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By H. R. Ogden

The notch sensitivity of titanium alloys is affected by impurity content, microstructure, and heat treatment. Using notch tensile properties to evaluate notch sensitivity, three commercial titanium-base alloys were investigated over the temperature range of -320o to 390°F. The alloys studied were Ti-5Al-2.5Sn, Ti-6Al-4V, and Ti-2Fe-2Cr-2Mo. Six interstitial levels were studied for each alloy in four mi-crostmctural conditions. The ff- 0 alloys were studied in both the annealed and heat-treated condition. All tests were conducted using 1/4-in. diam round tensile samples. The notched samples had a 50 pct notch with a notch sharpness (a/r) of 53, corresponding to Kt 6.3. Notch sensitivity was increased by increased interstitial content, low temperature, and acicular-type microstructures. The heat-treated, high-interstitial content - 13 alloys were more notch sensitive than the same alloys in the annealed condition. In addition, minima in the notch tensile-temperature curves were observed at temperatures near 32°F. These minima became more pronounced with increasing interstitial content. 1 HE increaseduse of titanium alloys in high strength applications at subzero temperatures requires that a better under standing of the low-temperature behavior of the alloys be obtained. At low temperatures, metals generally exhibit increased strength with lowered ductility and tohness. Notch sensitivity and the factors which influence it become more important as the strength level is increased and the temperature is decreased. Some of the factor s which affect notch sensitivity in ti- tanium alloys are composition, interstitial content, microstructure, and heat-treatment condition. In this paper, the results of a study of these variables on the notch sensitivity of three titanium alloys at temperatures from —320o to 390o are reported. The notch geometry selected for this program was chosen to provide a severe test of notch sensitivity. The ability of the metal to flow without initiating fracture under these severe conditions is reflected in the notch-strength values. Since notch strength is, in part, determined by the constraint exerted by the combined tensile stresses, the behavior of notch specimens reflects the properties of the material under combined stresses. For example, a material with a high notch-unnotch strength ratio may be expected to withstand the biaxial stresses encountered in a pressure vessel better than a material with a low ratio of notch-unnotch strengths. This implies that maximum strength alone is not a sufficient criterion for applications of this type. It further may be concluded that the various conditions that promote poor notch behavior also will affect adversely the performance of materials under combined stresses. In the alloys studied, these included low temperatures, high interstitial levels, and hasformed microstructures. EXPERIMENTAL PROCEDURES Three alloys, Ti-5Al-2.5Sn, Ti-6Al-4V, and Ti-2Fe-2Cr-2Mo, were purchased from commercial producers as 2-in.-dam rod stock. Oxygen and nitrogen were added to these alloys by remelting to obtain a variety of interstitial contents as shown in Table I. In order to Compensate for the much more potent strengthening effect of nitrogen compared with oxygen, an oxygen equivalent content is used to describe the total oxygen plus nitrogen contents studied. It has been suggested previously1 thatnitro-gen is approximately twice as effective in strengthening as oxygen, and carbon, to the extent it is in so-

Jan 1, 1962

By C. Elbaum

Specimens consisting of several crystals, each with a prescribed geometry and a controlled orientation with respect to both the extermally intposed stress and the highboring crystals, werer deformed in tension at room temperature. It is shown that the influence of a grain boundary on the plastic defolrmation of a mullicrystal depends on the extent to which the presence of the grain boundary, contributes to the necessity 01. multiple slip in the component crystals. MANY investigations were carried out in the past on the plastic deformation of aluminum single crystals, bicrystals, and polycrystals. The various studies of bicrystals aimed primarily at elucidating the influence of grain boundaries on the mechanisms of plastic deformation. In the earlier studies the emphasis was placed primarily on finding the "strength" contributed by a grain boundary. In more recent investigations it became apparent that the grain boundary does not contribute any strength per se but rather acts by influencing the mechanism of plastic deformation in the adjoining grains. The concept thus emerged of the plastic properties of a bi-crystal, and by extension of a polycrystal. depending solely on the mechanism of deformation prevailing in each grain. The contribution of the grain boundaries thus becomes limited to the type of restrictions imposed on each grain by its neighbors. The present investigation of the behavior of specimens consisting of more than two crystals was designed for the purpose of studying the influence of the grain boundary in simple aggregates. The findings of this study further support the concept that the restriction imposed on a deforming crystal by its neighbor constitutes the predominant factor in the plastic deformation of polycrystals. The term "multicrystal", in contrast with single and polycrystals, is used to describe specimens consisting of several crystals. Each one of the component crystals has a prescribed geometry and a controlled orientation with respect to both the externally imposed stress and the neighboring crystals. Two groups of multicrystals were prepared. All the component crystals of both groups of multicrystals had the axial orientation (isoaxial multicrystals) shown in Fig. 2, with the primary slip plane and slip direction both at 45 deg to the specimen axis. In the first group (hereafter referred to as group I) the component crystals were symmetrically oriented with respect to the plane of the grain boundary; the primary slip plane and slip direction were respectively at an angle of 60 and 30 deg to this plane. For the second group (group 11) the axial orientation remained the same and the relative positions of the primary slip plane and slip direction are shown in Fig. 3. EXPERIMENTAL METHODS The material used was aluminum 99.993 pct pure, according to the manufacturer. The specimens were produced by growth from the melt in a horizontal graphite container. In order to maintain the prescribed geometry of the individual crystals of a multicrystal, a technique described elsewhere was used.' The specimens were grown under a small, positive pressure of helium at a rate of approximately 1 mm per min. annealed in air for 24 hr at 640°C and cooled over a period of several hours to room temperature. All the multi-crystals were rectangular in cross-section, 6 by 18 mm (see Fig. 1) and from 150 to 170 mm long. In each group bicrystals, tricrystals and quadru-crystals were prepared as shown in Figs. 1 and 4.

