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By L. L. Swift

.It the present time there are four base metals being used for automo-tive bearing alloys. Of course there are numerous variations in the amounts of alloying elements added to each base metal and nearly all of these alloys have the conventional, if not classical, duplex structure; that is, they are composed of a hard constituent embedded in a soft matrix. The well-known theory is that the former will wear well, while the latter will be plastic enough to allow the bearing to be broken in and conform to the contours of the shaft. The requirements of the modern bearing have been most aptly described by W. M. Corse: In order to meet the engineering demands of today a good bearing metal must be able to carry the weight of the shaft and stand up under steady or suddenly applied loads, or even blows ill sorne types of service. A certain amount of plasticity is desired to compensate for minute irregularities in the shaft or bearing surface, and to permit yielding, thereby avoiding dangerous stresses in bearing and shaft and pre-venting overheating and rapid wear of parts. Less plasticity is required in a bearing tuetal if the surfaces of bearings and journals are machined accurately, aligned, and kept in alignment. It is desirable, of course, that a bearing metal have a low coeffi-cicnt of friction. Under most operating conditions the friction depends on the unit, pressure of the bcaring, the speed, the temperature, and the properties of the lubricant. A good bearing metal must have a low rate of wear to reduce the necessity for frequent replacements, and adjustment of the bearings. It must wear more rapidly, however, than the journal or shaft running on it, because replacement of the journal or shaft is more difficult and costly than replacement of the bearing.' The hardness of the bearing alloy is a property closely related to several of the foregoing. With a duplex microstructure, the measurement of hardness with any of the usual commercial devices means little. The Bierbaum method of measuring the hardness of the individual canstituents was developed to fill this need. MICROCHARACTER The Bierbaum MicroCharacter~,~ measures the scratch-hardness of a solid by pulling a weighted diamond point over the surface. The diamond point is ground so that it is the corner of a cube, and Mounted

Jan 1, 1939

By L. L. Swift

AT the present time there are four base metals being used for automotive bearing alloys. Of course there are numerous variations in the amounts of alloying elements added to each base metal and nearly all of these alloys have the conventional, if not classical, duplex structure; that is, they are composed of a hard constituent embedded in a soft matrix. The well-known theory is that the former will wear well, while the latter will be plastic enough to allow the bearing to be broken in and conform to the contours of the shaft. The requirements of the modern bearing have been most aptly described by W. M. Corse: In order to meet the engineering demands of today a good bearing metal must be able to carry the weight of the shaft and stand up under steady or suddenly applied loads, or even blows in some types of service. A certain amount of plasticity is desired to compensate for minute irregularities in the shaft or bearing surface, and to permit yielding, thereby avoiding dangerous stresses in bearing and shaft and preventing overheating and rapid wear of parts. Less plasticity is required in a bearing metal if the surfaces of bearings and journals are machined accurately, aligned, and kept in alignment. It is desirable, of course, that a bearing metal have a low coefficient of friction. Under most operating conditions the friction depends on the unit pressure of the bearing, the speed, the temperature, and the properties of the lubricant. A good bearing metal must have a low rate of wear to reduce the necessity for frequent replacements, and adjustment of the bearings. It must wear more rapidly, however, than the journal or shaft running on it, because replacement of the journal or shaft is more difficult and costly than replacement of the hearing., The hardness of, the bearing alloy is a property closely related to several of the foregoing. With a duplex microstructure, the measurement of hardness with any of the usual commercial devices means little. The Bierbaum method of measuring the hardness of the individual constituents was developed to, fill this need. MICROCHARACTER The Bierbaum microcharacter2.3 measures the scratch-hardness of a solid by pulling a weighted diamond point over the surface. The diamond point is ground. so that it is the corner of a cube, and mounted

Jan 1, 1938

By E. J. Nielsen, P. R. Strutt

A study has been made of the progressive changes in the distribution of etch-pit structures occurring during high-temperature creep in copper + 7 wt pct Al single crystals oriented with a [113] tensile axis. The two equally stressed glide systems with the highest Schmid factor would be expected to form subboundaries of the type predicted by Kear.2 The alignments of etch-pits on sections parallel to different (111} planes consistent with these types of boundaries were not observed. However, they were consistent with planar subboundaries (on a macroscopic scale). From an analysis of Amelinckx1 it may be shown that stable cross-grid dislocation boundaries may form in the primary slip planes. These boundaries form when dislocations with a Burgers vector not in the slip plane move into the plane by combination of climb and glide. THE geometry of subboundaries formed by the interaction of dislocations of two glide systems has been analyzed by Amelinckx,1 and the particular types produced by deforming fee crystals are predicted by ear.' In this paper types of boundaries which may be formed when climb as well as glide occur are discussed as this is relevant in high-temperature creep. It is assumed in the present investigation that the etch-pits observed in Cu + 7 wt pct A1 on surfaces parallel to {111} planes delineate the sites of dislocations. Although there is no direct evidence for this previous work on a-Cu/Al single crystals by Mitchell, Chevrier, Hockey, and Mon-aghan,3 would show this assumption to be reasonable. The alignments of etch-pits which form during creep are studied on sections parallel to each {111) plane. It is then deduced that these alignments are consistent with a specific type of planar subboundary. The Cu + 7 wt pct A1 single crystals had a [113] tensile axis and Fig. 1(a) shows schematically the relation of the slip planes and slip directions (as represented by tetrahedron ABCD) with reference to the tensile axis. The two equally stressed glide systems with the maximum Schmid factor namely ß-AD and (a-BD, from the analysis of Kear,2 would be expected to form the boundaries shown in Fig. l(a) and (b), also Fig. 5(a) and (b). EXPERIMENTAL PROCEDURE The a-Cu/Al single crystals were grown and annealed in a "gettered" argon atmosphere. Chemical analysis showed the aluminum content to be uniform in each crystal and the difference between crystals was maintained to an accuracy of ± 0.25 wt pct. The initial dislocation density and mean subgrain diameter after annealing was -106 cm-2 and 250 µ, respectively. Surfaces parallel to (111) planes were produced by specially developed electrolytic machining processes. The {111} faces were next electropolished for 5 min in a solution consisting of 25 g chromium trioxide, 113 ml glacial acetic acid and 40 ml water; the applied potential was 8 v. Dislocation etch-pits were revealed using l an etchant described by 1 ml bromine, 45 ml HCl, and - 250 ml water. RESULTS In crystals strained into secondary creep at higher stresses (443 and 750 g - mm-2 at 650° C aligned rows of etch-pits parallel to slip plane traces were evident in sections parallel to the (1111, (ill), and (111) planes, see Fig. 3. As well as the longitudinal alignments in Fig. 3, well formed randomly oriented arrays indicative of an equiaxed subgrain structure are evident. At the lower stresses (100 to 230 g . mm-2) only an equiaxed structure formed during creep. The sections in Fig. 3 are from a crystal crept for 70 hr at 650°C with a CRSS of 443 g.mm-2. Two identically oriented crystals were also deformed at the same temperature and stress for 5 min and 4 hr. In the crystal crept for 5 min, the etch-pits were randomly distributed with no tendency for directional alignment, see Fig. 2(a). As shown in Fig. 2(b) aligned arrays were evident after 4 hr creep but they were not nearly so well defined as in Fig. 3. The alignments (parallel to the arrows) in Fig. 3 are consistent with the existence of boundaries in the two main slip planes a and ß. The way in which this is deduced is seen by reference to Fig. l(c), where the existence of boundaries in the a and ß planes is verified by sectioning parallel to a,ß, and d. The (111) and ß(111) planes intersect the d(111) plane along BC [101 ] and AT [011] and alignments parallel to [101] and [011] are clearly evident in Fig. 3(c) in a section parallel to the d(111) plane. Similarly the a, and ß planes in Fig. l(a) intersect each other along DC [110] and hence there will be an alignment parallel to [110 ] in sections parallel to the a-plane and the ß-plane; this is evident in Fig. 3(a) and Fig. 3(b). It is interesting to note that alignments of etch-pits consistent with the boundaries predicted by Kear2 were not observed; see Figs. l(a) and l(b). The geometry of boundaries in {111} planes as shown in Fig. l(c) is discussed later. In Fig. 4(a) the individual etch-pits are resolved and the alignments are exactly parallel to the slip trace direction [101]. However, in some areas alignments deviate away from the slip trace direction by as much as 10 to 15 deg, this is evident in Fig. 4(b), and in Fig.

