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By Tong Guangxu

INTRODUCTION Throughout the world, the caving mining methods of ore-draw under the overlying waste rock are sublevel caving in Sweden, block caving in U.S.A. and forced block caving and sublevel caving with sill-pillar in U.S.S.R. These caving methods are of high efficiency, low cost and large production (especially the block caving method) when compared to opencast mining. From the ore production of all under- ground mines, the largest annual production of underground metalliferous mines in the world is caving methods. The sublevel caving in Kiruna Iron Mine of Sweden has reached annual ore production over 20 million tons in 1974. The block caving in Climax Molybdenum Mine and San Manuel Copper Mine of U.S.A. both have produced about 40 thou- sand tons of ore per day in 1971. At the same time, the productivity of Kiruna was 12 thousand tons of ore per man-year, Climax 42.8 tons (48.3 short tons) per man-shift and San Manuel 29.01 tons (32.1 short tons) per man-shift. The main feature of this group of mining methods is the underground extraction of ore from beneath overlying caveable waste rock. Since the loss and dilution of ore are inherent (sometimes to a great extent), the control of ore-draw in these methods as com- pared with other methods is very important. Consequently, concerned Universities and Research Institutes have devoted great amounts of research on ore-draw theory and control management which has provided positive results to mine production, and has apparently promoted the development of the caving methods. During 1979 in China, metalliferous underground mines accounted for 15.22% of the total iron ore produced, while also accounting for 56% of total non-ferrous production. According to the mining methods, sub level caving in the principal underground iron mines counted for about 56.74% of total principal underground iron mine production, but only about 1% of total non-ferrous underground mine production. Relative to forced block caving and sublevel caving with sill pillar, the Chinese non-ferrous under- ground mines estimated about 35% of total non-ferrous underground mine production from these two methods, mainly from the latter. From the trend of development of underground metalliferous mines in China, the percentage of production in caving will be increased in the future, especially in block caving and forced block caving which have already been given great attention in the mining circle. In these types of mining methods the ore is drawn from the stope under a large area of overlying waste rock, which complicates the basic regulation and control of ore-draw, but provides lower loss and dilution than sublevel caving. Because of these reasons, the Kiruna Iron Mine in Sweden is intending to change its sublevel caving by testing a sublevel shrinkage caving method and considering a large area of ore-draw beneath the stope as an advantage. Therefore, the basic regulation and control management of ore-draw under a large area, as practiced in China, will be discussed in this paper. BASIC REGULATION OF ORE- DRAW FROM CAVING STOPE The aim of studying ore-draw under a large area of overlying waste rock is to se- cure a planned draw schedule that guarantees a certain plane of interface between ore and waste rock, and controls the change of its shape in spatial position for reducing ore loss and dilution during the draw process. Presently, the ellipsoid theory is comparatively near the actual attitude of ore-draw from the cave. 1. Ore Drawn Out from Single Drawpoint Laboratory testing and practical experience all show that after a certain amount of ore has been drawn out from a drawpoint, its original shape in the stope before drawing is more or less similar to an ellipsoid, hence the name "draw ellipsoid." This draw ellipsoid is cut at the bottom by a horizontal plane corresponding to the raise of the drawpoint, and its volume can be calculated by the following formula:

