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By M. B. Bever, J. E. Reynolds

IN several alloys of iron, copper, and lithium as well as in some pure metals, martensite formed on cooling reverts to the parent phase upon heating to a temperature below the equilibrium temperature at which the parent phase becomes stable.' These martensitic transformations, therefore, are thermally reversible, although appreciable hysteresis may be involved. The martensitic reaction has long been

Jan 1, 1953

By A. L. Titchener, M. B. Bever

FROM their investigation of the martensitic transformation in Cu-Zn alloys, Greninger and Mooradian' concluded that there was no critical temperature at which martensite formation began in this system. Recent unpublished work by Gen-evray With two compositions of brass revealed the existence of a critical temperature, which is a function of composition and stress. In the work reported here the temperature range of the martensitic reaction was studied as a function of composition in high purity Cu-Zn alloys. The specimens were about 4 in. long with a diameter of 1/16 in.; their compositions are given in Table I. They were heated under vacuum for 5 min at 5" to 10°C below the temperature of incipient melting, and quenched into brine at about — 10°C. Specimens of alloys C, D, E and F were obtained with little or no precipitated a phase. Many attempts yielded only three usable specimens of alloy B, and even these contained appreciable amounts of a. All efforts failed to preserve metastable p in alloy A (containing 38.02 pct Zn and 0.002 pct each of Pb and Fe). The transformation was studied by measuring the electrical resistance during continuous cooling and heating of each specimen at similar rates. The cooling media were alcohol with dry ice from room temperature to — 78°C and a bath of petroleum ether and methyl cyclohexane (75:25), cooled by liquid nitrogen, from —78" to about —150°C. Readings were also taken at —195 °C in liquid nitrogen. Fig. 1 illustrates a typical experiment. The relative resistance is obtained by assuming the known

Jan 1, 1955

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce&apos; and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"&apos; multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately&apos;: — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce&apos; and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"&apos; multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately&apos;: — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Roscoe C. Clark

In October 1945. R. F. Farris. in an AIME paper entitled Method For Drtermining Minimum Waiting OIL Cenzent Time, presented a method for caiculating the minimum WOC* time required in oil well cementing operations. Briefly. this method consisted of shutting in a well. after the cement had been placed and noting the time required fur the wellhead pressure to reach a. maximum. This time was then multiplied by a factor of 1.5 to determine when the cement had reached sufficient strength to support the weight of the casing. As a result of this work, a number of areas have reduced their WOC time ~Wuirements with the subsequent saving of considerable rig time. The tests conducted by Farris were, for the most part, conducted under cementing temperatures in excess of 70°F. This was done because in the overwhelming majority of cases. cementing temperatures are in excess of 70°F (only in tile northern part of the country. primarily in the Rocky Mountain ares. in cementing surface casing are temperatures below 70° F. encountered, and such temperatures occur only during the winter months). The Stano-lind Research Laboratory since that time has performed a number of tests both in the laboratory and in the field to evaluate this WOC factor when cemeriting temperatures are lower than 70°F. The results of these tests indicated the need for greater WOC time in areas affeaed by abnormally low cementing temperatures. These tests indi.cated that a woc factor of 2 (Time from start to mix cement to maximum wellhead pressure x 2 = Time to drill plug) will allow sufficient time for the cement to develop adequate strength. A field test under abnormally low cementing temperatures (surface temyerature 35°F., mud discharge temperature <70°F. and cementing depth 500 ft.) in the Rangely Field, "* using the WOC factor of 2, indicated the time to drill the plug as 45 hours. Well conditions preventing getting back into the well until a 48-hour WOC time had elapsed. At this time, the plug drilled firm to hard indicating that the cement had reached its final set. It is contemplated that during next winter additional field tests will be performed to further check the results of the laboratory and field tests conducted to date,