Jan 1, 1969

By Rudolph G. Wuerker

THE scarcity of values of tensile strength of rocks has been explained by the lack of successful testing procedures. In the case of mine rock a description is given' of the difficulties encountered in testing a cylindrical specimen, such as a core, by conventional methods. Over a period of years the following method has given definite and reproducible results with the weakest as well as with the strongest rocks. It does not completely supersede the use of cores with special fixtures but is a supplement in all cases where cores cannot be obtained, as from soft rocks, or in cases where it is less expensive to prepare test specimens by cutting them out of the rock instead of drilling cores. Principle and equipment are the same as for the test for tensile strength of hydraulic-cement mortar.' The test specimen, Fig. 1, has the shape of a briquet. While in the original cement mortar test the briquet is cast in a special mold, it is prepared from rocks in different ways, depending on how easily they can be cut and shaped. Soft rocks, which cannot be core-drilled with a carboloy or diamond bit, are simply hand-cut. Only two dimensions need be watched. The first is the 1-in. diam at the narrowest cross-section of the briquet. The other critical measure is the radius of curvature of the waistline, as the roller supports in the grips have a fixed distance. This radius is ground out of the solid by means of a carborundum grinding wheel having a 3/4-in. radius. Medium hard rocks can be core-drilled with a carboloy bit. The resulting core can be used for nondestructive sonic testing first, and after that for any destructive test. By using an EX-bit and by carefully placing the coreholes, preferably by using a tenplate such as shown in Fig. 1, it is possible to obtain from the rock a punched sample from which numerous tensile briquets can be made. The outside radius of the EX-bit differs from the radius of curvature of the briquet by 1/8 in., but this still permits placing and aligning the specimen in the grips. In the case of bedded rocks the core might have bedding planes normal to the plane of the briquets, and rocks can be tested in any arrangement of the bedding planes desired. Hard rocks, limestones, igneous, and metamor-whic rocks can only be diamond-drilled or diamond-cut. Here the method of getting the tension briquets by accurate placing of EX-drill holes is especially economical. The tops of the briquets made from hard rocks cannot be rounded; they are straight cuts made with a diamond cut-off saw and rounded off on a polishing wheel. Results: As long as specimens broke over the waistline the results were considered acceptable. Further statistical treatment of the tests' showed a satisfactory percentage of standard deviation. The tensile strength values obtained by this method do not represent true values because of the stress concentration caused by the curvature of the side of the piece and because of the closeness of the grips. The ratio of maximum to average stress at the plane of failure has been determined to be about 1.75." All tensile strength values listed in Table I are corrected accordingly. To avoid this stress-concentration, if there are a sufficient number of cores, tensile strength can be measured by imbedding the cores in mortar in the two outer briquets in the gangmold.4 Strain-Measurements: The applicability of the briquet specimens for strain observations was tested in the case of sandstone and shale. Two element Rosette SR-4 strain gages were used. Young's modulus and Poisson's ratio, both in tension, were computed and found to be different from those in compression, determined during the same test series and from the same rock, see Table I. References 1 L. Obert, S. L. Windes. and W. I. Duvall: Standardized Tests for Determining the Physical Properties of Mine Rock. U. S. Bur. Mines R.I. 3891 (1946). 2 Test for Tensile Strength of Hydraulic-Cement Mortar, ASTM Standard C 190-44. S F. O. Auderegg, R. Weller, and B. Fried: Tension Specimen Shape and Apparent Strength. Proc. ASTM 11939) 39, pp. 1261-1269. 4 API Code 32.