Jan 1, 1981

By J. N. Breston, R. V. Hughes

Conclusions drawn by previous research workers with reSPect to the relation between Pressure gradients and/or velocity and oil recovery obtained by laboratory water flood tests have been in disagreement probably due to variable procedures and unnatural conditions and materials. The Bradford Laboratory of the Pennsylvania Grade Crude Oil Association as part of its secondary recovery research program has conducted nineteen water floods on two long cores of widely differing characteristics in an attempt to clarify this relationship and make it an aid in predicting flooding pressures in the field. Unlike previous research procedures the present experiments were conducted with the aim of duplicating field conditions as closely as possible by using long unextracted consolidated cores, a live crude, and natural brines for both flooding and, connate water content. Also, the pressure gradients and flooding velocities were representative of field conditions where similar sands were being flooded. Eleven floods on one core and eight floods on the other core showed increased recoveries and lower residual oil saturation with increased flood pressure gradients and flood velocities. A marked decrease in recovery was obtained from both cores at very low flood velocities. This pressure versus recovery relationship is shown to hold up to the point of water breakthrough and also up to the 100 and 1 produced water to oil ratio point. INTRODUCTION The possibility of water flooding oil sands was suggested by Carl1 of the Pennsylvania Geological Survey in 1880. It is not known when the practice was tried intentionally for the first time, but its beneficial effects were noted in the annual production rate of the Bradford field as early as 1907. The practice was illegal in Pennsylvania until 1921. Early water floods in the Bradford field usually consisted of shooting or splitting the casing secretly to permit subsurface waters to enter the producing sands under hydrostatic head. As it was noted that the benefits of water flooding seemed to be proportional to the quantity of water dumped into the well many also began to utilize surface sources after the practice became legal. It was probably during the middle 20's before many producers realized that the pressurehead of the water upon the producing sand determined the rate and quantity of water that would enter the sand. Hence, rate and quantity of production appeared to be a direct function of input pressures. By 1927 a few producers had ventured the installation of pressure pumps in order to increase water-input rates and production through the combination of hydrostatic and hydraulic pressures. The adoption of pressure flooding and the "five-spot" drilling pattern in the Bradford field were essentially simultaneous. Water-input pressures in 1930 seldom exceeded 300 p.s.i. at the well head or 1100 p.s.i. at the sand face. Since that time, water-flood producers in the Bradford-Allegany fields have gone to higher and higher pressure until today 600 p.s.i. at the well heads is called a low pressure flood. Many high pressure floods now operate at 1300-1400 p.s.i. at the well head. The limiting and advisable pressure at the sand face has been pronounced as that pressure just under what is required to lift the overburden or to cause formation parting: According to this rule any water flood operation utilizing well-head pressures nearly equal in pounds per sq. in. to 1.1 times the average depth in feet to the top of the producing sand would be considered as a high-pressure flood. Despite the higher pressure trends in the Bradford-Allegany field operations and the results of early laboratory water flooding research, the desirability and benefits of high input pressures are still questioned by many operators, particularly in midwestern water flood operations. The present paper recounts a series of 19 laboratory water floods using two long, consolidated cores of widely differing characteristics saturated with live crude and flooded with oil field brines in an effort to simulate field conditions under • various pressure gradients and flooding velocities. For both cores, higher recoveries and lower residual oil saturations were obtained at higher pressure gradients and flood velocities. This relationship is shown to hold up to the water breakthrough point and also up to the 100 to 1 produced water to oil ratio point.

Jan 1, 1949

By R. V. Hughes, J. N. Breston

Conclusions drawn by previous research workers with reSPect to the relation between Pressure gradients and/or velocity and oil recovery obtained by laboratory water flood tests have been in disagreement probably due to variable procedures and unnatural conditions and materials. The Bradford Laboratory of the Pennsylvania Grade Crude Oil Association as part of its secondary recovery research program has conducted nineteen water floods on two long cores of widely differing characteristics in an attempt to clarify this relationship and make it an aid in predicting flooding pressures in the field. Unlike previous research procedures the present experiments were conducted with the aim of duplicating field conditions as closely as possible by using long unextracted consolidated cores, a live crude, and natural brines for both flooding and, connate water content. Also, the pressure gradients and flooding velocities were representative of field conditions where similar sands were being flooded. Eleven floods on one core and eight floods on the other core showed increased recoveries and lower residual oil saturation with increased flood pressure gradients and flood velocities. A marked decrease in recovery was obtained from both cores at very low flood velocities. This pressure versus recovery relationship is shown to hold up to the point of water breakthrough and also up to the 100 and 1 produced water to oil ratio point. INTRODUCTION The possibility of water flooding oil sands was suggested by Carl1 of the Pennsylvania Geological Survey in 1880. It is not known when the practice was tried intentionally for the first time, but its beneficial effects were noted in the annual production rate of the Bradford field as early as 1907. The practice was illegal in Pennsylvania until 1921. Early water floods in the Bradford field usually consisted of shooting or splitting the casing secretly to permit subsurface waters to enter the producing sands under hydrostatic head. As it was noted that the benefits of water flooding seemed to be proportional to the quantity of water dumped into the well many also began to utilize surface sources after the practice became legal. It was probably during the middle 20's before many producers realized that the pressurehead of the water upon the producing sand determined the rate and quantity of water that would enter the sand. Hence, rate and quantity of production appeared to be a direct function of input pressures. By 1927 a few producers had ventured the installation of pressure pumps in order to increase water-input rates and production through the combination of hydrostatic and hydraulic pressures. The adoption of pressure flooding and the "five-spot" drilling pattern in the Bradford field were essentially simultaneous. Water-input pressures in 1930 seldom exceeded 300 p.s.i. at the well head or 1100 p.s.i. at the sand face. Since that time, water-flood producers in the Bradford-Allegany fields have gone to higher and higher pressure until today 600 p.s.i. at the well heads is called a low pressure flood. Many high pressure floods now operate at 1300-1400 p.s.i. at the well head. The limiting and advisable pressure at the sand face has been pronounced as that pressure just under what is required to lift the overburden or to cause formation parting: According to this rule any water flood operation utilizing well-head pressures nearly equal in pounds per sq. in. to 1.1 times the average depth in feet to the top of the producing sand would be considered as a high-pressure flood. Despite the higher pressure trends in the Bradford-Allegany field operations and the results of early laboratory water flooding research, the desirability and benefits of high input pressures are still questioned by many operators, particularly in midwestern water flood operations. The present paper recounts a series of 19 laboratory water floods using two long, consolidated cores of widely differing characteristics saturated with live crude and flooded with oil field brines in an effort to simulate field conditions under • various pressure gradients and flooding velocities. For both cores, higher recoveries and lower residual oil saturations were obtained at higher pressure gradients and flood velocities. This relationship is shown to hold up to the water breakthrough point and also up to the 100 to 1 produced water to oil ratio point.

