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By G. Derge, Ling Yang, G. M. Pound

The specific conductance and its temperature dependence were measured over the entire composition range of the molten Cu2S-CuCI system. At a typical temperature of 1200°C, 10 rnol pet of the ionically conducting CuCl reduced the specific conductance from about 77 ohm-lcm-l for pure Cu2S to about 32 ohm -1cm -1, and 50 mol pet CuCl reduced the conductance to that for pure CuCI—about 5 ohm 1cm1. The nature of electrical conduction in molten Cu2S, FeS, CuCI, and mixtures was studied by measuring the current efficiency of electrolysis at about 1100°C. The Cu2S, FeS, and mattes were found to conduct exclusively by electrons, but addition of 1 5 wt pet CUS to Cu2S produces a small amount of electrolysis. Addition of CuCl to Cu2S suppresses electronic conduction, and ionic conduction reaches almost 100 pet at a CuCl concentration of about 50 mol pet. These facts are interpreted in terms of electron energy level diagrams by analogy to the situation in solids. RESULTS of electrical conductivity studies on molten Cu-FeS mattes as a function of composition and temperature have been reported.' The specific conductances ranged from about 100 ohm-' cm-' for pure Cu2S to 1500 ohm-' cm-1 for pure FeS. This is in sharp contrast with the low specific conductance of molten ionic salts for which the transfer of electricity is by migration of ions in the field. In general, these ionically conducting molten salts, such as NaC1, KC1, CuC1, etc., have a specific conductance of the order of magnitude of 5 ohm-' cm-'. It was concluded on the basis of this evidence that molten FeS and Cu,S exhibit electronic conduction. Pure molten FeS has a small negative temperature coefficient of specific conductance, resembling metallic conduction, while pure molten Cu2S has a small positive temperature coefficient, resembling semi-conduction. The molten Cu2S-FeS mattes follow a roughly additive rule of mixtures, both with respect to specific conductance and temperature coefficient. Savelsberg2 has studied the electrolysis of molten Cu2S and Cu2S + FeS. He concluded that while molten Cu2S is an electronic conductor, there is some ionic conduction in molten Cu2S + FeS3 owing to the formation of the molecular compound 2Cu2S.FeS and its dissociation into Cu1 and FeS2-1 ions. The present work does not verify his results. Chipman, Inouye, and Tomlinson" have studied the specific conductance of molten FeO and report a high specific conductance, about 200 ohm-1 cm-1 of the same order of magnitude as that found for molten mattes, and a positive temperature coefficient. They interpret these results in terms of p-type semiconduction in the ionic liquid by analogy to the situation in solid FeO.1 imnad and Derne' detected appreciable ionization in molten FeO by means of electrolytic cell efficiency measurements. In order to verify the conclusion that electrical conduction in molten Cu2S and mattes is electronic, and to gain further insight into the structure of molten sulfides, the following investigations were carried out in the present work: 1) The specific conductance, s of the molten system Cu2S-CuC1 was measured as a function of temperature over the entire composition range. As discussed later, molten CuCl is an ionic substance. It was thought that if molten Cu2S were simply ionic in nature, addition of small amounts of CuCl might not have a catastrophic effect in lowering the high conductance of the Cu2S. On the other hand, if much electronic conduction occurs, addition of the ionic CuCl should have a large effect in destroying the electronic conduction. 2) The electrolytic cell efficiency of the following molten systems was measured at about 1100°C in specially designed cells: Cu3; Cu2S + FeS, 50:50 by wt; FeS; Cu2S + CuS, 15 wt pet; Cu2S + CuC1, 5.9 to 46.4 mol pet; and CuC1. This gives a direct measure of the fraction of current carried by ions in these melts. Further, the cell efficiency, extrapolated to zero ionic current, is given by cell efficiency = (s leasile + s elexstronic). [1] s lucile for molten CulS would be expected to be no greater than that for molten CuC1, whose s lonle is about 5 ohm-' cm-1, as will be seen in the following. u,.,,.,.,.......for molten Cu,S is of the order of 100 ohm-' cm-'.' Thus, a large increase in cell efficiency from 0 to values of 10 to 100 pet upon addition of CuCl to Cu2S would indicate destruction of the electronic conductance. Conductance Measurements Experimental Procedure—The apparatus and experimental method were the same as those described in detail in connection with the study of electrical conduction in molten Cu,S-FeS mattes.' A four terminal conductivity cell and an ac poten-

Jan 1, 1957

By J. Ruben Velasco, Roland B. Mulchay

CANANEA has long been recognized as a remarkable field for geologic study. The copper deposits and rocks of the district have been described by many geologists and engineers, but only the most general correlations have been made between Can-anea sedimentary rocks and other known sedimentary sections in the southwestern United States and northern Mexico. The present paper describes the Cananea sediments in greater detail than has been done before and attempts to fit the Cananea sedimentary section more closely into the geologic time table. The lack of well-preserved fossils has made it difficult to date the sediments accurately in geologic time, but it is possible to make tentative correlations between the Cananea sediments and the southeastern Arizona sections, based largely upon lithology and general position in the geologic column. It appears that sedimentation at Cananea and Bisbee may have been closely similar during Paleozoic time. Even such generalized correlations, however, may be subject to considerable modification in the future. The present study has led to the recognition of other problems of age and mineralization relationships in the Cananea district. Cananea is located in the north-central part of the state of Sonora, Mexico, at an elevation of 5270 ft. It is about 135 miles northeast of Hermosillo, the state capital, and 25 miles south of the international boundary. By road Cananea is 40 miles from the twin towns of Naco, Ariz., and Naco, Sonora, and about 50 miles from Bisbee, Ariz. It is served by the Nogales-Naco branch of the railroad, F.C. Pacifico, and is connected with Chihuahua and Mexico City by the Aeronaves airline. The headwaters of three rivers flowing to the Gulf of California are located in the Cananea Mountains: the San Pedro River, flowing to the north; the Sonora River, flowing south and west; and the Mag-dalena River, flowing west. Elenita Mountain, the highest point in the district, has an elevation of 8140 ft. The Cananea Mountains extend in a series of north-south to northwest-southeast spurs and ridges and are surrounded by gently sloping gravel plains. The mineralized area, lying across the southern and central parts of the range, is about 6 miles long and at most 2 miles wide. Elevations at the mines vary from 5300 ft at Cananea-Duluth mine at the southeast end of the district to between 6000 and 7000 ft at the west end of the mineralized area at Puertecitos-Elenita mines. Principal production has been from the intensely mineralized and altered area of Capote Basin in the central part of the district and the immediately surrounding area to the southeast. The district has produced over 2 billion lb of copper, substantial molybdenum, and minor amounts of lead, zinc, silver, and gold. Total production through 1949 is estimated at more than $300 million. In 1900 large-scale development was started at Cananea by W. C. Greene. Until World War II only high-grade ores were exploited; low-grade ores were extracted after the installation of a large concentrator in the early 1940's, and subsequent operations have been based upon mining and processing ores containing less than 1.0 pct copper from open-pit and underground workings. Mining and concentration of such low-grade ores, however, are made possible only by continued high copper prices, and active exploration for high-grade orebodies has been continued throughout the important mineralized areas. General Geology Study of the involved rock pattern at Cananea has indicated a complex geologic history for the district. Widespread alteration and mineralization have masked many of the salient features and have led to widely varying geologic interpretations over the years. Further work will probably disclose new information which will modify current beliefs. At Cananea a conformable series of sediments of probable Paleozoic age was deposited on an unknown basement. Following Paleozoic time there was an extended period of erosion common to many districts in the southwestern U. S., and there is no present evidence of marine sedimentation at Cananea after the Paleozoic. The eroded surface was eventually covered with a great thickness of extrusive volcanic rocks. The entire series of sediments and volcanic rocks was later intruded by a variety of deep-seated igneous rocks. These included the Cananea granite, the Cuitaca granodiorite, the El Torre syenite, the Tinaja diorite, the Campana diabase and gabbro and the Colorada rhyolite quartz porphyry. Faulting of early age, probably prior to the deposition of the volcanic rocks, may have been responsible for the present position of some of the intrusive rock masses. In the Capote mine on the third and fourth levels the northwest-striking Rick-etts fault zone, with apparent offset of about 800 ft, has been sealed by a dike-like mass of Cananea granite which gradually increases in size with depth. In lower levels of the mine the granite forms a large southeast-plunging mass generally following the course of the Ricketts zone. The granite is not known southeast of the Capote-Oversight mine areas and the Ricketts fault does not appear in the vol-canic~ southeast of Capote Basin, but several plugs of Colorada quartz porphyry cut the volcanics along the assumed general southeast trend of the Ricketts zone. These porphyritic intrusives may be the up-

