise and lower the mercury by applying vacuum from a mechanical pump, to the top of the tube and then to a bottle of mercury in which the bottom of the tube is immersed. The Apparatus The extraction is made in a Pyrex tube A, I in. i.d. It is drawn down at the top at N and an 8-mm. i.d. tube is welded on it. To this a Pyrex stopcock E, 4-mm. bore, is welded. The tube between N and E is preferably 8 in. long and is graduated in milliliters. The total length of A to the stopcock is 28 inches. Heat is supplied by a split-tube furnace. 0 in. long by 6 in. in diameter, hinged on the side. A short pyrometer couple P is inserted through the walls of the furnace. In use this is standardized by comparison with a standard couple in a I-in. tube, just opposite this short couple. In the I-in. tube A a glass rod R, flattened at one end, supports the sample S and the length of R is so adjusted that the sample is in proper place. (It may float in the mercury.) The tube A is inserted in a large rubber stopper to fit the bottle B and extends nearly to the bottom. It is so placed that the handle of the stopcock faces the operator. In this stopper also is a short tube D bent at right angles for the application of vacuum. Also in this stopper is an 8-mm. tube C reaching nearly to the bottom; this is bent so as to miss the heater and again bent to bring it in line with and as near as possible to the upper and reduced part of tube A. On this tube C is welded a 4-mm.-bore stopcock H. In order that the two tubes may be as near as possible, the handle of stopcock H faces the back, or is the reverse of stopcock E. The total height of II above the bottom is 28 in. As explained later, this is the pressure-measuring tube C. The bottle B is about half full of mercury. The mercury must cover the ends of A and C by about I in. when they are evacuated. By tees T and rubber tubing RT the tubes A, C and D, the latter through the three-way stopcock M, are connected to the vacuum pump. A sheet of asbestos at K prevents the stopcocks E and H from becoming so hot that they leak. A good grade of vacuum lubricant prevents leakage of E and H. In order to measure the pressure of the

Jan 1, 1945

By B. C. Wonsiewicz, G. Y. Chin

THE presence of deformation bands in cold-worked metals is known to influence the development of deformation textures1 but has not been considered in any theoretical treatments. At the present time the most rigorous theory of deformation textures appears to be based on Taylor's concept of homogeneous deformation of a crystal within a polycrystalline aggregate.' For each crystal the Taylor theory allows the operation of several equivalent combinations of five or more slip systems. Hence deformation bands can arise from the operation of a separate combination of slips in each of several portions within a crystal. On the other hand, a second type of band may occur as a consequence of slip on systems other than those selected on the basis on homogeneous deformation. This type appears to be associated with crystals of symmetrical orientations, such as the [loo] and [lll.] axial orientations in drawn wires of fcc single crystals studied by Ahlborn.3 In this note we propose a simple mechanism of deformation banding of the second type, and compare the theoretical results for wire drawing of [loo] and [Ill] with Ahlborn's observations. In outlini the model requires that the work to accomplish a given overall shape change by banding be less than or equal to the work to accomplish the same change by homogeneous deformation. While the work by homogeneous deformation, WH = ?T ;dri, can be calculated exactly by the equivalent methods of Taylor2 or of Bishop and Hill,4 the work by banding, WB, is less certain. The latter consists of 1) Wi, work by slip within a band, 2) Wb, work associated with formation of a boundary between bands, and 3) Wc, work to correct the difference in shape change arising from banding and homogeneous deformation. The Wi term can be evaluated explicitly for a band with an assumed set of slip systems, but a satisfactory analysis of Wb and Wc has not been obtained. Since WB = Wi + Wb + Wc WH, for banding to occur, however, a necessary condition is Wi = WH . Hence it seems reasonable to choose a band with the lowest value of Wi among competing bands consistent with Wi = WH, and then minimize Wb and Wc by arranging the physical configuration of the selected band. Wc is minimized by combining neighboring bands such that their net strain matches the macroscopic strain as closely as possible, and Wb is minimized by enforcing strain compatibility across the boundary between two neighboring bands, similar to the case of a grain boundary.5 It is realized that this procedure is not completely satisfactory, but it does seem to explain Ahlborn's observations reasonably well. The procedure is now outlined for the two corner orientations. a) [l00]. Fig. 1 shows a (100) stereographic projection. The results of the Taylor analysis for axi-symmetric flow by homogeneous deformation6 show that, while [loo] itself is unstable, the rotation of the tensile axis will nevertheless be confined to within about 15 deg from [loo]. Alternatively, less work may be expended by banding with slip on a pair of systems with primary-conjugate relationship, e.g., (ll1)[10l.I + (li1.)[110]. The latter represents minimum Wi for all possible bands.* Since there are four symmetrically

