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By Owen Thornton

Recently equations have been presented by Rose and Bruce' 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"' 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': — =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 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.' 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' 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's yield criterion the following equations must be satisfied:'," In the plastic zone,

Jan 1, 1963

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 Dilip K. Das, Douglas T. Pitman

ONE of the major uses of barium in metallic form is as a getter material in vacuum tubes. Because of the high chemical reactivity of the metal, Ba-Al alloys are extensively used. Numerous methods for the preparation of Ba-Al alloys have been published, a few of which1-4 are cited here. Most of these methods were found to be quite elaborate, involving the reduction of BaO, and not too well adapted for the close control of the final composition of small amounts of alloys prepared for laboratory use. A simple laboratory method for the preparation of Ba-A1 alloys in small batches starting from pure metals was devised, so that it was possible to control the desired compositions to within 1 pct. The pertinent features of the alloy system Ba-Al5 are 1) an intermediate compound BaAl, with the melting point of 1050°C, and 2) a eutectic between aluminum and BaAl4 at 98 pct Al. The accompanying sketch shows the experimental arrangement for the preparation of the alloys. Weighed amounts of aluminum and barium were placed in an alumina and a stainless steel crucible, respectively. According to the supplier's specification, the purity of the metals used in the alloys is as follows: a) aluminum rods—99.9 pct Al, and b) barium rods—99.5 pct Ba. The stainless steel crucible, tapered at the bottom and having a 1/16 in. diam hole, rested on top of the alumina crucible. The assembly was placed inside a graphite sleeve which rested on a refractory platform. The platform moved the assembly up and down through the field of a radio frequency coil. A glass bell jar was placed between the crucible assembly and the radio frequency coil to maintain a steady flow of helium around the melt. A small window was cut out on the wall of the alumina crucible to observe the progress of the re- action and to record the temperature with an optical pyrometer. The platform was first raised high enough to move the barium out of the radio frequency coil field in order to allow only the aluminum to melt. The assembly was then lowered so that the barium began to melt and flow out through the small orifice into the molten aluminum. In order to keep the violence of the exothermic reaction under control, the rate of flow of barium was carefully regulated by raising or lowering the crucible assembly. All the samples prepared by this technique were examined by a Norelco X-ray diffractometer using CuKa radiation, The diffraction specimens were prepared by placing the finely powdered samples in flat specimen holders. The Ba-Al alloys prepared with a high barium content were found to consist mainly of BaAl4. The structure of BaAl4 has previously been reported by Alberti and Andress.8 They found that BaAl4 was body-centered-tetragonal with an a0 = b0 = 4.530Å and c0 = 11.14Å. An alloy whose composition was found by chemical analysis to be almost 100 pct BaA1, was used to determine the relative intensities. The d-spacings were obtained from the same alloy to which a small amount of tungsten had been added as a calibrating material. Accurate values for a, and c, were calculated according to the method proposed by Taylor and Floyd.' The calculated values are: a, = b, = 4.566Å and c0 = 11.250Å. The measured d-values for BaAl4 are shown in Table I along with relative peak intensities above background and hkl indices. Acknowledgment The authors are grateful to L. J. Cronin, the head of the Techniques Dept., for suggesting the problem and for his constant interest. References 1Froges and Camargue: German Patent No. 809107, 1951. French Patent No. 935324, 1949. 2E. Bonnier: Annales de physique, 1953, vol. 8, pp. 259-312. 3M. Orman and E. Zemhela: Prac Institute of Metals; 1952, vol. 4, pp. 437-445. 4E. Fujita and H. Yokomizo: Reports Gov. Chemical Industrial Research Institute, Tokyo, 1952, vol. 47, pp. 291-297. 5E. Alberti: Ztsch. fur Metallkunde, 1934, vol. 26, p. 6. 6E Alberti and K. R. Andress: Ztsch. fur Metallkunde, 1935, vol. 27, p. 126. 7 A. Tnslor and R. W. Floyd: Acta Crystallographica, 1950, vol. 3, p. 285.

