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By Carll H. Samans, Charles R. Austiuon

It has been known for several years1 that certain alloys of the Konal type, containing commercial cobalt (99.32 per cent Co and 0.42 per cent Ni) and varying amounts of ferrotitanium, exhibit very high tensile strengths at 600°C. However, their proportional limits and yield pints are relatively low. published data' for the alloys quenched in water from 950°C. and then tested at 600°C. are summarized in the upper section of Fig. I. Similar specimens that were aged at 650°C. for 72 hr., after quench and prior to testing at 600°C., gave the result; shown in the: lower section of Fig. I. In the present work the investigation of the properties of these materials has been extended by a study of the tensile deformation characteristics in moderately longtime tests at 600°, 700' and 800°C. after quenching from various solution temperatures. In addition, some metallographic studies have been made to correlate with the deformation tests, and to obtain information on the quasi-binary system cobalt-Fe2Ti. The material, very kindly furnished by the Westinghouse Electric and Manufacturing Co. in the form of hot-swaged rods of 3/16-in. diameter, analyzed as shown in Table 1. The alloys, when originally made up,' were based upon an iron-titanium compound, Fe3Ti, as indicated by the work of

Jan 1, 1941

By Ming-Kao Yen, W. R. Hibbard

Various rationalizations of preferred orientations in cold worked polycrystalline metals have been based on the operation of at least two three2 five, an indefinite number, and all,6 slip systems of the type occurring in single crystals. Pickus and Mathewson3 suggested that the cold rolling texture in face-centered cubic metals could be rationalized on the basis of two or more operating slip directions symmetrically disposed about the direction of flow in such a manner that the resolved shear stress factor is equal for all operating slip systems and lattice rotations cancel each other. The importance of the direction of flow, the necessity for the operation of slip systems capable of producing the required changes in external dimensions, the maintenance of a common surface between adjacent grains and a symmetrical arrangement of the operating slip systems in order to produce an end orientation which is stable under additional deformation lead to the following rationalization of textures based on the type of slip systems operative in single crystals. The rationalization is intended to explain why certain orientations are suitable for deformational flow without a change in orientation and thus are stable end orientations or ideal texture orientations. It does not attempt to explain how the grains of a randomly oriented polycrystalline aggregate will reach this orientation. The rationalization is based on the following four postulates: 1. The ideal textures for polycrystalline aggregates are the result of reorientations of individual crystals toward the same stable end orientation at which no further reorientation will occur even during additional deformation. Since, in simple slip, the relative orientations of the stress axis and the active slip system determine the change in orientation during slip, it is considered that the orientation of the stress axis with respect to the ideal texture determines what slip systems must be active to retain the stable end orientation. Therefore the stable end orientation should be a symmetrical one around the stress axis with respect to the active slip systems such that lattice rotations resulting from slip will cancel each other and prevent a resultant change in orientation. (Rotational symmetry only—not translation, inversion, nor others—is considered here.) Thus a metal under a pure stress should develop a texture consisting of one or more of the crystallographically symmetrical directions, <100>, <110> or <111> for cubic metals or <0001>, <1010> or <1120> for hexagonal close-packed metals, parallel to the stress axis. 2. Since the active slip direction is the direction of glide during simple slip and thus the direction of maximum shear movement, in the ideal texture the active slip

