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By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By T. R. Graham, R. G. Feustel, J. R. Long, R. S. Dean

The comprehensive study of the copper-manganese-zinc alloy system in the Bureau of Mines Laboratories has so far been principally concerned with alloys that lie within the alpha solid solution field of the system. Two regions, one centering about 65 per cent copper, 10 manganese and 25 zinc, and the other centering about 70 per cent copper, 20 manganese, 10 zinc, have been carefully examined. These have indicated that when the alloys are made with electrolytic manganese considerable amounts may be readily introduced and that the strength and hardness are increased without excessive losses in ductility. In the course of the work of establishing the limits of the alpha solid solution range,3 enough of certain of the alloys was prepared to permit determination of their- physical properties at a future date. The 60 per cent copper alloys concerned here are part of that series. They cross through the alpha field and into the adjacent alpha plus beta and alpha plus X fields, and are of interest because they offer some information on the effects of manganese on alloys lying in these fields. Composition and Fabrication of Alloys The chemical composition of the alloys involved is given in Table I. They were intended to contain 60 per cent copper with manganese increasing from 5 to 25 per cent in 5 per cent steps and zinc decreasing from 35 to 15 per cent. The analyses are so close to the intended composition that the alloys mill be referred to hereafter by their norninal compositions. They were finished into sheet by cold-rolling and intermediate annealing procedurzs calculated to produce sheet $i6 in. thick, cold-reduced by 20, qo, 60, and 80 per cent in thickness. Physical properties were determined on standard flat tensile specimens with 4-in. gauge length, although the test gauge section used was 2 in. The properties were obtained on cold-worked material and on material annealed at temperatures ranging from 700' to r500°F. after 60 per cent cold reduction. Since an annealing temperature of 1200°F.

Jan 1, 1946

By J. R. Long, T. R. Graham, R. G. Feustel, R. S. Dean

The comprehensive study of the copper-manganese-zinc alloy system in the Bureau of Mines Laboratories has so far been principally concerned with alloys that lie within the alpha solid solution field of the system. Two regions, one centering about 65 per cent copper, 10 manganese and 25 zinc, and the other centering about 70 per cent copper, 20 manganese, 10 zinc, have been carefully examined. These have indicated that when the alloys are made with electrolytic manganese considerable amounts may be readily introduced and that the strength and hardness are increased without excessive losses in ductility. In the course of the work of establishing the limits of the alpha solid solution range,3 enough of certain of the alloys was prepared to permit determination of their- physical properties at a future date. The 60 per cent copper alloys concerned here are part of that series. They cross through the alpha field and into the adjacent alpha plus beta and alpha plus X fields, and are of interest because they offer some information on the effects of manganese on alloys lying in these fields. Composition and Fabrication of Alloys The chemical composition of the alloys involved is given in Table I. They were intended to contain 60 per cent copper with manganese increasing from 5 to 25 per cent in 5 per cent steps and zinc decreasing from 35 to 15 per cent. The analyses are so close to the intended composition that the alloys mill be referred to hereafter by their norninal compositions. They were finished into sheet by cold-rolling and intermediate annealing procedurzs calculated to produce sheet $i6 in. thick, cold-reduced by 20, qo, 60, and 80 per cent in thickness. Physical properties were determined on standard flat tensile specimens with 4-in. gauge length, although the test gauge section used was 2 in. The properties were obtained on cold-worked material and on material annealed at temperatures ranging from 700' to r500°F. after 60 per cent cold reduction. Since an annealing temperature of 1200°F.

