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By Arthur H. Wilson

INTRODUCTION The stratified deposits of the coal measures are strongly laminated and exhibit a high degree of anisotropy. The stronger rocks in the sequence possess joints and shear planes, the coal itself has a closely spaced cleat pattern, and the softer rocks are capable of flowage. To calculate the general distribution of stress in such a medium by analytical means based on the theories of elasticity is difficult, and has not yet been satisfactorily achieved. Nevertheless, some estimate is required to aid the design of supporting pillars and permit the correct siting of main roadways. This is important when laying out districts for longwall extraction, particularly if the results of previous experience are not available in the area to be exploited. Although elastic stress analyses, including finite element analysis, may not be very appropriate, the basic equilibrium conditions will apply. These, combined with logical deductions based on observed fact, can be used to give appropriate solutions which experience has shown to be capable of giving acceptable results in the design of pillars associated with longwall workings. Constancy of cover load is one of the fundamental equilibrium conditions. When mining below ground, the cover is not removed, therefore the average vertical load after mining must equal the initial cover load. If mining produces a local decrease in load in any particular area, it must be balanced by an equivalent increase in load nearby. Bending moments in the strata above are capable of compensating for the turning moments which this redistribution of load may produce, and the existence of a "rear abutment", much discussed between 1950 and 1960, is not an essential equilibrium requirement. If the distribution of vertical stress is plotted three-dimensionally, then the load on any small element of area 6S will be o.6S, where o is the average stress. This also represents the volume of the "stress envelope" which lies above 6s. By making the individual areas very small and summing together, it is possible to show that the total load on any particular area can be found by calculating the volume of the stress distribution envelope which lies above it. A similar consideration applies to the stress distribution in a two-dimensional situation. If the stress distribution curve is drawn, then the area below any portion will represent the load per unit depth of section. For example, Figure 1 represents the possible stress distribution across a caved waste and associated ribside. If AW is the load deficiency [ ] These loads must balance, therefore area AW = AS, and if one can be deduced, the other will then be known. Attempts have been made to measure stress distributions in the ribside and in the waste. Stress meters in soft rocks such as the coal measures have not proved very effective. Those based on the measurement of strain have experienced difficulty in strata capable of flowage, high modulus stress meters suffer from cross sensitivity, and overcoming to obtain absolute stress is almost impossible. Load measuring instruments left in the waste have also proved largely ineffective, mainly as a result of the difficulties of protecting the leads in a caving environment. Certain logical deductions, however, can be made about the conditions in the waste. CONDITIONS IN THE WASTE Over the area of the waste the surface trough which develops is remarkably consistent, despite the geological variations which occur from coalfield to coalfield. In Britain, an accuracy of 210% is claimed for subsidence prediction based on width of extraction and depth of cover (National Coal Board, 1975). The subsidence in the USA is more variable (Adamek and Jeran, 1981), particularly with respect to the point of inflexion, but the same general pattern occurs. At the shallower depths the somewhat harder roof strata involved in the caving in the USA may suffer less compaction, giving reduced values of subsidence. Subsidence at intermediate horizons below the surface

Jan 1, 1982

By R. L. Segall

AN unusual thermal etch figure in copper is described and an explanation in terms of twinning is suggested. A flat polycrystalline specimen of OFHC copper cut from a rolled sheet was electro-polished in orthophosphoric acid and annealed at 950°C in a vacuum of approximately 10-3 mm Hg for 2 hr. The specimen was found to be thermally etched, the markings on the surface being consistent with the assumption that they were the traces of the (111) planes which are developed preferentially because they have the lowest free energy. However, on one grain (the grain shown in Fig. 1) the traces formed an almost regular pentagon and at first sight it seemed unlikely that they could all be (111) traces. These traces were studied further because it was thought that they might be a type of growth spiral. A fringe pattern showed that this was not so, the grain being sensibly flat and the only features having steps were the striations and the faint curved line passing out from the center of the pentagons. To obtain some additional information, the specimen was deformed in tension. The effect of the stress was first to cause the appearance of lines running from the centers to the apexes of the pentagons and then to tilt the five segments so formed. At a much greater stress, appreciable slip appeared on the grain; these effects can be seen in Fig. 2. The micrograph was taken at a fairly late stage in the deformation and the tilting is quite marked. The magnification is the same as in Fig. 1, and although some slip can be seen it could be observed better by varying the illumination and using higher magnifications. In each segment of the grain, slip (which takes place on the (111) planes) was parallel to the side of the pentagon in that segment. The marked changes in direction of slip from segment to segment seemed to be incompatible with the presence of a regular array of subgrains. These results suggest that some of the five segments were twins. If this is so, since the twinning plane in copper is the (111) plane, the radial lines must be traces of the (111) planes on the surface. From the symmetry of the striations about the radial lines, these planes must be almost perpendicular to the surface. The angle between <III>directions in face-centered-cubic copper is 70&apos;32&apos;. If, in Fig. 3, OAB (triangle 1) is taken as matrix and OA, OB are (111) planes viewed edge on, then AB is in the correct direction to be the trace of either of the other two (111) planes on the surface. If triangle 2 is the twin (about the (111) plane perpendicular to the surface and containing OB) of triangle 1, then once again it can be shown that all lines are traces of (111) planes. Similarly, triangle 3 is the twin of triangle 2, 4 of 3, and 5 of both 4 and 1. (The sequence is, of course, quite arbitrary.) However, if this were the case there would be a discrepancy of 7&apos;20&apos; to be accounted for. It is suggested that the faint curved line passing outward from the center of the pentagon represents either a low angle boundary or a sixth small twin. The slight step shown by the fringes at this line might be an indication that the former is the case. This explanation does not account for the coincidence of obtaining a grain whose surface must be so close to (110) and obtaining the curious twinning described previously; it would be of interest to find a specific mechanism for this.