Jan 1, 1956

By M. F. Williams, L. G. Hendrickson

IN classification of pulps bearing magnetized ferromagnetic particles, depolarizing is of great importance. If size separation is to be effective, particles must be individual rather than in floes. Depolarizing is also practiced in heavy medium separations in which ferrosilicon or magnetite is the medium. When particles of ferromagnetic material have been removed from a magnetic field, residual magnetism causes agglomeration. The term depolarizing refers to the operation of reducing or eliminating this residual magnetism and may thus be considered magnetic deflocculation. The terms demagnetizing and randomizing are also used. At the Research Laboratory of Oliver Iron Mining Div. in Duluth a method was developed for measuring depolarization of the pulp of ferromagnetic material. Experiments were made with Mesabi taconite,' a natural magnetite of low coercive force. Ferromagnetic materials of higher coercive force, such as lodestone or the artificial magnetite produced by reduction roasting of hematite, present a more difficult problem, which was not within the scope of this investigation. It is possible, however, that some of the techniques evolved for measuring and calculating electrical characteristics of alternating current coils would be of use in depolarizing high coercive force material, particularly in conjunction with high-frequency alternating current, as proposed by Hartig and others.'," Properties of Ferromagnetic Materials:'7 Experimental work, described below, has shown that if a sample in the magnetized state is heated above the Curie point and cooled, much of the preferred orientation is destroyed and the sample is substantially depolarized. It has been thought that when the sample cools below the Curie point the domains cancel each other, leaving a zero net moment. However, such particles still exhibit a tendency to cohere, and undoubtedly this is caused by the forces of residual magnetism. -AS measured by the percent depolarization, this tendency is reproducible for any sample upon repeated heating above the Curie point and subsequent cooling and is independent of the initial state of magnetization. It is postulated, therefore, that as the material is cooled below the Curie point the domains in any particle do not completely cancel each other, but rather are preferentially oriented to some extent. Mechanism of Depolarizing with Alternating Current Magnetic Fields: It is believed that when ferromagnetic material is passed through an alternating magnetic field, depolarizing occurs in the decaying portion of the field. As the particles pass through the portion of highest intensity they become magne- tized. If the particles are not free to move, the polarities of the particles will be reversed (by a mechanism similar to that described above for magnetism) at a frequency equal to that of the applied field. As the material moves through the decaying field, intensity levels become such that a domain does not completely reverse, but stops on an axis of easy magnetization. By the time the material reaches the point of zero field intensity, a state of fairly random orientation of domains is achieved. If conditions are such as to give a completely random orientation, the particle will have little or no external magnetic field, and a pulp of such particles will be depolarized. Previous Work In 1918 E. W. Davis was granted a patent for demagnetization of magnetite pulps.' His method consisted of passing the pulp through a tapered coil, activated by alternating current of normal frequency (60 cycle). This method, with minor modifications, has been used almost universally in all pilot plants and commercial installations in which depolarization of low coercive force materials has been required. Hartig, Onstad and Foot2,3 avd made a detailed study of the factors involved in depolarizing both low (below 100 oersteds) and high (above 100 oersteds) coercive force material. They developed a method for evaluating the relative degree of depolarization of any pulp based on the settling characteristics of the pulp. Their standard of comparison was a sample heated to above the Curie point and cooled in a zero field, all in a neutral atmosphere.* For low coercive force material they found treatment.Thisprocedure is subsequently called, in this report,theCurie that results equivalent to Curie treatment could be

Jan 1, 1957

By B. C. Allen

Grain boundary grooving has been studied in chromium, molybdenum, and tungsten under a variety of conditions using high vacuum techniques and tantalum -gettered argon. The average surface free energy of solid chromium, and the chromium-liquid silver interface free energy were respectively found to be 2200 ± 250 and 500 i 130 ergs per sq cm from groove formation kinetics and estimates of pertinent volume difffusion coefficients. The results for chromium were unffected by variations in interstitial content ranging from 0.003 to 0.09 pct C, or 0.003 to 0.03 pct O. Surface diffusion is the primary mechanism of groove formation in chromium under 1 atm argon at 1200" to 140O°C, and is essentially unaffected by 0.003 to 0.09 pct C, 0.003 to 0.03 pct O , metastable nitrogen contents up to -0.01 pct, and up to 2 torr Ag vapor. At higher temperatures, the major mechanism is volume diffusion in argon or evaporation-condensation in stutic vacuum. Surface diffusion occurs in molybdenum at 0.5 to 0.96 and in tungsten at 0.5 to 0.9 of the absolute melting tempera -ture by a single mechanism, possibly by the migration of single adatoms or vacancies. Results were slightly affected by up to 23 tory Sn vapor, and in molybdenum were essentially unaffected by 0.5 Ti or carbon in the range 0.002 to 0.02 pct. Volume difffusion through the liquid is the mechanism of groove formation in chromium-liquid silver at 1200" to 1400°C and in molybdenum-, Mo-0.5Ti-, and tungsten-liquid tin at 1200" to 2000°C. The solid-liquid interface free energies involved were estimated from grooving kanetics. WHEN a grain boundary intersects a solid surface, a groove tends to form along the line of intersection at temperatures above about half the absolute melting point (0.5 TM). The groove progressively grows by preferential atomic migration either by diffusion or evaporation. Establishment of a groove angle occurs in accordance with the grain boundary and surface free energies involved. The motivation for groove formation is a reduction in the total surface free energy of the system. This study is a continuation of previous work on thermal grooving of chromium, molybdenum, and tungsten.&apos; The temperature ranges were extended, and the effect of metallic and interstitial impurities was evaluated. The results were such that certain interface free energies and surface self-diffusion coefficients were deduced from the grooving kinetics. EXPERIMENTAL WORK Materials and Preparation. As indicated in Table I, the 0.05-0.08-cm-thick chromium, molybdenum, and tungsten sheet used was nominally 99.99 pct after recrystallization. Two lots of molybdenum with about the same analysis, Mo-0.5Ti,* and tungsten were ob- *Alloy compsitions are expressed in weight percent . tained commercially. Extruded chromium rod,&apos; prepared from iodide process crystals, was warm rolled to sheet at 700°C. Sheet of three Cr-0 impurity alloys containing up to 0.03 pct 0 was prepared by warm rolling arc melted, extruded, and swaged rod. Two Cr-C impurity alloys containing up to 0.09 pct C were made by equilibrating unalloyed chromium with a known amount of CH4 for 24 hr at 1150°C in previously evacuated quartz capsules. Chromium containing nominally 0.015 and 0.06 pct N was similarly prepared by equilibration with NH3. The sheet was recrystallized to give a stable grain size about equal to the sheet thickness. Molybdenum and Mo-O.5Ti were recrystallized in a tantalum resistance furnace 1 hr at 1 x lo-5 torr at 2300" and 220O°C, respectively. Tungsten was similarly annealed for 1 hr at 2500°C. Chromium and its impurity alloys were outgassed at 1100°C and recrystallized 1 hr at 1700°C under 1 atm Ar. Except for nitrogen, the impurity content stayed roughly constant. Nitrogen in both alloys was reduced to <0.001 pct. In fact, over 80 pct of the added nitrogen was lost after outgassing at llOO°C and annealing sheet 1 hr at 1300°C in argon in the presence of tantalum. Such a rapid loss can be rationalized since -2 torr N are required for equilibrium with 0.04 pct N in solution,3 while the equilibrium pressure is ~10-5 torr over tantalum at 1300°C.4 The recrystallized sheet was cut into small coupons which were metallographically ground and polished on one side with a minimum of grain boundary relief. The surface roughness was on the order of 0.01 µ. The tin and silver used were nominally 99.999 spec-trographically pure. After being outgassed at 1100°C and equilibrated in a molybdenum crucible for 0.5 hr at 1800°C in argon, the tin contained 3 ppm 0, <0.3 ppm N, and 0.1 ppm H. Following outgassing at 900°C and equilibration in a chromium crucible 1 hr at 1400°C in argon, the gas content of the silver was 1 ppm O, <0.5 ppm N, and 0.3 ppm H. Grooving Under Argon or Vacuum. All specimens were placed in unsealed containers made from rod or sheet of the same alloy, thereby enabling the polished surface to achieve gas-solid equilibrium. The annealing fixtures are shown in Fig. 1. The specimen was placed in a resistance furnace with a tantalum or Ta-10W heating element plus tantalum fixtures or radiation shields. Chromium was outgassed at 1100°C, and molybdenum and tungsten were outgassed at 1900°C to 1 x l0-5 torr or at the grooving temperature, whichever was lower. In vacuum anneals, the specimen was then heated directly to the intended grooving temperature. In argon anneals, 99.996 Ar was admitted