Jan 1, 1946

By R. H. Richman

Coarse-grained Fe-Ni-C martensites formed at subzero temperatures were strained in compression at room temperature and the plastic deformation modes examined as a funclion of carbon content. At very low carbon levels, defovmation occurs hy wavy slip; commencing at about 0.05 pct C, mechanical twinning accounts for an increasing proportion of the plastic flow. Beyond approximately 0.4 pct C the deformation appears to be entirely by mechanical twinning. The habit planes of the operative twin modes were determined to be (113), (0131, and "(089)" in decreasing frequency of occurrence. Some of the implicaticms of Ihe o6served deformation modes upon the structure and properties of ferrous martensites are discussed. METALLURGISTS have long sought to explain the mechanical properties of ferrous martensites, particularly the extraordinary hardness and strength of the high-carbon varieties. Until recently the lack of precise knowledge of the structure of martensite crystals was the most serious barrier to understanding; however, the advent of thin-foil techniques for transmission electron microscopy has removed much of the mystery from martensite structure. Observations by Kelly and Nutting,"' and many others since, indicate that Fe-C based martensite crystals are internally twinned to a degree dependent upon the carbon content, and that a martensite plate containing 0.8 wt pct C or more consists of a stack of twin-related lamellae with each lamella on the order of l00A thick. Such a structure would be expected to influence greatly all aspects of metallurgical behavior, and many of the properties of Fe-C based martensites have been rationalized accordingly. Recent independent experiments led Winchell and cohen3 to conclude that the strength of ferrous martensite is derived primarily from solid solution hardening of the iron lattice by interstitial carbon atoms. Strength contributions from precipitation, dislocation-atmosphere interactions, clustering, short-range order, crystallite size, and so forth, were considered to be of secondary importance. In the view of Winchell and Cohen, the twinned structure of martensite serves mainly to limit the effective length of dislocation lines in the lattice, and thereby confers an added measure of hardening. Few properties of metallic crystals are as sensitive to metallurgical structure as are deformation mechanisms. It is somewhat surprising therefore, that, except for metallographic evidence of mechanical twins in strained martensite,4 no systematic examination of plastic deformation

Jan 1, 1963

By A. Andreas

New Mexico, after several years as the sixth ranking oil-producing state, was surpassed by Illinois and for 1939 ranks seventh in the United States. Oil production for 1939 was 36,746,840 bbl. Production for 1938 was 35,510,176 bbl., a gain of 0.033 per cent. Production for the year would have been greater had there been a pipe-line outlet for the Vacuum field. The complete shutdown during the latter part of August covering a period of 15 days meant a production loss of over 1,500,000 bbl. of oil. Daily production allowable as set by the Oil Conservation Commission has followed very closely the recommendations of the Bureau of Mines. It has been found that the recommended allowables as quoted by the Bureau of Mines do not always reflect the actual demand, as there is a considerable lag hetween the recommended amounts and the current demands. During the year the various operating companies have done considerable remedial work in setting packers to reduce the gas-oil ratios in the various fields. Six new fields were discovered in New Mexico during 1939; three in Lea County, two in Eddy County and one in Chaves County. In the early part of 1939 a committee composed of the various engineers and geologists recommended subdividing the old Artesia area into various producing pools. This division was accepted, therefore the total number of producing fields in New Mexico is considerably greater than the number of fields in 1938, but does not represent new fields discovered during the year. The southeastern area continues to he the largest producer of oil. During the year 2,716,551 bbl. were produced in Eddy County and 33,690,996 bbl. in Lea County. Total production ill the northwestern part of the state, which includes San ,Juan and McKinley Counties, was 338,293 bbl. At the beginning of the year the daily average nonmarginal well allowable for Lea County was 48 bbl. At the close of the year it was 49 bbl. The daily average production for the year was 97,313 bbl. During the year, 659 wells were drilled in the state, of which 565 were producing oil wells, 15 gas wells, 6 carbon dioxide gas wells and 73 dry holes. Summarized at meeting; manuscript received at the office of the Institute March 18, 1940. * State Geologist, member of New Mexico Oil Conservation Commission, Santa Fe, New Mexico.

Jan 1, 1940

By A. Andreas

New Mexico, after several years as the sixth ranking oil-producing state, was surpassed by Illinois and for 1939 ranks seventh in the United States. Oil production for 1939 was 36,746,840 bbl. Production for 1938 was 35,510,176 bbl., a gain of 0.033 per cent. Production for the year would have been greater had there been a pipe-line outlet for the Vacuum field. The complete shutdown during the latter part of August covering a period of 15 days meant a production loss of over 1,500,000 bbl. of oil. Daily production allowable as set by the Oil Conservation Commission has followed very closely the recommendations of the Bureau of Mines. It has been found that the recommended allowables as quoted by the Bureau of Mines do not always reflect the actual demand, as there is a considerable lag hetween the recommended amounts and the current demands. During the year the various operating companies have done considerable remedial work in setting packers to reduce the gas-oil ratios in the various fields. Six new fields were discovered in New Mexico during 1939; three in Lea County, two in Eddy County and one in Chaves County. In the early part of 1939 a committee composed of the various engineers and geologists recommended subdividing the old Artesia area into various producing pools. This division was accepted, therefore the total number of producing fields in New Mexico is considerably greater than the number of fields in 1938, but does not represent new fields discovered during the year. The southeastern area continues to he the largest producer of oil. During the year 2,716,551 bbl. were produced in Eddy County and 33,690,996 bbl. in Lea County. Total production ill the northwestern part of the state, which includes San ,Juan and McKinley Counties, was 338,293 bbl. At the beginning of the year the daily average nonmarginal well allowable for Lea County was 48 bbl. At the close of the year it was 49 bbl. The daily average production for the year was 97,313 bbl. During the year, 659 wells were drilled in the state, of which 565 were producing oil wells, 15 gas wells, 6 carbon dioxide gas wells and 73 dry holes. Summarized at meeting; manuscript received at the office of the Institute March 18, 1940. * State Geologist, member of New Mexico Oil Conservation Commission, Santa Fe, New Mexico.