Jan 1, 1958

By R. M. Goldhoff, J. W. Spretnak

IN connection with establishing the mechanism by which boron enhances the hardenability of heat treatable steels, this research work has been undertaken. Spretnak and Speiser1,2 indicated the need for studying high temperature effects in boron steels and, chief among these, the possible nonhomogeneous distribution of boron in iron grains. The occurrence of this effect may be of significance in explaining the mechanism of enhancement of hardenability by boron as well as in explaining some of the observed characteristics of boron steel behavior. Primarily, then, this work was undertaken a) to establish whether or not boron is adsorbed in ? solid solutions, b) to determine the nature of any such adsorption effects, i.e., whether it is positive or negative as well as its temperature coefficient, and c) to establish the magnitude of any such effect. While past literature on this specific subject is rather sparse, a number of authors have postulated that the observed temporary loss of hardenability as well as the occurrence of the characteristic boron constituent in these steels is due to the nonuniform distribution of boron in austenite.3-0 Experimental Techniques Attempts to obtain direct evidence of grain boundary effects in boron steels have been unsuccessful, both by using the technique of Chalmers&apos; in which small concentrations of solute made radioactive by irradiation are detected by autoradiographic means, and by means of studying cleavage fractures with the electron microscope.8 The present study attempts the design of experiments to measure the effect of boron on properties which might be subject to variation because of grain boundary effects. A study of the theoretical aspects of grain growth indicates that such studies may be pertinent. Another valid type of experiment involves the measurement in polycrystalline materials of properties whose values depend on the bulk of the grain, being negligibly influenced by grain boundaries. One such property is the lattice parameter measured by X-ray diffraction. The value of the lattice parameter reflects the average conditions which obtain over a relatively large number of atoms in a fixed crystalline lattice, and is therefore mainly dependent on bulk grain material. Measurement of lattice parameter variation over the austenite range of temperature in iron with and without boron should give evidence of concentration variations in the bulk grain material if adsorption effects are significant. Finally, use is made of the Grange and Garvey3 metallographic test for boron in which a characteristic boron constituent can be developed in austenite grain boundaries. The very occurrence of this phenomenon suggests grain boundary enrichment of boron and a study of the occurrence of this constituent and its varation with austenitizing temperature should help to detect grain boundary effects. Materials One lb ingots of pure iron, an Fe-B alloy, an Fe-C alloy, and an Fe-C-B alloy were prepared. The melting technique included an initial melting of electrolytic iron under vacuum followed by remelting under hydrogen and, finally, by melting under argon with the addition of alloying elements. Each ingot was surface machined between meltings. A quantitative spectrographic analysis was obtained on the pure ingot and, in addition, oxygen, nitrogen, and carbon were determined by the vacuum fusion method. The results of these analyses are given in Table I. Semiquantitative spectrographic analyses were performed on the alloy ingots, while quantitative determinations of the alloy additions were obtained. These analyses are shown in Table 11. The cast ingots were subjected to the following sequence of fabrication treatments: forging to 5/8 in. bars, swaging to 0.300 in. rounds, drawing to 0.025 and 0.010 in. wire. Portions of each ingot were retained in the swaged condition for experimental use. For certain portions of the work typical commercial steels were used. These materials were supplied by the Republic Steel Corp., Canton, Ohio, and correspond to AISI 8640 and AISI 86B40 compositions.

Jan 1, 1958

Jan 1, 1924

Jan 1, 1924

A plan which has just been approved by President Wilson, by, the Secretary of the Navy, and the Naval Consulting Board, provides for the active cooperation of the Associated Advertising Clubs of the World with the 30,000 engineers who will soon undertake the task of making a card index survey of American industry, so that it may be prepared for national defense, if need comes. Herbert S. Houston, President of the Associated Clubs of the World comments on the plan. "Through the great power of advertising we expect-to arouse manufacturers, workingmen, businessmen, in fact the whole country, to the vital need of making industry the basic line of defense so that, if necessity arises, it can supply munitions quickly and abundantly. "This is not a war measure, but a peace measure. The militarist will support it and so will the pacifist, as well as the great body of Americans in between. So the slogan `national defense and international peace, has been adopted believing that the two causes will be best served by linking them together. "While the primary thing, of course, is service to the country, it is manifest that this work of the engineers will be of the greatest service to industry in times of peace. If industry is mobilized for defense, it will be placed on a basis of efficiency to meet the keen competition that will surely follow the present war." Howard E. Coffin, one of the leaders of the American automobile industry, in outlining the far-reaching plans of his committee, the Committee of Industrial Preparedness of the Naval Consulting Board, said: "At the outset I wish to emphasize the absolutely non-partisan nature of this work. I am not even familiar with the political affiliations of the great majority of the members of the Board or of my committee. In setting out to, mobilize the industrial resources of the United States, we are concerned only with the benefit to the nation, and to that end we have called into being an organization made up of the best technical and business brains of the country, and that organization will work along business lines with strictly business methods. I think it reasonable to say that this is a movement perhaps unique in the history of national governments, and one geared up to the highest standards of twentieth century efficiency. "It is vitally necessary that American industry be made aware of the part it must play in the national defense. Our whole conception of warfare has been changed almost overnight. Our military heads at Washington are largely, of course, graduates of the very best technical schools, have been taught the profession of fighting, and are masters of that profession. As members of the Naval Consulting Board, we are unable to tell these men how to do their work. But while these departmental heads have lived with military problems all their adult years, we on the other hand have slept and eaten and lived with the industrial problems of the country. The two questions are wholly distinct, and the masters of one cannot possibly be the masters of the other. We are confronted then with the necessity of interlocking these two vast elements of our national life into a great working organization for the national defense. It is that which we are about to do.

