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By Irwin Roman

In a previous paper,l a method was suggested for determining the depth to a bed in the simple case of a uniform overlying layer of constant thickness. The main purpose of the present paper is to show how a slight modification of that method has been used to interpret specific data obtained in the upper peninsula of Michigan by the staff of the Depart- ment of Mathematics and Physics of the Michigan College of Mining and Technology. The method of Tagg2 has also been used on the same data, thus furnishing a comparison of the two methods, as well as a method of using the two methods jointly. The method of measuring the apparent resistivity is that suggested by Wenner,3 and illustrated in Fig. 1. A current I enters the earth at the positive pole C and leaves it at the negative pole D. The potential V of the high electrode A, with respect to the low electrode B is measured by suitable means. The separation of the collinear points in the order shown, DBA C, is I, the same for each interval. If the resistivity of the overburden is po, and that of the bed is pa, the apparent resistivity is given by

Jan 1, 1934

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By N. J. Grant, Masao Adachi

A number of Cu-SiO, and Cu-A1203 alloys of low oxide content, produced by internal oxidation of copper-silicon and copper-aluminum dilute solid solutions, were exposed at temperatures up to 1050°C for fairly long times to bring about partial or total re crystallization. The creep-rupture properties of these re crystallized alloys were compared to those in the as-extruded condition at 450° C. Some of the alloys were cold worked after re crystallization to note changes in creep-rupture properties, also at 450OC. SINCE the introduction of the SAP alloy in 1949,~ many studies have been carried out on similar oxide and intermetallic dispersion hardened alloys to determine properties and to establish the mechanisms involved in the strengthening process which led to stable, high-temperature behavior.'-' To date, it has been indicated that, however achieved, the structure should be composed of a continuous ductile metal matrix in which is dispersed a fine, submicron size, hard, insoluble second phase (or at least, essentially insoluble at temperatures very near the melting point), with a submicron or near submicron interparticle spacing. Stored energy, obtained by a high strain rate deformation process appears desirable, as an additional strengthening means beyond pure dispersion.=

Jan 1, 1961

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By H. Margolin, A. Coucoulas

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKcll radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuAl2, and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band.1,4 Europium in EuAl2 appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref. 1. One of the other phases was identified as Co5Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acia Cryst., 1959, vol. 12, p. '162. A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently hiher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1 week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By W. R. Kanne, P. R. Strutt, R. A. Dodd

A study has been made of the creep behavior of ß-NiAl of stoichiometric composition in the temperature range 475" to 775°C. Single crystal tensile specimens were deformed under a constant applied load. From slip line studies and tensile axis rotations it was concluded that the crystals deformed by pencil-glide on (100) and (110) planes with a (100) slip direction. Electron microscope thin-film studies showed evidence for profuse cross-slip, and the dislocation Burgers vector was determined to be (100). There was no tendency for the dislocations to lie in definite slip planes, although a strong alignment of segments of edge dislocations was frequently seen. The activation energy for creep in the temperature range 475" and 775°C was judged to be much lower than that for creep at temperatures above 775°C. It is possible that the rate-controlling process is the thermally activated cross-slip of screw dislocations. In recent years considerable interest has developed in the possible use of high-melting-point intermediate phases for high-temperature applications necessitating good creep resistance. Ordered alloys such as Ni3A1, modified by alloying additions, have received particular attention, culminating in the recent development by Pratt and Whitney of single crystal turbine blades.' The intermediate phase NiAl has considerable theoretical interest from a creep standpoint because not only is it ordered up to the melting point (-1650°C at stoichiometry) but it contains a high concentration of structural vacancies on the aluminum-rich side of stoichiometry. These vacancies are known to exert a strengthening effect under some conditions,' but in addition they might be expected to affect high-temperature creep rates through dislocation climb. The present paper deals with the slip line and dislocation structures developed during creep of stoichiometric NiAl between 475" and 775C, and with possible attendant creep mechanisms. MATERIALS AND TEST TECHNIQUES NiAl ingots of stoichiometric composition were prepared by induction melting 99.996 pct A1 and 99.98 pct Ni (kindly provided by the Kaiser Aluminum Co. and the International Nickel Co., respectively) in 100 cc pure alumina crucibles in a helium atmosphere. No chemical melting flux was used in order to avoid con- tamination of the alloy. Each ingot was slowly direc-tionally solidified to avoid porosity and to produce very large grains up to 2 in. in length. In this way, ingots were obtained which were suitable for sectioning into single crystal creep specimens. Chemical analysis indicated that all alloys were within the range 49.6 0.3 at. pct Ni. For the present investigation, identical rectangular single crystal blanks were cut vertically from one particularly large crystal in an ingot using a series of three diamond cut-off wheels with appropriate spacers. Thus, all sliced crystals had the same orientation with the tensile axis parallel to the long side of the rectangle; the initial orientation of the tensile axis is shown as S, in Fig. 1. The blanks were homogenized at 1250 to 1300°C for 48 hr and subsequently cooled slowly to room temperature. A gage length of rectangular cross section and about 0.75 in. in length was prepared on each specimen using an electrolytic lathe and a dilute nitric/phosphoric acid electrolyte. The gage length cross section was 0.250 0.0005 in. by 0.040 ± 0.0005 in. Holes to accommodate tensile grips were electrolytically machined using a rotating acid jet. After creep testing, this same technique was used to cut discs for transmission electron microscopy. Thus, all shaping was done electrolytically, the only exception being that (122) sections were spark-machined from some speci-