Jan 1, 1955

By D. T. Peters, S. Floreen

The age hardening behavior of an Fe-8Ni-13Mo alloy was studied after the matrix had been varied to produce either ferrite, cold u~orked ferrite, or nzassive nzartensite. The aging behavior of the cold worked ferrite and murtensite structures were very similar. The martensite aging kinetics were much different from those observed in earlier studies of aging of maraging steels, even though the martensite wzatri.r had the same dislocation structure as those found in maraging steels. The results suggest that the previously observed precipitation kinetics of maraging steels ?nay have been controlled by the nucleation be-haviov, which in turn were dictated by the alloy compositions and the resultant identities of the precipitating phases. IT is well known that the rate of precipitation from solid solution depends not only on the degree of super-saturation, but also on the density and distribution of dislocations in the matrix structure. These imperfections often act as nucleation sites, and may also enhance atomic mobility. 'Thus, the presence of dislocations is important since the type and distribution of precipitates may be determined by them. The precipitate density and morphology in turn affects the mechanical properties of the alloy. A number of studies have been devoted to the precipitation characteristics in various types of maraging steels.'-" These are iron-base alloys containing 10 to 25 pct Ni along with other substitutional elements such as Mo, Ti, Al, and so forth, that are used to produce age hardening. The carbon contents of these steels are quite low, and carbide precipitation is not believed to play any significant role in the aging reactions. After solution annealing and cooling these alloys generally transfclrm to a bcc lath or massive martensite structure characterized by elongated martensite platelets that are separated from each other by low angle boundaries, and that contain a very high dislocation den~it~.~~~~~~~~-~~ Age hardening is then conducted at temperatures on the order of 800" to 1000°F to produce substitutional element precipitation within the massive martensite matrix. Most of the aging studies to date have revealed several common traits in these alloys, regardless of the particular identity of the precipitation elements. Generally hardening has been found to be extremely rapid, with incubation times that approach zero. The agng kinetics, at least up to the time when reversion of the martensite matrix to austenite begins to predominate, frequently follow a AX/~~ = ktn type law, where x is hardness or electrical resistivity, t is the time, and k and n are constants. The values of n are frequently on the order of 0.2 to 0.5, which are well below the idealized values of n based on diffusion controlled precipitate growth models. Finally, the observed activation energy values are typically on the order of 30 kcal per mole, and thus are well below the nominal value of about 60 kcal per mole found for substitutional element diffusion in ferrite. The common explanation of these observations is that the precipitation kinetics are controlled by the massive martensite matrix structure. Thus, the absence of any noticeable incubation time has been attributed, after ~ahn," to the fact that the precipitate nucleation on dislocations may occur without a finite activation energy barrier. The low values of the activation energy are generally assumed to be due to enhanced diffusivity in the highly faulted structure. If this explanation that the precipitation kinetics are dominated by the matrix structure is correct then one should observe a distinct difference in lunetics between aging in a martensitic matrix and aging the same alloy when it has a ferritic matrix. Such a comparison cannot be made with conventional maraging compositions, but could be made with the alloy used in the present study. In addition, the ferritic structure of the present alloy could be cold worked to produce a high dislocation density so that one could determine whether ferrite in this condition would age similarly to martensite. EXPERIMENTAL PROCEDURE The composition of the alloy used in this study was 8.1 pct Ni, 13.0 pct Mo, 0.10 pct Al, 0.13 pct Ti, 0.012 pct C, bal Fe. The alloy was prepared as a 40 lb vacuum induction melt. The heat was homogenized and hot forged at 2100°F to 2 by 2 in. bar, and then hot rolled at 1900°F to $ in. bar stock. The aging lunetics were followed by Rockwell C hardness and electrical resistivity measurements. Samples for hardness testing were prepared as small strips approximately 2 by $ by 4 in. thick. Electrical resistivity was studied on cylindrical samples approximately 2 in. long by 0.1 in. diam. The method for making the alloy either martensitic or ferritic was based on the fact that the alloy showed a closed y loop type of phase diagram. At high temperatures, above approximately 24003F, the alloy was entirely ferritic. Small samples on the order of the dimensions described above remained entirely ferritic after iced-brine quenching from this temperature. In practice, a heat treatment of 1 hr in an inert atmosphere at 2500°F followed by water quenching was used to produce the ferritic microstructure. These samples were quite coarse grained and usually en-

Jan 1, 1970

By W. Weissberger, Frankiewicz, L. Pommier

Introduction In the U.S., about one-quarter of the fuel oil and natural gas consumption is associated with power production in utility and industrial boilers and process heat needs in industrial furnaces. Coal has been an attractive candidate for replacing these premium fuels because of its low cost, but there are penalties associated with the solid fuel form. In many cases pulverized coal in unacceptable as a premium fuel replacement because of the extensive cost of retrofitting an existing boiler designed to burn oil or gas. In the cases of synthetic fuels from coal, research and development still have a long way to go and costs are very high. Another option, which appears very attractive, is the use of solid coal in a liquid fuel form - coal slurry fuels. Occidental Research Corp. has been developing coal slurry fuels in conjunction with Island Creek Coal (ICC), a wholly-owned subsidiary. Both coal-oil mixtures and coalwater mixtures are under development. ICC is a large eastern coal producer, engaged in the production and marketing of bituminous coal, both utility steam and high quality metallurgical coals. There are a number of incentives for potential users of coal slurry fuels and in particular for coal-water mixtures (CWMs). First, CWM represents an assured supply of fuel at a price predictable into future years. Second, CWM is available in the near term; there are no substantial advances in technology needed to provide coal slurry fuels commercially. Third, there is minimal new equipment required to accommodate CWM in the end-user's facility. Fourth, CWM is nearly as convenient to handle, store, and combust as is fuel oil. Several variants of CWM technology could be developed for different end-users in the future. One concept is to formulate slurry at the mine mouth in association with an integrated beneficiation process. This slurry fuel may be delivered to the end-user by any number of known conveyances such as barge, tank truck, and rail. Slurry fuel would then be stored on-site and used on demand in utility boilers, industrial boilers, and potentially for process heat needs or residential and commercial heating. An alternative approach is to formulate a low viscosity pre-slurry at the mine mouth and to pipeline it for a considerable distance, finishing up slurry formulation near the end-user's plant. Finally, at the other extreme of manufacturing alternatives, washed coal would be shipped to a CWM manufacturing plant just outside the end-user's gate. Depending on fuel specifications and locations of the mine and end-user facility, any of these alternatives may make economic sense. They are all achievable in the near term using existing technology or variants thereof. The Coal-Water Mixture CWMs contain a nominal 70 wt. % coal ground somewhat finer than the standard pulverized ("utility grind") coal grind suspended in water; a complex chemical additive system gives the desired CWM properties, making the suspension pumpable and preventing sedimentation and hardening over time. Figure 1 shows the difference between a sample of pulverized coal containing 30 wt. % moisture and a CWM of identical coal/water ratio. The coal sample behaves like sticky coal, while the CWM flows readily. The combustion energy of a CWM is 96-97% of that associated with the coal present, due to the penalty for vaporizing water in the CWM. Potentially any coal can be incorporated in the CWM, depending on the combustion performance required and the allowable cost. CWMs are usually formulated using high quality steam coals containing around 6% ash, 34% volatile matter, 0.8% sulfur, 1500°C (2730°F) initial deformation temperatures, and energy content of 25 GJ/t (21.5 million Btu per st). Additional beneficiation to the 3% ash level can be accomplished in an integrated process. There are a number of minimum requirements which a satisfactory CWM must meet: pumpability, stability, combustibility, and affordability. In addition, a CWM should be: resistant to extended shear, generally applicable to a wide variety of coals, forgiving/flexible, and compatible with the least expensive processing. It was found that a complex chemical additive package and control of particle size distribution are necessary to achieve these attributes simultaneously, while maximizing coal content in the slurry fuel. Formulation of Coal-Water Mixtures A major consideration in the manufacture, transportation, and utilization of a slurry fuel is its pumpability, or effective viscosity. Most CWM formulations are nonNewtonian, i.e., viscosity depends on the rate and/or duration of shear applied. Viscosities reported in this paper were obtained using a Brookfield viscometer fitted with a T-spindel and rotated at 30 rev/min, thus they are apparent viscosities measured at a shear rate of approximately 10 sec-1. The instrument does reproducibly generate a shear field if spindle size and rotation rate are held fixed. By observing the apparent viscosities of several slurries at fixed conditions it is possible to obtain a relative measure of their viscosities for comparison purposes. A true shear stress-shear rate relationship at the shear rates at which the CWM will be subjected in industry may be obtained using the Haake type and a capillary viscometer. These viscometers are used for specific applications. However, for comparison purposes, apparent viscosities are reported.