Jan 5, 1916

By L. A. Wilson, N. H. Harrison, R. R. Clay, R. L. Reed. D. W. Reed

Experiments have been performed in a linear near-adiabatic system for the purpose of extending data on reverse and forward combustion from atmospheric pressure to 1,000 psig. Results obtained from reverse combustion appear to conform qualitatively with the existing description of the process when reaction kinetics are suitably modified to account for the increase in pressure, i.e., increasing tbe pressure decreases the peak temperature and increases the combustion zone velocity. Forward combustion appears to be a fuel dominated process wherein peak temperature and combustion zone velocity are not very sensitive to changes in pressure. The moderate effects of pressure that do exist at low flux virtually disappear at high flux providing all oxygen is consumed. With this provision. increasing the pressure decreases the frontal velocity and increases the peak temperature. Results me shown graphicaIIy which demonstrate the effects of presswe on peak temperature, rate of advance, oil recovery, air/oil ratio, carbon oxides produced and temperature distributions. INTRODUCTION Numerous field tests of oil recovery using the technique of underground combustion are now in progress. Operating pressures used are always substantially in excess of atmospheric pressure. Nevertheless, the literature contains no laboratory data pertaining to the effects of pressure except for those of Martin, Alexander and Dew.1 Unfortunately, these data appear to reflect heat losses which may have obscured some of the effects of increased pressure. The underground combustion processes are exceedingly complex, and general concepts relating to them have necessarily been described in relatively simple terms. Particularly with regard to forward combustion, the interaction between multiphase fluid flow, heat transport and various rate mechanisms is so involved that to date a rigorous treatment is not available. In this paper a linear near-adiabatic system is described which was found capable of operating at pressures up to 1,000 psig and temperatures of at least 1,100 F. Using this equipment, experiments on both forward and reverse combustion were accomplished at elevated pressures and the data presented as a function of air flux or temperature. It will be assumed that the reader is familiar with the papers of Wilson, Wygal, Reed, Gergins and Henderson on forward combustion and that of Reed, Reed and Tracht3 on reverse combustion, so that it is not necessary to repeat the details of the two processes. EQUIPMENT AND PROCEDURE It was decided to study the effects of pressure over the interval 0-1,000 psig using a near-adiabatic system. Since satisfactory operation of such a system requires very thin tubing walls, it proved necessary to insert the entire combustion tube and heater assembly into a high pressure jacket in such a way that the internal tube pressure could be counterbalanced by pressurizing the annulus. This meant that the numerous heater and thermocouple wires had to pass through gas-tight seals that required considerable effort to maintain effective. An unexpected difficulty arose in connection with the nature of the annulus pressuring gas. It turned out that the composition of this gas critically affected the functioning of the adiabatic control system. Operation of the equipment at elevated pressures was not particularly difficult. The problems that did arise were a direct consequence of the large numbers of connections and seals involved. EQUIPMENT The equipment consisted of the combustion tube which fitted within the pressure jacket. This jacket was in turn mounted on a wheeled carriage which facilitated movement and provided for rotation of the

By G. R. Speich, Morris Cohen

The growth rate of bainite has been determined by hot-stage metallography in five hypereutectoid high-purity iron-carbon, iron-carbon-chromium, and iron-carbon-nickel alloys. The studies have been confined essentially to lower bainite. The growth rate is independent of time at constant temperature, but both the edgewise and sidewise growth rates increase with increasing temperature. Increasing the carbon content, or adding chromium or nickel, decreases the growth rate without greatly affecting the temperature dependence. The results lead to separate diffusion-controlled models for the edgewise and sidewise growth rates. ALTHOUGH bainite has been subject of many detailed investigations,1,2 the growth mechanism of this intermediate transformation product of steel remains unclear. One difficulty has been that practically all the kinetic measurements have been restricted to studies of the overall reaction rate. Only a limited amount of information3, 4-6 is available on the growth process itself. The purpose of the present work was to investigate the effect of time, temperature and composition on the growth rate of bainite using hot-stage metallography. This method makes it possible to observe continuously the isothermal growth of individual bainitic units because of the surface upheavals accompanying their formation.3 This information is needed to test the existing growth models and to obtain a better understanding of the factors controlling the bainitic transformation. EXPERIMENTAL PROCEDURE Alloys—The compositions of the alloys used in the present work are shown in Table I. The five alloys were vacuum-melted and cast, and were prepared from high-purity materials. The three iron-carbon alloys were available from the work of Roberts et al.7 in the form of 3/8-in. diam rods.* To facilitate machining, the rods were ing. The rods were then tempered for 3 hr at 650°C to allow machining. The iron-carbon alloys in Table I were selected for investigating the effect of carbon on the bainitic growth rate. Due to the rapidity of the transformations involved, it was not feasible to measure the growth rates in iron-carbon alloys having carbon contents much less than 0.9 pct C. The iron-carbon-chromium and iron-carbon-nickel alloys were selected to study the influence of chromium and nickel on the growth rate at a carbon level of about 1.1 pct C, since this carbon content was intermediate among the iron-carbon alloys. The concentrations of chromium and nickel were chosen to match isothermal trans formation diagrams in the literature.8&apos;9 Hot-Stage—Since the iron-carbon alloys had such low hardenabilities, it was necessary to quench the hot-stage specimens drastically from the austentiz-ing temperature to the isothermal transformation temperature to prevent the formation of pearlite or proeutectoid constituents. A rapid-quenching metal-lographic hot-stage was built for this purpose. A maximum temperature of about 1100°C and quenching rates up to 500°C per sec could be attained with this equipment. The details of the apparatus are described in a recent publication. After being polished and mounted on the hot-stage, the specimen (0.020 in. thick) was protected from oxidation and decarburization during austenitizing by a vacuum of 10-4 to 10-5 mm. The quench to the reaction temperature was accomplished with a helium blast, and the isothermal run at this temperature was conducted in a helium atmosphere. A fine-wire thermocouple spot-welded to the sample and a high-speed

