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By Walter Rose

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

Jan 1, 1949

By W. H. Smith

IN the course of an investigation on chromium containing minor amounts of alloying elements, the information herein has been obtained on the crys-tallographic orientations resulting from arc melting, rolling, and annealing. The chromium used in this investigation was electrolytic flake obtained from the Electro Metallurgical Co. This material was heated for 20 hr at 1600°C in hydrogen with a dew point of about — 100°C. The oxygen and nitrogen content of the chromium after this treatment was 0.0003 pct 0 and 0.005 pct N. Five pounds of this chromium were arc melted in a water-cooled copper crucible. After arc melting, the oxygen and nitrogen contents were 0.002 and 0.025 pet, respectively. A section of this ingot is shown in Fig. 1. By means of a back-reflection Laue technique, the crystal habit of the cast ingot was determined. As expected, it was found that the [loo] was approximately the axis of the columnar grains. In this respect, chromium behaves like other body-centered-cubic metals in that a cubic axis is normal to the cold surface of the mold. A slab cut from this ingot was rolled at 600°C as follows: four 30 pct reductions were made with intermediate anneals at 1200°C for 15 min. Rolling was done with the [loo] of the columnar grains in the rolling direction. Following the final anneal, an 80 pct reduction was taken at 600 °C. The final sheet thickness was ten mils. By polishing and etching, the thickness was reduced to four mils and the grain orientation determined by the transmission Laue method using molybdenum radiation with a zirconium filter. Fig. 2 is the (110) pole figure for this material with the ideal (100) [011] and (111) [112] orientations indicated. The orientation is typical of most cold rolled body-centered-cubic metals having the [llO] of the grains approximately in the rolling direction and the (100) planes approximately in the plane of the rolled sheet. There is also evidence of some 10) [1 orientation. The grain orientation of sheet rolled 40 and 80 pct in the same direction as before at 600°C followed by recrystallization at 12000 C for 15 min was determined by a back-reflection Laue technique. A random texture was found in both cases. This 1200°C 15 min anneal was found to give complete recrystallization and some grain growth.

Jan 1, 1956

By M. B. Bever, A. B. Michael

THE structure of cast A1-Si alloys is altered profoundly by modifying agents. Sodium, in particular, reduces the size of the silicon particles in the eutectic and tends to change their shapes from plates to nearly rounded grains. This refinement is accompanied by a shift of the eutectic to higher silicon concentrations and lower temperatures. Similar effects can be attained by rapid solidification. Hypotheses advanced to explain modification have involved the formation of a ternary eutectic,1 the removal of oxides by fluxing,' and even a presumed allotropic transformation of silicon. Other hypotheses assume that the modifying agent causes an envelopment of the silicon particles by the aluminum-rich solid solution, but attribute this envelopment to different mechanisms. According to various explanations, the growth of the silicon particles is obstructed by an immiscible sodium-rich liquid," an adsorbed layer of sodium,' or a ternary compound;5 his obstruction has been conceived as purely mechanical or as a colloidal action.' It has also been proposed that sodium reduces the surface tension on the Al-Si interface, thus permitting the aluminum-rich solid to grow faster and to envelop the silicon particles.? Still other hypotheses stress undercooling and the attendant change in the rate of nucleation of silicon, but fail to ascribe any definite function to the sodium addition." '" Procedure High-purity alloys of aluminum and 3 or 7 pct Si were treated with modifying agents containing radioactive sodium tracers. The experiments were intended to investigate the partition of sodium between the primary aluminum-rich solution and the eutectic, and, if possible, to determine whether sodium is concentrated in or around the silicon particles in the eutectic. Radioactive sodium fluoride, alone or mixed with stable sodium chloride, was allowed to react with the alloy for 5 min immediately before solidification in the crucible. Modification could not be attained with additions of less than the equivalent of approximately 0.1 pct Na. Some alloys were not completely modified, but comparison of the structures of treated and untreated specimens indicated a very considerable reduction in particle size of the silicon in all of the former. A treated alloy is shown in Fig. 1. Radioactive sodium fluoride was prepared by bombardment with deuterons having an energy of 14 mev. This bombardment (totaling, for example, 6 microampere-hours in one run) produced radioactive Na24 (half-life 14.8 hr) by the reaction 11Na23 (d,p) 11Na24. The radioisotopes of fluorine also produced have short half-lives and were not detected. A half-life determination by counting confirmed that the measured activity was due to Na24. The distribution of the sodium in the solidified alloys was determined by an autoradiographic technique by which a suitable stripping film is attached to a very thin metallographic specimen. After exposure and development, this emulsion remains superimposed on the specimen and may be examined microscopically or photographed by reflected light. The emulsion of the autoradiograph can be correlated directly with the underlying surface by simple adjustment in focus. The details of this technique have been described elsewhere." Results Fig. 2 is a micrograph of the autoradiographic emulsion ("autoradiograph") lying directly above the area of eutectic in Fig. 1. Fig. 3 shows a similar autoradiograph of a region consisting of primary solid solution. The small black dots (tracks) in these autoradiographs are developed grains in the emul-