Jan 1, 1970

By C. E. Tsoutrelis

A new method for determining rock drillability in diamond drilling is discussed; the method takes into consideration both penetration rate and bit wear. The method is based on drilling a rock specimen under controlled laboratory conditions using a model bit. The technique used for determining the experimental variables is extremely simple, quick, and reliable. Drillability is then determined by the mathematics of drilling. In considering the different factors that affect diamond drilling performance, the nature of the rock to be drilled is of outmost importance since it affects significantly the drilling costs and such other variables as bit type and design, drilling thrust, and bit rotary speed. Many attempts have been made to study this effect by correlating actual drilling performances either to certain physical properties of the rock being drilled1-? or to test drilling data obtained under laboratory conditions.7-13 These attempts were aimed at providing a reliable method of predicting by simple means the expected rock behavior in actual drilling, thus giving the engineer a tool to use in estimating drilling performances and costs in different types of rock. The purpose of this paper is to describe such a method by which rock drillability (a term used in the technical literature to describe rock behavior in drilling) could be determined in diamond drilling. It is believed that the proposed simple and reliable method will cover the need of the mining industry for a workable method of measuring the drillability of rocks. It should be emphasized, however, that since drill-ability depends on the physical properties of rock and each drilling process (diamond, percussive, rotary) is affected by different or partly different rock properties,14-l6 the proposed method of determining rock drillability cannot be extended to the other drilling processes. The results presented in this paper form part of an extensive three-year research program carried out by the author in the laboratories of the Greek Institute of Geology and Subsurface Research. During this period the effects of the physical properties of rocks and of such operational variables as drilling thrust and bit rotary speed in diamond drilling were investigated in detail. DRILLABILITY CONCEPT The literature is not devoid of drillability studies. While there are a number of investigators1,3,5-7,9-0,12-13,17 who have attempted to establish by direct methods (i.e., drilling tests under laboratory conditions) or indirect (i.e., through a physical property of rock) an index from which the drilling performance in a given rock may be estimated, very few6-7,9,12, of the proposed methods seem to be of much practical value to the diamond drilling engineer and none to date has been universally accepted. Commenting on the proposed methods for assessing rock drillability, Fish14 remarks that "for a measure of drillability to be accepted it is essential that penetration rate at a given thrust and bit life are elucidated as otherwise the method is of little value." This statement should be examined in more detail by making use of the penetration rate-drilling time diagram obtained in drilling a rock under constant operational conditions. Furthermore, the merits of using this diagram to describe rock drillability will be pointed out. At the same time reference will be made to this diagram when discussing some previously proposed methods. Fig. 1 illustrates such a diagram for three rocks,A, B, and C, which have been diamond drilled under identical conditions. It is assumed here that rocks A and B have the same initial penetration rate, i.e., VOA = Vog, but since rock B is more abrasive than A, rapid bit wear occurs and as a result the fall of its penetration rate with respect to time is more vigorous than in rock A. This is shown graphically by a steeper V = f(t) (0 curve in this rock than in rock A. Rock C has a lower initial penetration rate, due to higher strength properties16 but since it is not very abrasive, only a slight fall of its penetration rate occurs during drilling (in this category are some limestone and marbles with compressive strength above 1000 kg per sq cm). It follows from the foregoing considerations that the characteristic for each rock curve (I) is a function of (i), the penetration rate of the rock Vo recorded at the instant of commencing drilling, which determines the starting point of the curve (1) on the y-axis and (ii), the abrasive rock properties which determine the rate of fall of Vo with respect to time. Thus, curve (I) provides an actual picture of the rock behavior in drilling for given operational conditions, and it can be used with complete satisfaction to assess rock drillability. It can be seen clearly from Fig. I that proposed methods for assessing rock drillability by measuring the