Jan 1, 1961

By Bengt Helmerson

A new tankhouse was started in January 1959 at the Copper Refinery of the Boliden Co., Skelleftehamn, Sweden. In early 1961 a semiautomatic machine for looping and straightening of starting sheets was introduced to substitute previous manual operations. The machine as well as consequent, racking and handling is described. Finally, economic benefits achieved and new constructions for the future are discussed. HISTORY Tankhouse operations at the Boliden Co. 's Smelter in Skelleftehamn started in 1932 on a scale that since then has been gradually increasing. In order to rationalize the operations, a new tankhouse was erected. It went into production in January 1959 and was designed for a yearly production of 35,000 metric tons at a current density of 16 amps per sq ft. Already from the beginning, however, the tankhouse has been run with a current density of 21.5 amps per sq ft, corresponding to a maximum capacity of 50,000 tons a year. During the time of planning of the new tankhouse, due consideration was given to the possibilities of mechanizing the operations. New ideas could be and were actually tested on full or pilot plant scale in the old tankhouse. In that way we developed a system for the cathode handling including washing, weighing, and transportation. A system using forklift trucks in combination with trailers and overhead cranes has been developed for transportation and racking of anodes and also for handling of anode scrap. With respect to the electrolyte, circulation and temperature control are partly automatic. Special attention was paid to the production of starting sheets, which operation normally requires a great number of man hours, and it was made the object of a particular survey as to the best ways of straightening starting sheets, attaching loops to the sheets, and so forth. As a result, a machine was designed during 1957-58 and built in our own shops. After a period of tests, the new equipment was put in operation commercially on the 10th of April, 1961. Since this date the machine has produced about 2 million starting sheets without interruption and has been the only source of looped starting sheets for the tankhouse. GENERAL DESCRIPTION Fig. 1 shows all the major parts of the system. These parts are: slitting machine with feeding table (I), standard roller leveler, type Ungerer (2), tilting roller table (3), conveyors for sheets and suspension bars (4, 7), storage of suspension bars (51, punching and stitching machine (6), two lift-turn-tilt tables (8) for discharging the starting sheets, two rack conveyors (9) for sheet assemblies. Included are a hy-daulic pump station and panels for pneumatic and electric controls. SLITTING AND STRAIGHTENING The machine is fed by hand by a man sitting in front of the slitting-machine table, Fig. 2. This operator inserts one sheet at a time into the slitter. After being trimmed, the sheet is automatically conveyed to the following step of handling, straightening. The slitting machine cuts away about 8 mm of the upper and lower parts of the sheet (in relation to its original position in the stripper section) for two reasons. The first one is to give the machine sheets of uniform dimensions; the second one is a matter of quality. Normally the starting sheets as stripped have a thick edge at the bottom end. This part would collect anode slimes and might also cause short circuits when inserted in the cells without trimming. The straightener used is of German construction

Jan 1, 1967

By N. J. Grant, B. C. Giessen, R. Koch

The system Nh-Ir was investigated over the complete concentration range by metallography and X-my techniques, using forty one alloys. The solubility limits of terminal and intermediate phases and the solidus temperatures were determined. Five intermediate phases were found: a Nb3Ir, cubic, Cr3O type; tetragonal, ofecr thorhomhic, isostruc-turn1 with (ta-Rh); and a Nhlr3. cubic, AuCu, type. a Nb3lr and a Nbfr3 melt congruently; three eutectic and three pentectic reactions occur. The phase diagram of the Nb-Ir system had not been fully treated in the literature; only surveys of intermediate phases were found.1"5 In this study, the details of the phase boundaries were investigated as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS The experimental procedures such as arc melting of powder compacts, heat treatments, solidus measurements, X-ray, and metallographic observation were identical with those used in the work on the Nb-Rh phase diagram.&apos; They will therefore not be repeated here except where the conditions differed. The purity of the niobium powder was as stated in Ref. 6; the iridium powder of 99.9+ pct purity from J. Bishop and Co., Malvern, Penn., did not contain impurities exceeding 100 ppm, except rhodium (200 ppm). The melting points and vapor pressures of both elements are very similar. This fact contributed to a very small weight loss on melting and facilitated preparation of homogeneous alloys. As shown in Ref. 6 for Nb-Rh, no oxygen pick-up exceeding 200 ppm had to be considered; this was regarded as valid also for Nb-Ir. A total of forty one alloys were used in the determination of the phase diagram; their concentrations are shown in Fig. l, which presents the phase diagram. The concentration limits as determined by the weight-loss method averaged <0.2 at. pct, and never exceeded 0.5 at. pct. Heat treatments were carried out as described in Ref. 6. Depending on the concentration, only tantalum, tungsten, or iridium containers were employed, avoiding oxide crucibles altogether. Alloys from 0 to 25 and from 65 to 100 at. pct Ir were homogenized at 2095°C for 15 hr, intermediate compositions from 25 to 65 at. pct Ir for 65 hr at 1780°C. A typical annealing-time schedule is presented in Table I. Solidus points were measured as described in Ref. 6 with the modification that samples rich in niobium were held between pieces of tantalum foil and samples of high iridium concentrations were held between rhenium platelets or in iridium wire. After each run it was ascertained metallographically that no reaction with the holder had occurred. Rhenium was selected as holder material after it had been shown in separate tests that the melting points of Re-Ir alloys rise continuously from 2440°C. Metallographic examination was carried out as described in Ref. 6, and the same procedure and etchants were used successfully. While metallographic discrimination between a Nb3lr and o was easily possible, X-ray diffraction was necessary to separate al and ct2. X-ray powder patterns were taken and evaluated as for Nb-Rh6 yielding the error limits indicated in Table 111, to be introduced later. For the determination of the invariant reactions and phase boundaries, the same techniques as for Nb-Rh6 applied. The general accuracy of invariant concentrations is regarded as somewhat higher than for Nb-Rh due to the small slope of most solvus lines.

Jan 1, 1964

By R. L. Rickett, S. H. Kalin, J. T. Mackenzie

Aluminum killed low carbon steel, § which is now used extensively for severe deep drawing or other difficult forming operations, is unusual in that its grain structure, after cold reduction and box annealing in accordance with conventional continuous sheet or strip mill practice, often is elongated, although at times it is equiaxed. Since this unusual structure has been found superior for many, but not all, severe forming operations, recrystallization of the steel, both at constant temperature and on continuous heating, was investigated and compared with that of rimmed steel in the hope that something might be learned about the mechanism of, and the factors controlling, the formation of such elongated grains. In this structure, the grains are elongated both in the lengthwise direction of the strip and transverse to this direction, even though nearly all of the extension in both hot and cold rolling is in the lengthwise direction. The grains are thus roughly pancake-shaped, being longer and wider than they are thick, as observed also by Burns and McCabe,1 and as illustrated by the typical structures shown in Fig 1. Fig la, representing a conventional longitudinal section, shows the length and thickness of the grains, whereas Fig Ib shows their length and width as seen by examining a section parallel to the sheet surface. Both illustrate the very irregular grain boundaries usually associated with the elongated grain shape. A finer equiaxed grain structure in this same grade is shown in Fig Ic. Either the elongated or the equiaxed structure may be present in the annealed product, and in rare instances the two types may coexist in a single specimen, as shown in Fig 1 d. Isothermal Recrystalliza-tion of Rimmed and Alamimum Killed Steel An aluminum killed steel known to have an elongated grain structure after conventional processing (Steel B, Table l), was selected for the initial recrystallization studies; for comparison, a rimmed steel, A in Table 1, was used. Samples of each in the form of hot rolled strip 0.075 and 0.095 in. thick, respectively, were cold rolled on a small laboratory mill in steps of about 0.010 in. per pass to obtain total reductions of 40 and 60 pct. Small pieces of the cold reduced strip were heated in lead at selected constant temperatures for one of several periods of time, then cooled in air. Rate of heating in the lead was, of course, very fast. Hardness of the cooled specimen was measured and a longitudinal section examined metallographically. Isothermal recrystallization curves for these two steels at 1050°F, based on hardness of the air cooled specimens, are shown in Fig 2 in which the amount of recrystallization corresponding to each plotted point is indicated. The marked difference in the behavior of these two types of steel is evident. After a corresponding amount of cold reduction, the rimmed steel recrys-tallizes in a much shorter time than the killed steel and the shape of its recrystallization curve, (plotted on a logarithmic time scale), is very different. The curve for rimmed steel indicates that recrystallization is analogous to isothermal transformation of aus-i.enite in that it proceeds at a progressively faster rate up to some 50 pct recrystallization, then at an increasingly slower rate. For the aluminum killed steel, however, the start of