Jan 1, 1985

By George M. Schwartz, Ian L. Reid

THE Soudan mine in the Vermilion district of northeastern Minnesota is the oldest iron mine in the state. It has shipped ore every year since 1884 and still contributes a yearly quota of high grade lump ore. No comprehensive report on the Vermilion iron-bearing district has appeared since Clements' monograph,' but Gruner2 discussed the possible origin of the ores in 1926, 1930, and 1932, and recently Reid and Hustad have added data on mining and geology .3, 4 For many years geologists of the Oliver Iron Mining Div., U. S. Steel Corp., have kept up to date a series of plans and vertical sections of the Soudan mine. In connection with mine operation considerable diamond drilling has been done, and this, together with the mine openings, has permitted a reasonably accurate picture of the structure of the orebodies and wall rocks. It has long been evident to geologists familiar with the mine that the ores were not a result of weathering, a point emphasized by Gruner in 1926 and 1930. As the deeper orebodies were developed it also became clear that replacement had played an important part in their development. In recent years it has been recognized that other iron ores were formed by replacement, as Roberts and Bartly5 have argued strongly for the deposits at Steep Rock Lake. On the basis of these facts G. M. Schwartz suggested to members of the Oliver staff that it would be desirable to study the evidence of replacement, particularly the possible alteration of the wall rock which would be expected if the replacement was a result of hypogene solutions. Rock Formations: The formations directly involved in the iron orebodies of the Soudan mine are few though far from simple. The country rock is largely the Ely greenstone of Keewatin age consisting of a mass of metamorphosed lava flows, tuffs, and intrusives which have been more or less altered by hydrothermal solutions. The predominant rock is chlorite schist. Interbedded with the original flows and tuffs are a series of beds and lenses of jasper to which the name Soudan formation has been applied. In the Vermilion district the term jaspilite has been used for interbanded jasper and hematite. According to modern usage these jasper or jaspilite beds do not comprise a formation separate from the Ely greenstone, inasmuch as the beds of jasper are interbedded with the flows and tuffs of the upper part of the greenstone. It would more nearly accord with modern usage to consider the Soudan beds a member of the upper part of the Ely formation. Because of incomplete rock exposure and exploration the number of interbedded jaspilite beds is unknown. In the mine, however, as many as nine major beds of jasper are known on a cross-section of one limb of the syncline, with an equal number on the other limb. In addition diamond drill cores show beds of greenstone down to half an inch in thickness. The thin beds are probably always tuffs. Structure: Rock structure in the Soudan area is complex, and because there are no recognizable horizons within the greenstone it is extremely difficult to work out the details. Generally speaking, the major regional structure is an anticlinorium, the axis trending east-west, with a westerly pitch. The Soudan mine is related to a synclinal structure on the north limb of the anticline about a mile from the west nose of the folded iron formation. The general structure at the mine is that of a closely folded minor syncline on the major regional anticline. A cross fault has dropped the east side so that the bottom of the syncline has not been reached, whereas to the west it is well shown by the mine openings and diamond drill exploration. Throughout the mine the beds of jasper, and ore-bodies that have replaced the jasper, normally dip northward at angles of 80" or steeper. In detail the jasper beds are extremely folded, probably as a result of deformation while they were still relatively unconsolidated. Orebodies: Ore in the Soudan mine is mainly a hard, dense, bluish hematite. Locally ore has been brecciated and cemented by quartz. The vugs commonly occurring near the borders of orebodies are lined with quartz crystals. They seem to have formed as part of the ore-forming process and are evidence that no folding or compression of the ore has taken place. The orebodies are numerous, varying greatly in size. Many lenses of high grade hematite are too small to be mined. Some of the larger orebodies have been followed vertically for as much as 2500 ft and horizontally up to 1500 ft. The large ore-bodies are extremely irregular in outline in the plane of the beds of jaspilite. In width they are more regular, as they are strictly governed by the width of the jaspilite beds and the greenstone wall rock, which seems to have resisted replacement by hematite. At many places the orebodies replace the jaspilite completely and have a footwall and hanging wall of greenstone. At other places either one or both walls may be jaspilite. Geologists who have studied the orebodies in recent years agree that evidence for the replacement origin of the hematite bodies seems conclusive. AS noted above, many of the orebodies replace jaspilite beds from wall to wall with no evidence whatever of compaction. The replacement origin is also supported by details of the banding which is characteristic of the

Jan 1, 1956

By G. A. Beske, P. Hilsch, J. Wulff

The effects of the growth precipitates on the su-perconduching properties of an Al- 15 al. pel Zu alloy have been studied using magneization, transition lem-perature, and residual resistivity measurements. Aging at 230C for 1/2 to 11 he produces an increase in Hfp, Ike field of first penetration, and tut increase in trapped flux. The upper critical field, Hc2 remains constant for such aging tunes. Aging at 200°C produces a decrease in Hfp and an increase in trapped flux. The transition temperature remains constant at Tc - 1.227° ± 0.02°K for aging at 220°C for tims of from 1/2 to 10 hr, and for aging at 200°C it remains constant at Tc. = 1.18° i 0.02°K for times from 1/2 hv to 26 hr. The observed behavior indicates that the superconducting matrix when aged at 220°C behaves tike a type U su-perconducior, but when aged at 200°C behares like a type I superconductor. The magnetization changes after aging can be attributed to the growth and clutnge in distribution of the precipitate in a matrix of fixed composition. IT has been realized for some time that the superconducting properties of alloys are highly structure-sensitive. This is evident in the work of Mould and Mapother1 who examined the properties of an aluminum alloy. Precipitation effects have also been briefly mentioned in other studies.2-4 Bonnin and coworkers5 have observed a sharp inc rease in trapped flux in an A1-Mg alloy when the residual resistivity reaches a value that indicates it is a type II superconductor. Recently Blanc, Goodman, and Nemoz5p have reported on precipitation effects in A1-Ag alloys. Detailed studies of precipitation in Pb-Sn and Pb-Cd alloys made by Livingston6 serve to show that the upper critical fields are enhanced by quenched-in solute. Furthermore. at various stages in the precipitation process? the upper critical field is determined largely by the remanent solute. The observed magnetic hysteresis and trapped flux in such alloys result from the interaction between precipitate and the flux filaments in the mixed state. The flux trapping appears to depend largely on the precipitate distribution and is greater if the superconductor is type II than if it is type I. To examine the effect of precipitation in another alloy system, particularly one in which the composition of the superconducting phase does not change significantly during the course of precipitation, the Al-Zn system seems interesting, especially in view of the transition temperature and resistivity studies of Chiou and seraphim.' Furthermore, the recent detailed electron-microscope studies of an Al-Zn alloy by Richards and Garwood8 provide a guide for relating superconducting properties to changes in structure. For these reasons, magnetization, transition temperature, and residual resistivity measurements for varying times of heat treatment at two temperatures were made with a -15 at. pct Al-Zn alloy. The results are reported in this paper. I) EXPERIMENTAL The alloy used was prepared by Cominco Products Inc. from 99.9999 A1 and 99.999 Zn. It was chill-cast, swaged, and drawn to 0.125-in.-diam rod. The analyzed composition was 15.6 at. pct Zn (31.1 wt pct). A jeweler's saw was used to cut the 0.125-in.-diam rod into the 0.875-in. lengths needed for magnetization measurements. The ends of the cylinders were slightly beveled to remove the sharp edges. A portion of the original 0.125-in.-diam rod was drawn into 0.010-in.-diam wire and used for transition temperature measurements. Specimens were suspended from wires within a vertical furnace during heat treatment. All were homogenized at 500°C for a minimum of 3 days and subsequently solutionized for times in excess of 6 hr. The solutionizing temperature was held constant to +3°C. Individual specimens were homogenized, quenched, and aged several times and no effects indicating loss of zinc were noted. The suspended specimens were quenched by cutting the wires and allowing the specimens to fall into a silicone oil bath held at the aging temperature. They were then isothermally transforked by aging in the same bath used for quenching. After aging for the required time (approximately 10 min aging was necessary before the upper critical field reached a fixed value), they were briefly (1 to 2 sec) dipped into an acetone bath at room temperature to remove adherent oil and then immediately transferred to liquid nitrogen where they remained until inserted into the helium bath (usually within an hour). The temperature of the aging bath was held constant to +3°C for longer aging times. The cryostat used for the measurement of superconducting properties consisted of outer and inner dewars for liquid nitrogen and liquid helium, Stokes 6-in. booster diffusion pump and Stokes Model 212 mechanical pump, temperature controller to measure and control the temperature of the helium bath, and a superconducting solenoid with inserted search coils to provide the magnetic field and measure the magnetic moment of the specimens. A schematic diagram of the cryostat is shown in Fig. 1. An ultimate temperature of 0.85°K was reached with this apparatus. The temperature controller used is similar to the one described by Blake and chase.' A 0.5 pct Allen-Bradley carbon resistor and a nichronle heater (200