Jan 1, 1970

By Erminio Ferraris

The development of the mining industry in Sardinia dates from the application of the mining law of 1859, which, following the example of the French mining law of 1810, declared prospecting to be free, and suppressed the liens which had previously attached the mine to surface ownership. The first ore-dressing plants were installed by German engineers upon the classic models of the Harz and of Freiberg; but in 1880 Sardinia commenced to open a new path in that industry, utilizing the refuse from the mining of rich, selected minerals, of poor deposits, and of mixed ores. The first experiments were attempte to adapt the existing apparatus to local conditions, but progress was rapid, as was demonstrated already in 1887 by the calamine-dressing mill of Monte-poni, which exhibited a large plant designed in accordance with the experience gained, and constructed entirely in the machine-shops of the country, after new models and designs.' This example was followed two years later by the Sociékté Malfidano, with a large plant of the same sort, and with the reconstruction of the old-fashioned dressing-mill, built in 1880 by the Austro-Belgian Company. In 1900, almost all the mines of Sardinia had adopted the new designs, and the island contained 32 concen-trating-works, employing 2,000 h.p. and 1,924 workmen. Since that time, there have been added a large dressing-mill for blende at Gennamari, and two for calamine, at San Giovanni and at Masua, while the establishments at other mines have been enlarged and perfected. For the treatment of intimately mixed ores, a large establishment has been built upon the new

Jan 1, 1909

By M. C. Fuerstenau

Each year during the AIME Annual Meeting, the MBD Division has its Business Meeting. Because many members cannot attend, it has be- come policy for the secretary of the Division to present highlights of the business conducted at the Meeting in Fine Grind. This year the Meeting was held on March 1 in the Americana Hotel. Five major items of business were brought up for discussion. These were: (1) the proposed name change for the Division, (2) institution of the Taggart Award, (3) a name change for a Unit Committee, (4) MBD funding of scholarships, and (5) authorship of Fine Grind articles. The Matter of What We Should Call Ourselves A lively discussion was held on the issue of a name change for the Division. Two names have been proposed: (1) Mineral Processing Division, and (2) Mineral Engineering Division. A number of strong reasons for changing the name from Minerals Beneficiation Division have been pointed out. Perhaps the most important of these is that the term "beneficiation" does not describe all of the functions that engineers in our Division perform. Further, there are inherent problems associated in the term, in that beneficiation is a long word which has the twofold disadvantage of being both difficult to pronounce and difficult to spell.

Jan 1, 1971

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

AUGUST began with a reminder that warfare was still in progress in the world, in that the Greeks, still at war with Turkey, threatened Constantinople in spite of the small British and French forces of occupation and opened a vista of international dangers. There was in this, moreover, a recollection that religious questions in India had prevented the British from permitting a real settlement of the Turkish question, wherein the absence of Russia as a great power is missed. Civil warfare also continued in Ireland and China. Even in the military way the world is far from being at peace. Bloody fighting between the Fascisti (anti-communists) and the com-munists in Italy led to several provinces being put under martial law, but after a while these disturbances were quelled. In the latter part of the month the assassination of Michael Collins in Ireland produced a great shock. From China, however, there came rather favorable news, indicating the early reintegration of that country, which sooner or later ought to play an important part in world affairs. Economically, instead of there being any improve-ment, there grew a clearer perception of how bad things really are. Italian politics were in chaos through inability to find anyone to accept the premiership and assume the all but hopeless task of averting national bankruptcy. The French, too, began to see their own position in true colors, and especially to see how in reconstruction they had incurred debts on the strength of what they hoped to collect from Germany, with at last the understanding that the Germans could not pay and that France herself was thereby put in a desper-ate economic position. As for the Germans, them-selves their Reichsbank defaulted on ordinary bills early in August. As the month wore on the value of marks fell more and more and at the end it appeared that Germany was on the verge of economic collapse. On Aug. 7, another international conference (with America again absent) was assembled in London, this being the thirteenth since the war, and there was a general feeling that it would be the last. The prime question was what is to be done about the German reparations, but underlying was the whole subject of the entente. The conference opened like a meeting of importunate creditors, doubtful whether the debtor had any tangible assets. On Aug. 14 this conference broke up without coming to any useful conclusion. Indeed, the acrimony among the premiers was so sharp that even the entente between Great Britain and France was endangered. The international situation was saved only by the Reparations Commission excusing the Germans from the payment of 50,000,000 gold marks that come due on Aug. 15 But although the entente was nominally preserved there is no longer any illusion about the interests of Great Britain and France being different and that henceforth they will play their own hands. The London conference was really an effort to maintain the partnership, and it failed.