Jan 1, 1950

By T. E. Schmieman, J. E. Miller, M. L. Rizzone

Both centrifugal and reciprocating-type pumps have been widely used in the transport of slurries. Although with some limitations, centrifugal pumps may be used, especially for short-haul systems, however, for the long pipelines the reciprocating pumps are better suited. A state-of-the-art review is presented in which a discussion of applications is made and some of the problems associated with meeting the proper design conditions for satisfactory service are discussed. Several developments underway give considerable promise of better pumps in the future, although the current level of development provides for an economical means to move slurries. The movement of liquids in pipelines necessarily occasions the use of pumps. The petroleum industry is familiar with the transport of solids through mud pumps and cementing and fracturing pumps where the movement of slurries is an everyday matter. In the drilling of an oil well, the circulating fluid utilized to remove drill cuttings is called drilling mud. This substance is usually a fairly sophisticated material designed to develop certain characteristics desirable in the drilling process. The cuttings are suspended in a moving column of this fluid and brought to the surface. The separation of the cuttings from the drilling fluids is accomplished by the use of shaker screens and settling pits; however, it is impractical to remove the cuttings completely and as a result they are pumped through the mud pumps back into the circulating stream. Over the years, mud pumps have been improved so that rather long life can be obtained from liquid end parts subject to the attritional effects of the abrasive-laden fluid. It is from this background that reciprocating-type slurry pumps have been developed. Centrifugal Pumps Centrifugal pumps have also been used to transport solids, where low heads are required, typically up to 200 ft or so, and for short hauls. The centrifugal pump is a hydrokinetic device wherein the increase in velocity of a fluid stream is converted to head, and to achieve high heads a large change in velocity is necessary. Abrasive laden fluids cause wear on impellers and casings as a result of erosion by the fluid and the suspended particles. Centrifugal pumps, therefore, can only be used where the internal velocity of flow is rela- tively low. The advantage of centrifugal pumps is their high capacity at relatively low capital cost and usually relatively small space requirement. One of the disadvantages of the centrifugal pump when used in slurry pipelining can be seen in its typical pressure-volume performance relationship, which tends to work against the application (see Fig. I). If an increase in pressure (head) is occasioned by flow restrictions in the pipeline, say by the dropping out of solids, a desirable characteristic of a slurry pump would be that it develop increased pressure to overcome the restriction. The centrifugal pump provides the increased pressure only at the expense of considerably reduced volume which then results in a lower flow velocity. With the reduced flow rate, adequate velocity to hold the material in suspension and keep it flowing in the line might not be achieved. If centrifugal pumps are considerd for the movement of solids in a long line, a series of pumps must be staged in order to provide the necessary motivating force. A large number of pumps in the line would be required, since each of the pumps could provide only a small pressure increment. An equal number of standby pumps

Jan 1, 1971

By R. F. Domagala, M. Hansen, D. J. McPherson

On the basis of metallographic analysis, incipient melting data, thermal analysis work, and X-ray diffraction, phase relationships in the 0 to 50 atomic pct Cr region were carefully resolved. Phase relationships in the 50 to 100 atomic pct region were outlined. A single intermediate phase, ZrCr,, was established in the system. A eutectic and a eutectoid were found in the zirconium-rich region of the system, while a eutectic was located in the chromium-rich region. Limited solubility of chromium in both a and a zirconium was observed. THIS is another in a series of papers on zirconium-base binary phase diagrams based on a program sponsored by the Atomic Energy Commission. The Zr-Sn,&apos; Zr-Si,&apos; and Zr-Mo and Zr-W" systems have already been published. Previous work on the Zr-Cr system includes a partial diagram by Hayes, Roberson, and Davies&apos; and a complete diagram by McQuillan." The phase relationships reported by these authors were determined with magnesium-reduced zirconium, whereas those reported herein are based on iodide metal. Some X-ray work on the intermediate phase in this system was also reported by Hayes et al., as well as by Wallbaum.&apos; Comparisons with these data are made in the appropriate sections. Thermal analysis, metallographic and incipient melting techniques were employed to accurately resolve phase relationships in the 0 to 50 atomic pct Cr region, while the remainder of the diagram is outlined on a basis of cast structures and thermal analysis. A description and analyses of the metals used in the preparation of alloys for this study are included in Table I. A "low-hafnium" zirconium crystal bar (Westinghouse "Grade 3") was used. This material was produced by the decomposition of a volatile iodide onto a hot zirconium filament. The as-received crystal bar was coated with corrosion product from a standard autoclave test by which its grade designation is determined. A sand-blasting and subsequent HF-HNO, pickling treatment was employed to remove this contamination. The bars were cold-rolled to approximately 1/32-in. sheet, pickled again, sheared to 1/4-in. squares, washed with acetone, and stored for use. Ingot chromium metal from National Research Corp. and electrolytic chromium flakes from Johnson, Matthey and Co., Ltd., were available as alloy additions. The ingot chromium was received in granular form. The large granules were sized by crushing, treated for iron removal, rinsed with acetone, and stored. The flakes were broken to approximately 1/8 in. with mortar and pestle, cleaned with acetone, and stored for charging. Experimental Procedure A nonconsumable electrode arc furnace identical to that described by Hansen, Kessler, and McPher-son,&apos; was used in this work. A 400 amp dc welding generator was the source of power. To insure homogeneity, ingots were melted in a water-cooled spun copper crucible, a total of four times without opening the furnace. No difficulties were encountered in the preparation of these binary alloys. Analyzed chromium contents were found to agree very well with the intended content. Melts of pure zirconium were interspersed in the course of preparing the alloys and their hardness was measured to keep a constant check on the melting technique. Vycor and quartz bulbs were used to contain the samples for isothermal annealing treatments. Vycor bulbs were employed for temperatures up to 110O°C, while quartz was used above this temperature. For treatments up to 950°C the bulbs were evacuated before sealing, but for higher temperatures a partial pressure of argon was admitted to the