Jan 1, 1949

By Gray L. L., Max Littlefield, Godbold A. C.

The West Edmond pool of Central Oklahoma, a limestone reservoir, has an area in excess of 29,000 acres and as of Sept. 15, 1946, had produced 53 million barrels of oil from 731 wells at an average depth of 6900 ft. Water has encroached into the reservoir along the west side of the pool and although the area of water invasion is large the net volume of water influx is small, because encroachment has been primarily into a fracture system. The most significant part of this study concerns the character of the Hunton reservoir. Geological study of cores of the producing section was made to supplement core-analysis data. It was determined that approximately 90 pct of the pore volume was contained in intergranular or sand-like porosity and 10 pct in fractures (intermediate porosity). The porous limestone is divided into blocks by the fractures, although in the strongly dolomitic parts of the producing section, fractures are less well developed. The low-permeability intergranular porosity, largely subsidiary to the high-permeability fractures, will produce oil into the fractures by evolution of solution gas. The fractures in effect serve as drainage channels for production of oil from the inter-granular porosity. Because of such a large difference in permeabilities of the two com-ponents, a high degree of by-passing will occur, and, accordingly, the economics involved in undertaking full-scale high pressure gas injection operations have been seriously questioned. Introduction The West Edmond Hunton pool, which covers portions of Canadian, Logan, Oklahoma, and Kingfisher Counties in Central Oklahoma, is the largest reservoir producing oil from a limestone in the state. The total area of the pool comprises about 29,240 acres and development is considered to be essentially complete. In all, 731 producing wells have been completed in the Hunton reservoir at an average depth of approximately 6900 ft, and have yielded a cumulative oil production in excess of 53 million barrels as of Sept. 15, 1946. In addition to wells completed in the Hunton limestone, 21 wells have been completed in the Bartlesville sand at a depth of approximately 6500 ft, which have produced a total of 730,000 bbl of oil. One small producer has been completed in the Cleveland sand at a depth of 5700 ft. However, a study of only the Hunton limestone reservoir will be presented in this paper. The most significant phase of this study concerns the special type of geological core examination that was made in an effort to ascertain the type and degree of porosity in the rock in accordance with lithologic types. Results of this geological study showed the west Edmond pool to be of such a complex nature as to appreciably affect the behavior normally associated with homogeneous reservoirs. Recognition of this condition in the

Jan 1, 1948

By Max Littlefield, Godbold A. C., Gray L. L.