Jan 1, 1961

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&apos; Eq. [I] which is used to compute Egb from the transverse displacement ITt of longitudinal marker lines is not given in the reference quoted,&apos;&apos; 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&apos;&apos; and "side". On the surface it is possible that the two sums could differ somewhat. In either event it is clear that the authors&apos; 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 R. B. Falk, F. E. Luborsky

Small iron particles in mercury pow by diffusion of iron atoms through the mercury. Iron particles, with diameters about 200Å, have been stopped from gvowing in size, even up to the boiling point of mercury, by the addition of a third metal. The metal additives were classified according to whether they produced 1) negligible inhibition, 2) some inhibition, or 3) marked inhibition of the growth rate. Metal additives which resulted in a marked inhibition of iron-particle growth form a stable monolayer on the iron particles. Only those metals which may form compounds with iron showed this pronounced effect. The one exception was manganese. Metal additives which resulted in no inhibition of growth, showed no evidence for adsorption and could not form compounds with iron. None of the added metals, even those which strongly inhibited particle gvowth and thus had adsorbed on the particle surface, actually formed any compounds with iron at room temperature at the concentrations required for complete inhibition of growth. ThE stabilization of the size and shape of metallic particles dispersed in liquid metals has important technological implications in "homogeneous" nuclear reactor systems and in elongated particle magnets and is directly related to the problem of corrosion by liquid metals. Growth in these par-ticulate systems may occur by diffusion of atoms from surfaces of high energy, corresponding to a small radius of curvature, to surfaces of low energy or large radius of curvature. Thus, small particles dissolve and large particles grow to increase the average diameter of the particles. reenwood&apos; has analyzed this diffusional growth of a system of particles containing a distribution of sizes and has obtained reasonable agreement with data on the growth of uranium particles in liquid sodium and UPb3 particles in liquid lead. Greenwood concluded from his analysis that the chief factors promoting stability of dispersed particles growing by a diffusion mechanism are large mean radius, high density, and low molecular weight with low values of the solute diffusion coefficient, the solubility, and the interfacial tension. In the case of elongated particle magnets the system of interest is that of iron particles dis- persed in mercury. Previous work,2 concerned with "spherical" particles in mercury, has indicated a diffusional growth mechanism similar to that discussed by Greenwood. It has also been shown3&apos;4 that the addition of certain metals to Fe-Hg dispersions results in the formation of a monatomic layer of adsorbed atoms on the iron particles. In this paper we will show that this adsorbed layer provides the decrease in the iron-atom flux through the mercury necessary for size stabilization. The general features of the stabilization of the iron particles in mercury through the formation of this "coating", with many different metals, will be described. EXPERIMENTAL RESULTS Iron particles in mercury were prepared by elec-trodeposition,2, 4 and measurements2, 4 of coercive force HCi) and saturation induction (Is) were used to follow changes in size and composition during thermal aging in the mercury in the presence of relatively small amounts of an added metal. In Fig. 1 is plotted the aging behavior of spherical particle samples in the presence of some of the added metals to be discussed. The iron particles have an initial average diameter of 180Å. Each sample was aged for 20 min at each temperature in succession in the presence of a twofold to threefold excess of added metal over that required to form a monolayer on the iron particles. These are the same samples used previously3 to study the adsorp-