Jan 1, 1954

By S. A. Spachner

An analysis of the powder patterns of the omega transition phase in three binary titanium alloys containing 8 pct Cr, 13 pet Mo, and 15 pet V, respectively, showed that all could be indexed on an orthorhombic unit cell. The unit-cell dimensions were all quite similar. There is evidence for the occurrence of more than one transition phase in Ti-Cr and Ti-V alloys. FOLLOWING the discovery of a new brittle phase in certain titanium-chromium alloys by Frost, Parris, Hirsch, Doig, and Schwartz,&apos; named ? by these investigators, much interest has developed concerning the identification of alloy systems in which this phase exists, kinetics of the transformation in such systems, and the crystal structure of the ? phases appearing. Omega has been found in alloys of titanium-manganese, titanium-molybdenum, titanium-iron,&apos; and titanium-vanadium.&apos; In the present work, a study was made of the powder patterns of the ? phase occurring in alloys of Ti-8Cr, Ti-13Mo and Ti-15V in an effort to obtain a basis of comparison for ? phases appearing in these different alloys. Comparison of Alloys for ?-Phases Two hundred mesh powders of Ti-8Cr, Ti-13Mo and Ti-15V were prepared. A portion of powder sufficient for three x-ray powder specimens was placed in a Vycor tube, evacuated to less than 0.1 µ pressure, filled with argon, and sealed. The tubes were then heated to 900°C, held at this temperature for 30 min, and water-quenched. Following this transformation to the ß phase, the specimens were quenched in lead or solder pots, held at the desired temperature for varying lengths of time and water-quenched. The heat-treatments used and the phases identified are listed in Table I. The intermediate water quench was used in lieu of direct downquenching from 900°C to the bath temperature desired to circumvent the possibility of transformation of the powder specimen from ß to (ß + a) while it was being moved from the homog-enization furnace to the lead bath. To check the possibility that upquenching to the bath temperature might bring into play a different mechanism than downquenching to this temperature, resistivity measurements were compared on Ti-8Cr rod specimens which were transformed isothermally at 400°C by downquenching from the solution-treatment temperature and those which were transformed at 400" C by upquenching ß specimens from room temperature. The results are shown in Fig. 1. No difference in transformation mechanism was noted. It soon became apparent that sufficiently detailed Debye-Scherrer photograms of the ? phase in the alloys which were to be used could not be obtained by the use of copper radiation. Although satisfactory photograms of ß and ß + a phases were obtained with this radiation, the ? phase appeared to exhibit mild fluorescence, making interplanar spacing computation virtually impossible. Molybdenum radiation appeared to offer promise in cutting down this fluorescent effect, the mass absorption of titanium for molybdenum radiation being 23.7 in contrast to 204 for copper radiation. The reduction in the accuracy in determining the location of the photo-gram lines caused by the shorter wave length of molybdenum characteristic radiation did not appear to be a significant factor. Utilizing a camera of 57.3 mm radius, best results were obtained for exposure times ranging between 30 and 40 hr. Tube potential

Jan 1, 1959

By L. A. Panek

Research on roof bolting has developed significant information with respect to the functions that can be performed by properly installed bolts and the methods that can be used to ensure that effective installation has been achieved. The present paper brings together results that are pertinent to the design of a bolting system for reinforcing horizontally stratified mine roof with vertical bolts. The design approach is based on the use of bolts to decrease the maximum bending stress within an arbitrary sequence of roof strata (see Fig. 2) in which the only loads are the weights of the individual beds. The use of rock bolts to achieve other objectives, such as to stabilize a fractured rock mass on the periphery of a mine opening,3 is excluded from consideration herein. Reinforcing effect of bolts consists of a friction effect and a suspension effect in combination. "Friction effect" refers to reduction of bending in a stratified roof due to clamping action of tensioned bolts, which compress the strata, thereby creating frictional resistance to displacement along planes of stratification. (The flexure of a sequence of strata is necessarily accompanied by horizontal displacement of each bed with respect to its neighbor, along mutual surfaces of contact.) Although the sliding of the beds tends to exert a shearing effect on the bolts, tests show that this has negligible influence on the bending stresses, probably because the bolts are so far apart. "Suspension effect" refers to the transfer of part of the weight of the weaker or thinner strata to one or more thick strata, which occurs when strata with differing tendencies to deflect are constrained to have equal deflection. The term "suspension" is used irrespective of whether the thin strata are above or below the thick strata, because tests show that the supporting effect of the flexurally more rigid roof strata is for practical purposes independent of their position in a bolted sequence of strata. An earlier paper4 dealt with a bolted unit in which all strata had equal flexural rigidity; bolting could develop a friction effect but no suspension effect. The present paper deals primarily with a bolted unit in which all strata do not have equal flexural rigidity, so that bolting can develop both a friction effect and a suspension effect. The reinforcing effect of the bolts was determined by a combination of experimental and theoretical stress analysis.4&apos;6&apos;7 The experimental method consisted of loading a model by rotating it in a centrifuge to simulate the gravity forces exerted about an underground excavation. Models were made from two different limestones, although the results are independent of the material because the elastic constants were taken into account in the data analysis. Electric resistance strain gages were bonded to the highest and lowest members of the bolted unit to determine the outer-fiber bending strains at the center and at the supports. The quantitative results presented herein are based on tests of 56 different models, which included a range of values for the structural parameters. Each model was tested several times, with different combinations of spacing and tension of the bolts. DESIGN EQUATIONS The effects of friction and suspension on the flexure of a bolted stratified roof can be expressed by the following equations, which give the maximum bending stress, the deflection, the friction effect, the suspension effect and the transferred load for any (the i-th) member of the bolted unit in terms of the structural parameters:

Jan 1, 1964

By K. Torssell, U. Lindborg

The kinetics of precipitation deoxidation is considered from a theoretical point of view. The size distribution and the total content of deoxidation products are estimated statistically as a function of time, taking into account Stokes and gradient collisions between the particles and separation at the top surface of the bath. The assumption is made that two particles coalesce into one larger particle as a result of a collision. General expressions are derived and calculations are carried out numerically for the case of silica particles in liquid iron. The analysis predicts a three-stage behavior for the removal of oxygen, an incubation stage, a stage of rapid separation, and a slow final stage where the content approaches the equilibrium value. The agreement with experimentally determined size distributions and deoxidation times is considered to be good. A quantitative estimation of such growth mechanisms as diffusion from the melt and redistribution of oxygen from small particles to large ones shows that these latter mechanisms cannot explain the experimentally observed gvowth of inclusions. This also indicates that collisions provide the important growth mechanism. OXIDE inclusions precipitate when a deoxidizer like silicon or aluminum is added to a steel bath. The inclusions grow and the large particles tend to separate from the bath. For each type of oxide the growth determines the sizes of the final inclusions as well as the total inclusion content of the steel. The mechanism of growth is controversial, however. It has been suggested that an inclusion grows principally by diffusion of atoms through the melt to the inclusion particle or principally by collisions and coalescence with other inclusions. Diffusion growth is always present to some extent but recent experiments and calculations by Torssell,&apos; Kniippel et &apos;a1.,2 Sano et al. and Miya-shita4 indicate that collisions may be more important than previously realized. A detailed analysis has so far been lacking. The present paper is a quantitative, statistical analysis of the growth and separation of inclusions and is based on a collision theory. Nuclea-tion is not considered. The numerical estimates are based on the experimental conditions of Torssell&apos;s&apos; investigation and comparisons are made with his observations. Torssell&apos; studied the growth and separation of silica particles in liquid iron. Samples were taken from a 0.6 kg iron bath at various times after the addition of silicon. By a particle-counting technique developed by Bergh and Lindber~the size distribution of the inclu- sions was determined. The number of particles at the first sampling, 10 sec after silicon addition, was of the order of 3 x lo7 to 10&apos; per cu cm, the largest particles having a radius of 2 to 4 pm. The volume fraction was 0.001 to 0.004; i.e., the dispersion was very dilute. During subsequent holding the largest particles increased their radius by a factor of 10 after about a minute, and the whole size distribution was displaced toward larger values. These results were obtained with allowance for precipitation of the equilibrium concentration of oxygen during solidification. The bath contained less than 0.01 pct of C. Figs. 1 and 2 show the typical appearance of the inclusions. Most particles are very closely spherical and appear to have been liquid or semiliquid in the melt. The observed number of inclusions, about 5x 10&apos; per cu cm, is of the same order of magnitude as found by ~er~h.&apos; This is a large value. It follows that the diffusion distances are very short and that the precipitation

Jan 1, 1969

By J. W. Marx, R. H. Langenheim

The injection of heat-bearing fluids may offer a wider application to secondary and tertiary recovery from conventional oil reservoirs than inderground combustion since the process is more easily controlled and the reservoir requirements, in general, are less critical. In all cares, conduction heat losses to overburden and un-derburden will impose an economic limit upon the size of the area which can be swept out from any one injection point for any given set of conditions. The present report describes a method for c.rtin~ating thermal invasion rates, cumulative heated area, and theoretical economic limits for sustained hot-fluid injection at a constant rate into an idealized reservoir. Full allow-ance is made for non-productive reservoir heat losses. Required solutions can be obtained directly from the numerical tables given here, as soon as all operating conditions are specified, withou extensive mathematica1 ~nanipulation on the part of the user. The injection of a heat-bearing fluid into a reservoir is frequently proposed as a means of secondary or tertiary oil production. This form of thermal recovery may offer a wider application to conventional oil reservoirs than underground combustion since the process is more easily controlled and the reservoir requirements, in general, are less critical. Because of its large gross heat capacity, steam appears to be the most efficient heat injection medium, although mixtures of steam and other gases, hot water, hot oil and hot non-condensable gases also have been employed. Whatever the nature of the injection medium, economic evaluation of such thermal recovery processes will depend upon thermal invasion rates, or rates of productive reservoir heating, at any given time after the start of heat injection. In all cases, conduction heat losses to overburden and underburden will impose an economic limit upon the size of the area which can be swept out from any one injection point, for a given set of reservoir conditions, at any given heat injection rate. The present report describes a method for estimating thermal invasion rates, cumulative heated area and theoretical economic limits for sustained heat injection at a constant rate into an idealized reservoir, making full allowance for non-productive reservoir heat losses. Required solutions can be obtained directly from the nu- merical tables given here, as soon as all operating conditions are specified, without extensive mathematical manipulation. It should be noted that ordinary water flooding may be used to move an annular-heated zone outward, even though the economic areal limit for straight heat injection has been reached. Thus well spacing need not be confined to the areal limits as determined here. However, the present calculations do not cover such supplementary heat scavenging programs. The operating element consists of a radial flow system, concentric about the point of injection, with the idealized step function temperature profile illustrated by the dashed line in Fig. 1. The solid curve shown in Fig. 1 gives a qualitative picture of the true radial temperature distribution. It will be shown later that the expressions given below, which are derived from the simplifying step idealization (dashed line in Fig. I), also can be interpreted in terms of the more realistic temperature distribution shown in Fig. 2. For this case, the thermal invasion radius is simply redefined as the distance from injection well to the mid-point of the temperature distribution.

By B. A. Shaw

Historically, microwave tubes have been fabricated from massive metal and ceramic components. The current trend is to lighten tibes for airborne applications. The reqciiremenls of light weight and also reduced cost have created a novel approach to tube structure in which thin-film technology plays a major role. Although the electrical requirements of thin-film circuits in microwave tubes differ from those required or se,niconductor integrated circuits. the technology is basically similar. The stringent requirements of the micvowave tube have created sophisticaled thin-film techniques thut are of interest to the integrated-circuit industry in general. This paper describes a nunzber of thin-jilm techniques recently developed and discusses in detail the application of the technology in microwave tubes. The particular areas of interest are: 1) ceramic mounted thin-film slow-wave structures; 2) thin-film secondary emitters; 3) suppression of tube environnental multipactor by semiconducting&apos; thin films; and 4) age-hardenable and dispersion-hardened thin metal films. SEVERAL thin-film techniques specifically applied to microwave power tubes are discussed in this report. There are two reasons for this work. One is the necessity of reducing weight and cost of microwave tubes and the other is related to overcoming problems in the tube operation by the use of applied thin-film technology. The major emphasis of this work has been on tube slow-wave structures. Other work in the area of secondary emission, either its suppression or its enhancement, is continuing; the most satisfactory results to date have been by utilization of thin-film technology. The requirements of high thermal and electrical conduction together with greater strength than normally obtained with elemental materials have led to the development of dispersion-hardened films. The paper will discuss: 1) ceramic-mounted delay-line microwave tubes; 2) multipactor and secondary emission; 3) hardened films. I) CERAMIC-MOUNTED THIN-FILM SLOW-WAVE STRUCTURES In a conventional crossed-field microwave tube, the slow-wave or delay-line structure is produced from two carefully machined components. One half of the structure is shown in Fig. 1. The other half is the mirror image of the first but is rotationally offset by a half a period. The combined structure now forms an interdigital type of slow-wave structure and is the anode of the tube as shown in Fig. 2. The period and finger length of an interdigital slow-wave structure are prescribed by the desired dispersion characteristics. The typical design is as shown in the first figure; it can be noticed that the finger width is several times greater than the finger thickness. Even assuming that it were mechanically possible to produce free-standing fingers of extremely small cross-sectional dimension, for example, 0.002 in. thick by 0.005 in. wide by 0.500 in. long, decreasing this finger width would increase the tube efficiency but would also decrease the thermal-conduction path, causing an increased temperature rise from intercepted rf current which in its extreme could easily cause finger melting. Hence, for free-standing lines of this type, the design is a compromise between mechanical capabilities, tube efficiency, and thermal dissipation. These structures are also expensive and tend to be heavier than purely electrical considerations would demand. In the present approach, we have transposed the three-dimensional structure previously shown into an essentially two-dimensional structure as shown in Fig. 3. The linear structure is used here for clarity of detail. The support member is a ceramic material and the line is deposited copper. The final tube design is shown in Fig. 4. Because of the backwall sup-

