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By S. R. Goodman, Hsun Hu

The formation of secondary - recrystallization tex-tlires in cube-textured 18-8 stain less steel (Type 304) Ilas been studied at three temperatures. Prolonged annealing at 100°'C protluces a PredoninanGly (520) [OOZJ-type texture, which is related to the cube te.ture of the primary lnatrix by a rotation of approxivzately 22 deg around the [001] axis in the rolling direction. Annealing at 1200 or 1300°C facers the formation of the (123)[272/-type texture, which is related to the matrix texture by a [111] rotation of app.voxiniately 40 deg. These observations suggest that in the secondary recrystallization of cube-texlut-ed stainless steel an apparent actilation energy for growth is higher for grains related to the tncrtuix Og [111] rotations thun those reloted by [100] rotations. THE formation of secondary-recrystallization textures in cube-textured primary matrices of fcc metals has been studied widely by various investigators. For Fe-40 pct Ni alloys, Pawlek' and wassermann2 reported that the orientations of secondary grains were related to the cube texture by rotations of 30 and 38 deg around [001] in the rolling direction. However, Rathenau and custers3 found that, while in one Fe-48 pct Ni alloy, most of the secondary grains were oriented with respect to the cube-textured matrix by rotations around [001] of 26.5 deg, in another alloy of a different origin, the orientations of secondary grains were related to the cube texture by rotations of approximately 35 deg around a [lll] axis. Similar orientation relationships were also observed between the secondary grains and the cube-textured primary matrices of copper.4"a No attempt was made to differentiate these two types of orientation relationships; reorientation by either a [111] or a [100] rotation was considered to be equally favored. The present investigation consisted of a study of the secondary recrystallization textures in cube-textured stainless steel. It was noted that the secondary grains formed in stainless steel were considerably smaller than those of Fe-Ni alloys or copper. This offered the advantage that the secondary recrystallization texture could be determined by the texture-goniometer technique, and a more detailed study of the textural development during the course of secondary recrystallization could be made. The effect of annealing temperature on the formation of secondary-recrystallization textures was also investigated. MATERLAL AND METHOD It was shown earlier"-" that a strong cube texture can be obtained in 18-8 stainless steels by rolling at 800°C to produce the copper-type deformation texture, followed by annealing at 800" to 1000°C for recrystallization. To improve the cube texture for the present study, a commercial-grade 18-8 stainless steel (Type 304) was rolled at 800°C first to 5 mm (0.2 in.) thick plates. Three of these plates were then stacked and welded together along the edges into a sandwich assembly. After annealing at 900°C for 20 min: the assembly was finally rolled at 800'C to 90 pct reduction in thickness with reheats and end-for-end reversals after each pass. Only the central strip, which was reduced from 5.0 to 0.50 mm (0.7 in. to 0.020 in.) thick, was used. The chemical composition of the steel in weight percent was as follows: C, 0.06; Mn, 0.38: Cr, 18.71; Ni, 9.56: P, 0.011; S, 0.009; and Si, 0.39. The purpose of rolling the strip in a sandwich assembly was to prevent direct contact between the central strip and the rolls. It was observed earlier" that, when the strip was rolled at 800°C without being enclosed in a sandwich assembly, the cube texture obtained by subsequent annealing at 900" or 1000° C for recrystallization was largely confined to the central section of the strip, while most of the recrystallized grains formed in the surface section of the strip were not cube-textured. This was obviously due to the fact that the actual temperature at the strip surface during rolling, as a result of direct contact between the strip and the cold and massive rolls, was considerably lower than 800°C. By using a sandwich assembly for hot rolling, the cube texture obtained upon subsequent annealing for recrystallization was found to extend through the entire thickness of the strip. After rolling, the central strip was taken from the sandwich assembly. and cut into specimens. Prior to annealing. the specimens were etched to 0.25 mm (0.010 in.) thick. A tube furnace provided with a purified, dry argon atmosphere was used for annealing. Textures were determined by the reflection technique. using a Siemens automatic texture-goniometer and ZrOz-filtered MoKa radiation. With a time constant of 4 sec. the preferred orientation of the secondary grains could be measured satisfactorily by the integrated intensities. Both (111) and (200) reflections were measured, and corresponding pole figures were constructed according to the techniques described previously.10 The agreement between results deduced from these two reflections was excellent. RESULTS AND DISCUSSION Secondary-Recrystallization Texture due to Prolonged Annealing at 1000°C. Fig. 1 shows the primary-recrystallization texture of a specimen annealed at 1000°C for 30 min. A substantial improvement in both sharpness and intensity of the cube texture, owing to the present processing method, can be noted readily by comparing Fig. 1 with similar pole figures shown earlier in Refs. 9 and 11. Secondary recrystallization