Jan 1, 1949

By N. K. Chen, C. H. Mathewson

Recrystallization of aluminum single crystals after plastic extension is carefully studied in relation to the structure of the deformed matrix. The shapes of the new grains are analyzed with regard to slip planes and to the presence or absence of deformation bands. A mechanism by which the orientations of the grains are related to the parent lattice is described. EXPERIMENTS previously reported&apos; have been extended to develop some of the characteristics of the new crystals which are formed on annealing axially strained crystals whose deformational characteristics had been documented with special care. Thus, the presence of deformation bands affects the growth contours of the crystals, some of the strained crystals produced single crystals anew, and some, polycrystals, on annealing, while others merely "recovered" or "polygonalized" after the 600°C annealing treatment generally adopted in these tests. In the matter of orientational relationships between new crystals and the strained matrix, the present experiments have added little to previous experience, which had demonstrated great variety in the range of orientations encountered and no simple theory or correlation. For example, there has been ample evidence for the predominance in various face-centered cubic metals of a favored orientational relationship; viz., a rotation of 30° to 40° around a <1ll> axis, between grains growing in a matrix with a strong single orientation texture and the matrix itself.&apos;-&apos; This reorientation has been interpreted by various investigators in support of both the "oriented nucleation" and the "oriented growth" hypothesis. In the case of axially extended single crystals of aluminum, no general relationship, such as the one stated above, can be used to correlate the orientations of the recrystallized grains with that of the original crystal. Thus, Carpenter and Elama and Burgers and Basart7 were content to assume that the orientational relationships so developed were random in nature. Mathewson, however, in the Campbell Lecture of 1943 "rgued on the basis of <112> slip that a complex strain, chiefly characterized by rotation around a variable axis in the slip plane combined with a principal rotation around the pole of the slip plane, could be responsible for such devious relationships. Nevertheless, owing to the limited data now available dealing with orientational relationships between new grains and the single crystals strained in tension from which they have recrystallized, no adequate examination of the above generalization could be made. Here, there is the disturbing preliminary condition that any desired orientational relationship may be expressed by means of two rotations about mutually perpendicular axes, so the process lacks a certain critical flavor and any successful choice of axes meeting certain theoretical requirements could be replaced by another differently selected pair. With this reservation clearly in mind the process of double rotations, as previously indicated, was used to relate the orientations of the single crystals which grew out of the strained single crystalline matrix and was construed as certain evidence in favor of the theory of incongruent shearing action proposed by Mathewsons as a necessary element in the (111) slip process with close-packed metals. There is here

Jan 1, 1953

By J. H. Fletcher, S. M. Cassidy

Air has been cooled, heated, washed, humidified and dehumidified for many purposes and in many industries. At a number of metal mines air is conditioned to reduce the high humidity and unbearable heat found in deep workings, and at some mines air is washed to allay siliceous dust. Steam is introduced into the intake air at many coal mines, particularly in winter, for the purpose of keeping loose coal dust so moistened that the hazard of an explosion is lessened. This paper will describe a further successful application of air conditioning in a coal mine, where, for over three years, all intake air has been cooled to a constant temperature for the sole purpose of preventing roof falls. Effect of Warm Weather on Mine Roof It is generally known by mining men that some, if not all, coal mines have more trouble from bad roof during the warm summer months than in winter. Also, it has been observed that roof on intake airways is usually worse than on the return entries, after the air has circulated through the mine. Some mines and some coal seams are much more affected than others. In the Clinton district of Indiana, the No. IV coal seam has a good, firm, gray shale roof except during the summer months, when it deteriorates badly and falls in small slabs 1 to 6 in. thick. Timbering is not very efficacious during this period because in time the roof will shear around the supporting prop or crossbar and either dislodge the timber or leave it supporting only a few inches of crumbly shale (Fig. 1). This action is renewed each summer, choking airways with fallen slate, tearing down trolley wires, hampering haulage, endangering men and adding considerably to the deadwork cost. Only when mines have been worked for a period of years and have been advanced a long distance from the shaft do the active workings become comparatively free of this trouble, and even then the intake entries are still a source of much deadwork. Such was the annoying situation at the mine of the Saxton Coal Mining Co. operated in the No. IV coal just north of Terre Haute, Ind. During the months of warm weather it was possible to stand at any quiet spot in the mine and within 10 min. hear at least two or three falls,