The West Edmond pool of Central Oklahoma, a limestone reservoir, has an area in excess of 29,000 acres and as of Sept. 15, 1946, had produced 53 million barrels of oil from 731 wells at an average depth of 6900 ft. Water has encroached into the reservoir along the west side of the pool and although the area of water invasion is large the net volume of water influx is small, because encroachment has been primarily into a fracture system. The most significant part of this study concerns the character of the Hunton reservoir. Geological study of cores of the producing section was made to supplement core-analysis data. It was determined that approximately 90 pct of the pore volume was contained in intergranular or sand-like porosity and 10 pct in fractures (intermediate porosity). The porous limestone is divided into blocks by the fractures, although in the strongly dolomitic parts of the producing section, fractures are less well developed. The low-permeability intergranular porosity, largely subsidiary to the high-permeability fractures, will produce oil into the fractures by evolution of solution gas. The fractures in effect serve as drainage channels for production of oil from the inter-granular porosity. Because of such a large difference in permeabilities of the two com-ponents, a high degree of by-passing will occur, and, accordingly, the economics involved in undertaking full-scale high pressure gas injection operations have been seriously questioned. Introduction The West Edmond Hunton pool, which covers portions of Canadian, Logan, Oklahoma, and Kingfisher Counties in Central Oklahoma, is the largest reservoir producing oil from a limestone in the state. The total area of the pool comprises about 29,240 acres and development is considered to be essentially complete. In all, 731 producing wells have been completed in the Hunton reservoir at an average depth of approximately 6900 ft, and have yielded a cumulative oil production in excess of 53 million barrels as of Sept. 15, 1946. In addition to wells completed in the Hunton limestone, 21 wells have been completed in the Bartlesville sand at a depth of approximately 6500 ft, which have produced a total of 730,000 bbl of oil. One small producer has been completed in the Cleveland sand at a depth of 5700 ft. However, a study of only the Hunton limestone reservoir will be presented in this paper. The most significant phase of this study concerns the special type of geological core examination that was made in an effort to ascertain the type and degree of porosity in the rock in accordance with lithologic types. Results of this geological study showed the west Edmond pool to be of such a complex nature as to appreciably affect the behavior normally associated with homogeneous reservoirs. Recognition of this condition in the

Jan 1, 1948

By R. K. Iyengar, G. C. Duderstadt

An investigation was carried out to determine the effect of Ca-Si additions on the dissolved oxygen content of liquid steel. An apparent equilibrium was reached after holding the melt for some time when the total oxygen content of the melt was identical with the dissolved oxygen. Results of the investigation show that for deoxidation with silicon and manganese the apparent equilibrium is reached after 8 to 12 min and the oxygen content of the melt is in good agreement with values reported in the literature for similar steel compositions. Ca-Si additions decrease the dissolved oxygen content appreciably below that obtained with Si-Mn deoxidation. It is postulated that some calcium dissolved in liquid steel at the time of its vaporization combines with dissolved oxygen to form CaO which then fluxes the manganese silicate, thereby lowering the activity of the deoxidation products. Slow flotation of calcium silicate inclusions is attributed to their slower growth rate. An addition of aluminum (to yield <0.005 pct Alsol) prior to introduction of Ca-Si improves the kinetics of removal of resulting deoxidation products. WITH the introduction of continuous casting of billets and blooms, application of calcium-containing alloys for deoxidation purposes has gained new interest. More so than in conventional ingot casting, the degree of control of the dissolved and total oxygen contents in steel for continuous casting can determine the success or failure of the operation because these affect both surface (pinholes) and internal quality of the billets. Of the available deoxidizers, only silicon has so far found wide application. However, in the typical range of application (0.20/0.30 pct Si), it is too weak a deoxidizer to suppress pinhole frequency to the level desirable for all but the least demanding appli-cations (approximately 10/50 pinholes per sq ft, de-pending on degree of subsequent reduction). On the other hand, Vincent&apos; has shown that it requires ap-proximately 0.007/0.008 pct A1 soluble in the steel to suppress pinhole formation to <10 pinholes per sq ft. In view of the difficulty of consistently maintaining this aluminum level and the associated problem of tundish nozzle constriction2 when aluminum is added to the ladle, steelmakers have searched for other de-oxidation alloys to circumvent the problem. Calcium-containing alloys offer such a possibility. When employed as a partial substitute for silicon, CaSi (30 pct Ca/60 pct Si) additions are reported to yield adequate pinhole contro1.3 Its use simultaneously preserves the "fluidity" of the steel and ensures good castability.4 Oxygen contents as low as 0.007 to 0.014 pct have been obtained with CaSi additions varying between 3 to 8 lb per ton.5-7 Due to the high degree of vaporization of calcium at the temperature of molten steel and the different methods used to introduce it into the liquid, the reported results show considerable scatter and lack of consistency. According to several investiga- deoxidation tors, the flotation characteristics of CaSi products are not as favorable as those found for alumi-num but are similar to those established for silicates with low alumina content.678 Thus, cleanliness ratings were improved when CaSi was replaced by a com-bination of Si + A1 followed by CaMnSi additions.5,9 In view of the lack of a comprehensive description of the deoxidation potential of CaSi alloys, a study was undertaken of the effect of CaSi additions on oxygen content in comparison to Si + Mn and Si + Mn + Al. The alloy chosen for this study contained 63 pct Si, 32 pct Ca, <3 pct Al, and 2.5 pct Fe. EXPERIMENTAL PROCEDURE The experiments were divided in three groups as shown in Table I. In each group, the CaSi addition was increased successively while maintaining the melt composition constant. The experiments in the third group were designed to determine the effect of prede-oxidation with small amounts of aluminum. Ingot iron, containing 0.02 to 0.03 pct C and 0.03 to 0.05 pct Mn, was melted in a 100-lb magnesia crucible. Pig iron was added to the melt under air in an induction furnace to attain the desired carbon content of 0.05 to 0.15 pct and thereby control the initial oxygen content of the melt between 0.04 and 0.015 pct. After removal of the slag, the furnace was sealed and argon was introduced through an opening in the graphite cover, Fig. 1. When the desired temperature was reached, electrolytic manganese was added to the melt and pin samples were taken (7 mm silica tubing) to establish initial oxygen content. To obtain maximum efficiency, CaSi and metallic silicon were introduced in a sealed steel pipe into the bath. This procedure assured minimum loss of calcium through vaporization as the deoxidants were always released at the bottom of the melt. Samples were taken at regular intervals and quenched in water. Temperature of the bath was measured with a Pt/Pt-10 pct Rh thermocouple. Portions of the pin sample were used for oxygen analysis; five determinations per sample were made to obtain average oxygen content. Oxygen analyses were made by the inert carrier gas fusion method with frequent cross checks with the vacuum fusion method.