Jan 1, 1967

IRVING. PERRINE, Hutchinson, Kans.-I think in reading this paper one should hear in mind its relation to Dr. David White's paper on "Some Relations in Origin between Coal and Petroleum."' In that paper he discusses the relationship between the percentages of fixed carbon in the coals, the gravities of the oils, and commercial gas possibilities. His paper has a map showing certain areas which Dr. White believes to be hopeless as far as oil and gas possibilities are concerned. THE CHAIRMAN (C. W. WASHBURNE, New York, N. Y.).-I. would like to emphasize one point brought out by Professor Schuchert.2 The southern hemisphere has had an exceedingly monotonous geological his-tory, except the northern border of Africa, the eastern border of Aus-

Jan 12, 1919

By F. R. Morral

INDUSTRY has yet to find a universal solution to the problem of engineer personnel selection. Today, the choice of the right man for the right job is even more pressing than ever before. The age of the hard apprenticeship seems to have passed. In its place one finds the interviewer who must determine through personal contact and evaluation of college grades whether a graduate engineer will fit into his company's scheme. The problem, as it is constituted today, may be broken into four parts: Need for better use of human resources (there is a shortage of engineers, scientists, and skilled workers), productivity with higher efficiency, encouragement of personal pride in work performed, and employee's happiness on the job and away from it.

Jan 4, 1953

By C. S. Barrett, O. R. Trautz

Previous investigations have shown that lithium is body-centered cubic from near its melting point to the temperature of liquid air.1,2,3 Nevertheless there was an incentive to search again for a transformation at low temperatures: C. Zener4.5 has remarked that the low value of the elastic modulus (C11 — Cl2)/z of body-centered cubic metals and alloys implies a rapid increase in free energy with decreasing temperature, which would favor the occurrence of a transformation; also the shear movement to which this modulus applies is one that can transform a body-centered cubic structure into a slightly distorted face-centered cubic structure. It was confirmed that lithium does not transform spontaneously at liquid nitrogen temperature, but it was found that a transformation can be induced at this temperature by cold working the metal,6 and at slightly lower temperatures a different transformation occurs spontaneously. Transformations were also found in solid solutions of magnesium in lithium. The Nature of the Transformations Before presenting a detailed treatment of the technique used and the specific data obtained, it would be well to give a brief survey of the general characteristics of the transformations. A new crystal structure begins to form spontaneously in a specimen when it is cooled below a critical temperature. In lithium the structure appears to be close-packed hexagonal; in theLi-Mg alloys most of the diffraction lines (but not all) are near those for hexagonal lithium. The transformation proceeds as the temperature is lowered and soon stops if the temperature is held constant or raised. The course of the transformation on cooling is indicated by the curve at the lower left of Fig -I. This curve is drawn in stepped fashion because the transformation goes by discrete steps with audible clicks. Because of the similarity to the decomposition of austenite into martensite in steels, it seems appropriate to designate the beginning of the spontaneous transformation on cooling as the Ms point. On heating to room temperature after the low temperature treatment only the usual BCC structure is found. On heating, the low temperature modification begins to disappear at a temperature which will be designated as Ac. The transformation on heating is halted when the rise in temperature is halted. The temperature must be raised 40 to 50°C above Ac before the reversion is complete—an interval which is sensitive to the rate of heating and to the time of holding at temperatures above Ac. This behavior on heating thus has similarities also to the formation of martensite in the cooling of steels.