Jan 1, 1954

By R. E. Maringer, A. Schwope

IT has been recognized that oxygen in minute quantities is extremely detrimental to the room-temperature ductility of molybdenum. Early fracto-graphic studies' of the cast metal indicated that oxides are formed preferentially at the grain boundaries. Additional verification of this preferential segregation has been obtained from internal friction studies on poly crystalline molybdenum (average grain diameter varied from 0.039 to 0.065 mm) and from observations of the effect of oxygen on specimens of extremely large grain size. Specimens A, B, and C, of 0.040 in. diameter commercial molybdenum wire (Lot FW 13-40) were heat treated in the vacuum furnace described by Few and Manning according to the specifications given in Table I. Internal friction studies of these specimens were carried out using a low frequency (approximately 1 cycle per second) torsional pendulum completely enclosed in a vacuum tank. As the pressure of oxygen in the heat treating atmosphere changed, the portion of the internal friction vs temperature curves ascribed to grain boundary relaxation changed correspondingly, Fig. 1. The decrease in the damping capacity at high temperatures as the pressure of oxygen in the heat treating atmos-

Jan 1, 1955

By W. Rostoker, S. Spachner

A N alloy of 50 pct Ni-50 pct Fe is currently manu- factured in tape thickness down to 1/8 mil. In the annealed form, this alloy produces an almost square hysteresis loop. This has generally been related to the fact that by proper rolling and annealing practice a sharp cube, (100) [OOl], texture can be developed. As part of a program directed toward an understanding of the relationships between magnetic properties and structure of tape core materials, analyses were made of preferred orientations in tapes of various thicknesses. Annealed tapes of this alloy in 2, 1, 1/2, ¼, and Y' mil gages were acquired from commercial sources. Pole figures constructed for the 2 and 1 mil tapes showed the expected sharp cube texture. However, the ½, ¼, and ? mil annealed tapes showed no evidence of any preferred orientations. A comparison of two transmission patterns is shown in Fig. 1. The origin of the absence of texture in the tapes of less than 1 mil thickness was explored in some detail. The basic questions were whether the heat treatment for the thinner tapes was wrongly selected, whether the initial cold worked textures were different, or whether the actual thickness of the tape exercised some influence on its annealing characteristics. Quantities of the five gages of tape were acquired in the as-rolled condition just prior to the final anneal. Pole figures of the cold worked textures were constructed for each of the tapes. Eye estimates of in-