Jan 1, 1965

By D. S. Tannhauser, I. Bransky

Measurements of the electrical conductivity, the thermal electromotive force, and the deviation from stoichiometry by thermogravimetry were made on ferrous oxide (wüstite) single crystals as well as on poly-crystalline samples in the temperature range of -900" to 1330°C. In the region defined by T 2 1000°C and 1.05 5 O/Fe 5 1.10 the electrical conductivity was shown to be proportional to the sixth root of- the oxygen partial pressure and to be linearly dependent on the deviation from stoichiometry. The absolute Seebeck coefficient of single and polycrystalline wüstite was shown to be independent of temperature in the above region and a p to n transition of the Seebeck coefficient was observed at O/Fe = 1.09 in polycrystalline wüstite. Analysis of the results showed that the predominant defects in wüstite in the above region were doubly ionized cation vacancies. The analysis also ruled out the existence of complexes of the type postulated by Roth, except that below 1000°C there is some evidence of &apos;association of defects. Of the three oxides of iron (FeO, Fe3O4, Fe2O3) only FeO (wüstite) can exist within a wide range of the ratio O/Fe. This has been shown by several investigations of the phase diagram using for instance chemical analysis of quenched samples&apos;-4 or thermogravimetric measurements. 5,8 Darken and Gurry&apos;s1 data for example in the temper- ature range 1100o to 1400°C show that the lowest O/Fe ratio obtainable for FeOl +. is about 1.045 and that the existence range extends to O/Fe = 1.20 at 1400oC. On the basis of detailed analysis of thermogravimetric measurements made by Vallet and Raccah6 the existence of three varieties of wüstite at elevated temperatures was suggested by these authors and by Kleman. It is well-established that wüstite has a NaCl structure with vacant cation sites.3, 8 From a neutron-diffraction study of wüstite samples quenched to room temperature Roth9 concluded that defects in wüstite are mostly complexes composed of two cation vacancies and one interstitial cation in a tetrahedral site. The atomic arrangement in the vicinity of such a defect is similar to that in magnetite, where each occupied tetrahedral site is surrounded by four vacant octahedral positions disposed at the corners of a tetrahedron, so arranged that each vacancy is shared by two tetrahedral cations. Thus there is an average of two vacancies per interstitial. Recent X-ray diffraction measurements made by Smuts10 on quenched wüstite samples confirmed the results of Roth&apos;s neutron-diffraction experiments. Roth&apos;s model of defects in FeO can be regarded as a solid solution of Fe3O4 in FeO; salmon1&apos; used this defect model to calculate the activity of Fe3O1 in FeO at high temperature and claimed good agreement with the results obtained experimentally by Darken and Gurry.&apos; Each missing cation in wüstite is accompanied by two trivalent cations, thus preserving charge neutrality. The "holes" which differentiate between the Fe 2+ and Fe3&apos; states of the ions in octahedral positions can overcome the attractive field of the cation vacancies, and are then free to move through the crystal as charge carriers. A similar picture holds for COO, NiO, andMnO.l2, 13 Localization of the charge carriers in transition

Jan 1, 1968

By L. S. Darken

Measurements of the electrical conductivity, the thermal electromotive force, and the deviation from stoichiometry by thermogravimetry were made on ferrous oxide (wüstite) single crystals as well as on poly-crystalline samples in the temperature range of -900" to 1330°C. In the region defined by T 2 1000°C and 1.05 5 O/Fe 5 1.10 the electrical conductivity was shown to be proportional to the sixth root of- the oxygen partial pressure and to be linearly dependent on the deviation from stoichiometry. The absolute Seebeck coefficient of single and polycrystalline wüstite was shown to be independent of temperature in the above region and a p to n transition of the Seebeck coefficient was observed at O/Fe = 1.09 in polycrystalline wüstite. Analysis of the results showed that the predominant defects in wüstite in the above region were doubly ionized cation vacancies. The analysis also ruled out the existence of complexes of the type postulated by Roth, except that below 1000°C there is some evidence of &apos;association of defects. Of the three oxides of iron (FeO, Fe3O4, Fe2O3) only FeO (wüstite) can exist within a wide range of the ratio O/Fe. This has been shown by several investigations of the phase diagram using for instance chemical analysis of quenched samples&apos;-4 or thermogravimetric measurements. 5,8 Darken and Gurry&apos;s1 data for example in the temper- ature range 1100o to 1400°C show that the lowest O/Fe ratio obtainable for FeOl +. is about 1.045 and that the existence range extends to O/Fe = 1.20 at 1400oC. On the basis of detailed analysis of thermogravimetric measurements made by Vallet and Raccah6 the existence of three varieties of wüstite at elevated temperatures was suggested by these authors and by Kleman. It is well-established that wüstite has a NaCl structure with vacant cation sites.3, 8 From a neutron-diffraction study of wüstite samples quenched to room temperature Roth9 concluded that defects in wüstite are mostly complexes composed of two cation vacancies and one interstitial cation in a tetrahedral site. The atomic arrangement in the vicinity of such a defect is similar to that in magnetite, where each occupied tetrahedral site is surrounded by four vacant octahedral positions disposed at the corners of a tetrahedron, so arranged that each vacancy is shared by two tetrahedral cations. Thus there is an average of two vacancies per interstitial. Recent X-ray diffraction measurements made by Smuts10 on quenched wüstite samples confirmed the results of Roth&apos;s neutron-diffraction experiments. Roth&apos;s model of defects in FeO can be regarded as a solid solution of Fe3O4 in FeO; salmon1&apos; used this defect model to calculate the activity of Fe3O1 in FeO at high temperature and claimed good agreement with the results obtained experimentally by Darken and Gurry.&apos; Each missing cation in wüstite is accompanied by two trivalent cations, thus preserving charge neutrality. The "holes" which differentiate between the Fe 2+ and Fe3&apos; states of the ions in octahedral positions can overcome the attractive field of the cation vacancies, and are then free to move through the crystal as charge carriers. A similar picture holds for COO, NiO, andMnO.l2, 13 Localization of the charge carriers in transition