Jan 1, 1970

By Arthur C. Spencer

IN extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,&apos; it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity applied to an elastic brittle mass offering strong resistance to deformation produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45° to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45°. This general conclusion, resting upon ana¬lytical mechanics, is completely supported by the results obtained by Daubrée in experiments upon the deformation of wax and resin prisms under compression. Let us then first con¬sider one of Daubrée&apos;s diagrams. In the case illustrated in Fig. 1, four sets of fractures in two appproximately right-angled pairs (that is to say, in conjugate sets) were produced by end-wise compression of the square cross-sectioned prisms. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45°. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism and place it between two fixed and

Nov 1, 1905

By H. R. Ogden, E. S. Bartlett, A. G. Imgram

Notched and unnotched tensile specimens of wrought and recrystallized, oxygmted and hydro-genated tantalum and columbium were tested over a range of temperatures selected to encompass the ductile-to-brittle transition. Increasing the oxygen content of tantalum and columbium increased their strength, and raised their ductility transition temperature, but did not cause a marked deterioration of notch properties below that of commercially pure material. The adverse effects of oxygen were more pronounced for recrystallized structures than for wrought material. The effects of hydrogen are complicated by strain aging or slow strain rate hydrogen embrittlement at -105°F. However, in general, hydrogen had only a minor effect an strength, but markedly increased the effective transition tem-terature and caused a deterioration of notch properties . BCC metals including the refractory metals in Groups Va and VIa (V, Cb, Ta and Cr, Mo, W) can be expected to undergo a ductile-to-brittle transition and exhibit brittle fractures at low temperatures.&apos; Notch embrittlement is associated with this phenomenon, and can be a serious design problem. Table I compares the tensile transition behavior and notch sensitivity of commercially pure Group Va and VIa refractory metals. The Group VIa refractory metals have considerably higher transition temperatures, and become notch sensitive at higher temperatures, than do the Group Va refractory metals. In addition, the Group VIa refractory metals are sensitive to metallurgical structure. Recrystallized structures generally have higher transition temperatures than wrought material of the same composition. The relatively poor transition behavior of the recrystallized structures of these metals is generally attributed to the segregation of interstitial impurity atoms at grain boundaries. Pronounced sensitivity to structure is not evident with commercially pure Group Va refractory metals, however. Since these metals have higher solubilities for interstitial elements than do the Group VIa metals ,4 it can be expected that higher total interstitial concentrations are necessary to develop a comparable degree of grain boundary segregation and to produce a similar sensitivity of transition temperature to structure. Increasing only the concentration of interstitial atoms in solution would tend to increase the flow stress of a metal in relation to its cleavage fracture stress and thereby raise its transition temperature, but would not be expected to cause a marked sensitivity of transition temperature to structure. A research program has been conducted at the Battelle Memorial Institute to evaluate the effects of interstitial oxygen and hydrogen on the transition behavior and notch sensitivity of tantalum and columbium, and to evaluate the effects of structure on "contaminated" material. EXPERIMENTAL PROCEDURES Notched and unnotched tensile specimens of oxygenated and hydrogenated tantalum and columbium with both wrought and recrystallized structures were tested over a range of temperatures selected to encompass the ductile-to-brittle transition Oxygen levels selected for study in both tantalum and columbium were nominally 500 and 1000 ppm, whereas nominal hydrogen contents were 150 and 500 ppm in tantalum and 150 and 300 ppm in columbium. Oxygen and hydrogen additions were made directly to 6-in. lengths of 1/2-in.-diam electron beam melted wrought bar stock, in a Sieverts Apparatus. Subsequent high-temperature annealing was required for homogenization of the oxygenated material, but was not necessary in the case of hydrogenated stock. The oxygenated and hydrogenated bars were then swaged to 1/4-in.-diam rods. Tensile specimen blanks were cut from the 1/4-in.-diam rods and annealed to achieve stress-re-