Jan 1, 1931

By T. L. McCall

THE late Walter Herd1 in 1929 gave a full description of past and present conditions in No. 2 mine, Springhill, Nova Scotia, developed theories regarding the cause of these bumps and made certain suggestions regarding possible methods of future development. Recapitulating briefly from Mr. Herd&apos;s paper, the seam is bituminous coal, averages 9 ft. in thickness and has a well defined parting containing fusain about 14 in. from the roof. This roof coal is somewhat stronger than the rest of the seam and has a tendency to cling to the roof. The pitch of the seam where it is now being worked is about 20°. The first manifestations of bumps began when the room and pillar workings had reached a depth of cover of 1900 ft. and under continuously increasing depth of cover these bumps increased to such an extent, both in number and severity, that in the year 1924 it became apparent that some change in the system of extraction was necessary. After closely studying all the factors involved and benefiting largely by valuable out-side advice obtained by the Provincial Department of Mines of Nova Scotia,2 the system of working was changed from room and pillar to longwall retreating. Mr. Herd&apos;s paper described in detail three remarkable bumps in the year 1928 in April, July and October that affected the 5700-ft. and 5900-ft. East levels, the last bump being so severe both in intensity and in extent of damage done that this district was abandoned. The longwall workings to the west of the slope had been stopped in the year 1926 owing to an inbreak of water, coming from the flooded waste of No. 3 seam lying some 400 ft. vertically overhead. This inflow was not excessive, but a large quantity of water being impounded in the old workings it was considered advisable to take the prudent course and not incur the risk of possibly increasing the flow by further working. This district has remained idle ever since.

Jan 1, 1934

By W. L. Fink, R. S. Archer

This paper describes results obtained on aluminum-beryllium alloys and aluminum-beryllium-copper alloys in the preparation of which aluminum of 99.95 per cent. purity was used. The constitution and structure of the high purity binary alloys are given. The aluminum-beryllium eutectic occurs at 0.87 per cent. beryllium and 645° C. The solid solubility of beryllium in aluminum at 631° C. is 0.05 per cent, beryllium, and at room temperature is less than 0.013 per cent. beryllium. The densities of the alloys are substantially the same as the values calculated on the assumption that the densities of the elements are not changed by alloying. All of the alloys age-harden at room temperature after a solution heat treatment, and the chill cast aluminum-beryllium-copper alloys age-harden at room temperature without a prior solution heat treatment. Hardness and tensile properties are given. Salt spray corrosion tests on sheet specimens are described. It is shown that beryllium docs not lower the corrosion resistance of aluminum to salt spray provided the alloy has received a solution heat treatment. Commercial Possibilities of Beryllium Alloys Beryllium has certain properties such as low density, high hardness, good corrosion resistance, low thermal expansion and fairly good electrical conductivity, which would indicate that it is worthy of consideration as an ingredient of light alloys. It was not until recently, however, that beryllium could be produced with sufficient ease to encourage research along this line. The production of beryllium by electrolysis from a fluoride bath has now developed to the stage where it could be used commercially if there were sufficient demand for the element. Claims made in certain newspapers and technical articles in regard to thc strength and corrosion resistance of thc aluminum-beryllium alloys are not justified by experimental results. Moreover, beryllium is an expensive metal ($200 a pound at the time this work was done) and, on account of the nature of its ore and the consequent difficulty of its extraction, it will in all probability continue to be a relatively expensive metal, although the cost would undoubtedly be a great deal less than $200 a