Jan 1, 1958

By L. D. Jaffe, R. K. Pitler

IT would clearly be advantageous to produce molten titanium, suitable for alloying and casting, directly from the relatively inexpensive tetra-chloride, without using a metallic reducing agent. Accordingly, a preliminary investigation has been made of the production of titanium by hydrogen reduction of the tetrachloride in an electric arc furnace. For the reaction: TiCl4(g) + 2H2(g) ? Ti(s) + 4HCl(g), Lockhart and his colleagues' have calculated equilibrium constants at 800" to 1500°K, based on tables of Brewer.' Extrapolating these data on the assumption that the heat of reaction varies linearly with temperature, and using Brewer's value for the heat of fusion, there is obtained for the reaction: TiCl4(g) + 2H2(g) ? Ti(l) + 4HCl(g) an equilibrium constant at 2100°K (100" above the melting point) Kp = (PHCl)4/pTlcl4 (Ph2)2 = 0.167 atm. If this is correct, starting with hydrogen saturated with TiC14 at 25°C, where the vapor pressure of the latter3 is 12.6 mm, and maintaining the overall pressure at 1 atm, 99 1/4 pct of the TiC14 would be reduced to Ti at equilibrium. An arc furnace designed for the melting of titanium and lined with water-cooled copper was used for the preliminary experimental check. Its inside diameter was 2 7/16 in. and height 6 in. The water-cooled electrode was tipped with 3/4 in. diam tung-sten. In the one run carried out, the furnace was charged with a starting batch of 293.35 g of scrap titanium,' analyzing 99.24 pct Ti. After the system was twice pumped out and flushed with argon to remove air, the arc was struck in argon and kept at 400 amp dc, electrode negative, for 1 min to melt the starting batch. Commercial tank hydrogen, dried by passing over silica gel and bubbled through technical grade TiC14 at room temperature, was then admitted to the furnace. The inlet tube directed this gas downward toward the arc and melt; the gas outlet was at the top of the furnace. The quantity of gas passed through was not measured accurately but is estimated to be about 50 liters per min at a few mm of mercury above atmospheric pressure. The arc was held in the H2-TiC14 mixture at 400 amp with little difficulty. After 10 min the arc burned through the copper lining above the melt, admitting water and ending the run. (This had happened frequently in straight melting runs under argon, and is not thought due to the atmosphere used.) In the furnace were found an ingot, several small pieces, and a little metallic powder, evidently formed when water entered the hot furnace. Some titanium also clung to the electrode. The portions were weighed and separately analyzed for titanium. Their total weight was 321.76 g of 94.82 pct overall purity. Much of the impurity consisted of tungsten broken off when the titanium was removed from the electrode. No detailed impurity analysis was made because the starting materials were impure and flooding the furnace introduced further contamination. Thus, the metal recovered contained 305.08 g Ti, as compared to 291.12 g in the starting batch. Titanium could not have been carried over from previous melting runs in the furnace, as the interior was sandblasted and the electrode ground clean before the run. Evidently at least 13.96 g of Ti were produced from TiCl4. Since this would require complete reduction of 430 liters of TiCl, gas at 12.6 mm of Hg, the efficiency of the process must have been rather high. Experimental work is continuing. No reason is seen why the process could not be scaled up to the size of a 30-ton steel-melting arc furnace. In a large unit there would be a large molten pool from which liquid metal could be withdrawn for alloying and casting. The problems of electrodes and power supply are similar to those arising in arc furnaces for melting titanium. Unreacted TiC14 and the HC1 in the exhaust gases could be recovered; unreacted H2 could be dried and re-used. The melt would be saturated with hydrogen, whose solubility in liquid titanium is unknown. Small amounts of hydrogen seem to have little effect on the properties of titanium.5 If the amount introduced was so large as to impair properties or cause casting difficulties, it could be reduced by holding the melt under an inert gas or by pumping on it, prior to casting. Acknowledgment The authors would like to thank I. Preble and M. Goldman for their valuable aid in the experimental work and the thermodynamic calculations, respectively. References 1R. J. Lockhart, J. J. Ward, M. J. Hussey, and J. W. Clegg: In unpublished report, "U. S. Air Force Project Rand. Titanium and Titanium Base Alloys." Battelle Memorial Institute (1949) 37-44. 2 L. Brewer et al: Chemistry and Metallurgy of Miscellaneous Materials—Thermodynamics. Ed. by L. L. Quill. pp 13-39, 60-192. (1950). McGraw-Hill Book Co. 3 K. Arii: Scientific Reports. Tohoku Imp. Univ. (1933) 22, 182. 4 R. S. Dean, J. R. Long, F. S. Wartman, and E. L. Anderson: Transactions AIME (1946) 166, 369-381; Metals Technology (Feb. 1946) TP 1961E. * R. I. Jaffee and I. E. Campbell: Transactions AIME (1949) 185, 646-654; Journal of Metals (Sept. 1949) TP 26813.