Jan 1, 1940

By H. T. Bowman

FOR more than 80 years the Bessemer process has depended upon the ability, skill, and judgment of the blower, although as early as the 1860's it was recognized that the process would benefit by some type of instrumental control.1 However, instruments with sufficient recording speeds did not exist, so the end-point determination was always dependent upon the blower's eye. This placed an obstacle in the way of precise experimental work, because of the absence of the necessary records and reference points as reported by Work.2 The use of the photocell provided the instantaneous record of the blow that made this experimental work possible and provided more scientific control for the process as discussed by Graham3' A brief description of the progress of the blow will illustrate the recording function of the instrument. The silicon in the iron is being oxidized during the first minutes of the blow, as pointed out by Henning4 in a table showing the order of metalloid elimination. The product of this oxidation is a solid that remains in the converter, so there is virtually no flame during this part of the blow. This low flame luminosity is illustrated by the flame recording shown in Fig. I, where the silicon blow is plainly marked. The dull flame of the silicon blow gradually gives way to the brilliant carbon flame as the increasing quantities of carbon monoxide formed inside the converter burn to dioxide upon contact with the atmosphere above the vessel. When the carbon reaches some low value under 0.20 per cent, there is insufficient monoxide formed to maintain the dioxide flame, so its intensity drops. Throughout the flame drop carbon continues to burn, until at some value around 0.05 per cent an arrest occurs in the recorded drop. This point has been designated as the end point. The period of time from this end point until the vessel is turned upon its side and blowing has stopped has been called the afterblow. This afterblow is used as a measure of the degree of metal oxidation, and uniformity demands that it be controlled within narrow limits. Iron and blowing conditions are likely to change several times during a turn, necessitating corresponding changes in end-point control. It is the purpose of this paper to discuss these changes, the factors that make them necessary, and their bearing upon the quality of steel. CARBON-FEO RELATIONSHIP In the Bessemer process oxidation relationships are precise. Fig. 2 shows a graph of the carbon-FeO relationship. The familiar "bomb-test" method, described by McCutcheon and Rautio,5 was used for obtaining these and all other dissolved FeO values herein reported, all tests being taken from the converter before deoxidation unless otherwise noted. All tests of 0.10 per cent carbon and above were obtained from metal blown for duplexing. McGinley and Woodworth6 reported iron oxide values for blown metal, but their tests were obtained by a different method than were those

Jan 1, 1942

By H. E. McCoy, C. J. McHargue

Single crystals of columbium containing various levels of oxygen, nitrogen, carbon, or hydrogen were deformed by slaw compression and impact loading at -196°C. For the slow deformation rates. 1500 to 1900ppm oxygen, 500 pprn nitrogen, or 150 to 200 ppm carbon completely suppressed mechanical twinning. Hydrogen in concentrations to 1000 ppm had no apparent effect on ease of twinning. Impact loading caused twins to form at all levels of contamination studied, and cleavage mucking on (100) planes occurred in specimens having higher interstitial contents. It is well established that, under some conditions, the bcc metals vanadium, columbium, tantalum, chromium, molybdenum, tungsten, and iron deform by formation of mechanical twins. In general it has been accepted that high strain rates, low temperatures, and large grain sizes are conducive to this kind of deformation.' Since interstitial impurity atoms have a relatively large effect on slip in bcc metals, one might sus- pect a similar effect on twinning. This could occur directly by the interstitials affecting the nucleation or growth of the twins or indirectly from their effect on slip. It has often been argued that the large increase in yield stress caused by interstitial elements enables the effective stress to exceed that necessary to cause twinning. The twinning stress has always been thought to be higher than the stress necessary to cause slip in pure metals.2 simonsens and Tipper and Hall4 found profuse twinning in very pure a iron even at room temperature, whereas Low and Fueste15 and Churchman and tottrell' observed twins in a iron containing carbon but none in highly decarburized specimens. McHargue7 reported mechanical twins to form readily in vanadium which contained 390 ppm interstitigs, while Clough and Pavlovic8 found twins only in the one or two grains adjacent to the fracture surface in vanadium which contained 1500 to 1700 ppm interstitials. In columbium, McHargue9 found high-purity single crystals to twin easily whereas Churchman,10 Adams, Roberts, and mallman,11 and Johnson12 studied less pure material and found far fewer twins. Although the results of Leadbetter and Argent13 showed oxygen to inhibit twinning, a study by sheely14 indicated the opposite to be true. Chromium exhibits this mode of deformation15,16 but there are no data regarding impurity effects. Lawley, Van den Sype, and Maddin17 observed twins in very pure molybdenum single crystals deformed at 77°K but none in less pure crystals. The work by Cahn18 and