Jan 1, 1970

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe&apos; using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"&apos; pure silwer and Ag-0.5 at. pct ~n;&apos; and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l&apos; Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele&apos;~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,&apos;~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,&apos; Gallaher,&apos; and Gallagher and Wash-burn.&apos; Ives and Ruff&apos; found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-&apos; because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:&apos; J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.&apos; As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA&apos; and CC&apos; define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970

By P. G. Sprang, S. Rosen

The Y-Al- C ternary phase diagram for the com -position range from 55 to 100 at. pct Y and for a temperature of 950°C has been constructed from metallographic and X-ray diffraction data. The significant features of the isothermal section which is presented are the small solubility of aluminum in the binary Y3C phase and the presence of a ternary carbide phase with a small homogeneity range around the composition Y3AlC. The similarity in structure and composition between these two carbide phases is discussed in the light of the misci-bility gap which exists between room temperature and 1300°C, which was the temperature range studied. THE occurrence and stability criteria of ternary T3BC, carbide phases having the L&apos;12 structure and the general formula T3BCx have been discussed in detail by stadelmaier1 and more recently by the present authors., Stadelmaier found many representatives of these phases formed between the T metals Mn, Fe, Co, and Ni and the B metals Mg, Al, Zn, Ca, Ge, Cd, In, Sn, Hg, T1, and Pb. The present authors reported on a new series of iso-structural carbide phases formed between the T metals of the Sc group and the B metal, aluminum. These new phases are unique in that many of the Sc group elements form stable binary carbide phases which occur about the composition T3C and which crystallize with a structure similar to that of the T9BCx ternary carbide phases. Furthermore, these binary and ternary phases are found to coexist in equilibrium with each other. The similarity in structure and composition between, for example, Y3C and Y3AlC in the light of the mis-cibility gap which had been found to exist between these two phases indicated a need for a more thorough knowledge of the phase relations which occur in alloys based upon these compositions. Consequently, an investigation of the phase equilibria in the yttrium-rich portion of the Y-A1-C phase diagram was undertaken. The limiting Y-A1 binary diagram determined by Lundin and Klodt3 and the results of Spedding et al.4 governing the Y3C phase were used as guides in , constructing the diagram. EXPERIMENTAL Alloys weighing about 10 g were prepared by arc-melting powder compacts made from the various components on a water-cooled copper hearth using a tungsten electrode in a gettered argon atmosphere. Good homogeneity was obtained by melting the alloys three times. The purity of the yttrium used was 99.9 pct (0.07 pct rare earths). The purity of the aluminum and the carbon was 99.99 pct. The results of chemical analysis on five representative alloys showed that losses during the alloying process were predominantly carbon losses and that in no instance did the measured concentration of this component differ by more than 3 at. pct from the intended composition. For this reason the alloy compositions which are reported are those of the charges prepared for melting. Three alloys which were analyzed for copper, tungsten, nitrogen, and oxygen compositions showed that no contamination had occurred either during casting or during the subsequent annealing treatments. For the major part annealing treatments were carried out on specimens which were placed in