Jan 1, 1963

By W. O. Philbrook, A. E. El-Mehairy

The reduction by hydrogen of individual particles of dense hematite implanted in beds of inert spheres is controlled by single-particle kinetics. No evidence of reagent starvation was found down to low flow rates established by pressure gradients as low as 0.01 in. H2O per- in. of depth in beds of spheres as small as 3/16 in. diam. The optimum size for most rapid reduction of beds of homogeneous ores results from the effect on reducing potential of the gas of competing factors of supply and consumption. A recent publication1 presented the results of a study of the rate of reduction of iron ore in a fixed bed by hydrogen introduced at constant pressure differential. Under these conditions the reagent flow rate varied directly with the bed permeability, which was a function of particle size and shape and bed voidage, and inversely with the temperature-dependent viscosity of the gas. The present note adds data from supplementary experiments designed to reveal whether or not any partial reagent starvation arising from a flow-dependent transport resistance in the gas phase might have been operative. Kinetic studies were made of the reduction of individual spheres of iron oxide inserted into beds of inert spheres, so that the reagent flow rate and aerodynamic conditions were again determined by bed characteristics and temperature. The experimental techniques and apparatus were similar to those previously described.&apos; The synthetic iron ore spheres were wet-rolled by hand from powdered, reagent-grade* Fe2O3 and subsequently dried and then fired in air at 1250°C. The indurated pellets has almost no porosity as indicated by their specific gravity of 5.10. The beds were made of dense alumina spheres, closely sized to the same dimension as the iron oxide spheres, in the following diameters: 3/16, 1/4, 5/16, and 3/8 in. Each bed was hand-packed of particles of a single size to a controlled voidage of 0.32 and depth of 3 in. within a capsule having an internal diameter at least 10 times the particle diameter. A few weighed iron oxide spheres were individually planted in the central plane of the bed of inert spheres at points away from the wall. Reduction was carried out at atmospheric pressure by purified hydrogen at 670°, 800°, and 985°c. The reagent was supplied at precisely controlled pressure differentials of 0.01, 0.02, and 0.03 in. of water per in. of bed depth. This gave a range of flow rates similar to that used in the study of beds of ore and comparable with blast-furnace practice in terms of mols of reducing gas per hr per sq ft of cross-section. Viscous flow prevailed in all beds under the experimental conditions of this study. The reduced particles were checked for loss in weight and then sectioned for metallographic examination. Occasional particles were found to have contained minute internal cracks that interfered with the concentricity of the reduction interfaces, and data for such particles were rejected. An experimental rate constant for the reduction of the imbedded Fe2O3 spheres was calculated on the assumption that the rate was proportional to the metal-oxide interface area by an equation that has been found by McKewan2 to describe the reduction of single spheres

Jan 1, 1962

By L. W. Saperstein, D. Yeung, L. B. Phelps

Introduction The success of preventive methods for the mitigation of coal mine drainage formation will require a marriage of the minimization of initial coal mine drainage formation, the minimization of toxic fluid formation after toxic material disposal, the minimization of the mobilization and transpor¬tation of formed toxic fluids, and the maximization of the rate of diultion and attenuation of the formed toxic fluids. This paper contributes to the understanding of factors af¬fecting mobilization and dilution and attenuation of formed toxic fluids. When water containing a salt content different from in situ pore water in the soil is passed through a body of soil, the concentration of salts in the outflow will gradually change composition in a manner that depends on the kinds of hydraulic processes that occur in the soil. These processes are molecular diffusion, lateral dispersion, longitudinal dispersion, chemical reactions or exchange, physical adsorp¬tion, and biological retardation. This note considers only the first three processes. These three microscopic processes can be analyzed statistically on a probability basis. Such results, confirmed experimentally, indicate that a tracer introduced instantaneously as a point source will tend to form a Gaussian normal distribution as it moves downstream (Todd, 1964). Dilution During Flow The closed-form soltuion for pulse or instantaneous injec¬tion of a tracer during confined flow in a homogeneous porous medium shows that the maximum tracer concen¬tration at a point in space, x, after the time interval, t*, is given by [ ] where Aa is the effective flow cross-sectional area; A is the column cross-sectional area; a is soil porosity; M is mass of the injected tracer; C is concentration of the tracer in the permeating fluid and is a function of x and t*; D is the longitudinal dispersion coefficient; and va is the interstitial fluid velocity (Klotz and Moser, 1974). Therefore, the following conclusion can be made: • For a medium with a constant longitudinal dispersion coefficient, D, a constant soil porosity, a, a constant cross¬sectional area, A, and a fixed mass of injected tracer, M, Cmax will decrease as the time of peak outflow concen¬tration t* increases. • For a medium with a constant longitudinal dispersion coefficient, D, a constant soil porosity, a, a constant cross¬sectional area, A, a fixed mass of injected tracer, M, and a constant interstitial fluid velocity, va Cmax will decrease as the distance of travel, x, increases. • For a medium of constant cross sectional area, A, con¬stant soil porosity, a, a constant mass of injected tracer, M, and a fixed distance of travel, x, Cmax will decrease as D/va increases. Klotz and Moser (1974) concluded that D is about proportional to no.3 where r) is the kinematic viscosity; D is about proportional to a-3 where a is soil porosity; D in¬creases with increasing grain size; D increases as grains become less spherical; D increases with greater grain rough¬ness and angularity; D increases with increasing uniformity coefficient; and D is significantly affected by grain size and uniformity coefficient. The remaining parameters are not significant. Numerical Simulation Studies Numerical simulation studies were used to investigate the nature of flow and the optimum length of a toxic package within a saturated porous medium of fixed dimensions and configuration (Fig. 1). The width and position of the package was maintained constant (Phelps et al., 1981). Results indicate that if the package extends throughout the length of the model, the flow is vertically downward and

Jan 1, 1984

By W. Rostoker, R. P. Elliott, B. W. Levinger

Phase equilibria in the Ti-Mn-Mo system have been investigated in the composition range 100 to 60 pct Ti and in the temperature range 550 to 1150°C. Three out of ten isothermal sections are presented as well as seven vertical sections, projections of the beta space and the surface of incipient melting. A STUDY of the system Ti-Mn-Mo was undertaken as part of a program to aid in the development of titanium-base phase equilibrium diagrams of potential technical importance to alloy development. The scope of the investigation included the composition range 100 to 60 wt pct Ti (all compositions refer to weight percentages) and the temperature range 550" to 1150°C. A surface of incipient melting was constructed from measurements of a large number of alloys. In the binary system Ti-Mo,&apos; the high temperature modification of titanium generally spoken of as the p phase is stabilized to successively lower temperatures with increasing alloy content. There are no known intermediate phases, and complete miscibility exists between body-centered cubic titanium and molybdenum. The u solid solution is limited to less than 0.8 pct Mo at temperatures between 885" and 600°C. An equilibrium diagram for the binary system Ti-Mn has been published.&apos; Manganese behaves as a p stabilizer but undergoes a eutectoid transformation at about 20 pct Mn and 550°C to a plus an intermediate phase. The structure of this phase has been found to be isomorphous with the a phase FeCr." Accordingly, the phase is assigned the formula TiMn, although its actual location on the composition scale has not been determined and may well be not exactly at the equiatomic composition. In disagreement with ref. 2, the origin of the TiMn phase has been shown&apos; to be a peritectoid transformation at a temperature between 900" and 1000°C. A second intermediate phase occurs at the atomic proportions TiMn,. The structure of this phase was originally established by Wallbaum" as having a hexagonal lattice (C 14 type, 12 atoms per unit cell) isomorphous with MgZn,. In this work, the structure determination was confirmed and lattice parameters determined to be: a = 4.815 kX, c - 7.901 kX. Because of the extensive range of the P phase, the ternary system was suited to the determination of the phase boundaries by the parametric method of Andersen and Jette." During the course of the investigation, this method was found applicable only to the P/a+P boundaries but not to P/P+ compound boundaries. Metallographic methods were used alternatively for delineating these phase boundaries. Preparation and Treatment of Alloys Over 70 alloys were prepared for the study of this system. Ten gram alloy buttons were arc melted in a nonconsumable electrode furnace using inert atmosphere protection, and a water cooled copper crucible. The construction and operation of this type of melting unit has been described.&apos; To insure complete solution of alloy additions, especially molybdenum, the buttons were remelted alternately on top or bottom as many as five times. This was accomplished by a suitable mechanism for "flipping" the ingots over. It was very difficult to obtain homogeneous melts in the region of less than 75 pct Ti because of the very high melting point of molybdenum and Ti-Mo master alloys and the comparatively low boiling point of manganese. Thus, the arc conditions for insuring complete solution of molybdenum were incompatible with the prevention of heavy losses of