Jan 1, 1963

By J. R. Long, T. R. Graham, R. S. Dean

ALTHOUGH considerable information has been published concerning manganese additions to the aluminum bronzes, these data refer principally to the two-phase alloys containing 8 to 11 pct aluminum, with some incidental information on the single-phase alpha solid solution alloys. Strauss1 gives an excellent review of the literature on aluminum bronzes up to 1927 and a bulletin2 of the Copper Development Association brings the bibliography up to 1938. The most extensive work on manganese addition is that of Rosenhain and Lantsberry,3 who investigated alloys ranging up to 10 pct aluminum and up to 10 pct manganese, and presented data on the physical properties of sand-cast, chill-cast, and several wrought alloys. The greater portion of the work, however, concerns alloys ranging from 7 to 10 pct aluminum in the cast condition and sheds little light on the properties of wrought single-phase alloys. Corson4 notes that alloys containing 10 pct manganese and 4 pct aluminum are not hardenable by heat-treatment, while one with 15 pct manganese and 5 pct aluminum can be hardened, but he gives no tensile data on it. In fact, no systematic study of the properties of single-phase wrought alloys containing substantial amounts of manganese has been reported. It should also be noted that most of the investigators worked with alloys containing significant amounts of iron and silicon, and that these impurities, whether intentionally added or accrued from the raw materials used in the preparation of the alloys, may be expected to have a direct bearing on the resultant properties. In the work on alloys made with electrolytic manganese, the Bureau of Mines has undertaken an investigation of the copper-manganese-aluminum system for the purpose of establishing the constitution and properties of high-purity alloys. In a recent paper5 the authors reported a metallographic investigation of the alpha solid solution area and the adjoining fields of the copper-manganese-aluminum system up to 50 pct manganese. This study established the alpha-phase boundaries at 50° temperature levels from 400° to 850°C. It was found that the addition of manganese to copper-aluminum alloys decreases the solubility of aluminum in the alpha phase (Fig I), curving the boundary toward the copper-manganese base line. The greatest change occurs in the first 20 to 25 pct manganese, which decreases the solubility of aluminum to approximately 4 pct. With larger amounts of manganese the alpha boundary tends to parallel the copper-manganese binary. At 1300°F and higher,

Jan 1, 1947

By A. U. Seybolt

RECENTLY, cases of coexisting ordered and disordered phase equilibria have been reported among face-centered cubic metals,1"3 but not on body-centered cubic systems.4 McQueen and Kuczynski5 showed a single line as the boundary between ordered solid solution of Fe3Al type and corresponding disordered solution in the Fe-A1 phase diagram based mainly on dilatometric and magnetic measurements. Such a single line would indicate a second or higher order transition. or an absence of coexisting order and disorder. The writer found previously a two-phase equilibrium region at 800°C consisting of ordered and disordered solid solutions of Fe3Si in a matrix of approximately 1-6 wt pct Si (Fe3Si is of 14.3 wt pct Si). A similar two-phase region of ordered and disordered Fe3Al solid solutions might be expected if the similarity between Fe3Si and Fe3Si structures hold true. In the present investigation, a wire of 22 at. pct Al, balance Fe and 0.0513 cm in diameter was subjected to electrical resistivity measurement in vacuum as a function of temperature between 300 and 800°C, see Fig. 1. There was excellent agreement between data taken on heating and on cooling: no hysteresis was observed. The Curie temperature was determined to be 640 °C which agrees with the finding by McQueen and Kuczynski.5 But in addition, there were two transitional points in the resistance-temperature plot at 510oC and 400 "C. The former is thought to be a connection with the transition from disordered state to a coexisting order and disordered equilibrium state; while the latter, from such coexisting state to ordered state. Fig. 2 shows a phase diagram where the suggested two-phase region lies between dotted lines. The solid lines are those of McQueen and Kuczynski.5 Since these authors found only a single-phase boundary between ordered and disordered Fe3 Al, it would seem likely that the dilatometric method used by these authors was not sufficiently sensitive to resolve the ordering reaction into the two-phase boundaries. In addition, their phase diagram conflicts with the statement they make on P. 1 of their paper: "The sharpness of the peaks indicates that ordering to Fe3A1 is a first order reaction." The suggestion of coexisting order plus disorder in Fe3A1 must be considered tentative until confirmed by high-temperature X-ray examination. If