By E. Miller, K. L. Komarek

Equatiorzs have been derived which related maximum solid solubilities in semicondcting compounds having retvograde solidus curves with 1iqllidus data. Liquidus curves in Lke Pb-Te, Pb-Se, ard PB-S systetris have been defermined by thertrzal aralyses. Fvotrz expevimental maximum solibilities ia CdTe, PbTe, uxd PbS vetvograde tetrperatures hale beep1 calculated. TIze resllts support the concept that under certaiz conditiots pronounced itjlections in the liquidis curves arc indzcatiz:e of retropade solidus curves and that the tenlperatltre of the lmaximum solid solubility will be close to the temperature of the point of inflection in the liquidus curve. The maximum solid solihility within a gvoup of homologous cottrpoods SeetlLs to increase with increasing flatness ol the liquidus curvres. The phenomenon of retrograde solubility in metals, i.e., maximum solubility in a solid terminal phase in equilibrium with a liquid phase, has been theoretically predicted by Van aar&apos; in his calculations of hypothetical binary phase diagrams. It was not until 1926, however, that retrograde solubility was experimentally verified in the Zn-Cd system.&apos; Since then many sys- tems with retrograde solubility have been found, so that at present approximately fifty binary diagrams with a retrograde solidus curve are known.3 Meijering4 has critically appraised the accumulated data and has presented calculations which alloy predictions as to whether or not a solidus line will be retrograde. Interest in retrograde solubility increased when it was found that the solidus curves of germanium and silicon alloyed with a great many doping elements are retrrade. The problem was treated thermody-namically by odkinson,% d all available data on solid solutions in germanium and silicon were summarized by Trumbore.7 Although it is to be expected that intermetallic compounds will also exhibit retrograde solubility, experimental evidence is much more limited. Until now retrograde solidus curves have been reported for the compounds de,&apos; be, Ps:" ne," SnSe," and SnS.13 All these compounds are semiconductors, and the solidus curves were usually obtained by determining the carrier concentration at room temperature of samples equilibrated at elevated temperatures and then quenched. It has been hown,&apos;&apos; however, that it is not always possible to quench in the equilibrium compositions from above a certain temperature. Theoretical discussions have either explicitly excluded intermetallic compounds4 or not treated them with respect to retrograde slubilit.j In the following a thermodynamic treatment of retrograde solu-

Jan 1, 1967

By H. P. Croft

[ ] Professor Hibbard&apos;s paper presents a very interesting theory concerning the influence of texture on the tendency of brass tube to stress-corrosion crack. I should like to present the result of some work done in 1941 which may throw further light on the subject. In the first place, in regard to his review of the influences of grain boundaries, we not only confirmed the findings which he quoted, but also were unable to crack single crystals of beta brass in the standard mercurous nitrate test in 50 hr under loads up to 18,500 psi. Samples containing two or more crystals of beta brass always cracked at grain boundaries and generally followed the same pattern as for alpha brass, although cracking occurred sooner than in alpha brass under the same conditions. Such a specimen is shown in Fig 4. Second, at the possible risk of repetition, we should like to call attention to the reported role of grain size as influencing the tendency to stress-corrosion crack. This phenomenon, originally mentioned by Dr. Allan Morris in the Transactions, AIME, 1931, is illustrated in Fig 5, showing the effect of variations in grain size on the tendency of drawn brass wires to crack under load in the mercurous nitrate solution. This was taken from my work published in Proceedings A.S.T.M. 41, (1941), 905.

Jan 1, 1948

By Charles S. Barrett, Robert F. Mehl

A study of the structures arising from the decomposition of the ß solid solutions in the Cu-Zn and the Cu-A1 systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution— the Widmanstätten structure—-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the ? phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series—that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-—which at present seems the only a1ternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the ß and in the precipit&apos;at.ion of the y phase from the y in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point, of view.

Jan 1, 1931

By G. W. Preckshot, N. G. DeLisle, C. E. Cottrell, D. L. Katz

MOST crude oils contain asphaltic substances that may be naturally or artificially precipitated. In the Greeley field, California, this asphaltic bitumen is precipitated during the flow of the oil from the reservoir to the stock tank. The mechanism of such precipitation is not well understood. This paper presents the progress that has been made by using the electron microscope as a new tool and by observing the effects of the streaming potential on the formation of bitumen particles. Crude oils at atmospheric pressure viewed in the electron microscope in very thin films under a vacuum showed no asphaltic particles. A technique of preparing slides of thin films by dilution of the oil with benzene and washing in petroleum ether was used at first, and these observations showed that the solvents caused the formation of the particles, varying from 0.01 to 0.2 micron in diameter. The electrical effects of fluids flowing through porous solid were studied, with emphasis on the formation of colloidal particles by the streaming potential. The streaming potential of crude oil flowing through sand was measured and was shown to be responsible for the formation of bitumen particles. These results bring out a new phenomenon, which may occur when crude oil flows through the porous oil reservoir.