Jan 9, 1922

By W. A. Backofen, D. H. Avery, G. A. Miller

An evaluation has been made of the relative importance of yield strength (?) and stacking-fault energy (y) to the rate of fatigue-crack growth in materials of fcc structure. Pure copper and its solid-solution al-loys with aluminum and nickel were chosen for the study because they provided sufficient range in both quantities of interest that either could be varied independently of the other. Experiments involved alternating tension and compression of flat specimens which were prepared with sharpened internal notches so that most, if not all, of the crack-nucleation interval could be eliminated. Growth rate (dC/dN) was concluded to be proportional to the square of the plastic-strain amplitude (€,,) over a strain range of approximately 6x 10-4 to 6 x 10-3. The factor, k, linking dC/dN and ep in dC/dN = kEp2 increased and decreased with corresponding variations in y, but it did not respond syste?>/atically to change in ay, indicating that y is the significant variable in crack growth at constant plastic-strain amplitude. In polycrystalline material, k varied by a factor of 5 over the available range of y. In a few single-crystal experiments on Cu-A1 alloys the growth rate responded less strongly to change in y. It has been suggested that single crystals behave somewhat differently than poly crystalline material because there is more extetnsive substructure near the grain boundaries in the latter, and this facilitates crack advance by separation along subgrain boundaries. A point of some controversy in current work on fatigue relates to the effects of strength and stacking-fault energy on crack growth. In recent experiments a separation was made between the cycling intervals for crack nucleation and the subsequent growth that eventually ends a specimen's fatigue life.' The study was carried out on Cu-A1 alloys primarily, fatigued in alternating four-point bending to constant deflection. A nucleation interval of about 10' cycles (at a total strain amplitude = 0.2 pct) was found to be insensitive to aluminum content in the range 0 to 7.5 wt pct, while the growth period was increased approximately forty fold over the same compositional range. The increase was not in any sense linear, however. Rather, most of the change occurred below 4 pct A1 or a stacking-fault energy, ?, of about 15 ergs per sq cm. It was argued that the plastic-strain amplitude was approximately constant, and therefore the effect of composition must have grown out of the reduction in stacking-fault energy. Several studies have shown that, with high ?, cross slip is encouraged, subgrain structure is introduced during fatigue, and cracking is aided through propagation along subgrain boundaries.1-5 Therefore, lowering ? sufficiently to interfere with substructure formation would be expected to retard growth rate. On the other hand, it is a general rule that resistance to fatigue cracking increases as strength is raised. Accordingly, there might still have been some doubt that Y was the controlling variable, since strength would be increased as y was lowered by the aluminum additions. To help in dispelling that doubt, an experiment was made on a polycrystalline Cu-Ni alloy similar in strength to the Cu-A1 alloys but of higher ?; the crack-growth interval was found to be essentially that of pure copper.' Further support for this position on stacking-fault energy as it relates to crack growth is derived from work by Boettner and McEvily,6 in which the actual crack-growth rate was measured on samples previously notched so as to minimize the nucleation period. Unfortunately, it was necessary in isolating strength level to compare different alloy systems and grain sizes. Recognizing the complication, it was still concluded that growth may be retarded by a reduction in y, per se. A related study has also been made by Roberson and Grosskreutz.7 The zinc content of a brass was systematically changed to alter strength and stack-ing-fault energy, although not below the 15 ergs per sq cm at which pronounced change in growth interval was found in the earlier work. The results were limited to more or less conventional S-N diagrams so that nucleation and growth events could not be separated. No definite conclusions were drawn, but