Jan 1, 1961

By James A. Barr

[CONTENTS PAGE Foreword. By JAMES A. BARRI A New Core Barrel for Prospecting for Phosphate in Florida. By I. M. LEBARON 2 Prospecting for Phosphate in Tennessee. By W. F. GUENTHER 6 Machine Prospecting in Tennessee Brown Phosphate. By H. O. PICKARD, JR8 Diamond Drilling through Flint Horizons in Tennessee. By HENDON R. JOHNSTON9] Foreword PROSPECTING methods used in Tennessee have gradually improved with the years, as required by depletion of the easily accessible and shallow deposits and the universal trend toward mechanization, and as necessitated by exploring deeper beds, often occurring under limestone and flinty overburden. In the early days it was a very simple matter to dig pits by hand, using a plentiful supply of local farm labor to expose relatively shallow deposits of "brown rock" under shallow clayey overburden that would stand up without timbering. Visual inspection of the exposed phosphate and expert judgment of the"grade" analysis, aided by a "biting" test to reveal presence of unwanted silica, furnished most of the information required. All this might be helped by a few samples sent to the local chemist[t] who supplemented his income by judicious trading or tanning a few bear skins. The extra curricula activities did not affect the accuracy of the analysis which hold up even under present day standards. Some shot and core drilling was done in Hickman County, mostly for the limestone-like blue Phosphate deposits. The next step was the use of a 4-in. posthole auger, hand operated as described by Guenther, followed by- a completely mechanized rig, as described by Pickard. Both these methods are practically adapted to the prospecting of the relatively soft brown rock deposits at moderate depths of clay overburden. For prospecting in areas of deeper overburden, such as are often found in Hickman County, up to 150 or even 200-ft depths, a modified core-drilling method is described by Guenther. Johnston describes a special diamond-drilling technique, developed by TVA, to penetrate flint horizons, which was adopted by the International Minerals and Chemical Corporation to prospect in Hickman County where deposits had previously been prospected at considerable expense and with difficulty, by Small, temporary, hand-dug shafts.

Jan 1, 1947

By C. G. Dunn

Nuclei that are formed during the recrystallization of a grain following plastic deformation generally have orientations that differ from the original. This aspect of recrystallization may be described in terms of orientation changes. It was shown previously, in an investigation on recrystallization in silicon ferrite,&apos; that the observed orientation changes were highly improbable on a chance basis, and that some mechanism must be involved. Analysis showed that the data could be satisfactorily classified into the smaller of two subclasses† of the 36 third-order twin transformations. No attempt was made at that time to classify the data within the special class of 12 third-order twin transformations, although results did indicate a greater probability for some of them to occur. A classification of this type would be more valuable, of course, with more data on orientation changes per old deformed grain. The present work fulfills this condition to some degree and also extends the scope of the investigation to include the effects of original orientation and the amount of plastic deformation. The effect of original orientation is of considerable interest because of the known effects of orientation on plastic deformation, particularly with regard to degree of fragmentation and the formation of deformation bands, and because the orientations produced by deformation should influence the orientations obtained through recrystallization. Barrett and Levenson2 reported that single crystals of iron deformed in the range 82 to 97 per cent could be put into three general classes; namely, crystals in class I maintained a reasonably sharp single orientation, those in class 2 transformed into two distinct orientations, and those in class 3 changed into a large number of major and minor orientations. Something similar would be expected for silicon ferrite crystals, and verification of this for a few cases of types class I and class 2 deformation has been reported elsewhere3 for single crystals of silicon ferrite cold-rolled in the range 10 to 20 per cent. As an example of class 2 deformation, it was shown that a crystal of silicon ferrite cold-rolled in a (110) plane in a <100> direction developed two layers, or deformation bands differing in orientation. When this happens it is possible to etch away one band and leave a single structure for use in studying the orientation changes that occur during recrystallization. when preferred crystal orientations are obtained in recrystallization, it is not particularly necessary to evaluate groups of common orientation, as was done previously (ref. I, Table 6); but an