Jan 1, 1968

By A. C. D. Chaklader, Ashok K. Kakar

The basic density equation originally dericed ' to predict the increase in density of a compact of spherical particles with the progressive deformation at the points of contact has been further modified to include the yield strength of the material. This has been done by assuming that the contact areas grow to stable sizes under a fixed stress which is equal to three times the yield strength. The final equation has the form: where Do and D me the initial and final bulk densities of the compact, u is the applied pressure, and Y is the yield strength of the material. This equation was tested with the data obtained on spheres of lead, K-Monel, and sapphire. The calculated yield strength t~alues for lead and sapphire are within the range of values reported in the literature. A few of the earliest hot pressing models proposed to explain the mechanism by Murray, Livey, and williams2 and then by McClelland3 are based on a plastic flow mechanism. However, more recent investigations suggest that the overall densification process is a combination of several mechanisms, such as particle rearrangement, fragmentation, plastic flow, and stress-enhanced diffusional creep. While fragmentation and particle rearrangement are considered to be responsible for the densification in the early stages,"475 it has been concluded that the final stages of hot pressing are controlled by stress-enhanced diffusional creep.516 The manner in which the densification takes place, i.e., by fragmentation, particle rearrangement, plastic flow, or stress-enhanced diffusional creep, would depend upon the type of material, the temperature, and the stress level used during the hot-pressing experiments. Metal compacts can be expected to have a much greater contribution from plastic flow than ceramic oxides. Also, plastic flow would be a significant contributing factor to densification at high temperatures and high stresses. Most of these works, directed towards elucidation of densification mechanism, have dealt with kinetics of the process. The results of most of the authors vary from one another and they have proposed either new empirical or semiempirical equations to fit their data. The densification rate was found to vary with the type of the powder, shape and size of the powder, initial packing density of the compact, and a few other factors such as rate of heating, pressure, and so forth. Beyond the initial stages, the densification process has been considered to be as time-dependent flow, controlled by a diffusional process, e.g., Nabarro-Herring creep. Palm our, Bradley, and johnson' have attempted to use modified creep rate equations to interpret the data of densification under hot-pressing conditions. Beyond the initial stages, however, the densification would be controlled by a process depending upon the temperature, pressure, and size of the powders. It is the authors' belief that such densification cannot be exclusively controlled by a single process and so attempts should be made to study some observable phenomenon like microstructure, yield strength, and so forth. The emphasis of this work has been toward studying the densification problem from a more fundamental point of view. Some of the principal variables, like initial packing density, mode of packing, and size of the powders, have been controlled to a great extent. The total strain produced on pressure application (instantaneous) in such a case can be considered to be due to plastic and elastic deformation. The elastic component of the strain can be determined by decreasing the load to the initial value. The strain remaining then can be correlated with the contact areas produced by deformation and the corresponding applied load. In a previous paper,' the possible deformation behavior of spheres in a compact has been theoretically analyzed and experimentally tested. The change in contact area radius a relative to the particle radius R was related to the bulk density and the bulk strain for simple and systematic modes of packing. Tt was found that a density equation relating the above parameters can be represented by: where D and Do are the bulk densities of the compact at any value of a/R and a/R = 0, respectively. This basic equation should hold for any material as it was derived from geometrical considerations alone. An attempt has been made in this work to include the yield strength in the above density equation, so that a knowledge of the properties of any material can be used in predicting the densification behavior during the hot-pressing process. THEORETICAL CONSIDERATTONS The deformation of two spheres in contact under a static load can be compared to the deformation occurring between a hard spherical indentor and the flat face of a softer metal. Tt has been shown theoretically by both ~encky~ and lshlinskyg and experimentally by ~abor" that, for a material incapable of appreciable work hardening, the mean pressure required to produce plastic yielding (for deformation occurring between flat face and a hemispherical indentor) is approximately equal to three times the elastic limit, Y, of the material (in tension or compression experiments). Tabor has further observed that the same relationship is valid in the case of work-hardening materials, if the elastic limit at the edge of the indenta-

Jan 1, 1969

By K. W. Nelson, John N. Abersold

INDUSTRIAL hygiene has been defined by Patty' as "the science and art of recognizing, evaluating, and controlling potentially harmful factors in the industrial environment." This definition implies thorough study of operations, evaluation of potentially harmful factors through air sampling, micro-analyses and other means and finally, appropriate medical and engineering control wherever indicated. The prevention of industrial health injuries is a vital part of operations of American industry today. Progress and interest in this field has increased steadily for many years, the most rapid progress having been attained, perhaps, during the last three decades. It is significant to note that there are now official agencies in 46 states actively concerned with industrial health problems and that a western field station has been established recently in Salt Lake City by the U. S. Public Health Service to augment its industrial hygiene services directed from headquarters of the National Institute of Health, Bethesda, Md. Many of the larger industries have found it advantageous to establish their own industrial hygiene departments. The American Smelting and Refining Co. is a world-wide organization engaged in the mining, smelting, and refining of lead, copper, zinc, silver, gold, by-product metals, including cadmium, arsenic, and others. In the United States there are 13 smelters and refineries, 11 secondary smelters or foundries, and a number of mines. Approximately 9000 workers are normally employed. It has long been the established company policy to seek out occupational hazards and provide safeguards for employee health. Protective equipment has been supplied to individual workers and exhaust ventilation installations have been in use in some operations for more than 40 years. All of the major units have their own medical departments which provide employees with excellent medical and hospital care. In 1937 full scale industrial hygiene studies were undertaken at the Selby Plant and were extended to most of the other smelters during the next three years. In 1945 the Department of Hygiene was organized with Professor Philip Drinker of Harvard University as Director and with Dr. S. S. Pinto as Medical Director. The department is responsible for coordinating and maintaining a program for the good health of all employees from top management down to the lowest paid day worker. It is essentially a service organization serving all of the United States plants regardless of location or size. Full and part-time physicians employed in all of the company's American plants and working in close cooperation with the Medical Director are responsible for de- termining the state of health of all the employees and giving treatment when necessary. In general, medical care is confined to accidents or illnesses occurring while the men are on the job. Among the duties of the doctors is the making of careful physical examinations of new employees and routine check-ups of old employees. In addition to medical care a primary responsibility of the department is the prevention of occupational illnesses. In this the main concern is with the working environment in relation to its effect on the worker. Environmental factors may be dusts, fumes, gases, toxic materials, heat, humidity, radiation, or noise. The objectives are: (1) Immediate control of these factors through the education of the worker, through providing the wearing of respirators or other protective devices, and through careful medical examinations and regular analysis of urine specimens; (2) a long range control program which may be accomplished by local exhaust ventilation, wetting of materials, changes in metallurgy, changes in methods of handling, or by use of special devices and special equipment. To accomplish these objectives a fine industrial hygiene laboratory was built in Salt Lake City and equipped to do routine and experimental work. Trained and experienced industrial hygienists obtain the facts by making frequent hygiene surveys. These surveys include tests of the air, studies of all processes, and careful investigation of ventilation, lighting, and general working conditions. Except in emergencies, the air contaminants and often the substances handled by the worker are sent to the laboratory for analysis by chemists and technicians specially trained in industrial hygiene methods. The findings are evaluated in terms of limits recommended by various State and Federal agencies, and in light of all available medical data. The methods used for studying the working environment involve all of the usual chemical and physical procedures employed in industrial hygiene. The Impinger, electric precipitator, thermal pre-cipitator, and filter paper sampler have been used to collect atmospheric dust and fume samples. Of special interest here is the filter paper sampler, shown in Fig. 1, which was developed by Dr. Silver-man at Harvard University. The instrument has been improved and is used very extensively in field studies. A water manometer connected behind an orifice is used to determine the rate of air flow. Calibration is effected by use of a standard gas meter or rotameter. The dust or fume is collected on a filter paper clamped between two rings, as shown in Fig. 2. The filter paper, such as Whatman No. 52, collects both dust and fume with a very high efficiency. The instrument is very convenient and easily transported. The solids collected on the filter paper are analyzed in the laboratory usually by use of a polar-ographic procedure. By this procedure it is possible to measure quantitatively in a single analysis the