Jan 1, 1951

By L. S. Richardson, N. J. Grant

REACTIONS of oxygen and nitrogen at low pressures with titanium have recently been studied by a number of investigators.1-3 Gulbransen and Andrew' noted that the reaction with nitrogen followed the parabolic rate law whereas the reaction with oxygen deviated slightly from this law in the temperature range 300° to 800°C. In the work reported here, commercial titanium (75 A) was used as the test material. Cylinders 2.5 in. long and 0.25 in. in diameter were machined from heavier bar stock. The test pieces were given a metallographic finish, immersed for 30 min in cold concentrated HC1, washed in water, then acetone, and dried with lint-free cloth. Reaction rates were determined in a modified Sieverts type apparatus by measuring the decrease in gas pressure of the reacting gas contained in a constant volume. The amount of gas added could be measured in a calibrated gas burette to an accuracy of 0.01 mm. During the course of a run the temperature never varied by more than 10°C and then only for brief moments. After placing the specimen in the furnace, the system was first evacuated for 12 hr at room temperature, and then flushed with purified argon five times, adsorbed gases being discharged during this period from the glass system with a high frequency spark coil. The flushing and discharging were repeated at 400°C. This rather involved procedure was found necessary after a number of trial runs indicated extraneous effects traceable to the system. Reaction periods up to 2 hr were used, at initial gas pressures of 0.2 to 0.5 atm. Experimental Results Fig. 1 shows the decrease in oxygen pressure for tests at 0.5 atm at various temperatures as a function of the square root of the time. Deviations from linearity are minor and the parabolic rate law is obeyed. Fig. 2 shows the same plot for the nitrogen reaction. A definite deviation from linearity is noted; however, it is probable that the higher initial rates are caused by the presence of small amounts of oxygen contamination, the initial faster rate changing to the slower rate after about 5 to 10 min. Calculations of the rate constants were made on the basis of the latter portion of the curves. The parabolic rate law constants calculated from these curves are shown for oxygen and nitrogen in Fig. 3. In spite of some scatter the average curves are quite definite. Changes in gas pressure of the order of 20 pct did not result in a measurable change in the rate law constants. The activation energy for the oxygen reaction was calculated to be 47,400 cal per mol (above 700°C), which is not in agreement with the value quoted by Gulbransen and Andrew' for lower temperatures, their value being 26,000 cal below 600°C. The activation energy for the nitrogen reaction was calculated to be 45,400 cal per mol above about