Jan 1, 1947

By C. G. Dunn

Nuclei that are formed during the recrystallization of a grain following plastic deformation generally have orientations that differ from the original. This aspect of recrystallization may be described in terms of orientation changes. It was shown previously, in an investigation on recrystallization in silicon ferrite,&apos; that the observed orientation changes were highly improbable on a chance basis, and that some mechanism must be involved. Analysis showed that the data could be satisfactorily classified into the smaller of two subclasses† of the 36 third-order twin transformations. No attempt was made at that time to classify the data within the special class of 12 third-order twin transformations, although results did indicate a greater probability for some of them to occur. A classification of this type would be more valuable, of course, with more data on orientation changes per old deformed grain. The present work fulfills this condition to some degree and also extends the scope of the investigation to include the effects of original orientation and the amount of plastic deformation. The effect of original orientation is of considerable interest because of the known effects of orientation on plastic deformation, particularly with regard to degree of fragmentation and the formation of deformation bands, and because the orientations produced by deformation should influence the orientations obtained through recrystallization. Barrett and Levenson2 reported that single crystals of iron deformed in the range 82 to 97 per cent could be put into three general classes; namely, crystals in class I maintained a reasonably sharp single orientation, those in class 2 transformed into two distinct orientations, and those in class 3 changed into a large number of major and minor orientations. Something similar would be expected for silicon ferrite crystals, and verification of this for a few cases of types class I and class 2 deformation has been reported elsewhere3 for single crystals of silicon ferrite cold-rolled in the range 10 to 20 per cent. As an example of class 2 deformation, it was shown that a crystal of silicon ferrite cold-rolled in a (110) plane in a <100> direction developed two layers, or deformation bands differing in orientation. When this happens it is possible to etch away one band and leave a single structure for use in studying the orientation changes that occur during recrystallization. when preferred crystal orientations are obtained in recrystallization, it is not particularly necessary to evaluate groups of common orientation, as was done previously (ref. I, Table 6); but an

Jan 1, 1947

By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy&apos;s law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy&apos;s law,

By Walter R. Hibbard, Harold Margolin

The effect of ten ternary additions on the aging of a Cu-Ag alloy was measured by X ray, microstructure and hardness. A supersaturated copper-rich transition structure was found. The effect of the ternary element was related to differences between transition and precipitate lattice parameters and analogies with solution and strain hardening. IN addition to the prerequisite of diminishing solid solubility with falling temperature, the theory of coherency hardening1 proposes that the principal source of hardening during precipitation is strain caused by coherency between the matrix and precipitate. For a given system greater coherency hardening would result from lengthening the period of coherent growth and/or increasing the number of nuclei, other things remaining equal. However, the hardness change during aging is a function of a number of phenomena in addition to coherency hardening, such as dispersion hardening, loss of coherency, solute depletion, matrix recovery or recrystal-lization, coalescence, and their relative time sequences. The present investigation was undertaken to study the effect of ternary additions on the age-hardening of Cu-Ag alloy. For this purpose a series of alloys were made containing as ternary constituents Mg, Al, Si, P, Mn, Ni, Zn, As, In, and Sb. These elements were added to a master 5 wt pct Ag in Cu alloy in such amounts as to obtain alloys listed in Table II containing the following approximate atomic percentages: 96 pct Cu, 3 pct Ag, 1 pct ternary addition. A 97 atomic pct Cu, 3 atomic pct Ag alloy was used as a comparison standard. There have been numerous investigations of age-hardening in Cu-Ag alloys2-lo but few of ternary Cu-Ag alloys. Pfister and Weist" found that 1 wt pct Ni reduced the solubility of Ag in Cu above 600 °C and that the rate of precipitation was slower than in polycrystalline Cu-Ag alloys of similar silver content. More recently Hodge, Jaffee, Dunleavy, and Ogden12 investigated the effect of ternary additions of Mg, Li, P, Cd, Zn, Zr and Be on strength properties of Cu-Ag alloys. Mg, Cd, and P were found to increase strength in the aged and cold-worked condition. Experimental Procedure Charges weighing 7.5 lb were melted in a closed carbon crucible under a reducing atmosphere* of nitrogen and hydrogen. A Durville-type casting procedure with a hot-top arrangement was used to obtain a sound casting, 2x2x43/4 in. Prior to rolling and annealing of the ingots, a trial solution anneal of rolled sections of the hot-top portions indicated that at 780°C melting was avoided except for the Cu-Ag-Sb alloy. This alloy could not be produced as a single phase within the limits of temperature control. i 3" to 5oC, since melting occurred at 64O °C, and below this temperature precipitation was