Jan 1, 1952

By C. B. E. Douglas

The following analysis was stimulated by a previous article on evaluation of the water problem at Eureka, Nev., which describes a method using formulas especially devised to calculate flow potential of extensive aquifers characterized by relatively even porosity and permeability throughout. The present discussion submits that the method was unsuitable for solving the kind of problem occurring at Eureka, where the amount of water available, rather than the flow potential, may have been the vital factor. IN an interesting article on evaluation of the water problem at Eureka, Nev.,1 W. T. Stuart describes how a difficult water problem, or one phase of it, may be evaluated by means of a small scale test. Test data are plotted by a method rendering, under certain conditions, a straight-line graph that can be projected to show how much the water table will be lowered by pumping at any specified rate for a given time. A formula is then used to determine the size of opening, or extent of workings, necessary to provide sufficient inflow to enable pumping to be maintained at that rate. At first glance this might seem the answer to a miner's prayer, but a word of caution is in order. It may not be the whole answer. Moreover, results obtained by the method described are reliable only for conditions approximating those assumed. Even where conditions do not meet this requirement, however, it may be possible to draw helpful inferences from the results, perhaps enough to facilitate another approach to evaluation of a problem. The two formulas Mr. Stuart used, the Theis formula and the one developed from it by Cooper and Jacob, were given field checks a number of years ago in valley alluvials by the Water Supply Div. of the U. S. Geological Survey and found to be reliable when the aquifer is very large in horizontal extent and sufficiently isotropic for the test well and observation wells to be in material of the same average permeability as the saturated part of the aquifer as a whole." Extensive valley alluvials, sands, and gravels can be evaluated in this way, and there are even cases in which the method could apply to porous limestones, such as flat beds of very large areal extent that have been submerged below the water table after extensive weathering. These are sometimes prolific sources of water for towns and industries. It is necessary for them to have been above the water table for some geologically long period of time in a fairly humid climate before submergence because the necessary high porosity and permeability, and large reservoir capacity, are the result of weathering, that is, of solution by the carbonic acid (H,CO3) in rainwater formed by the absorption of CO, from the air by raindrops, and this dissolving action must cease when all the H2CO3 has been consumed by re- action with the carbonate to form the more soluble bicarbonate. Consequently this weathering process is largely restricted to a zone that does not extend much below the water level, and submergence is necessary after the weathering to provide large reservoir capacity and good hydraulic continuity. On the other hand, water courses tend to form along faults and fractures in limestone, and to become enlarged by solution, well below water level when, as often happens, fresh meteoric water is circulated rapidly through them to considerable depth by hydrostatic pressure, as through an inverted syphon. Although the reservoir capacity of such water courses is relatively small they may extend far enough to tap more prolific sources. Cavities, and sometimes caves of considerable size, are found in limestones where the acid formed by the oxidation of sulphides has attacked them. This action can take place as deep below water level as surface water is carried by syphonic or artesian circulation, because the oxygen it carries in solution will not be consumed until it reacts with some reducing agent, such as a sulphide. Moreover, the formation of acid and solution of limestone in this way is not confined to the immediate vicinity of the sulphide. Oxidation of pyrite, for example, results in formation of acid in several successive stages, each taking place as more oxygen becomes available, as by the accession of fresh water into the circulation at some place beyond the sulphides. When the acid thus formed attacks the limestone, CO, is liberated and the ultimate effect of the complete oxidation of one unit of pyrite will be the removal of six times its volume of limestone as the sulphate and bicarbonate, both of which are relatively soluble. The reaction may be continued or renewed along a water course far from the site of the sulphides, where the small electric potential produced by contact with the limestone helped to start the reaction. Mr. Stuart refers2 0 caves in the old mining area in the block of Eldorado limestone southwest of the Ruby Hill fault at Eureka, Nev., and to the cavities encountered in drillholes in the downthrown block on the other side of the fault. Although he interprets these cavities as evidence that this formation was sufficiently isotropic (evenly porous and permeable) to give reliable results by the method he describes, they may, in fact, be entirely local conditions. There is reason to think they were probably formed

Jan 1, 1956

By C. T. Wei, A. Kelly

USING a recently developed X-ray method, reported by Schulz,2 it is possible to make a rapid survey of the perfection of a single crystal at a particular surface. This technique has the advantage of allowing a large surface of a specimen to be examined by taking a single photograph and it compares well with other X-ray methods in regard to sensitivity of detection of small angle boundaries. During the course of a survey of the perfection of large crystals of aluminum produced by a number of methods, an examination has been made of a number of single crystals produced from the melt using a soft mold (levigated alumina)." Crystals grown by this method are known, from an X-ray study carried out by Noggle and Koehler,3 to contain regions where they are highly perfect. In the present work, it has been possible to obtain photographs showing directly the distribution of low angle boundaries at a particular surface of these crystals. single crystals were grown from the melt using the modified Bridgman method with a speed of furnace travel of -1 mm per min. These were about 1/10 in. thick, 1 in. wide, and several inches long. The metal was 99.99 pct pure aluminum supplied by the Aluminum co. of America. The crystals were examined by placing them at an angle of about 25° to the X-ray beam issuing from a fine focus X-ray tube of the type described by Ehrenberg and Spear4 and constructed by A. Kelly at the University of Illinois. A photographic film was placed SO as to record the X-ray reflection from the lattice planes most nearly parallel to the crystal surface. The size of the focal spot on the X-ray tube was between 25 and 40 u, and the distance from the X-ray tube focus to the specimen (approximately equal to the specimen to film distance) was -15 cm. White X-radiation was used from a tungsten target with not more than 35 kv in order to reduce the penetration of the X-rays into the specimen. Exposure times were approximately 1 hr with tube currents between 150 and 250 microamp. The type of photograph obtained from these crystals is illustrated in Fig. 1, which shows a number of overlapping reflections from the same crystal. The large uniform central reflection is traversed by sets of horizontal white and dark lines. These two sets run mainly parallel to one another. Lines of one color are wavy in nature and often branch and run together. Large areas of the crystal surface show no evidence of these lines whatsoever. The lines are interpreted as being due to low angle boundaries in the crystal, separating regions which are tilted with respect to one another. A white line is formed when the relative tilt forms a ridge at the interface and a black line is found when a valley is formed. In a number of cases, the lines stop and start within the area of the reflection and often run into the reflection from the edge, corresponding to a low angle boundary starting from the edge of the crystal. The prominent lines run roughly parallel to the direction of growth of the crystal although narrow bands can run in a direction perpendicular to this; see Fig. 2. Although they may change their appearance slightly, the lines tend to occur in the slightly,Same place in the X-ray image and to maintain their rough parallelism when the crystals are reduced in thickness by etching. Thus the low angle boundaries can occur at any depth within the crystal. The appearance of the lines is unaffected by subjecting the crystal to rapid temperature changes, such as plunging into liquid nitrogen or rapid quenching from 620°C. From the width of the lines on the x-ray reflection, values can be found for the angular misorienta-tion of the two parts of the crystal on either side of a boundary. The values found run from 1' to 10' of arc, but values of UP to 20' have sometimes been found, e.g., the widest lines on Fig. 2. These mis-orientations are much less than those commonly found in crystals possessing a lineage structure. When a number of a and white lines occur, running in a roughly parallel direction across the image of a Crystal, the total misorientation corresponding to lines of one color is approximately equal to that corresponding to lines of the other color. The interpretation of the lines as due to low angle boundaries has been checked in a number of ways. Photographs taken with different specimen-to-film distances distinguish lines due to low angle boundaries from effects due to surface relief of the specimen. Normal Laue back-reflection photographs, taken with the beam irradiating an area of the surface showing a number of the lines, show white lines running through each Laue spot. Black lines are set to see by this method. X-ray photographs were also taken, using the set-up described by Lam-one et al.5 when the beam straddles regions giving rise to lines in the Schulz pattern, split reflections are observed within the Bragg spot. The misorienta-tions calculated from the separation of these reflections and that found from the widths of the lines on the schulz technique patterns show good agreement. An exposure was made with Lambot technique of an area of the crystal showing no evidence of low angle

Jan 1, 1956

By M. R. J. Wyllie, F. Morgan, P. F. Fulton

The importance of formation factor, F, not only in electric logging but as a fundamental rock parameter has recently been stressed.',: The desirability of investigating the range of variation of the resistivity index exponent, n, in the relationship I = S ;", where I is the resistivity index and Sw the water saturation as a fraction of the void volume of a porous medium, has also been urged.3 The magnitude and variation of n with saturation and rock texture is a subject not only of theoretical interest but also one of prime importance in the interpretation of electric logs. A simple technique has recently been developed which enables both F and u to he measured with high accuracy and which may also find acceptance as a convenient method for the determination of irreducible saturation attainment in the restored state method of core analysis. Experience has taught that reproducible measurements of F are possible only if the resistance measuring electrodes are so arranged with respect to a plane face on a porous medium that they are able to make electrical contact with substantially all entry pores in that plane. In practice this may be achieved by using a platinized-platinum gauze electrode backed by some absorbent material (such as felt) which has been saturated with a fluid identical with that used to saturate the porous medium. Applicatiorl of pressure to the electrode and absorbent material then forces the gauze against the plane face of the porous medium and simultaneously squeezes saline solution through the meshes of the gauze. By this means the electrode is in continuous aqueous contact with all pores and satisfactory and reproducible low resistance contact with the porous medium is achieved. Clearly this method, although satisfactory for measurements of F, cannot be applied to the making of continuous resistance measurements on a porous medium while capillary pressure desaturation is being carried out. However, accepting the principle that for satisfactory results electrical contact must be made between a measuring electrode and all pores adja- cent to that electrude, methods of bringing electrodes into intimate contact with the surfaces of porous media were investigated. Two methods were ultimately found to be satisfactory: in the one, the metal electrode is formed on the required portion of the porous medium by the use of a metal spray gun, while in the second the electrode is painted on with an ordinary camel's hair brush. The first method has the advantage of permitting the use of any metal which can be sprayed, but has the disadvantage of requiring rather elaborate and expensive equipment. The second method is presently limited to silver electrodes although in principle other metals, e.g. platinum or gold, could be used. Moreover, the method is so simple and cheap, and has been found to be so satisfactory that it will be described in some detail. The core being investigated is cut into a right circular cylinder and is extracted and dried in the usual manner. The ends are then lightly painted with silver conducting paint* of the type used in printed electrical circuits. The quantity of paint used is not critical but the recommended, minimum compatible with entirely coating the core ends is recommended, particularly on the end that contacts the barrier. The core is then dried at atmospheric temperature for one hour or for shorter periods at any suitable elevated temperature up to about 110°C. It will be found that silver coatings so prepared are not only strongly adherent but also permeable and the core may be the core may be desaturated by the ordinary capillary pressure technique through one of the coated faces. The same permeability is characteristic also of thin metal coatings formed using the spray-gun technique. An ordinary Lucite capillary pressure desaturation cell has been adapted to a form suitable for measuring the resistivity of the saturated silver faced cores both at 100 per cent saturation (i.e., F) and at intermediate saturations down to the irreducible minimum. This has been achieved as follows: A Coors porcelain barrier, having a displacement pressure of c 30 psi was grooved across a diameter. Dimensions of this groove were c 1 mm deep and 1 mm wide at the top. The groove was then painted thickly with silver conducting paint, the paint in the groove being extended lightly over the edges of the groove for a distance of c 1 mm on each side. A 30 gauge silver wire was then arranged in the groove in a form of a spring bow, each end of the silver being held at diamet~ically opposite ends of the groove by means of plastic cement. The arc of the bow at its highest point was arranged to be a millimeter or so above the face of the barrier, while one end of the bow wire was led by means of a pressure-tight connection through the wall of the capillary pressure cell. The groove in the barrier was then Surrounded by suitably cut portions of Kleenex in the conventional manner so as to ensure capillary continuity from core to barrier, and the core placed on the barrier. The weight of the core distorted the silver spring bow and good electrical contact was thereby made between the outside of the cell and the lower painted silver electrode. Electrical connection to tile top painted silver