Jan 1, 1955

By E. E. Anderson, R. L. Newacheck, J. Kohl

Radioactive materials were used underground before the advent of the nuclear reactor. Radium containing ores have been mixed with cements and other materials for later location in oil wells by gamma ray logging since 1940.1 Perforating bullets have been marked with radium salts,, and radioactive materials have been added to drilling muds to find the cause of "lost circulation."&apos; More recently colloidal suspensions of radioactive cobalt-60 and silver-1103 and solutions of 1-1314 have been used in waterflooding operatiorns to determine injection profiles, flow paths and water velocities. In this paper a recent and interesting underground tracer application is discussed. Development work and field engineering were carried out under the direction of Tracerlab, lnc., with assistance from personnel of the client. A gaseous tracer, argon-41, was used in an attempt to determine the cause of leakage from an underground gas storage reservoir. STATEMENT OF PROBLEM This gaseous tracer application was carried out for the Natural Gas Storage Co. of Illinois. This company has developed an underground gas storage field 1,750 ft below the surface of the earth near the village of Herscher, Ill., about 60 miles south of Chicago. The total volume of gas stored in the field was estimated to be about 13 billion cu ft in the spring of 1954. The field has a maximum estimated storage capacity of 90 billion cu ft. The gas is contained in the Galesville sandstone, previously a water bearing formation of about 25 per cent porosity. The water as it is pushed out by the gas forms a barrier for the gas around the edge of the reservoir. Over the top and beneath the bottom of the reservoir are located several layers of impervious rock, which barring cracks or unplugged and unknown wells should act as seals. Twenty-one injection and withdrawal wells were drilled into the Herscher reservoir and gas injection was begun during the summer of 1953. After a few weeks of gas injection, evidence of gas leakage was detected at the surface; water wells began bubbling and losing prime, and dry spots in the fields indicated gas leakage from uncharted oil wells. In every case, the leakage could not be traced back any further than the water bearing formations a few hundred feet below the surface. An extensive search was made to locate uncharted oil wells which were believed to be possible channels for the gas from the storage formation to the water containing formation. Long-time residents in the area assisted in the location of several abandoned oil wells. The wells when located were cleaned out and either used as vent wells to relieve the gas pressure in the water formations, or were plugged with cement. None of the wells even approached depths which would endanger the soundness of the storage reservoir. All of the injection wells were tested for leaks in the casings by conducting neutron surveys and by other techniques. To detect any leakage up through the cement-filled annulus surrounding the casing, a section of the casing wall in one well was milled out. Then, plugs were installed above and below the cut-out section and pressure applied to the annulus, which proved conclusively that the cement was sound in that well. The well was then plugged with cement and abandoned. In another well, ammonia was injected into the well and a temperature log was made. It was hoped that a leak would be re-

Jan 1, 1956

By R. W. Olson, A. L. Benham

Viscous fingering was studied as it occurred in an open Hele-Shaw model (1 ft x 4 ft x 1/16 in.); it was also studied in the same model packed with 80-mesh glass beads during miscible displacements under unfavorable viscosity ratio conditions. It was determined that the lengths of 20 elements of the front were distributed normally around the average position of the combined elements under all conditions. Represented by the normal distribution, the length of the viscous fingers grew linearly with the distance traveled from the point of finger formation, increased with displacement velocity, and increased with increasing mobility ratio. Results obtained during the first few inches of displacement were of little or no use in predicting finger growth and/or finger length throughout the 4-ft model since the point of finger initiation cannot be predicted and would often occur several inches from the point of injection with either positive or apparent negative coordinates. The fingering occurring during a miscible slug displacement was much greater than would be predicted based upon the actual mobility ratios between in-place fluid and slug and between slug and following fluid, using the results described above for miscible displacement in the absence of a slug. Many of the experiments in the packed model showed that the rate of growth of the viscous fingers was diminishing toward the end of the displacement in the 4-ft long model, indicating that microscopic mixing, such as diffusion or dispersion, was decreasing the viscous fingering effect. INTRODUCTION Viscous fingering is a manifestation of a finger-shaped interface between displaced and displacing fluids occurring during typical miscible displacement projects for oil recovery. Its cause may be traced to the instability of a viscous fluid being displaced by a more mobile fluid. Viscous fingering takes on important significance in the miscible slug process 1.2 where it may be a dominant factor in determining minimum slug size. Experimental1-3 and theoretical4-7 studies of viscous fingering have been made by other investi- gators. However, an exhaustive study of the variables affecting viscous fingering had not been made. The present study was undertaken in an effort to determine the effects of some of the more obvious variables—such as mobility ratio, displacement velocity, distance displaced, and packing—upon viscous finger length and growth in a small laboratory model. It does not necessarily follow that conclusions reached by studying the results of this model study may be applied to the field. Future studies would have to evaluate the effect of model size on extension of these results. EQUIPMENT AND EXPERIMENTAL PROCEDURES A flow diagram for the equipment used in this study is shown in Fig. 1. Basically, it consisted of (1) a constant-rate pump for the injection of displacing fluid into (2) a model made up of two flat transparent plates spaced a small distance apart and (3) provisions for the production of fluid into a calibrated graduate. The displacing fluid contained a dye which allowed visual observation of finger spacing and length. The pump performed at rates from 2.5 cc/hr to 480 cc/hr, while pumping a light mineral oil into a bladder in a closed glass container holding the displacing fluid. The model was made up of two plates of 1-in. Plexiglass with dimensions 1-ft wide by 4-ft long. These were spaced 1/16 in. apart so that the internal model dimensions were 1-ft wide x 4-ft long x 1/16