Jan 1, 1968

By A. S. Venkatadri, H. B. Bell

The equilibrium sulfur distribution between molten iron and Ca0-Mg0-Al203 slags containing iron oxide was investigated at 1550°C. The results were used to derive the iron oxide activities at low iron oxide concentrations in the slag by combining the sulfide capacity data obtained from gas-slag work with the free energies of both the sulfur solution in iron and the iron oxide formation in slag. The derived ferrous oxide activities were compared with values based on Tem-kin&apos;s kin&apos;s and Flood&apos;s ionic models. One difficulty in using these models is that the nature of the aluminate ion in slag is uncertain. Nevertheless, such indirect methods, in particular, those described in the present paper, are of value because of the difficulty of measuring small amounts of oxygen in liquid iron in equilibrium with slag. It is shown that these methods confirm the consistency of thermodynamics data on liquid iron and slags. It is well established that decreasing the iron oxide activity in the slag increases the desulfurization of molten iron at constant slag basicity. This effect is most pronounced at the very low iron oxide activities, characteristic of blast furnace slags. Yet a precise quantitative determination of the significance of low iron oxide contents in slag in blast furnace desulfuri-zation is not possible for the following reasons: a) difficulty of separation of iron "shots" from the slag, and b) errors in chemical analysis of small amounts of iron oxide in slags. In view of these obstacles, one must resort to indirect methods of calculating iron oxide activities. EXPERIMENTAL TECHNIQUE The apparatus for providing the sulfur equilibrium data has been described previously1 and was similar to that used by ell&apos; in connection with the study of slag-metal manganese equilibrium. The procedure consisted of: a) melting about 50 g of Armco iron in a magnesia crucible in a platinum furnace, b) adding a mixture of about 15 g of lime-alumina slag and varying amounts of Fe2O3 and CaS, and c) maintaining the temperature at 1550°C for more than an hour in an atmosphere of argon to enable the sulfur equilibrium to be attained. Several melts were made using lime-alumina slags with basic composition 55, 50, and 45 pct lime. During the experiment the temperature was controlled manually using a Pt/10 pet Rh-Pt thermocouple. After the experiment, the Power was shut off and the flow rate of argon was increased to freeze the melt as quickly as possible. The analysis of sulfur in the metal was carried out by the oxygen combustion method3 using uniform drillings from the top and bottom of the metal button. After crushing and grinding and removal of any iron particles with the aid of a hand magnet, the slag was analyzed for sulfur by the CO2 combustion method.4 The E.D.T.A. method was employed for the analysis of lime5,6 and magnesia,= the ceric sulfate method7 for the analysis of slag iron oxide, and the perchloric acid dehydration method5 for the analysis of silica. The remaining amount was taken to be Al2O3 precipitation with ammonium hydroxide in several preliminary melts had confirmed the propriety of using this simple procedure. RESULTS The activity of iron oxide in binary, ternary, and more complex slags has been the object of numerous investigations, and the two experimental methods for its determination are: 1) Equilibrating the metal with the slag in question and measuring the oxygen content of the metal. The ferrous oxide activity is then given by aFeO L%OJSat where [%0]sat is the oxygen content of the metal in equilibrium with pure iron oxide slag. This method was used by Chipman et al.8,9 2) Equilibrating the slag in iron crucibles with known partial pressures of H2/H2O or CO/CO2 mix-tures.10-12 This method is limited to temperatures between 1265" and 1500°C. The very low oxygen content of the melts in this investigation made it impossible to derive the ferrous oxide activity by the first of these methods. Therefore, the iron oxide activities were computed by means of: Sulfide capacity data from the gas-slag work" Temkin&apos;s concept14 Flood&apos;s approach15 a FeO from Sulfide Capacity. The method of calculating the aFeO involves the sulfide capacity of the slag (c,), the sulfur distribution coefficient (Ls), the free energy of dissolution of sulfur in iron, and the free energy of formation of iron oxide in the slag. Bell and Kalyanram13 have investigated the sulfur absorption characteristics of lime-alumina slags containing magnesia by the Carter-Macfarlane method16 (based on comparing the sulfide capacity of the slag in question with that of a standard slag of unit lime activity) and have derived lime activity values. The relation between sulfide capacity and their lime activity a&apos;CaO is given by: Cs= 3—: Xa&apos;CaO at 1500°C