Jan 1, 1951

By M. R. J. Wyllie, F. Morgan, P. F. Fulton

The importance of formation factor, F, not only in electric logging but as a fundamental rock parameter has recently been stressed.',: The desirability of investigating the range of variation of the resistivity index exponent, n, in the relationship I = S ;", where I is the resistivity index and Sw the water saturation as a fraction of the void volume of a porous medium, has also been urged.3 The magnitude and variation of n with saturation and rock texture is a subject not only of theoretical interest but also one of prime importance in the interpretation of electric logs. A simple technique has recently been developed which enables both F and u to he measured with high accuracy and which may also find acceptance as a convenient method for the determination of irreducible saturation attainment in the restored state method of core analysis. Experience has taught that reproducible measurements of F are possible only if the resistance measuring electrodes are so arranged with respect to a plane face on a porous medium that they are able to make electrical contact with substantially all entry pores in that plane. In practice this may be achieved by using a platinized-platinum gauze electrode backed by some absorbent material (such as felt) which has been saturated with a fluid identical with that used to saturate the porous medium. Applicatiorl of pressure to the electrode and absorbent material then forces the gauze against the plane face of the porous medium and simultaneously squeezes saline solution through the meshes of the gauze. By this means the electrode is in continuous aqueous contact with all pores and satisfactory and reproducible low resistance contact with the porous medium is achieved. Clearly this method, although satisfactory for measurements of F, cannot be applied to the making of continuous resistance measurements on a porous medium while capillary pressure desaturation is being carried out. However, accepting the principle that for satisfactory results electrical contact must be made between a measuring electrode and all pores adja- cent to that electrude, methods of bringing electrodes into intimate contact with the surfaces of porous media were investigated. Two methods were ultimately found to be satisfactory: in the one, the metal electrode is formed on the required portion of the porous medium by the use of a metal spray gun, while in the second the electrode is painted on with an ordinary camel's hair brush. The first method has the advantage of permitting the use of any metal which can be sprayed, but has the disadvantage of requiring rather elaborate and expensive equipment. The second method is presently limited to silver electrodes although in principle other metals, e.g. platinum or gold, could be used. Moreover, the method is so simple and cheap, and has been found to be so satisfactory that it will be described in some detail. The core being investigated is cut into a right circular cylinder and is extracted and dried in the usual manner. The ends are then lightly painted with silver conducting paint* of the type used in printed electrical circuits. The quantity of paint used is not critical but the recommended, minimum compatible with entirely coating the core ends is recommended, particularly on the end that contacts the barrier. The core is then dried at atmospheric temperature for one hour or for shorter periods at any suitable elevated temperature up to about 110°C. It will be found that silver coatings so prepared are not only strongly adherent but also permeable and the core may be the core may be desaturated by the ordinary capillary pressure technique through one of the coated faces. The same permeability is characteristic also of thin metal coatings formed using the spray-gun technique. An ordinary Lucite capillary pressure desaturation cell has been adapted to a form suitable for measuring the resistivity of the saturated silver faced cores both at 100 per cent saturation (i.e., F) and at intermediate saturations down to the irreducible minimum. This has been achieved as follows: A Coors porcelain barrier, having a displacement pressure of c 30 psi was grooved across a diameter. Dimensions of this groove were c 1 mm deep and 1 mm wide at the top. The groove was then painted thickly with silver conducting paint, the paint in the groove being extended lightly over the edges of the groove for a distance of c 1 mm on each side. A 30 gauge silver wire was then arranged in the groove in a form of a spring bow, each end of the silver being held at diamet~ically opposite ends of the groove by means of plastic cement. The arc of the bow at its highest point was arranged to be a millimeter or so above the face of the barrier, while one end of the bow wire was led by means of a pressure-tight connection through the wall of the capillary pressure cell. The groove in the barrier was then Surrounded by suitably cut portions of Kleenex in the conventional manner so as to ensure capillary continuity from core to barrier, and the core placed on the barrier. The weight of the core distorted the silver spring bow and good electrical contact was thereby made between the outside of the cell and the lower painted silver electrode. Electrical connection to tile top painted silver

Jan 1, 1951

By Robert T. Ault

The nature of fracture in unnotched tensile and notched tensile sheet and round specimens and V -notched and precracked Charpy-type sheet specimens of both wrought stress -relieved and re-crystallized molybdenum was investigated over the temperature range of -78° to 300°C. The sharp rise in fracture stress, for unnotched tensile samples, as the temperature is increased above the brittleness transition temperature (Tb), is found to be a result of an increase in flow stress due to plastic constraint and an increased strain rate which results from the onset of necking at Tb . Quasi-brittle fracture in notched tensile samples is found to occur when the tensile stress at the elastic-plastic interface, beneath the root of the notch, reaches a maximum critical value, which is independent of test temperature over the range from —78° to 25°C, but dependent on microstructure. In the temperature range between 150° and 300°C, unnotched tensile and notched tensile samples alike are found to fracture by a ductile fibrous tearing process which is discontinuous in nature, as a result of the competition between the processes of tearing, through continued plastic flow, and local work hardening. Results from the V-notched and fatigue-cracked Charpy-type impact tests demonstrate that crack initiation is the governing factor in the low-temperature (-78° to 25°C) fracture process for molybdenum. In recent years, there has been considerable interest, and a commensurate number of investigations, concerning the duc tile-to-brittle transition in refractory metals. There has not developed, however, a satisfactory explanation for the uniaxial tensile fracture-stress transition which accompanies the well-known ductility transition. This matter therefore warranted investigation. In a similar manner, the increased importance of notched tensile strength values in evaluating materials and in design criteria requires a better understanding of the factors which control the fracture behavior of notched tensile samples. In a previous investigation1 of the nature of initial yielding and fracture in notched sheet molybdenum at room temperature, it was suggested that plastic constraint was the controlling factor in governing the fracture behavior of notched samples. The final portion of this investigation was concerned with the fracture toughness of molybdenum. Of particular interest was the comparison of effective surface energies for fracture in V-notched samples with fatigue-cracked, Charpy-type samples in order to ascertain the relative importance of the initiation and propagation phases of the fracture process. MATERIALS AND TEST PROCEDURE Sheet tensile, notched tensile, and V-notched Charpy specimens were prepared from 50-mil, stress-relieved molybdenum sheet.* Half of these specimens were vacuum-annealed for 1 hr at 1200°C and 7.5 x l0-5 Torr and furnace-cooled to produce a relatively uniform grain size of 0.30 mm diameter. Round notched and unnotched tensile specimens were prepared from warm-rolled and swaged 5/8-in.-diam bar.* These specimens were vacuum-annealed for 1 hr at 1350°C and 5 x lom5 Torr and furnace-cooled to produce a grain diameter of 0.11 mm. Material analyses in ppm were: C N O H Sheet 290 10 4 1 Bar 50 30 30 2 The unnotched tensile sheet specimens had a 1/4-in. gage width and a 1-in. gage length. The unnotched tensile round specimens had a 9/32-in. gage diameter and a 1-1/4-in. gage length. The sheet and round notch tensile specimens are shown in Fig. 1. All of the notched tensile specimens tested were tandem-notched in order to study the location and mode of fracture initiation. The tandem-notched specimens were carefully machined so that the largest variation in notch depth on a single specimen was 0.001 in. Thus, when fracture occurs, the extent of plastic deformation that exists in the un-fractured notch section is that which exists just prior to fracture. All of the tandem-notched sheet specimens were electrolytic ally polished and chemically etched prior to testing. The V-notched Charpy-type specimens machined from the 50-mil sheet material had the standard dimensions of 2.125 in. long, 0.394 in. deep, and a 0.010-in. root radius. The unnotched tensile and notched tensile tests were conducted over the temperature range of -78° to 300°C, in a 10,000-lb Instron Universal Testing Machine, at a constant crosshead speed of 0.020 in. per min. The V-notched Charpy-type