Jan 1, 1949

By Roscoe C. Clark

In October 1945. R. F. Farris. in an AIME paper entitled Method For Drtermining Minimum Waiting OIL Cenzent Time, presented a method for caiculating the minimum WOC* time required in oil well cementing operations. Briefly. this method consisted of shutting in a well. after the cement had been placed and noting the time required fur the wellhead pressure to reach a. maximum. This time was then multiplied by a factor of 1.5 to determine when the cement had reached sufficient strength to support the weight of the casing. As a result of this work, a number of areas have reduced their WOC time ~Wuirements with the subsequent saving of considerable rig time. The tests conducted by Farris were, for the most part, conducted under cementing temperatures in excess of 70°F. This was done because in the overwhelming majority of cases. cementing temperatures are in excess of 70°F (only in tile northern part of the country. primarily in the Rocky Mountain ares. in cementing surface casing are temperatures below 70° F. encountered, and such temperatures occur only during the winter months). The Stano-lind Research Laboratory since that time has performed a number of tests both in the laboratory and in the field to evaluate this WOC factor when cemeriting temperatures are lower than 70°F. The results of these tests indicated the need for greater WOC time in areas affeaed by abnormally low cementing temperatures. These tests indi.cated that a woc factor of 2 (Time from start to mix cement to maximum wellhead pressure x 2 = Time to drill plug) will allow sufficient time for the cement to develop adequate strength. A field test under abnormally low cementing temperatures (surface temyerature 35°F., mud discharge temperature <70°F. and cementing depth 500 ft.) in the Rangely Field, "* using the WOC factor of 2, indicated the time to drill the plug as 45 hours. Well conditions preventing getting back into the well until a 48-hour WOC time had elapsed. At this time, the plug drilled firm to hard indicating that the cement had reached its final set. It is contemplated that during next winter additional field tests will be performed to further check the results of the laboratory and field tests conducted to date,

Jan 1, 1949

By J. Gordon Parr, D. H. Polonis

RYSTALLOGRAPHIC relationships between martensitic a&apos; (close-packed-hexagonal) and retained fi (body-centered-cubic) have been studied in binary alloys of titanium with manganese, molyb- denum, chromium, and iron.&apos;" In these investigations, the habit planes of the martensitic phase were determined, as well as the orientation relationships between martensitic and parent phases. In each alloy

Jan 1, 1957

By J. E. Burke

THE origin of recrystallization textures continues to be a matter of controversy. One explanation is that a recrystallization texture occurs because only grains having a limited range of orientations ever appear in the deformed matrix—the oriented nuclea-tion* hypothesis. Another explanation is that grains essentially having all orientations are nucleated but that those having certain orientations grow much more rapidly than any others in the deformation texture, and thus only the rapidly growing grains survive when recrystallization is complete. There has recently appeared a great deal of evidence&apos;- indicate that recrystallized grains of face-centered cubic metals are frequently related to their parent grains by rotations of 20" to 40" about a common [lll] direction. Furthermore, it has been observed that the growth rate of the new grains depends upon their orientations with respect to the matrix, and that the most rapidly growing grains lie within the stated range of orientations. In a recent note, Beck7 has concluded from observations of this type that oriented growth alone is responsible for the appearance of preferred orientations in re-crystallized metals. It should be pointed out. however, that many of the available data indicate that oriented nucleation operates in addition to oriented growth. Thus, while oriented growth may permit a selection to be made among nuclei of several orientations, only a limited number of orientations are available in the first place for such selection.