Jan 1, 1970

By C. H. Bowen

NDUSTRY needs a generally applicable means of defining average grain size and grain size distribution. Students of sediments hade explored this field, employing methods that might also prove useful in engineering problems. Before attempting to solve specific problems it is well to review the derivation of commonly used grade scales and the reasons for their selection. This aspect of the problem seems largely to have been lost, and a review of basic factors may suggest causes for failures in using size analysis data. Three facts are implicit in selection of a grade scale: 1) Most particulate mixtures are continuous distributions of sizes, and any grade scale that may be employed is an arbitrary means of visualizing that distribution. 2) For purely descriptive purposes, any grade scale, regardless of the rationality of the class intervals, will be satisfactory if it is accepted by a sufficient number of workers. 3) For analytical purposes, class intervals must be small enough to define the continuous distribution accurately. Further, where statistical studies are involved, a fixed relationship should exist between classes or grades. An argument in favor of geometrically related size grades lies in the fact that most particulate mixtures contain such a wide range of sizes that use of an arithmetic diameter scale is practically impossible. Udden, who recognized this fact in 1898,&apos; proposed one of the first grade scales based on a regular geometrical interval. Udden used 1 mm as his basic diameter and a ratio of 2 (or 1/2) between classes. In 1922 Wentworth2 re-examined Udden&apos;s grade scale, retaining the same class interval and basic diameter, but extending the scale in both directions and renaming the classes. In 1930 (Ref. 3, p. 82) the American Society of Testing Materials proposed what is now known as the U.S. Standard fine sieve series, also based on the 1 mm diam, with a v2 ratio between sieves. This, then, is a one fourth Udden-Wentworth series in the sizes below the 4 mesh sieve. The U.S. Standard coarse sieve departs from the 1 mm base and uses inches; hence it is not a direct continuation of the fine series. The U.S. Standard series would thus seem to possess all the attributes of a good grade scale, which it is. It has a large number of classes (sieves). in fact too many for practical use in its entirety. This v2 subdivision of the Wentworth grades has led to the common use of two v2 sieve series, the half-Wentworth and the engineers&apos; series. Geologists and sedimentologists favor the half Wentworth, or 18, 25, 35, 45 sieves, etc., whereas the engineers, preferring round numbers, utilize the other half of the U.S. Standard grade scale in the 16, 20, 30, 40 sieves, etc. The fixed geometrical ratio between classes is an advantage in statistical analysis, but the unequal classes cause some complications in calculations. This is especially true when moment measures are used. It was to simplify these calculations that Krumbein in 1934 devised the phi scale. Phi is defined as being equal to —log2 of the diameter in millimeters. Selection of logarithms to the base 2 relate the phi scale directly to the Wentworth grade scale in such a manner that the whole or fractional diameter values 2, 1, 1/2, 1/4 mm, etc., become rational whole numbers, —1, 0,1, 2, etc. Since this is an arithmetic rather than geometric series, calculations are facilitated. When the logarithm is multiplied by —1 the phi values below 1 mm become positive, those coarser than 1 mm negative. Because of its relationship to the Wentworth grade scale (and in turn to the U.S. Standard fine sieve series) it is not necessary to use the transformation equation to calculate the phi value for each individual sieve; this can be done graphically as shown in Fig. 1. It should be noted that this graph may be extended in either direction to include the range of sizes most commonly used by the individual worker. Application to Statistical Analysis Any attempt at systematically relating size analysis data to properties involves a statistical study whether it is recognized as such or not. Since this is true it would seem more logical to use measures and devices related to the general body of statistical theory. Several methods are available for studying particulate mixtures. One of the most commonly employed, and also the most often misused, is the histogram or block diagram. If its limitations are recognized and provided for, the histogram is a very useful tool. According to conventional practice, the bars of equal width are plotted and the values noted in terms of diameters, when in point of fact, log diameter is implied by such notation. Further, the histogram is sensitive to choice of grade scale and size of class interval, either of which may color the result. Grade scales whose classes are not related by fixed intervals are particularly difficult. Another basic weakness of the histogram is that it pictures a continuous distribution as a series of discrete grades.

Jan 1, 1957

By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase &apos;fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,&apos; hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.&apos; It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

By R. A. Davidson, L. Silverman

RESIDENTS of many urban centers are becoming increasingly aware of the obscuring effect of fume and smoke discharge from power, metallurgical, chemical, and other industries; and they, as well as the legislatures of these affected cities, are agitating for cleaner air. Management&apos;s most pressing problem is to find an economical way to reduce process effluents in response to the growing pressure from population and legislative demands. The removal must be done, if possible, without handicap to the current operation, since the costs of relocating are often excessive or prohibitive. In fume recovery or disposal, an important item to consider is whether or not the material being discharged has any value. If it has commercial value, the cost of its recovery may offset or aid amortization. For this reason, in making a study of the specific problem in hand, a major factor was the nature of the material emanating from the stack: in particular, its particle size, size range, and its chemical and physical composition, as well as its potential value and utility when recovered (in either a wet or dry state). Should the product have no commercial value, it must be disposed of at minimum cost in a way to prevent recontamination. Initial studies were therefore made to determine stack concentrations and volumes of material evolved from the operations. The next phase of the study concerned the physical and chemical nature of the collected fume. The third portion of this paper describes the wet and dry collector studies undertaken to recover the fume. Cleaning Requirements for Ferroalloy Furnace Operation The basic need for any effluent collection equipment is the highest possible efficiency and the lowest tolerable resistance when the power consumption involved is considered. Since the electric furnace effluent is largely composed of fume of small size (less than 0.5u), it has high light obscuring properties, and even low concentrations will cause some loss of visibility and be evident to nearby residents. The permissible limit for fly ash emission in many cities is based on a weight value (viz, approximately 0.4 grains per cu ft), but the smoke density values are dependent upon a shade of color. In the case of the Los Angeles County code, emission is restricted to pounds per pound of material processed per hour basis (but not exceeding 40 lb per hr for any one given plant operation). If an average particle size of the fume from ferro-silicon alloy electric furnaces is assumed to be 0.4u (as shown later, this is the approximate mean size) and an average loading of 1 grain per cu ft (stp), each cubic foot of stack gas will contain approximately 75x10 10 particles (based on assumed, and confirmed, spherical shape and a standard deviation of unity). When it is realized that the air in metropolitan areas, which are also general industrial areas, contains approximately 5x108 particles, the tremendous light scattering effect of this concentration becomes apparent. Consequently, nearly 100 pct collection would be necessary to equal the average concentration. Fortunately, however, discharge from a high point above ground (50 to 100 ft) will result in at least a thousandfold dilution, or the stack concentration reaching the ground in the foregoing case might result in a ground concentration of &apos; particles. If the concentration at the source could be reduced by a factor of 100 (99 pct efficiency of collection), then a concentration of 75x10" particles would be diluted to 7.5x10&apos; which would be very satisfactory. An efficiency of 90 pct (factor of 10 decontamination) at the source would result in a discharge of 75x109 articles which upon dilution yields 75x10 which is still 15 times the general air value. Another approach to this consideration is to use the value of concentration of 0.005 grains per cu ft for the value of a visible effluent as cited by Kayse.1 To attain this value with an average loading of 1 grain per cu ft would require an efficiency of 99.5 pct. Since the foregoing value is not based on any reported size of fume particles, it is felt that the numbers&apos; approach given previously is more reliable. These calculations serve to indicate the desirability of thorough cleaning, preferably at the source, and with efficiencies well above 90 pct, preferably above 95 pct (dilution 1:20). One of the most important items in any control program is to reduce the concentrations as close to their sources as possible. The use of better furnace design, deeper coverage over the electrodes, and the prevention of blows or breaks in the surface all help to reduce dissemination; consequently, all of these improvements should be made, if possible, to cut down the effluent load. In addition, in order to minimize the volume of contaminated air that has to be cleaned, the furnace should be enclosed as much as possible. Test Arrangements Before fundamental studies with collectors were made, a furnace stack selected for the test program was sampled to determine the gas temperatures and