Jan 1, 1952

By H. M. Howe

On commencing the construction of the Orford Company&apos;s copper smelting works, at Bergen Point, N. J., I endeavored to convince our President, Mr. W. E. C. Eustis, by actual tests, that at the pressure of from 15 to 18 ounces per square inch, employed by us in smelting, less power was consumed in delivering a unit of blast by a Baker blower than by a fan blower. I attempted to prove this in the following manner: Across the mouth of a No. 5) Baker blower I firmly fastened a board with two round holes, 6 inches in diameter, cut in it. The board was fastened so tightly that no air could escape except through the holes. I then drove the blower at several differerent speeds, observing the pressure at which the air excaped through the two openings for each different speed of the blower, and also indicating the engine, whose only work at that time was to drive the blower. From this I calculated the quantity of power required to deliver, with a Baker blower, sufficient air to keep the pressure at a given point, while it escaped freely through the two six-inch apertures into the open air; or, in other words, to deliver air at a given pressure through these two openings. From the total power so consumed it was, of course, necessary to deduct the power which was required to drive the engine itself. This was ascertained by removing from the engine the belt which drove the blower, and then noting the quantity of power consumed in simply turning the engine over without any

Jan 1, 1882

All the Technical PUBlications and Preprints published in 1932 are available at Institute headquarters. They are also on file in public, university and technical libraries and, when so indicated in the list, may be found in the Transactions. Copies of the Technical Publications have been mailed to those members of the Institute who are registered in the different classes: A-Metal Mining; B-Milling and Concentration; C-Iron and Steel Division; D-Nonferrous Metallurgy; E-Insti-tute of Metals Division; F-Coal Division; G-Petroleum Division; H-Nonmetallic Minerals; I-Mining Geology; K-Mining Administration; L-Geophysical Prospecting. Other members may obtain copies by writing to the Secretary. Copies of Preprints may also be obtained from the Secretary&apos;s office. Additional copies are sold at the rate of 1 cent per page; minimum charge, 25 cents. Nonmembers may purchase the papers at the prices mentioned. Metal Mining Technical Publi- Title Author Meeting Trans. cation Volume No. and Page* 484-A.45 Propeller Type Mine Fan at Moose A. S. Richardson New York 102, 88. 95 F.52 Shaft. Butte. Montana (13) Feb.. 1932 487-A.46 Progress in the Improvement of Max H. Barber New York. Methods and Equipment at Feb., 1932 Open-pit Iron Mines on the Lake Superior Iron Ranges (9) Pre. Sand Filling through Pipes and Lucien Eaton New York, 102, 33, 41 Boreholes (9) Feb., 1932 Milling And Concentration 445-B.37 Soap Flotation of the Nomulfides Will H. Coghill New York. H.19 (18) J. Bruce Clemmer Feb., 1932 461-B.38 Principles of Flotation—An Experi- I. W. Wark New York. mental Study of the Effect of A. B. Cox Feb.. 1932 Xanthates on Contact Angles at Mineral Surfaces (48) Iron and Steel Division 447-C.81 Electrochemical Potentials of Nitri- Shun-ichi Satoh New York, fied Steels (31) Feb.. 1932 450-C.82 Reaistanoe of Iron-aluminum Alloya N. 9. Ziegler New York. 100, 267. 670 E.143 to Oxidation at High Tempera- Feb., 1932 tures (8) 451-C.83 Pressure Welding of Low-carbon C. H. Austin New York. Steela with Theoretical Con- W. S. Jeffries Feb.. 1932 siderations on the Mechanism of Such Welding (42) 453-C.84 Inclusions—Tbeir Effect, Solubility C.E.Sims New York, 100, 154, 176 and Control in Cast Steel (24) 0. A. Lillieqvist Feb., 1932