Jan 1, 1967

By H. J. McQueen, G. C. Kuczynski

ThE useful properties of k6-Alfenol and the thermenol alloys (summarized by J. E. Nachman and W. J. Buehler') have encouraged research into those alloys which, having compositions near 25 at. pct Al, 75 at. pct Fe, undergo an ordering transformation between 500° and 550°C. The equilibrium diagram of the iron-rich iron-aluminum alloys was first determined by Bradley and Jay.2,3 They distinguished three structures: the disordered, which is bcc; FeAl, which is simple cubic with one Fe atom and one Al atom per lattice site; and Fe3Al, which is fcc with three Fe atoms and one Al atom per lattice site. This last structure may be conceived as eight body-centered cubes with Al atoms at the centers of alternate ones, so that Al atoms have only Fe as first and second nearest neighbors. Later, Osawa and Murata4 determined the boundaries of the different superlattice regions in the iron-rich Fe-Al solid solution by dilatometric and X-ray methods. Two of the six phases, which they found between 0 and 50 at. pct Al, were never identified by other workers. A. Taylor and R. M. ones,' concurrently with and independently of this research, redetermined this diagram by measuring lattice parameters at temperature. Further reference will be made to their results. EQUILIBRIUM DIAGRAM A) Experimental Procedure—The alloys were prepared from NRC gas-free iron (99.9 pct Fe) and 99.99 pct Al. They were melted in alumina' crucubles under vacuum in an induction furnace. If the ingots were unsound or showed more than a 3 pct weight loss, they were rejected. The ingots were homogenized at 1100°C for 24 hr before hot-rolling at 700" to 900°C from 1 in. to 0.25 in. thick. It is interesting to note that alloys containing more than 28 at. pct Al were able to take an 80 pct reduction of area in the ordered FeAl region. The dilatometer specimens and specimens for chemical analysis were cut from these plates. A Leitz dilatometer was used to measure the coefficient of linear expansion as a function of temperature. The specimens were slowly cooled from 900" to 300°C where they were annealed for 10 hr before slowly cooling to room temperature. The expansion was recorded photographically as the alloys were heated and cooled at 1.5oC per min between 100" and 1000°C. The magnetic measurements determining the Curie points were performed on the dilatometer specimens in the dilatometer, by using direct current in the furnace windings both to heat the specimen at 1.5°C per min and to serve as the primary coil. The regular specimen holder was replaced by a thin alundum tube on which was wound, as a secondary, a closely spaced coil of fine copper wire. A reversal of current in the furnace windings produced, in the secondary, an emf which was proportional to the induction in the specimen, and which could be detected on a galvanometer. In this way, it was possible to determine the Curie points of alloys to within * 5°C. B) Results and Discussion—The coefficients of linear expansion, as obtained from the dilatometer curves, are plotted as a function of temperature and composition in Fig. 1. Since in many cases the heating and cooling curves were superimposed, it was decided to measure slopes of heating curves only. Definite high peaks, due to the transformations, were observed on each curve between 400" and 520°C, and, for alloys containing more than 23 at. pct Al, a second set of smaller peaks at temperatures above 660°C. The sharpness of the peaks indicates that ordering to Fe3Al is a first-order reaction. The compositions and the temperatures of these peaks are listed in Table I. When these temperatures are plotted as a function of the composition, the result is the constitution diagram presented in

Jan 1, 1960

By Walter Morley

This paper is a record of the first of a series of tests on sulfide minerals to be made by the metallurgical department f the University of California. The purpose of the tests here recorded is to determine the action of standard oils, oil mixtures, and addition agents on the flotation of pyrites. The question of the commercial value of pyrite was not considered. Of the many factors affecting flotation, only two-the oil and the other agent used-were made variable. The flotation agents used are given in the accompanying table. PENSACOLA TAR AND TURPENTINE CO. (PENTARCO) NON-POL., SP. Dis. REF. PER No. KIND GR. POINTS INDEX ?VISC. CENT. 200 Refined wood creosote oil 0.965 105-275 1.5096 1.7 7-8 350 Crude pine wood oil 1.019 70-345 1.525 2.9 4 75 Crude wood turpentine 0.887 65-217 1.456 0.9 10-12 80 Crude pine oil 0.911 70-232 1.4894 1.1 8 750 Heavy pine tar oil 1.063 165-350 1.557 41.0 400 Wood creosote oil 1.025 190-360 1.4977 2.9