Jan 1, 1953

By Paul A. Beck

THE occurrence of the (100) [lOO] or "cube" texture upon annealing of cold-rolled copper has been much investigated.&apos; The conditions favorable for its formation were found to be a high final annealing temperaturez or long annealing time," a high reduction of area in cold rolling prior to the final anneal,&apos; and a small penultimate grain size." The effects of penultimate grain size and of rolling reduction were found by Cook and Richards4 to be interrelated in such a way that any combination of them giving lower than a certain value of the final average thickness of the grains in the rolled material leads to a fairly complete cube texture with a given final annealing time and temperature. Also, according to the same authors, at a higher final annealing temperature a larger average rolled grain thickness, i.e., a lower final rolling reduction, is sufficient than at a lower temperature. These somewhat involved conditions can be understood readily on the basis of recent results obtained at this laboratory. Hsun Hu was able to show recently by means of quantitative pole figure determinations that the rolling texture of tough pitch copper, which is almost identical with that of 2s aluminum: may be described roughly as a scatter around four symmetrical "ideal" orientations not very far from (123) [112]. In the case of aluminum, annealing leads to retain-ment of the rolling texture with some decrease of the scatter around the four "ideal" orientations, and to the appearance of a new texture component, namely the cube texture." A microscopic technique, revealing grain orientations by means of oxide film and polarized light, showed that the retainment of the rolling texture is achieved through two different mechanisms operating simultaneously, namely "re-crystallization in situ," and the formation of strain-free grains in orientations different from their local surroundings, but identical with that of another component of the rolling texture. Thus, a local area in the rolled material, having approximately the orientation of one of the four "ideal" components of the texture, partly retains its orientation during annealing, while recovering from its cold-worked condition, and it is partially absorbed at the same time by invading strain-free grains of an orientation approximately corresponding to that of another "ideal" texture component. The reorientation here, as well as in the formation of the strain-free grains of "cube" orientation, may be described as a [Ill] rotation of about 40°, see Fig. 1 of ref. 6. The preferential growth of grains in such orientations is a result of the high mobility of grain boundaries corresponding to this relative orientation.&apos; " It appears very likely that in copper the mechanism of the structural changes during annealing is similar to that observed in aluminum (except for the much greater frequency of formation of annealing twins in copper). In both metals the new grains of cube orientation have a great advantage over the new grains with orientations close to one of the four components of the rolling texture. This advantage stems from their symmetrical orientation with respect to all four retained rolling texture components of the matrix; they are oriented favorably for growth at the expense of all of these four orientations. As a result, the growth of the "cube grains" is favored over the growth of the others, as soon as the new grains have grown large enough to be in contact with portions of the matrix containing elements of more than one, and preferably of all four component textures. It is clear that this critical size is smaller and, therefore, attained earlier in the annealing process if the structural units, such as grains and kink bands, representing the four matrix orientations are smaller, i. e., if the average thickness of the rolled grains is smaller. Hence, for a given annealing time and temperature, a smaller penultimate grain size and a higher rolling reduction both tend to increase that fraction of the annealing period during which the above condition is satisfied. Consequently, the percentage volume of material assuming the cube orientation increases. The same is true also for increasing time and temperature of annealing when the penultimate grain size and the final rolling reduction are constant, since the average size attained by the new grains during annealing increases with the annealing time and temperature. For the same reason, at higher annealing temperatures a given volume percentage of cube texture can be obtained with larger rolled grain thickness (larger penultimate grain size, or smaller rolling reduction) than at lower annealing temperatures. The well-known conspicuous sharpness of the cube texture may be interpreted as a result of the fact that selective growth of only those grains is favored that have an orientation closely symmetrical with respect to all four components of the deformation texture and exhibit, therefore, a high boundary mobility in contact with each. The effect of alloying elements in suppressing the cube texture, as described by Dahl and Pawlek,&apos; appears to be associated with a change in the rolling texture. For face-centered cubic metals, such as copper, which do exhibit the cube texture upon annealing, the rolling texture is always of the type described above, i. e., scattered around four "ideal orientations" of approximately (123) [112]. The addition of certain alloying elements, such as about 5 pct Zn or 0.05 pct P in copper, has the as yet unexplained effect of changing the rolling texture into the (110) 11121 type. This texture consists of two fairly sharply developed, twin related components. In such cases, as in 70-30 brass and in silver, the annealing texture again is related to the rolling texture by a [lll] rotation of about 30°, however, because of the different rolling texture to start from, it has no cube texture component. At higher temperatures, both in brassm and in silver," grain growth leads to a further change in texture: A [lll] rotation of the same amount, but in reversed direction, back to the original rolling texture.