Jan 1, 1967

By E. L. Kamen, H. D. Kessler, M. Hansen, D. J. McPherson

The highly reactive Ti-Mo and Ti-Cb alloys were prepared and heat treated under protective conditions. Phase diagrams were established based on micrographic and X-ray diffraction analysis and detection of incipient melting. ß titanium forms a continuous series of solid solutions with both molybdenum and columbium, whereas these metals are only slightly soluble in the a titanium modification. PREVIOUS work on the Ti-Mo and Ti-Cb systems was very limited and is discussed in succeeding sections of this paper relating to the respective phase diagrams. The diagrams in the present work were determined principally by micrographic analysis, because other methods such as thermal analysis and dilatometry are not suitable, due to the low diffusion rates of these alloys in the transformation range. X-ray analysis was believed less useful than micrographic analysis because: 1—On quenching certain high titanium alloys from above their transformation range, the body-centered cubic ß phase decomposes into acicular a (hexagonal close-packed) which room temperature X-ray diffraction techniques cannot differentiate from isothermal a. 2— High temperature X-ray techniques might be used, but are difficult to apply and are subject to error because of the high reactivity of titanium with gases such as oxygen and nitrogen. Although metallo-graphic study was the basic method used, X-ray diffraction analysis was applied to a limited extent, to further substantiate the findings. The transformation ranges on the titanium side of the Ti-Cb and Ti-Mo systems were studied both with DuPont Process A (magnesium-reduced) titanium alloys and with iodide titanium alloys. The Process A metal was used chiefly to bracket the transformation range in order to reduce the number of alloys given a particular treatment for the more accurate final study with iodide titanium alloys. Experimental Procedure The analyses of the metals used in the preparation of alloys for this study are presented in Table I. Melting Practice: Early in the work, a consumable electrode, arc melting furnace was used in the preparation of the Process A Ti-base Mo and Cb alloys. This type of furnace has been described by other investigators.&apos;, &apos; One of the major difficulties of the consumable electrode melting process was the prep- aration of homogeneous electrodes (with the mixture of coarse titanium sponge and fine powder alloying addition) which would give homogeneous ingots. Composition gradients encountered may have been due to a tendency for powdered alloying metals to drop away from the electrode in handling. This difficulty in the preparation of homogeneous alloys was overcome by the use of a nonconsumable electrode furnace for later work. This furnace is similar to the one used by Mc-Pherson and Fontana a Ohio State University. A diagram of the nonconsumable electrode arc furnace is given elsewhere.&apos; The source of power was a 400 amp dc welding generator. Electrode tips of tungsten (% in. in diam) were used for all columbium melts and for a limited number of molybdenum melts. Molybdenum tips were used for the majority of molybdenum alloy melts. Columbium tipped electrodes were tried, but disintegrated rapidly at currents above 300 amp. In the Process A titanium melting practice the metals were charged into the water-cooled spun copper crucible in the following forms: l—titanium: sponge (—4 + 16 mesh); 2—molybdenum: sections of 0.003 in. sheet (approximately ½ in. sq); and 3— columbium: powder compacts (? in. lumps broken from large section). After alternately evacuating and purging the furnace several times with argon or helium, the arc was struck against the metal charge,

Jan 1, 1952

By J. S. Aronofsky

The results of polentiometric model studies and numerical computations are described. The purpose of these studies was to determine the influence of the mobility ratio on flooding efficiencies during water encroachment in petroleum reservoirs, in systems of regular well geometry. The direct line drive well pattern having relative spacing distances of one and one-half to one was investigated for water to oil mobility ratios of 10. 1. and 0.1. The results of these studies indicate that the pattern Sweep efficiency i.; very dependent upon the mobility ratio. INTRODUCTION The almost universal occurrence of water in the immediate neighborhood of oil-hearing sands lends considerable emphasis to the desirability of having a rational analysis of water encroachment into petroleum reservoirs. This problem has 1)become increasingly important with the accelerated use of water injection for secondary recovery operations. The water encroachment problem has been studied from both the theoretical and experimental viewpoints by Muskat.&apos; He has formulated, in a precise manner, differential equations to express flow in a water encroachment system, and rigorous analytical solutions have been developed for the linear, radial, and spherical cases.&apos; However, it becomes exceedingly difficult to solve the encroachment problem rigorously for any general two-dimensional system in which the shape of the two-fluid interface is not immediately evident from the geometry of the system. The difficulty lies in the fart that a rigorous analytical solution requires that the shape of the two-fluid interface be known simultaneously with its instantaneous posititon and with the pressure distribution on both sides of the interface. Although this paper concerns the study of the two-fluid system of oil and water. the methods described in the paper are generally applicable to other systems of incompressible and immiscible fluids in which the displacing fluid sweep-the displaced fluid down to a residual value. In each region it is assumed there is only one mobile fluid and its mobility is constant throughout the region. The Same procedure. with minor alteration, is applicable for gas injection systems provided the assumption can be made that both the displaced and displacing gases can be described by steady state formulas. For the particular two-fluid problem considered in this paper, there is a relative permeability. K, and a viscosity. p. associated with the water zone, and a different permeability and viscosity associated with the oil zone. The K/p (mobility value associated with a particular volume element of the porous medium. at any instant of time. will depend upon whether the element is ahead of. or behind the advancing interface. It is assumed that all volume elements ahead of the interface are characterized by the K/p value for oil, while all the elements behind the interface are characterized by the K/p value for water. That is. the K/p value in the oil zone is constant throughout the oil zone. and the K/p value in the water zone is also constant but different from the value in the oil zone. The symbols are defined at the end of the paper. The well pattern chosen for initial study is the direct line drive; the swept-out area at breakthrough was determined by two different methods which are described in the section on theory. These are: 1. Potentiometric analyzer 2. Numerical computation The use of the potentiometric analyzer for studying water flooding problems is adequately described in the literature, particularly for cases where the mobility in the water zone is assumed equal to the mobility in the oil zone." &apos; 5