Jan 1, 1964

By J. Lewis, J. Harper, M. F. Ashby

A grain boundary in a metal interacts with second-phase particles, which exert a pinning force (first estimated by Zener) on the boundary opposing its motion. We have computed the shape of boundaries which interact with more or less spherical second-phase particles and have constructed a soap-film model to reproduce the shape of the boundary surface. An important result is that measurement of this shape allows the pressure, or driving force, on the boundary to be measured. We hare applied this technique to grain boundaries in two alloys and hate measured the pinning force exerted by single second-phase jwrticles on the boundaries. It is in good agreement with Zener's estimate. J\. boundary between two grains, or two bulk phases, interacts with small inclusions or particles of a second phase, whether they are gas or solid. This interaction means that the boundary, forced to migrate by a difference in free energy between the material of the two grains or phases which it separates, exerts a force on a particle which it touches, tending to drag it forward. (The movement of inclusions through metals under the influence of this force, has, in fact, been observed. 1-3) Equally, the particle can be thought of as exerting a pinning force on the boundary, tending to hold it back. Zener (in a celebrated private communication4) first realized that this interaction, and the resulting pinning force, existed. His calculation of its magnitude was crude but adequate: a spherical inclusion of radius r blanks off an area nr2 of the boundary on which it sits; since the boundary has an energy of rMM x per unit area, the blanlung-olf decreases the energy of the system by MM: this energy is returned to the system if the boundary is pulled free from the inclusion— a forward movement of the boundary by a distance r will do this—so that the maximum pinning force is Trrym.M- A similar argument can be made for inter-phase boundaries. The nature of the particle itself did not enter this, or two subsequent treatments.5,6 When it is considered, tic leifthe energyoftheb a) The boundary may enter and pass through the particle if the energy of the boundary is lower within the particle than in the matrix. Fig. l(r/). Certain coherent precipitate particles behave like this. h) More usually, the boundary will bend round the particle, enveloping and bypassing it. Fig. l(b). In doing so, it changes the structure and energy of the interface between the particle and its matrix. This means that the boundary does not touch the particle surface at right angles, as early treatments assumed,5'9 but at some angle a which depends on this change in surface energy of the particle, and can be calculated from the equilibrium of surface tensions. Most precipitate particles and inclusions behave like this. Gas bubbles or liquid drops can be regarded as belonging to either group. The progress of bypassing is conveniently measured by the angle shown in Fig. 1. When the nature of the particle is ignored, its maximum pinning force is exerted when - 45 deg. When it is considered, this critical value of is found to depend on a and thus on the nature of the particle. The maximum pinning force lies between nryMM and 2jtjMM (Appendix 1). not very different from Zener's result. In reality, a boundary between crystals has a specific energy and tension which varies with the orientation of the boundary. Furthermore, recent experiments7 indicate that such a boundary is not atom-ically smooth, but has steps on it: migration of the boundary corresponds to the sweeping of these steps across the boundary surface, like the Frank model of crystal growth from the vapor. This means that the interaction of a boundary with particles should really be considered in terms of the way in which particles hinder the movement of these steps. To suppose a grain boundary or interphase boundary to be smooth, and to ignore the variation of its energy with orientation, is to liken it to a soap film. The advantage of this soap film approximation, which we have used throughout this paper, is that interaction energies and boundary shapes can be calculated easily. We have done this by numerical computation and by using a soap film model, and have compared the results with grain boundaries in an aluminum-based and a copper-based alloy. It turns out that the shape of the boundary which bulges between particles allows the pressure an it to be calculated; that is, the local driving force an the boundary can be measured. This has allowed us to check the Zener relationship experimentally.

Jan 1, 1970

By H. W. Meyer, H. N. Lander, F. D. Delve

A method of calculating the changes in blast-furnace performance brought about by burden and/or blast modifications is presented. Essentially the method consists of three simultaneous equutions derived from materials and heat balances. These equations can be used not only to evaluate quantitatively the effect of changes in process operating variables on furnace performance, but also to provide a useful means of evaluating changes in process variables which cannot be measured directly. It has been customary for a number of years to use simple heat and materials balances as a basis for assessing blast-furnace practice. A good example of the method used to set up these balances is that proposed by Joseph and Neustatter.1 This approach to process assessment has limited utility, however, in that it cannot be used to predict the furnace coke rate or production under new operating conditions. Using an approach based on multiple correlation of blast-furnace variables, R V. Flint2 has developed an equation which may be used to predict the change in coke rate that will result from some changes in operating conditions with a reasonable degree of accuracy. Although this equation has useful applications in production planning, it cannot be used to study the relationships between the operating variables and the fundamental thermochemi-cal characteristics of the process. In attempting to analyze the blast-furnace process quantitatively, the idea of dividing the furnace into zones3 may at first appear attractive. In our present state of knowledge, however, it is not possible to define with any accuracy the physical limits of such zones in relationship to their temperatures or to the reactions which may occur in them. Although its application is restricted, the zonal approach to blast-furnace analysis is useful in some instances. For example, the change in the calculated flame temperature in the "combustion zone" caused by injecting steam constitutes information which is helpful in understanding why the addition of steam to the blast is best accompanied by an increase in blast temperature. The zonal approach cannot, at the present time, be used to establish the relationships between process variables and process performance if the whole process rather than part of it is to be considered. One of the earliest approaches to the problem of relating blast-furnace operating variables to pro- duction and coke rate was that developed by Marshall.4 Essentially Marshall's work showed that it was possible to estimate the performance of a furnace by solving three simultaneous equations which consisted of rudimentary carbon and heat balances plus a further equation relating the production, wind rate, and the carbon burned at the tuyeres. Although these equations did not include all of the chemical and thermal variables of the process, their derivation and application seems to be the earliest attempt which achieved any success in relating prior furnace operating data to the calculation of furnace performance under different blast conditions. Work carried out in Germany has been directed mainly towards prediction of coke rates using material and thermal balances rather than statistical methods. wesemann5 used prior furnace operating data as part of the basis for predicting the change in coke rate accompanying a change in burden composition. This author employed a method of successive approximations to estimate the secondary changes in slag volume and stone rate brought about by the change in coke rate. The most recent analysis, which seems to have been developed concurrently with the thermochemical model presented in this paper, has been described by Georgen.6 This author has succeeded in improving on Wesemann's approach by expressing the total changes in the slag volume and stone rate in terms of the change in coke rate itself. This is accomplished in a manner similar to that used in the thermochemical model described in this paper. Although Georgen makes use of a calculated furnace heat loss, he does not relate the heat loss per unit of hot metal to the production rate as is done in the present work. Georgen's approach may be used to calculate the changes in materials requirements accompanying changes in furnace operation; it cannot be used to assess the resulting changes in production. The fact that blast-furnace behavior can be interpreted by consideration of the heat requirements of the process was demonstrated by Dancy, Sadler, and Lander.7 In the analysis of blast-furnace operation with oxygen and steam injection these authors showed that it was possible to account for the changes in production and coke rate

Jan 1, 1962

By Charles L. Mantell, Kurt Straler

The hydrogen reduction of Cr2O3 to chromium metal was found to be feasible at very low water-vapor concentrations, corresponding to dew points of -38° to -24°C, over a temperature range of 1130" to 1490°C. Hydrogen reduction under these conditions was predicted by the calculated equilibrium curves which also indicated that CrzOs is reduced directly to chromium without forming the intermediate oxide, CrO. This reduction path was confirmed by X-ray diffraction analysis. The percent reduction of Cr2O3 at each reaction temperature was constant with time, suggesting an inhibiting effect of water vapor. A small increase in the residual water-vapor concentration of a single temperature, 1490°C, strongly retarded the rate of reduction This effect was expressed by an empim'cal equation which indicated a direct relationship between "distance from equilibrium" and the rate of reduction. me effect of temperature over the range of 1130" to 1490°C was expressed in an Arvhenius plot of log rate vs reciprocal absolute temperature. From this curve the apparent enthalpy of activation was found to be 29,600 cal. Based on the hypothesis that the rate of reductiun is contvolled at the oxide-metal interface, an over-all rate equation consistent with the experimental data and the thery of absolute reaction rates was formulated. A simplification of this expression to an Arrhenius equation was justified by the overriding effect of temperature on the rate of reaction for the minimum water-vapor concentration range. MOST of the metals in Subgroup V1 of the periodic table can be prepared commercially by direct reduction of their oxides by hydrogen or carbon monoxide, at temperatures considerably below the melting points of both the metals and their oxides. Chromium is an exception, being generally reduced from its ore, Cr2O3 . FeO, by silicon in an electric arc furnace which operates above the melting point of the Fe-Cr alloy or above the melting point of chro- mium if a chromium oxide be the starting material. In reduction of chromium oxide by hydrogen, either reduction does not occur at all or the rate of reduction is extremely slow. Theoretical considerations based on the high, exothermic, free energy of formation of Cr2O3 compared to the oxides of the other Subgroup VI metals, molybdenum, tungsten, and uranium, would also suggest a slow rate of reaction and a high activation energy. Interest in the direct gaseous reduction of fine-powdered ores in fluidized beds was considered justification for examination of this reaction. In order to develop a basis for a continuing study of the commercial feasibility of the direct gaseous reduction of chromite, a study of the kinetics of the reduction of Cr2O3 with hydrogen was undertaken. To the authors' knowledge no accurate kinetic data for this reaction have been obtained. Neither has an activation energy been determined nor has an attempt been made to establish a mechanism of reaction. LITERATURE Maier10 compared the data of I. Y. Granaat,6 H. von Wartenburg and S. Aoyama, and G. Grube and M. Flad7 with that derived from calorimetric and ther-modynamic properties for the equilibria for the reduction of Cr2O3 with hydrogen. These results, plotted as the log of the equilibrium constant vs absolute temperature for the reduction of Cr2O3 and the intermediate oxide, CrO, to chromium, show agreement between the differently derived data. In both cases the equilibrium constants were extremely low. Maier showed that, over a temperature range of 1000° to 2000°K, Cr2O3 is more readily reducible than CrO. Granat assumed that CrO was preferentially formed from Cr2o3 above 1100°C. Grube and Flad's analysis of their reaction products in the 895" to 1000°C range indicated the coexistence of only Cr2O3 and chromium. The hydrogen reduction of the other Subgroup VI metals, molybdenum, tungsten, and uranium, shows that reduction of the higher oxide proceeds through all of the intermediate oxides before being reduced to the metal. Since evidence pointed to an anomaly in the reduction behavior of Cr2O3, the authors investigated the reduction path of Cr2Os.to chromium. This was done theoretically with more recently available free-energy data and experimentally by X-ray diffraction analysis. This work reinforces Maier's conclusion.