Jan 1, 1949

Jan 1, 1902

Jan 1, 1967

By C. S. Barrett, O. R. Trautz

PREVIOUS investigations have shown that lithium is body-centered cubic from near its melting point to the temperature of liquid air1,2,3 Nevertheless there was an incentive to search again for a transformation at low temperatures: C. Zener4,5 has remarked that the low value of the elastic modulus (11 - C12)/2 of body-centered cubic metals and alloys implies a rapid increase in free energy with decreasing temperature, which would favor the occurrence of a transformation; also the shear movement to which this modulus applies is one that can transform a body-centered cubic structure into a slightly distorted face-centered cubic structure. It was confirmed that lithium does not transform spontaneously at liquid nitrogen temperature, but it was found that a transformation can be induced at this temperature by cold working the metal,6 and at slightly lower temperatures a different transformation occurs spontaneously. Transformations were also found in solid solutions of magnesium in lithium. THE NATURE OF THE TRANSFORMATIONS Before presenting a detailed treatment of the technique used and the specific data obtained, it would be well to give a brief survey of the general characteristics of the transformations. A new crystal structure begins to form spontaneously in a specimen when it is cooled below a critical temperature. In lithium the structure appears to be close-packed hexagonal; in the Li-Mg alloys most of the diffraction lines (but not all) are near those for hexagonal lithium. The transformation proceeds as the temperature is lowered and soon stops if the temperature is held constant or raised. The course of the transformation on cooling is indicated by the curve at the lower left of Fig I. This curve is drawn in stepped fashion because the transformation goes by discrete steps with audible clicks. Because of the similarity to the decomposition of austenite into martensite in steels, it seems appropriate to designate the beginning of the spontaneous transformation on cooling as the Ms point. On heating to room temperature after the low temperature treatment only the usual BCC structure is found. On heating, the low temperature modification begins to disappear at a temperature which will be designated as Ac. The transformation on heating is halted when the rise in temperature is halted. The temperature must be raised 40 to 50°C above Ac before the reversion is complete-an interval which is sensitive to the rate of heating and to the time of holding at temperatures above Ac. This behavior on heating thus has similarities also to the formation of martensite in the cooling of steels.

Jan 1, 1948

By Cyril Smith

A COMPLETE discussion of the literature on the subject of the influence of copper on iron and steel will be published elsewhere.1 The present paper is concerned especially with the precipitation-hardening of copper steels, and brief mention will be made here only of the work of Kin-near,2,3 Nehl4 and Buchholtz and Koster,5 who alone have studied this phase of the subject. Kinnear found that normalized low-carbon steel castings containing about 1.0 per cent copper on drawing at temperatures in the neighbor-hood of 530° C. (1000° F.) increased in tensile strength and yield point, with little decrease in ductility. The maximum effect was obtained with about 0.9 to 1.0 per cent copper, and when the copper exceeded 3 per. cent no improvement occurred on reheating. Kinnear did not study the effect of time of reheating-an all important factor where precipitation is concerned. Nehl,6 who apparently was unaware of Kinnear's work, recognized the change as due to precipitation and studied the interdependence of time and temperature of reheating, the temperature of the initial solution heat treatment, and the speed of cooling necessary to retain the bulk of the copper in supersaturated solu-tion and to give an increase in hardness and tensile strength on reheating. Nehl found that if the final rolling or forging temperatures exceeded 700° C. (1300° F.) it was not necessary even to normalize the steel, but full precipitation occurred on merely reheating the forged or rolled shapes at 500° C. (930° F.).