Jan 1, 1942

By J. A. Brierley, Roshan B. Bhappu, D. H. Reynolds, P. H. Johnson

Although the economic importance of recovering copper by leaching of mine work dumps from open-pit operations has been realized for some time, serious attempts to understand and to improve such operations through scientifi research has been made only in recent years. This progress report covers the results of chemical, physical, and biological studies pertaining to the dump-leaching process and discusses salient features and parameters that may be helpful in improving such operations. The dump leaching of low-grade copper ores, as an integral part of the open-pit mining operations in the Southwest, has been practiced for the last 50 years and is increasing in importance as one of the major sources of copper. The recent acceleration in dump leaching can be attributed to: (1) the greater tonnages of low-grade ores mined and dumped at newer mines as well as resulting from increased stripping ratios at the older mines, (2) the relatively small investment required for dump leaching facilities per pound of copper recovered contrasted with expansion of milling facilities to recover equal amounts of the metal by raising tonnage throughout, (3) low labor requirements needed for leaching, and (4) the simple and continuous nature of the process needing little close supervision of trained operators. In the past, the mining companies have not worried about efficiency in dump leaching but have been satisfied with whatever metal recoveries could be made without much effort. However, because of the huge amounts of metal accumulating in the low-grade waste dumps, compared to the relatively small amount recovered annually, an operator today cannot leave dump leaching to chance. What appears to be a simple, empirical process is actually a very complex one involving a large number of critical factors that encompass Several Scientific disciplines, such as physics, chemistry, geology, biology, and hydrology. It is imperative that

Jan 1, 1970

By M. A. Scheil

Austenitic stainless alloys are susceptible to stress-corrosion cracking which may occur under certain corrosion environments irrespective of their susceptibility to intergranular corrosion. Test samples are described for investigating stress-corrosion susceptibility of alloys for industrial equipment. A laboratory test using a solution of magnesium chloride boiling at 309 F. was found to produce transgranular cracks in several alloys investigated and in types 347 and 316 stainless steel tubing a residual stress of the order of 10,000 psi. was observed to initiate cracking. The susceptibility to stress-corrosion cracking as judged by the boiling magnesium chloride test indicates that alloys may be selected which will withstand a high stress in service Stressed specimens of stainless alloys included in a corrosion testing program will aid in determining the acceptibility of these fabricated alloys, when stressed, to the service conditions.

Jan 1, 1945

By D. W. Gillmore, C. C. Wright

DEWATERING is a major problem in the preparation and utilization of fine-sized coals now being recovered in increasing amounts from colliery effluents, refuse banks, and silt ponds. Of the various methods which have, been proposed for dewatering fine coal, gravity drainage is probably the oldest and most widely used, and yet little information on this subject has been published. Consequently a laboratory investigation of gravity drainage phenomena was undertaken not only to provide basic data for predicting the drainage behavior of fine coals in cars, bunkers, basins, and silos, but also to obtain some understanding of the moisture retention properties of fine coal. Because of practical interest in the problem, a reproducible laboratory technique, which simulated plant conditions as closely as possible, was developed for the evaluation of drainage variables. The ap- paratus selected consisted of vertically-mounted lucite columns, nominally 4 to 8 ft in length and 2, 3 or 6 in. in diam; the bottom of the column was provided with a rubber stopper through which was inserted a -in. diam drainage tube; a wad of glass wool was placed on the upper part of this outlet tube to retain the coal and a plug was temporarily located at the lower end to prevent drainage during charging of the column, see Fig. 1. The most satisfactory testing procedure is as follows: 1—The fine coal, which has been thoroughly

Jan 1, 1953

By E. Gregory, C. G. Goetzel

The outstanding elevated temperature properties of materials made from sintered aluminum powder have been well established in recent years.1,2 and considerable investigation has been carried out on the structures which appear to be responsible for this type of strengthening.2,3 The maximum operating temperature of such materials is severely limited, however, by the low melting point of the aluminum matrix; and, therefore, considerable interest was aroused in methods of introducing the

Jan 1, 1959

CLEAR sunny skies that prevailed all through the 175th General Meeting of AIME were not the 1east of the details that resulted from the many months and man-hours of p1anning by the Southern California Local Section. Some 2600 persons left the 1953 Annual Meeting technically enlightened, having had a choice of over 300 papers presented by 400 authors to listen to, learn from, and criticize. During the meeting, Mike Haider turned over the Presidency of AIME for 1953 to Andrew (Drew) Fletcher.