By A. D. Rich

The term "bleaching clay" or "bleaching earth," as used in the oil industries, refers to clays that in their natural state, or after chemical or physical activation, have the capacity for adsorbing coloring matter from oil. There are three common types of bleaching clays: fuller&apos;s earth, activated clays, and activated bauxite. Fuller&apos;s earth, or naturally active clay, is prepared from bentonites (see Chap. 5) that possess natural activity. It is not activated commercially; in fact, earths of this type ordinarily do not respond satisfactorily to acid activation. Fuller&apos;s earth is prepared in pulverized as well as granular form for use in the contacting and percolation processes, respectively. Acid-activated clays also are of bentonitic origin. The basic raw clay, however, is of a type that has a very low natural activity but is highly activable by treatment with mineral acid. Commercial acid-activated clays generally possess several times the decolorizing power (bleaching efficiency) of the best quality of fuller&apos;s earth. The former are prepared commercially only in the pulverized grade because of the difficulties in obtaining a satisfactory granular product, and hence are used only in the contact process. Activated bauxite is made by heat-treating bauxite ore, which in its natural state has very little natural activity. The commercial product is prepared in granular form for use in the percolation process on petroleum oils. For the most part, bleaching clay is used commercially in the decolorization of animal, vegetable and petroleum oils, fats and waxes. It is applied in two ways: (1) by the percolation method and (2) by the contacting method. Percolation refers to the passage of oil through a bed of granular clay whereas contacting refers to direct agitation of oil and pulverized clay followed by removal of the clay from the oil by filtration. In either case, the decolorizing effect is obtained by intimate contact between the liquid oil and the solid adsorbent. Petroleum oils are treated commercially by either the percolation or the contact process. Animal and vegetable oils are treated by the contact process only. Composition The raw clays from which both fuller&apos;s earth and acid-activated clays are prepared are composed of hydrous aluminum silicates containing varying quantities of magnesium, iron, calcium and other elements. These raw materials are usually nonswelling bentonites derived from volcanic ash or lava by weathering and hydrothermal chemical reactions. The bentonites have as their chief mineral constituent montmorillonite, which has the formula [(OH)4Si6A14O20•nH2O], according to Grim. (See Chap. 5, ref. 6, p. 91.) The underlying reasons are not fully known for the natural activity of the fuller&apos;s earth type of clay and its usual failure to further activate with mineral acid in contrast to the natural inactivity of the activatable type of clay. However, it may be said that the bentonites that are responsive to the acid-activation treatment generally have not undergone any drastic metamorphism. The chemical composition is not a reliable means of discrimination between a nonactive, a naturally active, and a nonactive but activable clay, therefore it is not possible to forecast the ultimate quality of a clay on the basis of the raw-clay analysis alone. Table 1 gives typical analyses of representative clays of the foregoing classifications.

Jan 1, 1960

By E. F. Ketterer, D. B. Collyer, A. B. Wilder

The microstructural stability of 59 carbon and low alloy steels after 34,000 hr exposure at 900&apos; and 1050°F, including the weld heat-affected zone, is discussed. The tensile and creep rupture properties of the parent metal of many of the steels before and after 10,000 hr exposure are presented. SEAMLESS pipe has been used for many years at elevated temperatures. When seamless first began to be used, operating temperatures and pressures were relatively low and the steel produced adequately met the existing requirements. The need for knowledge of creep properties and graphitiza-tion was nonexistent. Today the requirements for tubular products have changed considerably. Operating temperatures and pressures are increasing continually and corrosion, particularly at high temperatures, presents a problem. Carbon steels have, under these conditions, certain economic advantages particularly in oil refinery use. However, the use of low alloy steels in the generation of steam power has increased appreciably due to the influence of molybdenum on creep strength and the control of graphitization with chromium. The behavior of carbon and certain low alloy steels after long periods of exposure at 900° and 1050°F (480° and 565°C) has been investigated. The steels were examined before and after 10,000 to 34,000 hr exposure. Results obtained with material exposed at 1200°F (650°C) are not presented due to the severe oxidation and resulting decarburiza-tion after long periods of exposure. The graphitization characteristics of carbon and low alloy steels are of fundamental concern to the users of these materials. This is particularly true where welded joints are employed. In order to evaluate properly the behavior of steels at elevated temperatures, it is desirable to employ not only long periods of exposure under controlled conditions, but to use material with known properties and steelmaking practices. The purpose of this investigation has been to study the microstructure of the weld and the tensile and creep rupture properties of the parent metal after long periods of exposure at elevated temperatures. In the report&apos;.&apos; of a previous investigation data were presented on the microstructure, impact strength, hardness, and oxidation characteristics after 10,000 hr exposure at elevated temperatures. When this investigation was planned, methods for controlling the graphitization characteristics of steel were not established and, therefore, a number of special alloy steels were included in the study. During the exposure of these steels, the influence of aluminum in accelerating the rate of graphitization and the inhibiting power of chromium were established by various investigators. Also, the vanadium-bearing steels, because of their outstanding creep properties, received attention. As a result of these developments, considerable progress has been made in the field of high temperature tubular products, and the necessity for special alloys to prevent graph-itization has been restricted largely to the use of chromium. Material Chemical analysis, deoxidation treatment, and austenitic grain size of the 59 steels discussed in this paper are shown in Table I. The steels were forged to 1x1 in. bars with the exception of steels 12B, 12DX, 12DY, 12DZ, 70, 70A, 72 to 78, 82, and 83 which were machined from heavy wall pipe. All bars were surface ground before exposure. Heat treatment before exposure is shown in Table 11. The majority of the steels included were melted in either a basic open hearth or basic electric furnace; how-