Jan 1, 1933

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-A1 alloys has been measured up to the solubility limit for formation of aluminum nitride using the Sieverts method. The activity coefficient of nitrogen decreases slightly with increasing aluminum content in the range of 0 to 4 wt pct Al. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from fhe elements dissolved in liquid iron has been determined to be: ?F" = -59,250 + 25.55 T in the range from 1600º to 1750ºC. The solubility of nitrogen in liquid iron alloys and the interaction of nitrogen with dissolved alloying elements in liquid iron have been the subject of a number of research investigations.' Most of this work, however, has been reported for concentrations well below those necessary for the formation of the alloy nitride phase. Data in the concentration region near the solubility limit of the alloy nitride, particularly for systems exhibiting stable nitrides, are important in evaluating the denitrifying power of various alloying elements. They are also useful in determining the stability of a given nitride if it is to be used as a refractory to contain liquid iron alloys. In view of the importance of aluminum as a deoxidizing agent in commercial steelmaking and the fact that its nitride, AIN, is a highly stable compound and has merited some consideration as an industrial refractory, the following investigation was undertaken. The use of the Sieverts technique provided a measurement of the equilibrium nitrogen solubility in liquid Fe-A1 alloys as a function of nitrogen gas pressure up to 3.85 wt pct A1 in the temperature range of 1600º to 1750°C. The values obtained by the Sieverts method were checked by means of a quenching method in which liquid iron was equilibrated with an A1N crucible under a known partial pressure of nitrogen gas, and the solubility of A1N in liquid iron determined by chemical analysis. EXPERIMENTAL PROCEDURE The theoretical considerations involved in determining the solubility product of a solid alloy nitride phase in liquid iron by measuring the point of departure of the nitrogen gas solubility from Sieverts law have been discussed by Rao and par lee.' The principal problem is to determine the variation of nitrogen solubility in an alloy as a function of the pressure of nitrogen gas over it with sufficient precision to establish the break point in the curve at the solubility limit of the alloy nitride phase. A fairly large number of data points are required to do this. A second problem is the determination of the composition of the precipitated solid nitride phase. This is necessary in order to define completely the thermodynamic relationships. The Sieverts apparatus used to make the nitrogen solubility measurements in this investigation is of essentially the same design as that described by Pehlke and E1liott.l The charge materials were Ferrovac-E high purity iron supplied by Crucible Steel Co. and 99.99+ pct pure aluminum. Recrystal-lized alumina crucibles were used, and were not attacked by the liquid alloys. The hot volume of the system which was measured for each melt ranged from 46 to 50 standard cu cm and was found to decrease linearly with decreasing pressure and with increasing temperature. The temperature coefficient of the hot volume at 1 atm pressure of argon gas was essentially constant for all experiments at a value of -6 X 10-3 cu cm per "C. The melt temperature was measured with a Leeds and Northrup disappearing filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature scale was calibrated against the observed melting point of pure iron taken as 1536°C. The emissivity of all melts was assumed to be that of pure iron, taken as 0.43. The charge weights ranged from 110 to 140 g and the range of aluminum contents covered was from 0 to 3.85 wt pct. Aluminum additions were made as 12 to 15 wt pct A1-Fe master alloys previously prepared in the system under purified argon. The compositions of the master alloys were checked by chemical analysis and found to be in agreement with the charge analyses. Vertical cross sections of the master-alloy ingots were used as charge material for the equilibrations in order to minimize the effect of any segregation which might have occurred during solidification of the master alloys. Determinations of the solubility product of

Jan 1, 1964

HOW the Engineers' Memorial clock and carillon at Louvain has impressed the people of that city is indicated by the following letter sent by the Secretary of the University of Louvain to the Secretary of the United Engineering Society. We are still full of the memories of that splendid July 4, when we came into such .delightful contact with our American friends and more specially with the representation of the engineering societies of the United States. It was a great joy for all the members of the University to see those, American friends who have given to us such a splendid memorial in honor of- the brave men who fell in the Great War.

Jan 1, 1928

By R. E. Smallman, J. C. Terry

J. C. Terry and R. E. Smallman (Llniuersity of Birmingham, England)—In a recent publication53 Wood and Westbrook have reported the results of an investigation of the tensile behavior of fl-phase AgMg alloys. These results agree in broad outline, but differ in the details, with those obtained in the above laboratory and, consequently, some discussion of their paper would seem appropriate. In our experiments, tests were carried out on extruded wires, 2 mm diam, in a hard-beam tensile machine, and while an oil bath was used for the tests up to 150°C, above this temperature the oil bath gave rise to serious contamination of the specimens and hence tests above 150°C were made in vacuo. This procedure is different to that adopted by Wood and Westbrook. The ß-phase alloys exhibit differences in mechanical behavior when they are tested in different temperature ranges. In agreement with Wood and Westbrook, three characteristic ranges are observed which may be classified as low, intermediate, and high temperatures, respectively. Our experiments show that in the low-temperature region, the shape of the stress-strain curves is similar to that reported. However, in addition, it is observed that the temperature at which the low-temperature region ends is markedly dependent on strain rate, and increase with increasing strain rate as shown in Fig. 18. The temperature at which a transition from the low to the intermediate temperature takes place is about 0.4 to 0.45 of the absolute melting point, Tm. This transition temperature coincides with that at