Jan 1, 1955

By D. H. Davis, I. Fatt

Oil bearing rocks, usually found at depths of 2,000 to 10,000 it, are elastically deformed by overburden pressure. Although the change in porosity with pressure in a number of example rock.: has been shown to be small, it was thought that overburden pressure might have a significant effect on permeability. This note presents results of an investigation to determine the magnitude of the change in permeabilty with pressure. In routine core analysis permeabilities are measured on rock samples which are not under overburden pressure. If permeablity measured in this way differs from permeabilities measured under overburden pressure, a systematic error is introduced into well productivity calculations. The experiments described in this report were made to determine the magnitude of the change and thus to give an estimate of the error introduced into the calculations. The error introduced by the neglect of the change in permeability when overburden pressure is removed may account for part of the difference between well productivity calculated from core analysis and the actual well productivity. The results obtained in this investigation have only quali-tative significance because of the difficulty in reproducing in the laboratory the stress conditions on the rock buried in the earth. The assumption which is usually made is that the rocks in the earth are under a uniform pressure equal to the weight per unit area of the vertical overburden column from the rock in question to the surface of the earth less the pressure of the liquid in the pores of the rock. For an overburden consisting of sandstones and shales (of assumed average specific gravity of 2.3) and for a liquid pressure equal to the pressure in a salt water column (of specific gravity 1.0) reaching from the rock to the surface, the resulting net pressure on the rock is approximately 0.56 psi per ft of depth. EXPERIMENTAL METHOD Clean, dry sandstone core plugs one in. in diameter and about three in. long were mounted in a copper foil jacket as shown in Fig. 3 or molded in a Lucite jacket as shown in Fig. 4. All cores except those labeled "2" in Fig. 1 and "8" in Fig. 2 were measured in the copper foil jacket. Cores "2" and "8" were measured in the Lucite jacket. The jacketed core was placed in a high pressure hydraulic bomb in which the liquid pressure outside the jacket could be raised to 15,000 psi. Flow lines from the core were brought out of the bomb through special fittings in the bomh head and connected to a laboratory type gas permeameter. Measurements were made with nitrogen gas; the maximum mean gas pressure in the core was 16.1 psia. RESULTS The specific permeability of sandstone decreases with in. crease in overburden pressure. Most of the decrease takes place over the range of zero to 3,000 psi overburden pressure. If the net pressure on the rock is assumed to be 0.56 psi per ft of depth as discussed above, 3,000 psi of overburden pressure is equivalent to about 5,000 ft of overburden. At 3,000 psi overburden pressure, the permeability of the eight sandstone core samples tested ranged from 59 to 89 per cent of the permeability without overburden pressure. Figs. 1 and 2 show the permeability reduction as a function of overburden pressure. The permeability of the eight cores without overburden pressure ranged from 4.35 md to 632 md; these permeabilities are listed in Figs. 1 and 2. REFERENCES 1. Carpenter and Spencer: "Measurements of Compressibility of Consolidated Oil Bearing Sands," U. S. Bureau of Mines, R.I. 3450, (1940). * * *

Jan 1, 1952

By D. W. Fuerstenau

In 1940 Schuhmann1 showed that the size distribution of a comminuted material can be expressed by the following empirical relationship: y = 100 (|f [i] where y is the cumulative percentage of material finer than size x, k is a size modulus, and a is a distribution modulus which is constant for a given material and machine. During the past few years, considerable emphasis has been given to the investigation of the extent of size reduction resulting from the expenditure of mechanical energy in crushing and grinding. Recently Schuhmann' presented a derivation of the energy-size reduction relationship by postulating that comminution in a device such as a ball mill can be considered to be the summation of many single comminution events, each of which yields a size distribution of particles following the Schuhmann size distribution equation. By grinding