Jan 4, 1953

By T. A. Rickard

The earlier paper (Trans., xx., 463) describing this Victorian mining district, to which the present is supplementary, was mainly confined to the consideration of the "saddle-reefs," as scientifically the most interesting and economically the most important of the

Jan 1, 1893

By D. W. Gillmore, C. C. Wright

DEWATERING is a major problem in the preparation and utilization of fine-sized coals now being recovered in increasing amounts from colliery effluents, refuse banks, and silt ponds. Of the various methods which have, been proposed for dewatering fine coal, gravity drainage is probably the oldest and most widely used, and yet little information on this subject has been published. Consequently a laboratory investigation of gravity drainage phenomena was undertaken not only to provide basic data for predicting the drainage behavior of fine coals in cars, bunkers, basins, and silos, but also to obtain some understanding of the moisture retention properties of fine coal. Because of practical interest in the problem, a reproducible laboratory technique, which simulated plant conditions as closely as possible, was developed for the evaluation of drainage variables. The ap- paratus selected consisted of vertically-mounted lucite columns, nominally 4 to 8 ft in length and 2, 3 or 6 in. in diam; the bottom of the column was provided with a rubber stopper through which was inserted a -in. diam drainage tube; a wad of glass wool was placed on the upper part of this outlet tube to retain the coal and a plug was temporarily located at the lower end to prevent drainage during charging of the column, see Fig. 1. The most satisfactory testing procedure is as follows: 1—The fine coal, which has been thoroughly

Jan 1, 1953

By Clarence Zener

Contents Page General Principles................................................................. 551 Equilibrium Diagrams......................................................... 551 Nucleation................................................................... 553 Kinetics of Phase-boundary Propagation......................................... 553 Kinetics of Growth of New Phase............................................... 556 Spheroidization............................................................... 560 Pure Iron-carbon System........................................................... 561 Formation of Pearlite.......................................................... 561 Interlamellar Spacing........................................................ 562 Pearlite C-curve............................................................. 563 Bainite Formation............................................................. 565 Formation of Martensite....................................................... 570 Loss of Tetragonality of Martensite.............................................. 570 Effect of Alloys upon Decomposition of Austenite..................................... 572 Pearlite...................................................................... 572 Bainite and Martensite......................................................... 574 Time-temperature-transformation Curves............................................. 576 Appendix A............................................................. ......... 579 Appendix B....................................................................... 580 Appendix C....................................................................... 580 The present investigation started in an attempt to understand certain details of the decomposition of austenite, and of the effect of alloying elements thereon. As the investigation proceeded it became apparent that not only these details, but all the general features of austenite decomposition, could be understood in terms of fundamental physical principles. Since the direct applicability of these physical principles has not been previously recognized, it was decided to incorporate the original results of the investigation into a review of the general subject of the kinetics of austenite decomposition. This review constitutes the present article. An extended summary of the results is given on pages 576 to 579. This article, which deals with the kinetics of phase transformations, may appropriately be considered as a sequel to two recent articles1,2 from this laboratory on the equilibrium relations in medium alloy steels.