Jan 1, 1965

By Pradeep K. Rohatgi, Clyde M. Adams

Structures produced upon solidification of the eu-tectic composition (33 wt pct Cu) aluminum copper alloy have been examined as a function of freezing rate dfs /d? , the rate of change of fraction solid (fs) with time (8). Slow (dfs/d? = 0.0016 sec-1), intermediate (dfs/d? = 0.02 sec-1) and rapid (dfs/d? = 0.4 to 7.30 sec-1) freezing rates were used. The lamellar Al-Cual2 eutectic is arranged in the form of rod-shaped colonies at rapid freezing rates. The colonies are aligned parallel to the direction of heat flow, whereas the lamellae within the colonies are aligned at various angles, as high as 90 deg, to the direction of heat flow. The colony spacing (C) is proportional to the square root of inverse freezihg rate. The relationship is C = 15.5(dfs/d?)-1/2 where C is in µ and 8 is in sec. The ratio of colony spacing to lamellar spacing is greater than 20.0 and increases with a decrease in the freezing rate. A duplex dendritic structure is produced at intermediate freezing rates. A fine lamellar eutectic is arranged within the dendrites (exhibiting side branches at an angle close to 60 deg from the main stem) and a coarse irregular eutectic appears in the interdendritic regions. The duplex eutectic structure is also produced at slow freezing rates. However, at slow freezing rates there is a Platelat of CuAl2, along the center of the main stem of each dendrite and the other lamellae are arranged perpendicular to the central platelet. THE eutectic between CuA12 and a! aluminum has been reported to freeze in a lamellar form by several workers.&apos;-3 chadwick4 has measured the interlamel-lar spacing as a function of growth rate. Kraft and Albright2 have reported on irregularities in the lamellar structures, and have proposed growth models which account for the formation of faults during solidification. In certain instances the lamellar eutectic has been found to exist in colonies. The colony formation315 has been attributed to the breakdown of a planar liquid-solid interface due to rejection of impurities. The aim of the present work is to study the structures produced from the eutectic aluminum-copper alloy under relatively fast solidification rates, such as encountered in casting and welding operations. The solid-liquid interface presumably remains planar under conditions of slow unidirectional freezing which produce lamellae aligned parallel to the direction of heat flow. The local growth velocities are the same over the entire interface and are equal to the rate of growth of the all-solid region. The spacing between the eutectic lamellae is inversely proportional to the square root of the growth rate of the all-solid region. Under the freezing conditions used in the present study, the solid-liquid interface is cellular or dendritic and the local growth velocities are different in the different regions of the interface. The relationship between the growth rate of the all solid region and the local growth velocities varies with the location and the shape of the interface. The growth rate of the all-solid region is, therefore, an inadequate parameter to describe the eutectic micro-structures which depend upon the local growth velocities. For this reason the structures have been examined as a function of freezing rate, dfs/d?, where fs is the fraction solidified at time 0. The freezing rate was varied by a factor of 4000. The relationship between the freezing rate, dfs/d?, and the growth velocit of the all solid region depends upon the specimen geometry and the shape of the interface. EXPERIMENTAL PROCEDURES The A1-33 pct Cu alloy used throughout this study was made in an induction furnace, using electrolytic copper and aluminum of commercial purity (99.7 pct), the primary impurities being silicon (0.12 pct), iron (0.14 pct), and zinc (0.02 pct). Three ranges of freezing rates were investigated: 1) A spectrum of rapid freezing rates (ranging from 0.40 to 7.30 sec-1) was obtained in arc deposits made on 2-in. thick cast plates of the eutectic alloy. The arc was operated at constant power and was made to travel at constant velocity on the surface of the plate that was in contact with the chill surface during solidification. The pool of liquid metal formed under the moving tungsten arc solidified rapidly by heat extraction through the unmelted plate. Conditions of unidirectional heat flow were achieved near the fusion zone interface, especially in the center of the arc deposits. The great advantage of the arc technique is that rapid cooling and freezing rates can be varied in a qualitative way. The correlation between the arc parameters and the solidification rate is given by the following relationship:6-8