Jan 1, 1961

By C. W. Chen

MARTENSITE transformations in ß Cu-Al alloys have been studied by Greninger1 and other investigators. According to Greninger, the parent phase ß1 an ordered body-centered-cubic structure obtained from ß phase by suppressing the eutectoid decomposition, transforms into an ordered hexagonal-close-packed phase in composition containing 12.9 to 14.7 pct Al. The M, temperature decreases with increasing aluminum content; for the alloy containing 14.5 pct Al, for example, the ß1??' transformation occurs below room temperature. More recently, Kurjumow2 studied the transformation in ß Cu-Al alloys with the addition of nickel. His report stimulated new interest in the subject due to the observation of completely reversible transformation without hysteresis in the transformation temperature ranging from 10° to —10°C. In the present paper some characteristics are described of the transformation of Cu-Al-Ni alloys that were partly studied by Kurjumow. Experimental Procedure High purity copper (99.999 pct) and aluminum (99.99 pct) and electrolytic nickel were used in the preparation, by the Bridgman technique, of single crystal specimens which contained aluminum and nickel of 14.5 and 0.5 to 3.0 pct, respectively. Polished surfaces were prepared mechanically. Specimens were then chemically etched to remove distorted material, homogenized at 1000°C for several hours, and quenched drastically to room temperature in a 10 pct NaOH bath to produce the parent phase ß1. The transformation was studied under a microscope and, in some cases, recorded by means of motion pictures. A device similar to that designed by Greninger and Mooradian3 was used to cool and reheat the specimens. Results and Discussion When the specimens were cooled below room temperature, the ß1 to ?' transformation began at 10°C with the appearance of ?' crystals In relief, Fig. la. As the specimen temperature dropped further, the transformation continued, either by the growth of the ?' crystals, with the ß1 — ?' interface moving into the ß1 phase, Fig. 1c and 1d, or by the formation of new ?' crystals, Fig. 1b. As a consequence of the former process, banded structure is observed as a common feature of the low temperature phase. According to the theory of the formation of martensite by Wechsler, Lieberman, and Read,' the bands of ?' phase are probably twin-related, as is the case in the diffusionless phase change of In-T1 alloys,5 but this was not revealed by X-ray tech- niques. New ?' crystals, in needle form, often emerged suddenly across the ?' bands during the transformation. These acicular crystals then grew, both in length and in width, see Fig. 2a through 2d. The transformation on cooling is completed at about -35°C. Upon heating, the reverse transformation started at —10° C, in a manner nearly opposite to the transformation on cooling, and completed at 35°C. There was no noticeable change in the transformation temperature when the nickel content was varied within the limits previously mentioned. Through control of the specimen temperature, the transformation can be started, stopped, or reversed at will. This phenomenon has frequently been observed in the martensite transformation of many nonferrous alloy systems. Other systems are Au-Cd6 and In-Tl.5 ow-- ever, in the latter systems, the transformation is accomplished by single interface motion if the specimen composition is homogeneous and the temperature gradient in the specimen is uniform and sharp, whereas in the Cu-Al-Ni specimens, only multiple interface transformation is observed. The speed of the interface motion appears to be a functionof the rate of temperature change and the temperature gradient across the specimen length. In one case, in which the temperature increased at the rate of 10°C per min and there was no temperature gradient along the specimen axis, the speed of the disappearance of a ?' plate was determined, by the study of the motion pictures made, to be 26 µ per sec. Quench markings were observed on the polished surfaces of specimens. The markings were grouped into one or more sets of different orientations, and were parallel in each set. The ?' plates formed in subsequent transformation were parallel to the markings, indicating that the ?' plates and the quench markings had the same geometric relation-ship to the ß1 matrix. The quench markings on two intersecting surfaces of a specimen were therefore used in the determination of the habit plane of transformation, by the trace method suggested by Barrett.' Results obtained from five sets of markings in three specimens indicate that the habit plane is an irrational plane about 2" from one of the {221} planes. This is very close to the habit plane (3" from 221 planes) of ß Cu-Al alloys containing more than 13.0 pct Al.1 The martensite transformation of Cu-Al-Ni alloys is reproducible. No sluggishness was found between consecutive transformation cycles, although a slight difference in the distribution pattern of the ?' plates was observed, compare Figs. Id and 2d. The transformation can be strain-induced. This characteristic has been tested by a simple method. When a specimen was elastically strained slowly in a vise, ?' plates were gradually produced in the same fashion as during transformation on cooling, This test was done at room temperature, and thus above the M,

Jan 1, 1958

By H. W. Paxton, C. C. Busby

IT has been shown previously' that strain aging can markedly improve the tensile properties of low carbon martensites, especially the yield-tensile ratio, without seriously affecting the ductility. In view of interest in high strength steels, an investigation has been made of the effect of strain aging following tension or rolling on the tensile properties of A1S1 4340 in an attempt to obtain a tensile

Jan 1, 1957

By W. Rostoker, R. P. Elliott

TWO intermediate phases enter into equilibrium with the primary solid solutions of titanium.' The TiMn2 phase was identified by Wallbaum2 as of the C14 type isomorphous with MgZn2. Contrary to Maykuth, et al.,¹ the phase occuring at about the 50-50 atomic proportion has been shown to derive from a peritectoid reaction.:' A 30 day anneal at 900°C of an alloy containing 52 wt pct Mn developed sufficient of the new phase to give a clear and predominant diffraction pattern. The powder pattern was taken in a 14 cm diameter powder camera using filtered Cu Ka radiation. In all, 75 lines were recognized and measured. Interplanar spacing and observed intensities for the first 26 of these are given in Table I.