Jan 7, 1921

By NEWTON B. KNOX

THE Guianas region is a geological unit, consisting of the northern lobe of the Brazilian Shield, but political accident and the fact that rivers act as the principal means of transportation have divided the region between five separate sovereignties. Brazilian and Venezuelan Guiana have already been considered. The French, Dutch, and British colonies consist of a coastal plain some fifty miles wide, which, together with the lower reaches of the principal rivers, support the greater part of the population. Inland from this tidewater region is a wide area of low, forest-covered hills, under-lain by gneisses, schists, granites, and pegmatites of the Shield. As in Venezuelan Guiana, these rocks are overlain by a thick series of horizontal continental sediments intruded by moderately basic magmas. Gold, bauxite and diamonds have been the principal products of the colonies. The first metal is quite widespread in the hill country. The quartz mines are small, though occasionally rich; probably the greater number of veins remain undiscovered because of the thick mantle of decomposition product that covers the schists and gneisses. The greater proportion of the gold, therefore, is derived from placers which are exploited in all three colonies. Some geologists claim that they occur in two belts parallel to the coast; whether this feature has its origin in the location of the primary mineralization or in the gradients of the rivers is not clear. In some instances the river gravels grade into auriferous laterite. The laterites are well developed in the Guianas and represent the weathering products of the more basic rocks.

Jan 1, 1946

By S. A. Bradford

Internal-oxide precipitates in decarburized a iron alloys were studied by microscopic and X-ray methods. Diffusion of oxygen is primarily trans-granular, although large amounts of manganese or PhosPhorus cause preferred grain boundary dimsion at temperatures below 1450OF. Transgvanular internal oxidation follows the parabolic rate law with an apparent activation energy of 60 kcal per g-atom for decarburized rimmed steel and around 50 kcal per g-atom for higher alloy contents. The internal oxide is (Fe,Mn)0. Evidence was found for a miscibility gap in the FeO-MnO system. UNTIL very recently, the internal oxidation of metals was studied primarily as a scientific curiosity or, in a few cases, as a means of strengthening alloys by precipitation hardening. However, with the recent development of low-carbon enameling sheet steel, internal oxidation has become a problem of practical importance to the steel industry. For example, in 1961 it was reported1 that internal oxidation of steel can occur during decar-burization by open-coil annealing and will reduce the notch ductility of the sheet unless the process is carefully controlled. The present study was therefore undertaken to learn more about the rates and mechanism of oxygen diffusion and oxide formation in iron alloys. BACKGROUND The process of internal oxidation has been well-defined in the literature:',' oxygen dissolves in an alloy, diffuses inward from the surface of the metal, and reacts to form a precipitate with the alloying element that will provide the most stable oxide. he growth of the finely divided so-called subscale, i.e., the internal-oxidation zone, depends on the diffusion rates of both the oxygen and the reactive element.4 Investigators have generally found that increasing the temperature increases the size of the oxide particles, the rate of subscale growth, and the tendency to transgranular diffusion. With very few exceptions, the square of the thickness of the internal oxide layer is directly proportional to the reaction time. Given two conditions easily satisfied for iron systems— a) an oxygen solubility much less than the concentration of the alloying metal and b) an oxygen-diffusion rate to the oxide boundary much faster than that of the alloying element—then the general expression developed by Rhines and co-workers5 for the parabolic growth rate of the internal-oxide zone can be simplified to the following form: where Co and CM are, respectively, the solubility of oxygen and the concentration of the alloying element, DO is the diffusion coefficient of oxygen, O/M is the weight ratio of oxygen to metal in the precipitated oxide, and x is the thickness of the internal-oxide zone after an annealing time t. Both the oxygen solubility and diffusion coefficient can be approximately expressed as functions of temperature by Arrhenius-type equations: in which H and Q are, respectively, the heat of solution and the activation energy of diffusion. Consequently, the apparent activation energies calculated from Arrhenius plots are the sum of the heat of solution of oxygen in iron and the activation energy for diffusion of oxygen. The data, if not the interpretation, of Schenck et al.8 bear out the fact that oxygen diffuses in the atomic form. The general rate law for atomic diffusion is: the reaction rate being proportional to the square root of the pressure at low pressures. Benard and Moreau8 studied both the surface oxidation of Fe-Ni alloys and the gradual penetration of oxygen into the metal. They observed that oxide particles first form along grain boundaries and then grow to form continuous films that eventually envelop the grains. The parabolic rate law does not usually apply in these cases, especially at the higher temperatures. The oxide formed is wustite which gradually transforms into Fe3O4 and finally into Kennedy and coauthors8 examined Fe-Ni alloys with 26, 75, and 84 pct Ni oxidized at 800°C and