Jan 1, 1955

By L. R. Page, J. J. Norton

EFFECTIVE methods for determining grade and reserves of pegmatites in advance of mining have been developed in recent years. When intensive work began on the economic geology of pegmatites during the early years of World War 11, it was widely believed that grade and reserves could be estimated only in a most general way. The literature indicated that not all pegmatite deposits are unpredictable, but statements emphasizing unpredictability and irregularity seem to have been more widely accepted. Many standard references reflect the prevailing opinion that minerals: are unsystematic in their occurrence in pegmatites. Pegmatites have been described as "notorious for their irregular structure," and minerals within pegmatites as "irregularly distributed." "irregularly disseminated," of "erratic occurrence," "proverbially erratic in distribution," "characterized by extreme irregularity in ... size and distribution of the essential minerals, and variety and proportion of the accessory minerals," and "spotty.&apos;"" Over many years, however, geologic techniques have been applied with increasing success to economic analysis of pegmatites. Investigations, chiefly since 1939, have shown that mineral distribution and structure of pegmatites are largely systematic and that detailed geologic study can be used to predict the size and shape of mineral deposits in pegmatites. Because the writers are most familiar with the pegmatites of the Black Hills, S. D., examples cited are from that area." Pegmatites mined in other dis- * All examples are described more cornpletely elsewhere.: tricts are similar to those in the Black Hills," and the techniques described here have been applied by geologists and engineers working in other districts. In actual practice few pegmatite mine operators attempt to make accurate estimates of grade and reserves in advance of mining. Many deposits are too small for mining except on a very small scale; few pegmatite mines have more than ten employes. Hence there is little systematic preparation for mining, and the capital outlay may be so small that only a general knowledge of reserves is necessary. Technical personnel are rarely employed by pegmatite mine operators to make such estimates. In the future, however, as capital outlay becomes larger, estimates of grade and reserves will have to be more accurate. Geologic Aspects of Determining Grade and Reserves Estimating grade and reserves requires that the type of pegmatite, the size and shape, and the internal structure be determined by detailed geologic mapping and careful mineralogic study. The wide variations in the texture and distribution of minerals within many pegmatite deposits make a thorough geologic study of this kind necessary before it is possible to decide what sampling methods should be used to determine mineral content or grade. Types of Pegmatites: The first step in economic appraisal of a pegmatite is to determine the min-eralogical and structural type. In general, pegmatites may be classified into two groups: 1) those in which component minerals are more or less evenly distributed throughout the entire body and show relatively minor variations in texture, and 2) those in which component minerals have been segregated into units with recognizable differences in texture, mineralogy. or both. Johnston" has classified these types of pegmatites as homogeneous and heterogeneous, respectively. Cameron et al.10 have used the terms ~inzoned and zoned for similar types. The difference between the homogeneous and heterogeneous types is of great commercial importance. Homogeneous pegmatites can seldom be mined where the products are concentrated by the hand methods now commonly used, but they have been mined in a few places where a milling process has

Jan 1, 1957

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick&apos;s First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood&apos;s analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner&apos;s diffusion-controlled kinetics is based upon the same form of mass balance using Fick&apos;s First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By C. S. Corbett

EARLY in the development of every oil field, the operators of relatively large tracts of land must decide upon a spacing plan for the wells to be drilled upon their respective tracts. Usually it is desirable to have a system of regular spacing laid out over the entire tract, making such adjustments as may be necessary near land boundaries. Unless the dip of the producing formation is very steep, the equilateral triangular arrangement is the one most generally preferred, for the very good reason that it gives the maximum amount of drainage area for the wells up to the limit at which mutual drainage interference begins. Assuming that the equilateral triangular pattern is to be used, there still remains to he decided the matter of distance between wells. Many variable factors enter into the problem of proper spacing, some of which are physical and some economic. It is not the purpose of this paper to discuss these factors, as that has been done in several comprehensive articles during the past few years. In the end the decision must be based upon an estimate of the relative importance of various factors which apply to the field in question and to economic conditions in the oil industry at the time the development is getting under way. Even if the best possible spacing distance should be chosen when the problem arises, changing economic conditions and variation in physical conditions in different parts of the field may cause the original choice to become more or less unsatisfactory. Obviously, it is advantageous, once a spacing plan has been adopted, to avoid alteration of it as the field becomes better known or as conditions in the industry change, and yet be able to vary somewhat, the acreage per well in extending the area of development. Or, it may be desired to provide for an ultimate spacing considerably closer than conditions seem to warrant early in the development of the field. With these contingencies in mind, it is of interest to examine the possibilities which the equilateral triangular system affords. Orientation of Coordinate System In this system the well locations may be considered as the inersectionst of three sets of coordinate lines, the lines of each set intersecting those of the other two sets at 60. For convenience in placing such a system

Jan 1, 1930

By Charles Wurms, Robert Steinitz

DURING an investigation to determine the compatibility of several metals with tungsten, the degree of reaction between tungsten and lead was determined. A literature survey showed considerable disagreement between the results of various earlier investigators. Information presented by M. Hansen1 states that, according to S. Inouye,2 tungsten has very poor resistance against attack by molten lead, even at the low temperature near the melting point of lead. A phase diagram in the same reference indicates a solubility of 30 wt pct W in molten lead at 1300°C. Contrary evidence was shown by Parkman and shepard3 in their investigation of materials for use in heat transfer systems containing liquid lead alloys; they performed experiments at 980°C for times up to 50 hr without noticing any appreciable attack on the tungsten. Tungsten sheet was immersed in molten lead contained in Vycor tubes evacuated to at least 10-4 mm Hg. R. Bernard4 and R. I. Jaffee5 also indicate that no reaction occurs between molten lead and tungsten. However, no experimental data were included in these reports. In order to settle the question of the solubility of tungsten in molten lead, tungsten powder with an average Fisher subsieve particle size of 6µ was pressed in a double-acting die at 6 tsi to small compacts. They were then sintered in an atmosphere of hydrogen for 2 hr at 1700°C, resulting in a sintered density of 64 pct of theoretical with final dimensions of 0.260 in. in height and 0.245 in. in diameter. For all tests, the tungsten pellets were immersed in molten lead. Table I is a summary of the experimental procedures showing atmospheres, temperatures, and times. The first experiments were performed at 650°C; at this temperature, the liquid lead should wet the porous tungsten better than at its melting point, and penetrate into the pores. The lead was heated in a graphite crucible with a graphite cover. No protective atmosphere was used, as it was expected that the formation of CO would be sufficient to prevent oxidation. This, however, proved to be wrong, and all tungsten samples showed a slight oxide film after treatment. The tungsten samples were immersed in the molten lead for times of 5 min, 10 min, 1/2 hr, 1 hr, and 2 hr. After this time, the melt was poured into a form and the

Jan 1, 1962