Jan 1, 1963

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.' They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

By Frederick Laist

I. INTRODUCTION The new slime-concentrating plant at the Washoe Reduction Works, Anaconda, was put into operation during March, 1914. This plant, which has a capacity of 26,000,000 gal. of slime pulp carrying 2,500 tons. of solid matter per day, consists of Dorr thickeners and Anaconda multiple-deck slime concentrators.' This plant is the culmination of a great deal of experimental work extending over a considerable period of time, which work will be described briefly in the following pages.

Jan 8, 1914

By Allan Martin, R. A. Swalin

Diffusion rates of manganese, aluminum, titanium, and tungsten in nickel were measured at temperatures between 1100° and 1300°C. Activation energies, Q, and values of the frequency factor, Do, were calculated for each system. Values of Q were found to be within 15 pet of that for self-diffusion of nickel in agreement with present theories of diffusion. ONE of the most interesting problems in diffusion concerns factors governing the order of diffusion coefficients of various solutes in a common solvent metal at low solute concentrations. An early suggestion by Rhines and Mehl' was that diffusion coefficients might each approach that of the self-diffusion coefficient of the solvent itself. Later Thomas and Birchenall' pointed out correlations between the order of the diffusion coefficients and the freezing point depressions of the solvent by the various solutes. Other correlations have been sought. To settle this question it seems likely that much more data will be needed and, in particular, data collected at low solute concentrations. This type can be obtained by special analytical techniques as well as by use of radioactive tracers. The following study was made of diffusion of manganese, aluminum, titanium, and tungsten in a common solvent, nickel, at relatively low solute concentrations: 1—Production of alloys of nickel with manganese, aluminum, titanium. and tungsten at concentrations of the order of 1 atomic pet. 2—Use of pressure-welded diffusion couples in cylindrical form. 3—Diffusion anneals in the temperature range of 1100" to 1300°C. 4—Lathe sectioning of the diffused couples. 5—Spectrophotometric analyses of lathe turnings for the solute being studied. 6—Calculation of the diffusion coefficient for each of the solutes as a function of temperature. 7—Interpretation of results with current theories of diffusion. Experimental Work Materials—Two types of nickel were used in this research. The grade designated as Vacuum melted Mond nickel was used for all diffusion systems except the Mn-Ni system for which the Vacuum melted electrolytic nickel was used. Analyses of the two grades are given in Table I. The manganese used in making alloys was 99.9 + pet pure, aluminum 99.99 pet pure, titanium 99.9 pet pure, and tungsten of C.P. grade powder. Alloys used in this investigation were prepared by melting in vacuo or under a low pressure of argon. After melting, all heats except those of nickel-manganese were poured into a cylindrical copper mold 3 in. long and 1 in. ID. In the case of nickel-manganese, the alloys were solidified in the melting crucible. For nickel-aluminum heats alumina crucibles were used and for all other heats, zirconia crucibles.

Jan 1, 1957

By Clyde Evarts Weed

SOME one once affirmed his great belief in luck, adding that he had found that the harder he worked the more luck he had. Clyde Weed is a firm believer in this method of courting the fugitive lady. He is at work early and late, often leaving his staff at Anaconda's offices at 25 Broadway breathless trying to keep up with the ideas teeming from a fertile brain and the actions those ideas entail. Miles ahead of his assistants much of the time, he still manages to be an agreeable fellow to work with, no small accomplishment as many can testify. Mr. Weed arrived in the world at Moorestown, Mich., on Aug. 8, 1890. Sixteen years later he entered Michigan Agricultural College, a lowly freshman. The following year, with the experience and wisdom expected of a sophomore, he transferred his studies from the reaping of a harvest on the surface of the earth to delving into the deeper, unpredictable bowels of the earth, his studies now shifted to the Michigan College of Mines. Last June his alma mater conferred upon him the degree of Doctor of Engineering.