Jan 1, 1952

By O. Katz, A. Spilners, M. Simnad

THE oxidation of titanium has been studied in recent years by a number of investigators.&apos;-W ne of the most important aspects of the reaction of titanium with oxygen, which has been observed by several of the investigators, is the extremely high solubility of oxygen in the metal. A detailed study of the Ti-0 systeml% as shown that the solubility limit of oxygen in a-titanium is approximately 14.5 wt pct 0 from 800" to 1700°C. The unusual oxidation behavior of titanium may be ascribed to this phenomenon, since part of the oxygen uptake enters into solid solution in the metal and only a part is available for scale formation. A more complete study of the kinetics of oxidation of titanium would require information on the influence of oxygen in solution in the metal upon the oxidation rate. Such information would also be of interest in regard to the theory of oxidation of metals. The authors have measured the oxidation rates of oxygen-saturated and oxygen-free titanium between 800" and 1200°C and have found appreciable differences in their rates of oxygen uptake and in the activation energies. The experimental set-up was similar to that described in a previous paper.u The course of oxida-dation was followed continously by attaching the specimen to a sensitive spring balance and observing the extension of the spring with time of oxidation. High purity electrolytic oxygen was used and precautions were taken to purify the gases employed. The specimens were prepared from iodide titanium and were ground on metallographic polishing papers to a fineness of 4/0. The furnace was first evacuated and filled with argon; the specimen was lowered into the furnace, which was then evacuated and filled with oxygen, after the specimen had reached the oxidation temperature in argon. The samples were presaturated with oxygen by means of the following procedure: Each specimen was first heated in oxygen at 1200°C until its increase in weight indicated 13.8 pct by weight uptake of oxygen. The furnace was then immediately evacuated and filled with purified argon five times. The specimen was heated in the argon atmosphere for a period of 72 hr at 1200°C in order to saturate the metal with oxygen by complete absorption of the scale. The temperature was lowered to the oxidation temperature, the furnace was evacuated and filled with oxygen, and the oxidation rate was followed by noting the extension of the spring balance. No oxide film was visible on these specimens at the start of the oxidation experiments. Titanium samples in the oxygen-free as-received condition were also oxidized and their oxidation rates measured. The results are shown in Figs. 1, 2, and 3, which indicate that the initial rates of uptake of oxygen by both the oxygen-saturated and oxygen-free specimens are parabolic at these temperatures. The rate of uptake of oxygen is, however, appreciably lower

Jan 1, 1956

By L. D. Wooddy, Robert Moscrip

The simultaneous solution of the volumerric balance and the unsteady-state equation has been used for several years to make performance calculations for combination drive reservoirs. This method makes possible the calculation of volumetric changes of fluids in the gas cap, oil zone, and aquifer which occur as a result of withdrawals and reservoir pressure changes. It does not provide a means for the determination of reservoir fluid distribution changes corresponding to these vollrmetric changes. A knowledge of the fluid saturation distribution in the reservoir at various stages of depletion is important for the determination of the efficiency of gas and water as oil-displacement media and, therefore, for the reliable predicrion of ultimate oil recovery. To provide this knowledge, the displacement equations are solved simultaneously with the volumetric balance and unsteady-state equations. The described calculation procedure has been used satisfactorily to analyze the past performance and to predict the future behavior of combination drive reservoirs under both primary and pressure-maintenance operations. INTRODUCTION The three basic mechanisms by which oil is displaced from a reservoir are: (1) dissolved gas drive—the displacement of oil by the expansion of liberated solution gas, (2) water drive—the displacement of oil by water which enters the oil zone from the aquifer, and (3) gas cap drive—the displacement of oil by gas which ex- pands into the oil zone from the gas cap. The action of gravitational forces may be effective in increasing the efficiency of the basic drive mechanisms. Gravitational forces favor the segregation both of gas and oil and of oil and water, thus tending to shorten the transition zone between oil and displacing fluids. Most reservoirs produce under the influence of a combination of these drives and are designated "combination drive reservoirs". Fig. 1 is a cross section of a typical combination drive reservoir. A calculation procedure for analyzing the performance of combination drive reservoirs has been developed by combining the displacement equations&apos; with the volumetric balance equation&apos; and the unsteady-state equations. The pressure-production performance and the positions of the gas-oil and oil-water contacts are calculated for several stages of reservoir depletion by solving these equations simultaneously, thus affording a basis for: 1. Determining instantaneous and ultimate oil, gas, and water production under various operating conditions. 2. &apos;Establishing a maximum efficient rate of production, 3. Determining the advantages of pressure maintenance and unitization, and 4. Designing surface installations necessary for primarv and pressure-maintenance operations. DEFINITIONS The calculation procedure for combination drive res-