Jan 1, 1970

By G. Y. Chin, W. L. Mammel

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of&apos; virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law&apos;), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.&apos; Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor&apos;s original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*&apos;8 showed that Taylor&apos;s least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen&apos; obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3&apos;) a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;&apos; hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.&apos; This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,&apos;. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal&apos;s stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

By Cyril Stanley Smith

Jan 1, 1949

By Cyril Stanley Smith

Jan 1, 1949

By D. C. Porterfield

-4s a result of world economic conditions brought about by the European war and the consequent loss of European markets for Venezuelan crude, production in Venezuela decreased from 205,433,000 bbl. in 1939 to 186,134,000 bbl. in 1940, or 9.4 per cent. This decline interrupted a steady annual increase in production from the country, which had been continuous since 1932. The Maracaibo Lake Basin in western Venezuela accounted for 135,738,000 bbl. during 1940, or 73 per cent of the total, as against eastern Venezuela&apos;s production of 50,396,000 bbl., or 27 per cent of the total for the country. Corresponding figures for 1939 were 167,688,000 bbl., or 82 per cent of the total from the Lake Basin, and 37,744,000 bbl., or 18 per cent from the east. These comparisons indicate the increasing importance of the newer developments in eastern Venezuela, but it is unlikely that production from the east will ever exceed that from the west. In all, 429 new wells were completed in Venezuela during 1940 as compared to 438 in 1939. Of the 1940 completions, 411 were in proved areas and 18 were wildcats; 389 (95 per cent) of the exploitation wells drilled were producers, I was a gas well and 21 were dry holes, while 6 (33 per cent) of the wildcats drilled were producers and 12 (67 per cent) were dry; 263 of the exploitation wells and 4 of the wildcats were in the Maracaibo Lake Basin and 148 exploitation wells and 14 wildcats were in the east, mostly in the State of Anzoategui. Exploration of the light-oil areas in the Tia Juana and Lagunillas fields was con- tinued during the year with favorable results. Along the lake shore, drilling was confined principally to fill-in wells in the La Kosa, Tia Juana, Laguni!las and Bachaquero fields, although some important semi-exploratory drilling was done in the Pueblo Viejo area between Lagunillas and Bachaquero fields. The only other developments of particular interest in the west were the successful completion of a step-out well lying to the south of the former southern limit of Mene Grande field, which adds considerable proved acreage to that field; and the failure of two wildcats that were drilled near the Colombian border to determine whether the productive sands of the Petrolea field in the Barco Concession, Colombia, extend into Venezuelan territory. In the east no new fields were discovered during the year, although five wildcats were completed as producers. Three of these, Guario No. I, Jusepin-56 and LM-I (Leona), discovered important extensions to previously proved areas and the remaining two, Cantos-I and SPN-I (Socororo), were subsequently proved to have tapped productive sands of small extent and operations in these areas have been suspended. The greatest activity in the east was concentrated in the Oficina field, where 105 new wells were completed during the year and production was increased from 22,540 bbl. per day during January 1940 to 57,627 bbl. per day during December 1940. Important development work was also done in the Jusepin. San Joaquin and El Koble fields.