Jan 1, 1954

By K. A. Natarajan, M. K. Yelloji Rao

Significance of grinding media wear and its effect on chalcopyrite flotation are discussed. Laboratory marked ball wear tests were conducted grinding chalcopyrite ore and quartzite dry, wet, and with collector added during grinding. The effects of oxygen and nitrogen on ball wear were evaluated by the addition of chalcopyrite mineral while grinding quartzite. The effect of dry and wet grinding on chalcopyrite flotation was also studied. Results show abrasive wear is greater in quartzite grinding than in grinding chalcopyrite. Oxygen increases the corrosive wear of high carbon low alloy steel balls in the presence of chalcopyrite ore. Chalcopyrite flotation was retarded due to wet grinding in the presence of oxygen. Though collector reagent increased the media wear, it improved the flotation of chalcopyrite. Probable electrochemical reactions encountered in a grinding mill are outlined.

Jan 1, 1991

By J. Gordon Parr, D. H. Polonis

IN a previous study of hypereutectoid Ti-Ni alloys' a substructure was observed in quenched powder specimens when the constitution was 100 pet retained ß body-centered-cubic phase. The alloy powders were quenched from 1000°C by a blast of helium gas and precautions already described were observed throughout the work, to minimize contamination. Ogden et al.2 have previously observed subboundaries in the ß phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-rich a precipitation. The nitrogen content of the Ti-Ni alloys does not exceed 0.02 pet and the quenching rate was sufficiently rapid to suppress precipitation reactions. Since X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon, it seems unlikely that this substructure is explicable in terms of nitrogen content. Fig. 1 shows the substructure in adjacent grains of 100 pet ß phase in a quenched 6 atomic pet Ni alloy. Fig. 2 shows adjacent ß grains in a similarly treated alloy; one grain contains marked intracrys-talline boundaries and the other is completely free from any substructure. The suberystals appear to have fairly regular shapes, suggesting a regular orientation relationship among them. Tempering the retained ß structure at temperatures below the eutectoid eliminates the substructure at an early stage of ß decomposition. At the present time it is possible only to guess at an explanation for this subboundary phenomenon, since very little work has been reported on substructures resulting from phase changes. It is believed that the present phenomenon is due to poly-gonization resulting from unrelieved stresses set up

Jan 1, 1957

By R. A. Deju, R. B. Bhappu

The basic structural unit of all silicate minerals is a tetrahedron with a silicon atom at the center and four oxygen atoms at the corners. The oxygen-silicon distance is about 1.6 & and the oxygen-oxygen distance about 2.6 &. The different types of oxygen-silicon frameworks in the various silicates are based entirely on the combinations of the tetra-hedral oxygen-silicon groups through sharing of oxygen atoms. In recent years, infrared spectroscopy has permitted estimation of the ratio of the ionic character of the oxygen-silicon bond to be a few times that of the oxygen-carbon bond and the ratio of electro-negativity of the two bonds has also substantiated this finding. On this basis, it is generally accepted that the oxygen-silicon bond is the strongest one occurring in silicate minerals. As the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, there is increasing oxygen-to-metal bonding. Upon the fracturing of a silicate mineral crystal, the oxygen-metal bond, which is almost entirely ionic in character, should break more easily than the stronger oxygen-silicon bond, resulting in a greater number of unsatisfied negative forces on the surface. If, then the mineral is immersed in a liquid containing hydrogen ions, these negative forces should tend to be neutralized by hydrogen ions from solution, resulting in a change of the pH of the solution. An increase in the degree of adsorption of hydrogen ions is to be expected as the oxygen-silicon ratio in the crystal structure increases. This study attempted to correlate the oxygen-silicon ratio for various representative silicate minerals to the adsorption of hydrogen ions. Experiments to determine the effect of surface area on this adsorption and to investigate the effect of surface iron were also conducted. It is believed that such studies of the surface properties of silicate minerals will supply pertinent information about their behavior in froth flotation systems. EXPERIMENTAL PROCEDURE Ion Exchange: Carefully selected, hand-picked samples of the minerals investigated were dry-crushed in a ceramic ball mill and sieved to obtain a minus 100 plus 200-mesh sample. The sized samples were then run through the electro-magnetic separator to remove any iron-bearing particles. A 10-g sample of each mineral was placed in 100 ml of freshly deionized water previously adjusted to a pH of 3.50 with HCl. The beaker containing the sample and the water was placed under a bell jar from which the air was displaced at once by nitrogen gas from a tank. All experiments were carried out in a nitrogen atmosphere. The sample and solution were stirred gently but continuously during the entire experiment, the stirring speed being kept about the same for all runs. Changes in pH were followed with a Beckman Zeromatic pH meter and recorded on a