Jan 1, 1952

By M. C. Fuerstenau, A. M. Gaudin

A homogeneous suspension is viewed by X-rays. The radiation density seen, affords a measure of the extra absorption due to the solids contained. This radiation density, at a predetermined depth, varies with time. The chart of this relationship gives the desired determination. s it is frequently necessary to know the distribu-rt tion of particle sizes in various products used in industrial applications, a number of means have been devised for these determinations. Some of them include direct microscopic measurement, screening of product, extraction of samples from a settling slurry, air and liquid elutriation, adsorption of gases and liquids, and light absorption. The absorption of light as a means for particle size analysis has been known and employed for some time. X-ray absorption has not received the attention that light has enjoyed primarily because of the complex and costly instrumentation involved with X-rays. In 1954, Brown and Skrebowskil suggested the use of X-rays for this type of determination but did not supplement their suggestion with experiment. In 1958, the authors conducted size analysis experiments on suspensions of quartz with the Trans-viewer: an X-ray unit specifically adapted for sedimentation research, and Rossa conducted experiments in a similar manner in 1959 with a stable gamma emitter, AmZ4l, on suspensions of uranium oxide. To illustrate the applicability of X-ray absorption for analyzing particle size distributions, an essentially mono-energetic and well collimated X-ray beam was used as a source. The beam was made mono-energetic by placing a zirconium filter before the counting window together with feeding the pulses from the proportional counter into a reverter, a device capable of discriminating against pulses of various heights. The sketch in Fig. 1 shows the collimation arrangement in more detail. As shown, the X-ray beam was collimated by inserting a 3/8-in. ID pipe into one of the ports of the X-ray tube and further by two small steel plates with slits 3/32-in. wide and 1/2-in. long placed in front of the window of the Geiger-Mueller (G-M) tube. One of the plates was located 1/2 in. and the other 2 1/2 in. from the window of the counter; both plates were contained in an aluminum holder mounted on the box containing the G-M tube. This type and degree of collimation should eliminate any intensity due to scattered radiation; the transmitted intensity would then be solely a functior. of the absorption by the suspension at that level. Experimentally, homogeneous suspensions of finely ground quartz were prepared, Daxad (a sulfo-nated compound made from wood) was added as dis-persant, and the transmitted X-ray intensity measured as a function of time at a fixed depth in the suspension. In more detail, the experimental procedure involved the following: 1) measuring the transmitted X-ray intensity through the Daxad solution at a predetermined position or settling depth in the absence of solids, 2) placing a known amount of dry solids into the vessel and agitating thoroughly, 3) measuring the transmitted X-ray intensity at time zero (i.e., immediately upon cessation of stirring), and 4) measuring the transmitted X-ray intensity as a function of time (a 10-sec counting interval being chosen and counting being started 5 sec before the desired time). Since a linear relationship exists between percentage solid in a slurry and the logarithm of transmitted intensity for a homogeneous material, the cumu-

Jan 1, 1961

By J. Gurland

The effects of variations of carbon content on the constitution and properties of sintered WC-Co alloys were studied. The grain growth of tungsten carbide during sintering was measured and it was shown that it takes place mainly by solution and reprecipitation of the carbide in and from the binder at the sintering temperature. It was found that the decomposition of W3C03C by carburization during sintering is responsible for the formation of very large grains. THE properties of sintered WC-Co alloys are critically dependent upon their final composition and structure. Slight changes of cobalt and carbon contents and small variations of grain size result in marked changes of mechanical properties and performance of products. Previous investigators have studied the microstructure as a function of composition&apos; and have dealt with the influence of cobalt upon properties.&apos; The present work is concerned with the effect of carbon content upon constitution, microstructure, and grain growth during sintering, as well as upon the physical properties of sintered compacts. Phase Boundaries at the Sintering Temperature The WC-Co section through the ternary diagram W-Co-C has been studied by Wyman and Kelley,&apos; Takeda,V andford and Trent," and Rautala and Norton." Two phases, namely WC and a cobalt-rich solid solution (P), appear in the sintered structure if the carbon composition corresponds very nearly to the theoretical carbon content of WC (6.12 pct C). But small deviations from the ideal carbon content will bring about the occurrence of either graphite or the double carbide W,Co3C (7) . The 7 phase was long believed to be metastable, this conclusion being based mainly on the work of Takeda. More recent studies have shown that it is a stable phase of the ternary system,"5 but the actual phase boundaries have not been established and there has been some discussion as to whether or not the 7 phase occurs at some stage of sintering in the fully carburized alloys." In view of this uncertainty it was thought advisable to undertake an investigation of the phases present during the sintering of WC-Co alloys. Commercially available tungsten, cobalt, and carbon powders were used in the present study. A typical analysis of impurities in a sintered compact is reported in Table I. The desired carbon compositions were attained by varying the amount of carbon added to the tungsten during carburization and controlling the composition during sintering by packing the compacts into beds of mixed alundum-carbon powders of suitably selected ratios. The alloys were sintered in a hydrogen tube furnace at 1400°C, then brought to equilibrium at the temperature under investigation and quenched in water. The high temperature phases were identified by metallographic and X-ray diffraction techniques. The samples were etched with a 10 pct solution of alkaline potassium ferricyanide. The phase boundaries, established by metallo-graphic examination, are shown in Fig. 1, which is a vertical section through the ternary diagram at 16 pct Co. The temperatures of the invariant planes, at 1298" and 1357°C were established by Rautala and Norton. The vertical section shows that the three-phase field, WC + 7 + L, extends into the two-phase field, WC + L, but does not include the stoichiometric composition of WC. In practice this means that the 7