Jan 1, 1941

By D. C. Porterfield

-4s a result of world economic conditions brought about by the European war and the consequent loss of European markets for Venezuelan crude, production in Venezuela decreased from 205,433,000 bbl. in 1939 to 186,134,000 bbl. in 1940, or 9.4 per cent. This decline interrupted a steady annual increase in production from the country, which had been continuous since 1932. The Maracaibo Lake Basin in western Venezuela accounted for 135,738,000 bbl. during 1940, or 73 per cent of the total, as against eastern Venezuela&apos;s production of 50,396,000 bbl., or 27 per cent of the total for the country. Corresponding figures for 1939 were 167,688,000 bbl., or 82 per cent of the total from the Lake Basin, and 37,744,000 bbl., or 18 per cent from the east. These comparisons indicate the increasing importance of the newer developments in eastern Venezuela, but it is unlikely that production from the east will ever exceed that from the west. In all, 429 new wells were completed in Venezuela during 1940 as compared to 438 in 1939. Of the 1940 completions, 411 were in proved areas and 18 were wildcats; 389 (95 per cent) of the exploitation wells drilled were producers, I was a gas well and 21 were dry holes, while 6 (33 per cent) of the wildcats drilled were producers and 12 (67 per cent) were dry; 263 of the exploitation wells and 4 of the wildcats were in the Maracaibo Lake Basin and 148 exploitation wells and 14 wildcats were in the east, mostly in the State of Anzoategui. Exploration of the light-oil areas in the Tia Juana and Lagunillas fields was con- tinued during the year with favorable results. Along the lake shore, drilling was confined principally to fill-in wells in the La Kosa, Tia Juana, Laguni!las and Bachaquero fields, although some important semi-exploratory drilling was done in the Pueblo Viejo area between Lagunillas and Bachaquero fields. The only other developments of particular interest in the west were the successful completion of a step-out well lying to the south of the former southern limit of Mene Grande field, which adds considerable proved acreage to that field; and the failure of two wildcats that were drilled near the Colombian border to determine whether the productive sands of the Petrolea field in the Barco Concession, Colombia, extend into Venezuelan territory. In the east no new fields were discovered during the year, although five wildcats were completed as producers. Three of these, Guario No. I, Jusepin-56 and LM-I (Leona), discovered important extensions to previously proved areas and the remaining two, Cantos-I and SPN-I (Socororo), were subsequently proved to have tapped productive sands of small extent and operations in these areas have been suspended. The greatest activity in the east was concentrated in the Oficina field, where 105 new wells were completed during the year and production was increased from 22,540 bbl. per day during January 1940 to 57,627 bbl. per day during December 1940. Important development work was also done in the Jusepin. San Joaquin and El Koble fields.

Jan 1, 1941

• The Venezuelan Trade Mission to the United States announced that Bethlehem Steel Corp. will begin exporting iron ore from its El Pao concession, south of the Orinoco River in Venezuela, in about three months. The ore will be transported by rail from the mines to barges on the Orinoco and transshipped to ore vessels at the coast for shipment to the Sparrows Point, Md., plant. The Latin American business men warned that projected increases in the United States tariff on petroleum imports from Venezuela would force that country into bilateral trade agreements with other countries and would mean drastic curtailment of Venezuelan imports from this country. •Bethlehem, South American Gold and Platinum Co., and U. S. Steel are investigating the possibilities of securing American foodstuff for their South American mining camp commissaries through the International Basic Economy Corp. IBEC buys in quantity to supply its subsidiary companies operating in Venezuela and Brazil. The mining companies will rid themselves of this burdensome task as well as realizing a saving from the bulk purchases of IBEC. •Oliver Iron Mining Co. has begun construction of a fine ore and taconite agglomeration plant at Virginia, Minn. It is expected to be ready in six months. The plant will be used to experiment with the making of clinker cakes and egg-sized lumps by sintering machines and nodulizing kilns respectively; about 1 million tons per year will be produced. • Roof pinning has been adopted at the iron mines of TCI, near Birmingham, to support overlying strata as mining progresses. Favorable results have been obtained in that dilution of the ore has been reduced by 50% which is attributable to this method of supporting the roof. •An American mining engineering team has gone to Turkey for a two-year assignment assisting Turkish government agencies in the $45 million ECA development, mechanization, and construction of cleaning plants for the Zonguldak coal field, 200 miles east of Istanbul on the Black Sea. The group consists of James Beeley, John E. Good, John S. Lambright, David Renshaw, and Charles R. Weir, all of the Paul Weir Co. •Arthur F. Taggart describes a new way of training engineers by emphasis on broad, basic engineering courses on page 460 of this issue. •Lawrence T. Tierney, chairman of the National Bituminous Coal Advisory Council, released a report stating that the increase in oil imports since the latter part of 194$ has caused significant damage to the U. S. fuel economy. It has reduced the strength of and employment opportunities in the coal, domestic petroleum, and transportation industries, as well as in related service and supplier fields. •Women, camels, and donkeys are the beasts of burden of the Sahara, according-to the UNESCO World Review. •Increased demand for magnesium sheet in airplane construction ana other phases of the national security program have led Alcoa to establish a sheet magnesium rolling division at its New Kensington, Pa., works which will begin operation shortly. Novel prospecting methods being used by the USGS in its search for uranium include: shock-mounted instruments in light trucks,. Geiger-counter probes lowered into augur holes, and experimental airborne prospecting.

Jan 4, 1950