Jan 1, 1932

By R. Lingle, E. Hardin, M. Board, H. Pratt, W. Ubbes, M. Voegele, N. Barton

A 2 m. cube of jointed, Pre Cambrian biotite gneiss was subjected to uniaxial and biaxial loading at ambient and elevated temperature. The effects of different boundary conditions on the following rockmass properties were investigated: deformation modulus, joint stiffness, dynamic modulus, coefficient of thermal expansion, thermal diffusivity and conductivity, and joint permeability. Test conditions ranged between 0 and 6.9 MPa uniaxial and biaxial load, and 12° to 74°C mean block temperature. The tests were performed as part of the Office of Nuclear Waste Isolation program for evaluating site charterization test methods for measuring the hydro-thermal-mechanical properties of rock masses. The fracture flow experiments discussed in this paper were described in detail in a similar paper given to this symposium in 1981 (Voegele, 1981). DEFORMATION MODULUS Horizontal deformation measurements oriented parallel to the loading direction were made at the block surface. Several instrument types were employed: surface short-rod extensometers, bonded strain gauges, vibrating wire strain gauges and the Whittemore caliper strain gauge. Two vertical and two slant borehole extensometers measured vertical displacement. Loading history, especially during uniaxial loading, was critical to interpretation of observed deformation and fracture flow data. This important tendency has been observed in other large-scale laboratory (Bandis, 1980) and field tests (Pratt, et al., 1977). Excavation of the block resulted in minimal disturbance to the intrinsic condition of the sample. Even so, permanent, unrecovered "set" was imparted to the block beginning with the first low-stress biaxial load cycle to 3.45 MPa (Table 1). Unloading

Jan 1, 1982

By J. C. Uy, A. A. Burr

IN the primary solid solutions of zirconium-base alloys, there is a striking regularity of the effect of solute valence on the stabilization of the allotropic phases.1 The valences derived by pauling2 are for elements as they are bonded in the solid metallic state. Effects of variations in isotopes, alloying elements, and allotropes on their valences are difficult to determine and such data are presently unavailable. Pauling&apos;s values are somewhat empirical and approximate, but if some definite correlations can be found between those values and experimental observations, this will lend support to the tacit assumption that the possible variations in valence mentioned above are small. Pauling has amassed a large amount of evidence of such correlations. It is the purpose of this technical note to show another application of the Pauling valences and to offer a possible explanation for this observation. The relationship between the Pauling metallic valence of the solute and the stabilization of allotropic phases in zirconium is shown in Table I, which has been compiled from available data in the literature3 plus the results of work done at Rens-selaer Polvtechnic Institute.&apos; The chemical valences are included for comparison. It can be seen that a solute whose metallic valence is lower than that of the solvent tends to stabilize the a phase while one whose metallic valence is higher than that of the solvent tends to stabilize the 0 phase. It should be noted that, inasmuch as the Pauling valences are periodic with atomic number, this is tantamount to saying that the elements in groups I-A, 11-A, III-A, III-B, IV-B, V-B, and VI-B are a stabilizers while those in groups IV-A, V-A, VI-A, VII-A, VIII-A, I-B, and 11-B are ß stabilizers. The chemical valences do not show such consistency. Although the zirconium-rich end of the Zr-Au diagram is not available, it call be expected that gold, having a metallic valence of 5.56, would stabilize the ß phase. At absolute zero, the Fermi energy level is the criterion of equilibrium, i.e., the structure having the lower Fermi level will be more stable. Conse- quently, allotropic transformation occurs in a metal when thermal excitation raises the Fermi level to a point at which the atoms can be better accomodated by a different structure which yields a lower Fermi level.4-6 Thus in allotropic transformation, a change in structure occurs as a result of the change in the energies of the bonding electrons. Since the Pauling valence is the number of bonding electrons per atom, and these are the only electrons whose energies are affected by thermal excitation,* it can be inferred that the introduction of a solute which has a higher Pauling valence than that of the solvent raises the initial Fermi level; consequently, the transformation temperature is lowered. The converse is also true. The fact that at the transformation temperatures this statement is still fairly valid implies that the contribution due to the difference in specific heat terms of the two allotropes is comparatively small.

Jan 1, 1962

By B. H. Caudle, A. B. Dyes

In a recent publication&apos; it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n &apos;. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/q, = 1/(1 + y) y and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The resrilts obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce all infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of diflerent permeabilitv and thicktress or two lnyers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when wing only data over early years 01 decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index INTRODUCTION As a result of both experimental work with models and theoretical deductions, it was recently concluded&apos; that wells having a free surface in a homogeneous reservoir producing by pure gravity drainage should have a hyperbolic decline with n = 2. The present report details efforts to extend this work on ideal homogeneous reservoirs to actual field cases. It should be remembered that both the previous work and the present extension are based on the assumption that the reservoir is at very low pressure, and hence, nearly all the potential available for driving fluid to the well is the gravity head. Attempts to apply conclusions of this study to reservoirs which have considerable pressures supplementing the gravity drive may lead to difficulty. WELLS WITH NO FREE SURFACE In a dipping gravity-drainage reservoir such as that shown in Fig. 1, some of the down-dip wells have no free surface. The previous study&apos; showed that the up-dip wells, which have a free surface, should follow Eq. 1. The following approximate analysis, of a type which was justified experimentally for up-dip wells in the work just mentioned, leads to results for the down-dip wells.