Jan 1, 1947

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By Edgar L. Weinberg, W. Horatio Brown

The Austinville-Ivanhoe lead-zinc deposit occurs in the Lower Cambrian Shady dolomite. This deposit is located in southwestern Virginia in the faulted and folded Appalachian Valley and Ridge province. The ore bodies resemble the chimmey and manto deposits of northern Mexico and are formed by replacement and filling. They are confined to certain favorable zones of the Austinville and Ribbon members of the Shady. Structural and stratigraphic factors combine to control the location and form of the ore bodies. In certain places secondary oxide enrichment of the zinc minerals has contributed to the economic development of the area. It is concluded that the ore is epigenetic and is deposited by hydrothermal solutions rising through the fault "plumbing." Classification is epithermal-telethermal.

Jan 1, 1968

By Carl Wagner

This paper contains solutions of the differential equation of diffusion in binary alloys if the diffusion coefficient is an exponential function of the concentration of one of the components. THE general differential equation for one-dimensional diffusion in a binary system can be written as: where c is the concentration of one of the two components in any suitable units; x, the distance from a reference plane; t, time; and D, the diffusion coefficient. Hartley and Crank&apos; have pointed out that eq 1 with conventional length units for measuring the distance x holds only if the alloy can be regarded as a rigid framework. In general, this is not the case, especially if the lattice parameter varies appreciably with composition. If a modified coordinate system is used instead of an orthodox system based on the centimeter a:: length unit, eq 52 is obtained, which has the same general form as eq 1 and is generally valid. The necessary transformations are presented in the appendix. If&apos; D is independent of concentration, analytical solutions of eq 1 are known for numerous boundary conditions. If D depends on concentration, solutions based on known analytical functions are not available. Among others, Boltzmann2 and Matano3 have shown that the concentration c depends only on (x/t1/2) in the case of diffusion between two semi- infinite spaces with uniform initial concentrations: c = c, for x < 0, t = 0, i.e., x/tl/2 = — x [21] c = c2 for x > 0, t = 0, i.e., x/tl/2 = + a Moreover, Boltzmann and Matano have shown how D may be calculated as a function of concentration over the whole range of composition from c -c, to c = c2 if c as a function of (x/t1/2) for the initial conditions stated in eq 2 has been determined experimentally. Thus, for instance, in principle, the diffusion coefficient in silver-gold alloys may be calculated as a function of concentration for the whole range of composition from only one diffusion experiment with a couple of pure silver and pure gold welded together. If the diffusion coefficient D as a function of concentration c is known, a solution of eq 1 for boundary conditions as stated in eq 2 with arbitrarily chosen values of c, and C2 may be wanted. For instance, if the diffusion coefficient in an alloy A-B as a function of concentration has been derived from an experiment with a diffusion couple involving 0 and 30 pct B as initial. concentrations, the calculation of the concentration distribution in a diffusion couple involving other initial concentrations, e.g., 5 and 20 pct B, may be desired. This problem may be solved by numerical or graphical integration of eq l. The solution of an ordinary differential equation of second order, which results from using (x/t1/2) as an independent variable, can be computed quite rapidly if two conditions for the same value of the independent variable are given. In eq 2, however, two conditions are given for two

Jan 1, 1953

By Cyril Smith

FOR several years an investigation has been in progress in the research laboratory of The American Brass Co. to determine the thermal and electrical conductivities of most copper alloys of commercial importance and several of scientific interest. This paper contains such data on the binary alloys of copper with silicon, aluminum, manganese and nickel, and on a large number of ternary or more complex alloys. Some inter-esting general relationships between the thermal and electrical conductivi-ties for all copper alloys at all temperatures are pointed out. The data for the copper-zinc, copper-phosphorus and copper-tin binary systems have already been published1,2 ? except for the electrical conductivity at 200° C., which is given in the appendix of this paper.

Jan 1, 1935