Jan 1, 1970

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for OFHC copper, and for a series of binary solid solutions of high purity copper with zinc, gallium, germanium, arsenic, and silicon, to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity. The apparatus used was of the torsional pendulum type developed by KeI1 modified so that the specimen and vibrating system could be maintained in a high vacuum. The activation energy for grain boundary relaxation in copper is 33,000 cal per mol. This is considerably less than the activation energy for self-diffusion, in disagreement with Ke's theory2 that the two activation energies should be the same. All the alloying elements increase the activation energy for grain boundary relaxation to approximately 44,000 cal per mol, increasing the grain boundary viscosity at a given temperature. The results are discussed in terms of theories of grain boundary slip put forward by MottQ and by Ke.+ Experiments have also been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. EXPERIMENTS described in this paper were designed to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity, using the internal friction method developed by Kel for measuring grain boundary viscosity. It was considered desirable to make the system under investigation as simple as possible by making experiments on a comprehensive series of binary alloys of copper with the elements immediately following it in the periodic table, i.e., zinc, gallium, germanium, and arsenic. These elements are within the range of favorable size factor for solution in copper, and the systems have been extensively investigated by Hume-Rothery and his co-workers." Later, in order to study the effect of the relative size of the solvent and solute atoms, experiments were made on a series of Cu-Si alloys, since the apparent atomic diameter of silicon when in solution in copper—the diameter necessary to assign to the solute atoms to account for the lattice constant of the solid solutiona—is almost the same as that of the solvent atoms. Preliminary experiments were made to measure the variation of internal friction with temperature for pure copper. Ke made some experiments on copper," but found that the curves obtained were not reproducible in consecutive experiments. The copper was maintained in an argon atmosphere during the experiments but, although he took precautions to exclude oxygen, Ke came to the conclusion that the precautions were not entirely satisfactory, and that the lack of reproducibility must be due to absorption of oxygen by the copper. Experiments have therefore been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. Previous Work Ke made extensive experiments on high purity aluminum and was able to show that the grain boundaries behave viscously at high temperatures. He found that the relative rate of movement of the grains could be expressed as Where v is the velocity of slip, A is the constant, u is the shear stress, H is the activation energy, R is the gas constant, and T is the absolute temperature. By assuming that the boundary layer was one atom thick, he obtained a value for the viscosity which, when extrapolated to the melting point, gave good agreement with the viscosity of the liquid metal at the melting point. Ke also made experiments on other high purity and commercial purity metals:, and on some alloys." " He came to the conclusion2 that the activation energy for grain boundary slip was the same as for self or volume diffusion and for steady state creep in single crystals. Rotherham, Smith, and Greenough" have shown recently that the activation energy for grain boundary slip is not the same as for self-diffusion in tin,

Jan 1, 1957

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By J. G. Early, F. V. Lenel, G. S. Ansell

The isothermal shrinkage rates of copper-powder compacts were determined in the temperature range from 760o to 1060oC. The rates for compacts fabricated from a pure spherical copper powder were compared, on the one hand, with those fabricated from a spherical powder containing a dispersion of aluminum oxide in the copper matrix and, on the other hand, with those fabricated from a pure copper powder having irregularly shaped particles. The irregular copper-powder compacts shrank much faster than the spherical copper-powder compacts and these, in turn, shrank faster than dispersion -strengthened copper -powder compacts. The experiments were run under a small external load. By varying this load, the stress dependence of the isothermal shrinkage rate could be measured for compacts from spherical-copper powders. This stress dependence was found to be approximately proportional to the 4th (dispersion-strengthened alloys) or 4.5th (pure metals) power of the stress. It is concluded that the material-trans port mechanism is due to dislocation climb rather than to Herring-Naharro creep. In this investigation the isothermal shrinkage rates of compacts made of copper powder with an average particle size of 70 g in the temperature range from 780o to 1060°C were studied. The aim of the investigation was to determine the mechanism of material transport responsible for the shrinkage of these compacts. Since the phenomenon observed in this investigation was shrinkage of compacts at high temperatures, it will be necessary to consider all the material-transport mechanisms possible in sintering. It is unlikely that evaporation and condensation, surface diffusion, or even volume diffusion of vacancies, in which surfaces of small radius of curvature are vacancy sources and those of larger radius of curvature vacancy sinks, will materially contribute to a sintering process involving shrinkage, i.e., one in which the centers of adjacent particles move towards each other. The two principal mechanisms which were considered were the so-called Nabarro-Herring mechanism and a plastic deformation mechanism by dislocation movement. Both of these mechanisms were originally conceived to explain creep, i.e., the plastic deformation of metals at elevated temperatures under a constant applied stress. The shrinking of metal-powder compacts which was studied in this investigation can be readily treated as a creep process. This means that the shrinkage rates observed are considered as creep rates under the influence of an applied stress. It is true that the stresses in sintering experiments are generally not constant but decrease continually with time, but, by considering creep rates or shrinkage rates over a relatively short time interval, the small changes in stress during this time interval can generally be neglected. Nabarro-Herring microcreep is a high-temperature deformation mechanism which is caused by a diffusional flow of vacancies from boundaries under a tensile stress towards those under a compres-sive stress. Herring1 has shown that in this type of microcreep the strain rate e is proportional to the applied stress and follows an equation of the form ma, aexp(-Q/RT) [l| where <j is applied stress, Q is the activation energy for self-diffusion, R is the gas constant, and T is the absolute temperature This type of creep can explain the shrinkage of a porous compact. The surface of the pores are subjected to the tensile stress of surface tension, while the grain boundaries are under a compressive stress also due to surface tension. Vacancies diffuse from the pore surface through the lattice to the grain boundaries, where they are eliminated. In order to maintain vacancy equilibrium at the pore surface the vacancies leaving the region of the pore surface are replenished from the volume of the pore, which means that the pores shrink.

Jan 1, 1964