Jan 1, 1964

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By C. E. Brukl, E. Rudy, St. Windisch

The ternary-alloy system Nb-Mo-C was investigated by means of X-ray, melting point, DTA, and metallo-graphic techniques; a complete phase diagram for temperatures above 1500°C was established. Above 1960°C, niobium monocarbide and the cubic (Bl) high-tenzperature phase in the Mo-C system form an uninterrupted series of solid solutions. The ternary range of the pseudocubic q MoCl-, is very restricted. Dimolyb-denum carbide dissolves up to 44 mol pct Nb2C (2240°C), whereas the maximum solid solubility of MO2C in Nb2C does not exceed 5 mol pct. The order-disorder transformation temperatures in Mo2C and Nb2C are lowered by the mutual metal exchanges. Six invariant (p = const) reactzons occur in the ternary system; three correspond to class 11-type four-phase reactions involving a liquid phase, one to a class I (eutectoid)-type, and two further isotherms are associated with limiting tie lines. The results of the Phase diagram investigation are discussed, and the thermodynamic interpretation identifies the low relative stability of the binary sub-carbides in conjunction with the large stability diflerences between niobium and molybdenum carbides as the cause for the formation of a stable equilibrium between the monocarbide and the metal phase in the ternary reson. Due to their refractoriness, the carbides of the high-melting transition metals have received increased interest in recent years as base materials in composite structures for aerospace applications at high temperatures and for the development of self-bonded cutting tool materials; other novel fields of application include power reactors, where operation at high temperatures becomes essential for attaining high power efficiencies. In these applications, the increased reaction rates at high temperatures require a close consideration of the chemical interactions between the alloy constituents. As a consequence, a detailed knowledge of the phase relationships in the alloy systems is required in order to provide a sound basis for developmental -type work. Partly as a result of the considerable experimental difficulties associated with the investigation of this high-melting alloy class, no complete studies of ternary metal-carbon systems have been performed until recently. Even the high-temperature phase relationships in the binary transition metal-carbon systems have been delineated only during the past few years to a degree of accuracy required for a more detailed study of ternary or higher-order alloys. In recent investigations of binary and ternary systems of refractory transition metals with carbon, boron, and silicon,&apos; alloys from the ternary systems Nb-Mo-C became of interest because of the demonstrated possibility2,3 of obtaining compatible composites based on metal + monocarbide combinations. In the meantime, however, studies in other, but related, ternary metal-carbon systems, such as Ta-W-C, have shown that the solid-state equilibria may change significantly toward higher temperatures (>2000°C), and that extrapolations based on low-temperature equilibrium data are, in general, not very reliable. Although the lower-temperature (<2000°C) phase relationships in the Nb-Mo-C system are similar to those found in Ta-W-C, a cursory thermodynamic analysis of the equilibria indicated4 that complete solid-solution formation between Mo2C and Nb2C should not occur at higher temperatures. The present work was conducted in order to experimentally verify these expectations and, in addition, to provide phase equilibrium data in the melting range of the alloys. In the boundary systems, niobium and molybdenum are known to form a continuous series of solid solutions.576 The continuous solubility was also confirmed by Kornilov and Polyakova,7,8 who also observed a minimum melting point at 22 at. pct Mo and 2345°C. The phase diagram investigations of the Nb-C system by Storms and Krikorian9 and Kimura and Sasaki10 were recently supplemented by Rudy et al.11,12 The system contains a high-melting monocarbide with the B1 structure, Table I, and a subcarbide, Nb2C, which exists in at least two different states of sublattice order at low temperatures47"-&apos;3 and a disordered state above approximately 2500°C.11,12 The melting-point measurements by Rudy et al .11,14 are in close confirmation of the data by Kimura and Sasaki.10 The rather complex phase relationships in the Mo-C system were only recently Clarified.15,18 The system is characterized by three congruently melting, intermediate phases, MozC, ? MoC1-x and a Mol-,, Table I, of which only Mo2C is stable at temperatures below 1650°C. Substoichiometric MozC exists in several states of sublattice order which interconvert in homogeneous phase transitions. Hyperstoichiometric compositions cannot exist in the ordered state. Upon cooling through a critical temperature range, the

Jan 1, 1968

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole&apos;&apos;) and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-&apos;) is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-&apos; using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- &apos; torr, Maiya and lakel measured y as 39 kcal mole-&apos; using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-&apos;: there is evidence also for a low temperature value of about 20 kcal mole-&apos;. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.&apos;-&apos;&apos; Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A&apos;, C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2&apos;3 M = mass of an evaporating molecule

Jan 1, 1970

By Lee Hillard Meltzer, Ralph E. Davis

INTRODUCTION During the past few years emphasis has been placed upon methods of estimating the future expectancy of gas production from natural gas fields. Before technical methods were applied, the production expectancy over future years was based upon the knowledge of gas well behavior, learned through long experience and embedded in the "know-how" of men long in the gas producing business. It is doubtful that a technical study of future expectancy of a gas field or a group of fields was ever prepared for the preliminary planning of a natural gas pipe line system built prior to about five years ago. The decline in well production capacity was naturally recognized by all familiar with the business since its earliest beginnings more than 75 years ago. In 1953, the Bureau of Mines published Monograph Number 7, "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices," which gave to the industry the first technical analysis of the decline in production of individual gas wells. This method affords a means of estimating the future production in relation to decline in reservoir pressure. The demand for technical determination of expectancy of future gas productivity from fields or a group of fields led technical men to the application of the knowledge of well behavior to the problems. The decline in a well&apos;s ability to produce as pressures declined could be estimated by the use of the curve known as the "back-pressure potential curve" as developed by the Bureau of Mines. A field containing few, or even numerous, wells could be analyzed on the basis of the sum of potentials of all wells. In most studies of this nature, the problem is to estimate the rate of production that can be expected, not only from present wells but also, from wells that will in the future have to be drilled into the reservoir being studied. The "back-pressure potential" method requires that the following data be known or estimated: (1) Proved gas reserves. (2) Current shut-in pressures and rate at which shut-in pressures change with production. (3) Back pressure potential data on wells in the source of supply. (4) Ultimate number of wells which will supply gas, and their potential. (5) Limitations on productivity such as line pressures against which the wells will produce, friction drop in the producing string, and so forth. It is evident that the resulting estimate of gas available in each year for a future of say, 20 years, contains many uncertainties. While the method may have considerable merit for a field that is fully developed, it cannot be completely dependable in fields that are only partially developed. In such cases, some of the data upon which it is based can only be estimated or assumed. In the study of this problem during the past few years, a method has been developed which we believe has great merit, especially when applied to fields subject to substantial future drilling, and when applied to the study of fields which, on the average, appear to have characteristics similar, in general, to the average of the fields used in the development of the "yardstick" outlined herein. From an analysis of the production history of 49 reservoirs which are depleted, or nearly depleted, a curve has been constructed which shows the average performance of the reservoirs during the declining stages of production. When properly applied, this "average performance curve" can be used to determine the stage of depletion at which a reservoir or group of reservoirs will no longer be able to yield a given percentage of the original reserves. "AVAILABILITY" AND "AVAILABILITY STUDIES" The rate at which. a reservoir will yield its gas depends basically upon physical factors, such as the thickness and permeability of the sand, the effect of water drive, if any, and other conditions, and upon economic factors, such as the number of wells drilled. Within the ranges set by the physical conditions, a rate of delivery tends finally to become established. The rate (or range of rates) represents a balance between the interests of the operator, who desires the maximum return from his property and of the pipe line owner, who desires to maintain a firm supply for his market. This balance, which is influenced by the terms of the contract, determines the capacity which will be developed by the operator, and the time and rate at which the decline in production is permitted to occur. Thus the "availability" of gas

Jan 1, 1953