Jan 1, 1956

By J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young&apos;s modulus and a value of approximately 0.5 for Poisson&apos;s ratio. A value of % for Poison&apos;s ratio with finite Young&apos;s modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By D. L. Kelley

High-viscosity water injection has been proposed for use in reservoirs containing high-viscosity crude oils. Previous publications have largely ignored the possible effects of the connate water on the proposed process. This paper describes experimental work which indicates that the connate water will be forced ahead of the injected water to form a bank of low-viscosity water. This decreases the oil recovery which would be expected if such a bank were not formed. These effects are shown for a range of fluid mobilities and connate-water saturations for a five-spot injection system. In general, oil recoveries using viscous water are significantly greater than for untreated water even though they are less than would be expected if no connate water bank were formed. INTRODUCTION The effect of mobility ratio on the oil recovery of wa-terfloods has been known for many years. Muskat first pointed out that the fluid mobilities (k/µ) in the oil and water regions would affect the performance of the water-flood, and he estimated the general effect of these variables.&apos; Since this early work, studies of the effect of mobility ratio on secondary recovery have been reported where mathematical,&apos; potentiometric3 and scaled flow models&apos; were used. These studies have shown that a reduction in the mobility ratio between the oil and the displacing fluid would cause additional oil recovery when water-flooding reservoirs containing viscous crude oils. Studies reported by Pye- nd Sandiford 8 have indicated that chemicals to increase injection water viscosity are now available and can be used to reduce the over-all mobility ratio of a waterflood. Where mobility ratios are controlled by the injection of viscous fluids, the connate water of the reservoir can play an important part in the displacement of the reservoir oil. The purpose of this study was to determine the effect of the connate-water saturation in waterfloods where viscous waters are used for injection. DISPLACEMENT OF THE CONNATE WATER Russell, Morgan and Muskat7 were the first to recognize the mobility of connate waters in waterflooding. They conducted waterfloods on oil-saturated cores containing 20 and 35 per cent irreducible water saturations, and found that from 80 to 90 per cent of the "irreducible" water was produced after only one pore volume of water was injected. However, their experiments were conducted at rates of flow significantly higher than those ordinarily occurring in waterfloods. Also, the cores were only from 4.0 to 8.5 cm long. Brown 4 studied a 100-cm linear sand pack which had been prepared to contain connate water and oil. He used 140- and 1.8-cp oils with injection water of essentially the same viscosity as the connate water. He found that all of the connate water was displaced by the injection water in both cases. However, the injection volumes required for complete displacement of the connate water were considerably higher in the case of the more viscous oil. To verify the results of the foregoing experiment, a 10-ft-long linear model was constructed by packing 250-300 mesh sand in a 1/2-in. diameter nylon tube. The model was evacuated, saturated with a brine of 1-cp viscosity, and flooded with a 41-cp mineral oil to the irreducible water saturation of 10.9 per cent. The model was then waterflooded by the injection of a water solution which had an apparent viscosity of 42.6 cp. The solution consisted of 0.5 per cent methylcellulose in distilled water. The viscosities of the oil and connate water were measured with an Ostwald viscosimeter. The viscosity of the polymer solution was calculated by Darcy&apos;s law using pressures measured during actual flow conditions. The ratio of the mobility in the oil region to the mobility in the inject ion-water region was approximately 0.32. The mobility ratio of the oil region to the connate-water bank was approximately 14. The mobility ratio between the connate-water bank and the injection water region was 0.024. Approximately 84.5 per cent of the recoverable oil was produced before water breakthrough. Immediately following breakthrough, oil and connate water were produced at an increasing water-oil ratio until the viscous injection water broke through. At viscous-water breakthrough, 96 per cent of the original connate water had been produced. After breakthrough of the viscous water, there was no additional production of connate water or oil. The near-

Jan 1, 1967

By K. H. Hiller

A rotational viscometer has been designed which perrnits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described. The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensiom at high temperatures and pressures, are presented. Data are also presented for the flow behavier of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. INTRODUCTION The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin.1 The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.&apos; Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids. The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.3 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro- duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress 7 and the rate of shear D is given by the following equation: where is the plastic viscosity and 4 the yield point. If 4 = 0, the equation for simple Newtonian flow, 7 = pD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known. For this reason a high-pressure, high-temperature rhe-ometer has been designed to measure the plastic viscosity the yield point +, and the static gel strength S, at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress t at any given rate of shear D. This is possible only if t and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde." The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fie. 2. which revresents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. For measurements of dynamic flow properties, the rotating cup is driven by a 1/2-hp electric motor, which operates through a Vickers

By J. Szekely, G. P. Martins

A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.&apos; Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble&apos;s ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The &apos; &apos;anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at

Jan 1, 1970