Jan 1, 1957

By C. W. Spencer, F. N. Rhines, R. J. Knight

Ametallographic study has been made of the peritectoid transformation as it occurs in two Ag-A1 alloys, containing 6.0 and 6.9 wt pct Al, respectively. After equilibrating at 475°C, these alloys were transformed isothermally just below the peritectoid temperature which lies at about 450°C.1-3 Peritectoid transformation in this alloy system consists in the reaction of a and 5 to form µ. The crystal structures of the a, µ, and 5 phases have been determined as face-centered-cubic, 6 manganese, and hexagonal-close-packed, respectively. At the peritectoid temperature their equilibrium compositions are approximately 5.85, 7.02, and 7.24 wt pct (19.92, 23.2, and 23.8 atomic pct) aluminum."" The transformation might be expected to occur principally at the interface between the a and 5, but such is not the case. Instead, the major part of the transformation occurs by the direct (and perhaps initially diffusionless) conversion of 5 to µ. The composition range of the forming µ nearly overlaps that of the parent at the temperature of transformation" so that little, if any, composition change is required. Transformation proceeds by the nucleation of µ at points upon the external surface of the sample and sweeps through the 5 phase, leaving the a initially almost undisturbed. Subsequently, the a phase participates in the transformation by being partly or totally converted to µ. Specimens approximately 1/4 x 1/4 x 1/16 in. were cut from cast ingots, previously equilibrated 68 hr at 588°C. The specimens were held for 3 hr at

Jan 1, 1958

By B. F. Peters, J. Gordon Parr, E. R. Macgregor

A SERIES of seven hypoeutectoid alloys, up to 18.2 atomic pct Mn, was made by the levitation melting technique. The loss of weight on melting was considered to be entirely due to volatilization of manganese, and compositions were computed on this basis. Filed samples (—200 Tyler mesh) were helium quenched from 1000°C after soaking for 5 min by a technique already described.&apos; Quenched Alloys -Assessments of the amounts of a phase produced and the hardness of the quenched alloys are summarized in Fig. 1. The experimental techniques and calculations involved have been described previously. The amount of a decreases as manganese content increases, until at 10.6 pct Mn only a trace of a&apos; is observed. Previous

Jan 1, 1957

By Stephen Krickovic

AS it is commonly understood in the bituminous coal mining industry, pillaring means removal, as completely as is practical, of all pillars formed in the development of headings and rooms on first mining. The degree to which this can be accomplished, termed percent of recovery, is of course dependent generally upon the physical conditions of the bottom and the overburden, the system of min-

Jan 1, 1956

By F. D. Wright, H. D. Fara

The solution to the plastic and elastic stresses around a circular shaft in a hydrostatic stress field that has appeared in two editions of a widely used book on rock mechanics1 is in error. Although this is a relatively minor matter, the correct solution was not found by a literature survey, so it appears worthwhile to present it. For a homogeneous, isotropic, rigid plastic-elastic body in plane strain which obeys Tresca&apos;s yield criterion the following equations must be satisfied:&apos;," In the plastic zone,