Jan 1, 1964

By C. S. Smith, W. M. Williams

THE quantitative study of grain shape in three dimensions has been a difficult one from the practical standpoint. Experiments on grain shape have usually been based on indirect observations of two-dimensional metallographic samples or on grains separated by intergranular corrosion or fracture. The latter method was used in particular by Deschl in 1919 in observing the shapes of ß-brass grains which had been separated with mercury. The similarity in detail of shape and packing that exists between bubbles in a soap froth and metal grains was noted by Desch who remarks that: "Surface tension has an. important share in determining the form of the crystal grains in a solidifying metal and such grains have a tendency to assume the shape of foam cells." More recently the relation between grain shape and grain growth has been studied by Harker and Parker.' The importance of surface tension forces in determining microstructure has been discussed by Smith," and an analysis of the topologi-cal rules that apply to such structures has been made by the same author.' Biologists have made valuable contributions to the general problem of shape and form in an assembly of space-filling cells subject to surface tension forces. Particular mention must be made of the extensive researches of Lewis5,8 on botanical and anatomical tissues, and Matzke and Nestler,7,8 who have made painstaking studies of bubble shapes in different kinds of foam. The present paper introduces a new method of studying individual grains in particular alloys—a method which may well find use in other metallurgical researches, and which seems also to be applicable in biological problems. Metal Grains in Three Dimensions The individual grains in a piece of metal or the bubbles in a soap froth must satisfy two conditions —they must be in juxtaposition so as to fill space and their interfaces must conform to the laws of surface tension. If a further restriction is imposed, namely, that only one type of polyhedron be used, then the sole possibility is an assembly of "minimal" tetrakaidecahedra," each polyhedron having eight doubly-curved hexagonal faces and six plane quadrilateral faces, the angles between adjacent faces being 120". Such cells could be stacked on a body-centered cubic lattice and would be quite stable. For many years it was believed that soap bubbles actually possessed the shape of this ideal body, and the hypothesis was the starting point for several investigations on the shapes of soap bubbles, biological cells, and metal grains. These investigations have shown, what might have been obvious in the beginning, that if the condition of symmetry is relaxed the tetrakaidecahedron is almost never found. If we retain only the rule that all contacts should be in local surface tension equilibrium and that the assembly should fill space, metal grains may then take a nearly infinite variety of shapes and no single one may be regarded as an archetype. These two conditions, which are fully discussed in one of the previously mentioned papers,' lead us to think of a typical grain in an annealed metal as having the following characteristics: 1—A grain may have any number of faces, but usually between nine and eighteen. The faces (each of which is, of course, shared by two grains in the assembly) may have any number of edges, but usually between four and six. Pentagons are by far the most frequent. 2—In the assembly of grains each edge is shared by three faces and by three grains. Each vertex is a point shared by four grains, six faces, and four