Jan 1, 1956

By H. Papazian, Robert A. Lad

SINCE it can be shown both theoretically'' : and experimentally that disordered Cu3Au has a greater internal energy than the ordered alloy, it might be expected that its chemical reactivity would be greater. Experiments were initiated' to test this hypothesis. This note will describe some recent results obtained in the study of the rates of corrosion of ordered and disordered polycrystalline Cu3Au by aqueous FeCl., The work of Robertson' has indicated that the attack by such solutions is intergran-ular and highly orientation dependent. It was of interest to see whether the order-disorder effect was great enough to overcome the variations from specimen to specimen which would arise from this type of attack. The polycrystalline alloy specimens (0.020 in. wire, 1¾ in. long) were preannealed in ½ atm H, at 700°C for 2 hr. The subsequent heat treatments to produce order and disorder were performed in M atm He. Disordered specimens were obtained by heating at 450°C for 2 hr and quenching in water. Ordered specimens were produced by heating for 2 hr at 450°, furnace cooling to 380°, and soaking at 380°C for 80 to 90 hr. Room temperature was reached by cooling to 150" at a rate never exceeding 7" per hr, and water quenching from 150°C. The specimens so produced exhibited electrical resistivities characteristic of the two states; of the order of 11.27x10 ohm-cm for the disordered, and 4.28x10 ohm-cm for the ordered specimens. The corrosion rates were studied at 30°C in ferric chloride solutions of several concentrations (?,¼, 1.5, and 1 molar). The specimens were attached to a stirrer during the tests. Tests were interrupted at intervals, and the specimen weight change was determined after washing and drying. Analysis of the solutions showed that the attack was limited to the copper. The higher corrosion rate for the disordered alloy, as illustrated in Fig. l, is typical of the results obtained. The effect of variation in ferric chloride concentrations is indicated in Table I for typical specimens. The variations in the ratio of reactivity for disordered and ordered specimens at the different concentrations are within experimental error, and the best value is estimated to be near 1.4. The experimental variation was due in part to the mode of attack, as mentioned, and in part to the fact that films were formed on the specimens under some conditions. Electron diffraction patterns of the films were very complex and indicated the presence of metallic iron, as did chemical analysis. In an attempt to eliminate the difficulties arising from the mechanism of attack, single crystal specimens were used. A greater reaction rate was again measured for the disordered specimens, but the reproduci-bility was no better than that for the polycrystalline metal. This would indicate that film formation was primarily responsible. It was concluded that the reaction with aqueous ferric chloride served to demonstrate that the reactivity of disordered Cu3Au is greater than that of the ordered alloy. However, the difficulties with film formation did not permit determinations of a precision great enough to warrant extension of the study to partially ordered alloy systems.

Jan 1, 1957

By C. G. Dunn, F. W. Daniels, M. J. Bolton

Recent observations on grain boundary movements in sihcon iron have indicated the possibility of studying grain growth phenomena in two-grain specimens in which several variables affecting growth are readily controlled. These variables are (1) the energy per unit area (?) in the grain boundary, (2) the orientation relationship of the two grains, and (3) the radius of curvature (7) of the moving boundary. Ideally, one grain A should be a narrow rectangular parallelepiped adjacent to a second grain ß as shown two dimensionally in Fig 1. Such a two-grain group becomes unstable when one end of grain A is shaped according to the dotted line. Since the width w of grain A remains constant during growth of grain B, T should also remain constant. The other vari- ables mentioned above can be controlled in the preparation of each two-grain specimen.l,2,3 For a parLicular orientation of each grain, is not necessarily fixed; ? may also depend on the orientation of the grain boundary, but this may be controlled to some degree. The energy relationships for the gowth of grain ß may be derived from the more simple arrangement of two grains A' and B' shown schematically in Fig 2. Here B' largely surrounds A'. Assume these grains are oriented with a common plane parallel with the flat

Jan 1, 1950

By Wolfgang Gartner

METALLURGISTS engaged in the pulling of single crystals of germanium and silicon, and their zone purification and zone levelling for transistor and diode production, have found that the lifetimes of minority carriers in low resistivity samples tend to be shorter than in high resistivity material, although equal care is taken in the crystal preparation. In other words, it is more difficult to obtain long lifetimes in single crystals of low resistivity semiconductors. It is the purpose of this note to point out that this phenomenon follows directly from the Hall1 and Shockley-Read' theories of lifetimes in semiconductors." In general, the recombination mechanism may be very complicated,' but experiments seem to indicate that the simple formula2 for the lifetime of excess carriers given by n0 + n3 Pn + P1 T = Tpo,------------------+ Tjpu ----------------------- [ 1 ] nu + pn na+ + Pa is a good representation of the situation prevailing in transistor grade semiconductors. In this formula, no and pa are the equilibrium densities of electrons 6+ - E./ET and holes, n1 = N,e is the number of electrons E1- E2/KT in the conduction band, and p1 - N,e is the number of holes in the valence band, both for the case in which the Fermi level falls at the trap level, E1. N,. is the effective density of states in the conduction band; E1, the recombination level; E1, the lower edge of the conduction band; k, Boltzmann's constant; T, absolute temperature; N,., effective density of states in the valence band; and E,., the upper edge of the valence band. t,.,, denotes the lifetime of holes injected into highly n-type material, and The indicates the lifetime of electrons injected into highly p-type material. Eq. 1 holds for nondegenerate semiconductors in which only one recombination level is active and the charge in the recombination centers is neglected. It is further assumed that the number of injected ex-

Jan 1, 1957

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