Jan 1, 1955

By M. R. Annis

Drilling mud rheological and gel property changes due to elevated temperatures frequently cause problems in drilling deep wells. A laboratory investigation of the effects of time, temperatures up to 3001; and mud composition on these properties was made with concentric-cylinder, rotational viscometers of the Farm type. The viscometers were sealed from the atmosphere to prevent dehydration of the sample. Gel strengths were found to be more sensitive than viscosities to changes in temperature and mud cornposition. The high-temperature gel strengths of bentonitic clay drilling fluids were not predictable from low-temper.atl4t-e measurements. At high temperatures, [lie clay flocculates. The floccu-lation temperature depends on the concentration and type of solids in the mud and the degree of chemical defloccula-tion. As the bentonite content of a mud increases, floccrrla-tion temperature decreases. Lignosulfonnte treatment raises the flocculation temperature. To minimize adverse high-temperatrrre effects on mud properties, the mud should be maintainted at minimum solids content, properly treated with. a defloccullant which is stable at the maximum ten?perature encountered and maintained at a pH high enough to insure activation of the deflocculant for the duration required. The Methylene Blue Test for cation exchange cnpacity of a clay was found to be a useful guide in deter.niinirig when a mud contains a dangerously high clay conWnt. INTRODUCTION In drilling a well it is desirable, for several reasons, to know the effects of time and temperature on the rheological and gel properties of the drilling fluid in the hole. Problems associated with drilling fluids normally occur down-hole: so it is reasonable to be interested in the properties of drilling fluids at the conditions which exist down-hole. It has long been observed that high pump pressures are often needed to start circulation after a trip and that the "bottom-up" mud that is circulated back to the surface is usually more viscous than it was before "cooking" at the bottom of the hole for several hours. Burk-hardt&apos; showed that a knowledge of rheological proper-ties of muds under down-hole conditions is necessary to predict pressure surges. He showed that the viscosity of a mud greatly influences the magnitude of pressure surges and the likelihood of lost returns. McLean et aL~ showed that the rheological properties of a mud under down-hole conditions are very important to cementing operations. This paper presents data showing the effects of time and temperature on rheological and gel properties of water-base drilling fluids. Measurements of gel strengths and rheological properties were made with two different concentric-cylinder rotational viscometers of the Fann type. One was the conventional six-speed viscometer modified to operate at temperatures up to 350F and at the vapor pressure of the liquid at test temperature. The other viscometer was newly designed to operate at temperatures up to 500F and pressures up to 1,000 psi. Tests with both instruments were made under essentially the same operating conditions. The new viscometer is shown in Fig. I. In this investigation, great emphasis has been placed on the rheological properties of clay suspensions, since clays are largely responsible for a mud&apos;s thixotropic and gel-

By J. R. Kyte, C. C. Mattax

Previous workers have developed differential equations to describe oil displacement by water imbibition, but have not explicitly defined the relationship between recovery behavior for a single reservoir matrix block and its size. In the present work, imbibition theory is extended to show that the time required to recover a given fraction of the oil from a matrix block is proportional to the square of the distance between fractures. Using this relationship, recovery behavior for a large reservoir matrix block is predicted from an imbibition test on a small reservoir core sample. The prediction is then extended to analyze recovery behavior for fractured- matrix, water- drive reservoirs in which imbibition is the dominant oil-producing mechanism. Experimental data are presented to support the basic imbibition theory relating matrix block size, fluid viscosity level and permeability to recovery behavior. INTRODUCTION Imbibition has long been recognized as an important factor in recovering oil from water-wet, fractured-matrix reservoirs subjected to water flood or water drive. l-3 Recently, two approaches have been published which might be used to predict imbibition oil-recovery behavior for reservoir-sized matrix blocks. Graham and Richardson4 used a synthetic model to scale a single element of a fractured-matrix reservoir. lair,&apos; on the other hand, used numerical techniques to solve the differential equations describing imbibition in linear and radial systems. This latter method requires auxiliary experimental data in the form of capillary pressure and relative permeability functions. These two approaches, i.e., synthetic models and numerical techniques, have been used to study a variety of reservoir fluid-flow problems. One pur- pose of this work is to present, with experimental verification, a third method for predicting imbibition oil recovery for large reservoir matrix blocks. This method uses scaled imbibition tests on small reservoir core samples to predict field performance. The imbibition tests are easier to perform than the capillary pressure and relative permeability tests required to apply the numerical method. Furthermore, when suitably preserved reservoir-rock samples are used, the properties of the laboratory system are the same as those of the field. This offers an important advantage over the use of synthetic models because there is usually some question as to how accurately reservoir-rock properties can be duplicated in such models. Based on the recovery behavior for a unit matrix block, an analysis is presented to predict oil recovery for a fractured, water-drive reservoir made up of many such unit blocks. In the analysis, it is assumed that the flow resistance and the volume of the reservoir fracture system are negligible compared with that of the porous matrix. These assumptions are generally consistent with observed characteristics of many fractured-matrix reservoirs, and have been employed in previous studies.2,3,6-8 further assumed that the effect of gravity on flow in the matrix blocks is negligible. On first thought, the latter assumption might appear to seriously limit application of the method. However, in a fractured reservoir, the effect of gravity on flow in a matrix block will be restricted by the height of the block. Furthermore, matrix permeabilities are often very low (10 md or less) in such reservoirs. This means that capillary or imbibition forces will be large, thus tending to minimize the relative importance of gravity. For these reasons, imbibition should be the dominant oil-recovery mechanism in many fractured-matrix, water-drive reservoirs. The predictive method presented in this report is applicable to such reservoirs. SCALING IMBIBITION THEORY The "scaling laws" applicable to the operation.

By R. J. Sandrea, S. M. Farouq Ali

The results of an experimental and theoretical study of the effects of rectilinear impermeable barriers and highly permeable channels on the sweep efficiency and conductivity of a five-spot network are presented. The study was carried out using Hele-Shaw, and conductive sheet analogs for both. normal and inverted flood patterns. A functional relationship was developed which provides quantitative prediction of the above parameters; i.e., sweep efficiency and conductivity, for the nonhomogeneous system. To evaluate this, it is necessary only to measure the interference modulus of the obstacle using a simple expression. The results indicate that impermeable barriers, with an interference modulus greater than zero, always cause a decrease in the conductivity and the sweep efficiency of the pattern. On the other hand, permeability channels do not have a significant effect on these parameters, unless they are located along the streamlines. The study also discusses a method of formulating the difference equations pertaining to the two-dimensional Laplacian in a system containing rectilinear barriers. In addition, a technique is described for tracing the progress of a free surface, using marked particles, in a stream containing discontinuities SuCh as those occurring at the extremities of barriers. The above computational scheme was used in a digital computer program to simulate results of the Hele-Shaw analog. The computed values of sweep efficiency mere in good agreement with the experimental values. INTRODUCTION At the present time waterflooding remains the most widely used technique for the secondary recovery of oil. Among the numerous factors that affect the performance of a waterflood, the areal sweep efficiency constitutes one of the most critical parameters. It is a function only of the geometric distribution of the wells for a homogeneous medium and unit mobility ratio. Geological considerations, however, such as the presence of sealing faults or solution channels in the rock matrix, would generally exert an adverse effect on the areal sweep efficiency of a waterflood network. Surprisingly little information is presently available on the quantitative implications of such permeability interferences. It was the object of this investigation to consider the presence of rectilinear, impermeable and highly permeable interferences in an otherwise homogeneous five-spot pattern, and to analyze their effects on the resulting sweep efficiency and pattern conductivity. The experimental phase of the study was conducted using two different models: the Hele-Shaw flow cell and the field plotter. For experimental convenience, the geometric boundaries of the five-spot were assumed to constitute streamlines even in the case where the interference was asymmetrically placed with respect to a repeated five-spot pattern. A second object of the study was to develop a computational scheme for numerically calculating the pressure distribution in a five-spot flow pattern containing rectilinear, impermeable barriers, and to use this distribution to compute the sweep efficiency. EXPERIMENTAL PROCEDURE HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remains valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates. The model used in this study was composed of

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,&apos; the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968