Jan 1, 1953

By G. C. Kuczynski

Two particles in mutual contact form a system which is not in thermo-dynamical equilibrium, because its total surface free energy is not a minimum. If such a system is left for a certain period of time, the bonding of the two particles will take place in order to decrease the total surface area, even though the temperature is lower than the melting point. This phenomenon of bonding of two or more particles with the application of heat only and at temperatures below melting point of any component of the system will be called sintering, although the powder metallurgists use this term in a broader sense, including the presence of molten phase and pressure. It is the objective of this paper to study this process and the mechanisms involved in it. This problem is of utmost importance to powder metallurgy and powder ceramics, and its technological aspects have been studied for a good many years. However, the powder metallurgical operations are too complex and include too many superimposing mechanisms, and too many variables for a direct study. It was therefore advisable for the purposes of this study to reduce the variables to a minimum. In this work the radius of the interface formed during bonding in a simple system composed of a spherical particle and a large block of the same metal was studied as a function of time and temperature. It is believed that the mechanism involved in this simple process is fundamental to any sintering operations. Previous Work J. Frenkell was the first to make a serious attempt to develop a theory of sintering. He assumed that the process consists of a slow deformation of crystalline particles under the influence of surface tension which reduces to a viscous flow where the coefficient of viscosity n is related to the self-diffusion coefficient D by the following equation 1 _ D D6kT [1] where 6 is interatomic distance, k the Boltzman constant, and T the absolute temperature. This type of viscous flow of a crystalline substance is essentially different from the ordinary plastic flow. The latter is a specific propcrty of crystals and cannot take place in amorphous bodies. According to Frenkel this viscous type of flow is due to the diffusion of the holes or vacancies arising in the lattice. He was able to derive an equation relating the growth of the interface between two spherical crystalline particles or between a particle and a semi-infinite crystal (Fig 1) to time t at constant temperature. This relationship can be written as follows: x²— 3/2 a/nt [2] where x is the radius of the interface assumed to be circular, a the original radius of the sphere and a surface tension of the material. The other assump- x tions are that x is less than 0.3 and that during the period 1 the original radius, a, of the metallic particle did not change appreciably. A. J. Shaler and J. Wulff2 followed closely the ideas of Frenkel in their theory of sintering of a mass of metallic powder. Neither Frenkel nor Shaler has validated his theoretical speculations with conclusive experimental data. Two measurements reported by

Jan 1, 1950

By J. Spreadborough, D. LaW. King, E. Anderson

Tmzsile tests were performed on Armco iron samples, at various ternpe.ralures and strain rates, ocer a wide range of grain sizes. Analysis of the data suggests that the plot of the lower yield stress, against d-1/2,where 2d is the acerage grain diameter, is not linear (as is often assumed) but is concave toward the d. axis over the range of d-from 7 to 53 . The different values of the parameters obtained by other workers can be explained, in part at least, by the observed curvature. This curvalure is shown to be consistent with a model of yielding based on dislocation pile-ups; however, the values of obtained by fitting our data to this model differ appreciably from the values generally reported. The equation proposed by Cottrell, viz.: is a plausible empirical fit to the experimental results. The purpose of this paper is to comment on the validity of the widely used linear relationship first proposed by all' and Petch and coworkers2"4 between ay, the lower yield stress, and 2d, the average grain diameter, for bcc metals, viz.: Many workers, see Refs. 2 to 7 and Table 11, have fitted this equation to their experimental results and have obtained acceptable fits over the relatively narrow range of grain sizes used by most of them. Indeed, in some cases, so few data points were available that any more sophisticated fit would have been irrational. In most of the interpretations,'-' oi is thought to be a measure of the friction stress accompanying dislocation movement, and ky was originally inter- preted as a measure of the dislocation locking but is now believed by Cottrell" to be a function of the dislocation creation rate. In the "unpinning" theories, k, is equated to where od is the unpinning stress and 1 is the average distance from the boundary of the grain where yielding is taking place to the nearest dislocation source in an unyielded grain. Other considerations (see, for example, Refs. 11 and 12) lead to equations with a similar form to [I] where different meanings may be attributed to the parameters. While there are doubts as to the physical significance of the parameters i and k, they continue to be used by many workers; interpretations of the variations in the behavior of ferrite materials following certain treatments, e.g., aging,'3 neutron irradiation,14 have been given frequently in terms of these parameters. Some theories of the mechanical behavior of bcc metals are based on this relationship. We have investigated experimentally the oy - d-'lZ relationship for Armco iron over a wider range of grain sizes and with more data points than those given in published results. The analysis of our data suggests that the oy—d-'" relationship is not linear but is in fact concave towards the d-'I2 axis. RESULTS AND DISCUSSION The experimental work was carried out on 3-mm-diam Armco iron rods which were prepared by wire drawing from 5-mm-diam rods. By annealing in vacuum at temperatures between 7000 and 1200°C for various times, grain sizes from 7 to 20,000 grains per sq mm were obtained, the grains in all cases being regularly shaped. Grain sizes were measured by lineal interceptand by area methods; only specimens with Amax/A values of 3 to 6 were used in the Petch-Hall plots (where A is the average area of a grain and Amax is the area of the largest grain observed). For all the specimens used, the number of grains in a cross section exceeded 50, which should be adequate to avoid grain size effects.'= Tensile tests were performed at 296", 219, and 17l°K, using

Jan 1, 1969