Jan 1, 1947

By M. Muskat

A theory has been developed describing the behavior of wells and reservoirs producing by the action of bottom water drives. It is assumed that the pressures are maintained above the bubble point, and that the permeability to viscosity ratio of the water in the flooded zone is the same as for the oil in the oil-saturated pay. Accordingly, the treatment is based on the homogeneous fluid potential theory. The effect of the difference in density between the oil and water is neglected. .4fter deriving the proper potential distrihutions, the nature of the rise of the water-oil interface below the producing wells is calculated. The primary clean-oil-production phase is expressed in terms of the displacement efficiency, defined as the fraction of the pay flooded out by the rising water table at tlle time of first water entry. The variation of this displacement efficiency is calculated as a function of the well spacing, pay thickness, the ratio of the horizontal to vertical permeability, and the well penetration. The important parameter, other than the well penetration, is found to be the ratio of the well separation to the thickness of the oil pay multiplied by the square root of the ratio of vertical to horizontal permeability. It was found that the displacement efficiency continually decreases as this parameter increases, and for values of the latter >3.5, the efficiency varies inversely as the square of the parameter. It also increases with decreasing well penetration. Perhaps the most striking result of this phase of the analysis is the conclusion that in order to explain the delay in entry of water in wells producing by bottom water drives for periods longer than a few days normal production, with drawdowns large compared with the differential density head between the oil and water, it is necessary to assume that the vertical permeability is a very low fraction of the horizontal permeability. An analysis is also given of the production history after the water has broken through, on the assumption that the production mechanism and details of the flow distribution continue to be the same as during the phase of clean-oil production. As is to be expected, it is found that the water cut will increase at an accelerated rate as production proceeds. However, the initial differences between systems of different well penetrations or well spacings with respect to the total clean-oil production gradually decrease in terms of the variation of the water-oil ratio with cumulative production. In particular, by the time the water-oil ratio has reached values of the order of 5 or greater the cumulative recoveries will generally differ much less among various producing systems than their corresponding clean-oil recoveries. Introduction On the basis of elementary geological principles, one may classify effective water-drive fields in two groups. In the first, the entry of water into the oil-producing formation may be characterized as an edge-water encroachment. This term is used to suggest that the motion of the water proceeds largely in a direction parallel to the planes of stratification. This type of water intrusion occurs usually in thin producing zones and in strata lying along structural flanks of appreciable dip. In the second group—"bottom water-drive" fields—the water-oil interface lies in a plane of zero or slight inclination to the

Jan 1, 1947

By M. Muskat

A theory has been developed describing the behavior of wells and reservoirs producing by the action of bottom water drives. It is assumed that the pressures are maintained above the bubble point, and that the permeability to viscosity ratio of the water in the flooded zone is the same as for the oil in the oil-saturated pay. Accordingly, the treatment is based on the homogeneous fluid potential theory. The effect of the difference in density between the oil and water is neglected. .4fter deriving the proper potential distrihutions, the nature of the rise of the water-oil interface below the producing wells is calculated. The primary clean-oil-production phase is expressed in terms of the displacement efficiency, defined as the fraction of the pay flooded out by the rising water table at tlle time of first water entry. The variation of this displacement efficiency is calculated as a function of the well spacing, pay thickness, the ratio of the horizontal to vertical permeability, and the well penetration. The important parameter, other than the well penetration, is found to be the ratio of the well separation to the thickness of the oil pay multiplied by the square root of the ratio of vertical to horizontal permeability. It was found that the displacement efficiency continually decreases as this parameter increases, and for values of the latter >3.5, the efficiency varies inversely as the square of the parameter. It also increases with decreasing well penetration. Perhaps the most striking result of this phase of the analysis is the conclusion that in order to explain the delay in entry of water in wells producing by bottom water drives for periods longer than a few days normal production, with drawdowns large compared with the differential density head between the oil and water, it is necessary to assume that the vertical permeability is a very low fraction of the horizontal permeability. An analysis is also given of the production history after the water has broken through, on the assumption that the production mechanism and details of the flow distribution continue to be the same as during the phase of clean-oil production. As is to be expected, it is found that the water cut will increase at an accelerated rate as production proceeds. However, the initial differences between systems of different well penetrations or well spacings with respect to the total clean-oil production gradually decrease in terms of the variation of the water-oil ratio with cumulative production. In particular, by the time the water-oil ratio has reached values of the order of 5 or greater the cumulative recoveries will generally differ much less among various producing systems than their corresponding clean-oil recoveries. Introduction On the basis of elementary geological principles, one may classify effective water-drive fields in two groups. In the first, the entry of water into the oil-producing formation may be characterized as an edge-water encroachment. This term is used to suggest that the motion of the water proceeds largely in a direction parallel to the planes of stratification. This type of water intrusion occurs usually in thin producing zones and in strata lying along structural flanks of appreciable dip. In the second group—"bottom water-drive" fields—the water-oil interface lies in a plane of zero or slight inclination to the

Jan 1, 1947