Jan 1, 1963

By B. L. Averbach, M. Cohen, G. P. Conard

IT has been frequently observed that, when metal crystals are bent and annealed or when they are bent at elevated temperatures, the asterism of the Laue spots is split discontinuously into tiny intensity maxima. This finding indicates that segmented crystallites or subgrains are produced, which are relatively undistorted within themselves but which differ slightly in orientation from their neighbors. The following viewpoints have been put forward concerning the nature of this segmentation process: 1—Crussard&apos; has described the phenomenon as "re-crystallization in situ." According to this mechanism, the deformed lattice recrystallizes on heating into an aggregate of comparatively strain-free subgrains separated from one another by low-angle boundaries and having nearly the same orientation as the original crystal. This process differs from the classical type of recrystallization in that the latter involves the formation of grains having quite different orientations from that of the mother crystal. 2—A similar but more detailed picture has been advanced by Cahn&apos; who adopted the term "polygonization." In this interpretation, the plastic bending of lattice planes results in an excess of dislocations of one sign, but at suitable temperatures these dislocations migrate along slip planes and collect in localized regions to form an array of low-angle boundaries. Concurrently, the lattice segments between the boundaries lose their curvature and elastic strain. 3—The "cell formation" concept of Wood and co-workers: unlike the two hypotheses cited, postulates that the segmentation of the lattice is basically a mode of deformation and is not an annealing phenomenon. Cell formation appears to compete more effectively with respect to the normal slip process as the deformation temperature is increased and as the strain rate is decreased. The present work was performed on 3.2 mm diameter 99.99&apos; pct Zn single crystals, grown from the melt in a gradient furnace. The major impurity was 0.003 pct Fe. The crystal orientations ranged from those with basal plane parallel to the rod axis to those with the basal plane almost perpendicular to the rod axis. The specimens were bent on templates to effective radii varying from 14.2 to 1.3 cm at the temperatures from —196" to 100°C. In each case, the axis of bending was parallel to the basal plane. Subsequent annealing was carried out at temperatures from —196" to 400°C. Back-reflection Laue pictures were taken on the convex surface of the bent specimens, before and after annealing. This procedure was found to yield better resolution of the detail in the diffraction spots than did the previously used Laue transmission technique. Some X-ray pictures of rods bent at —196" and —78°C were taken at these respective temperatures without intermediate warming to room temperature. In addition, bent crystals were acid cut" parallel to the basal plane, and double-crystal spectrometer rocking-curves were obtained from the etched (0001) face before and after increment an-

Jan 1, 1954

By L. J. Klinkenberg

It is pointed out that the current concept of pore size distribution is not unequivocally defined and that different methods aiming at a determination of such a distribution therefore do not lead to the same results. A pore size distribution should not be based on the idea that a core should, under all circumstances, behave as a bundle of straight non-interconnected capillaries of the same pore size distribution. This is illustrated by calculations and experiments on the displacement of miscible liquids. INTRODUCTION The introduction of the concept of pore size distribution has been an attempt to characterize the intricate geometry of the flow channels in porous media. As pores in a porous medium are interconnected it is impossible to describe exactly what is meant by a "pore" and, therefore, the term pore size distribution requires further amplification. In the visual method for the determination of pore size distribution "the pore" is considered to be the hole between the grains as observed on thin sections or on a polished surface of the rock under a microscope. In all other presently known methods,1,2 a displacement process is studied and it is ascertained what as- semblaae of straight cylindrical capillaries would show the same behavior. The distribution of the capillary diameters of this assemblage is said to represent the size distribution of the pores of the actual porous medium. From the foregoing it is already apparent that it is useless to try to decide which process or which method of investigation leads to a "correct" pore size distribution. To illustrate this further a displacement process in which a fluid is displaced by another miscible with it will be discussed and the results will be interpreted in terms of a pore size distribution. DISPLACEMENT EXPERIMENTS WITH MISCIBLE LIQUIDS OF NEARLY IDENTICAL VISCOSITY AND DENSITY Interpretation in the Form of a Pore Size Distribution If distilled water is displaced from a homogeneous unconsolidated sand pack by, for instance, a dilute solution of NaCI, the breakthrough recovery i.e., the amount of distilled water produced at the moment the first trace of NaCl can be detected in the effluent water, is between 95 and 100 per cent of the pore volume of the pack. This result can be understood by following in imagination the course of one particle of the liquid. Imagine a length, ?l, at the end of which a liquid particle has an independent chance of a renewed choice of pores of different diameters. In other words, the particle has a choice of traveling time, at, for any length ?l; instead

Jan 1, 1958

By Jack L. Lytton, Oleg D. Sherby

RESULTS of recent investigations1 on the creep of metals at high temperatures have revealed that the activation energies for creep of pure metals, AH,., about equals the respective activation energies for self-diffusion, hHD. This fact strongly suggests that the rate-controlling process in creep at high temperatures might be that of dislocation climb, as first postulated by Mott.&apos; It would be desirable, however, to relate the creep rate of a metal at a given temperature and stress with actual diffusivity data, rather than with a comparison of the tempera-

Jan 1, 1957