Jan 1, 1967

By H. F. Dunlap, R. R. Hawthorne

A method of calculating formation water resistivities from chemical analyses is presented which is somewhat faster and more accurate than previously described methods. For 26 formation water samples taken from wells in the Texas Gulf Coast, the average deviation of calculated from measured water resistivities was 3.3 per cent, with an average bias of + l.l per cent in the calculated values. This compares with average deviations of 4.6 per cent and 7.8 per cent, with corresponding average biases of +3.2 per cent and -6.3 per cent, for the two methods previously described in the litera-

Jan 1, 1951

By R. R. Hawthorne, H. F. Dunlap

A method of calculating formation water resistivities from chemical analyses is presented which is somewhat faster and more accurate than previously described methods. For 26 formation water samples taken from wells in the Texas Gulf Coast, the average deviation of calculated from measured water resistivities was 3.3 per cent, with an average bias of + l.l per cent in the calculated values. This compares with average deviations of 4.6 per cent and 7.8 per cent, with corresponding average biases of +3.2 per cent and -6.3 per cent, for the two methods previously described in the litera-

Jan 1, 1951

By J. J. Arps

This paper is a study of the effect of temperature on the electrical resistivity of sodium chloride solutions based on the published resistivity and density data in the International Critical Tables. This temperature effect is of considerable importance in quantitative interpretation of electric logs, where it is frequently necessary to correct mud resistivities measured under surface conditions to temperatures existing at the bottom of the bore hole. An empirical approximation formula was developed for this conversion which has proved to be very useful and seems to provide results well within the range of accuracy of the data involved. This approximation formula states: sistivities of sodium chloride solutions at temperatures of t and t degrees Fahrenheit, respectively. INTRODUCTION Research by various investigators during the past 20 years has clarified the physical principles of the phenomena which cause the natural or spontaneous electric potential in rotary drilled bore holes. The basic relationship which is most commonly used reads: in which the SP deflection, as measured from the shale base line, is expressed in millivolts. K is a constant, which appears to vary between 50 and 110; the low value applying to shaly sands, whereas the higher values are more common in carbonate rocks. A good average value for K = 70. for which value there is considerable theoretical justification." In order to calculate the resistivity of the connate water R and to estimate its "equivalent salinity" (as NaCl) from an electric log by means of this SP relationship from a knowledge of the static self potential and of the resistiv- ity of the mud filtrate R it is necessary to first correct the resistivity of the mud filtrate measured under surface conditions to the resistivity of this same mud filtrate in the well bore at a different temperature. In order to make this temperature conversion for the mud filtrate the variation of the electrical resistivity of sodium chloride solutions with temperature is commonly used. Since some discrepancies were found in the charts ordinarily used for this purpose, it was felt desirable to make a new study of this relationship based on the published measurement data. Because of the fundamental nature of these relationships and as an aid to other workers in this field, an attempt has been made in this study to show every step in the calculations. CONDUCTIVITY VS MOL CONCENTRATION The most complete published reference on the temperature relationship of sodium chloride solutions of different concentrations is provided in the International Critical Tables.' The basic measurement data on the electrical conductivity of aqueous sodium chloride solutions, at different temperatures, as given in these tables, are reproduced in Table 1. The electrical conductivity values in this Table 1 are expressed as 10' times the specific conductivity k in ohm-'cm'l per unit of concentration in milligram mols per liter of solution C, or: RESISTIVITY VS MOL CONCENTRATION These conductivity values from Table 1 were first converted to the corresponding electrical resistivity values (R) , expressed in ohm-meters, as is conven-

Jan 1, 1953

By M. J. Sinnott

WITH the advent of nodular iron as an engineering material, considerable interest has been shown in developing this material for various applications. Generally the strength, hardness, or ductility are the more common properties used for design purposes but occasionally applications involving a knowledge of the thermal conductivity of the material is required. A search of the literature showed, rather surprisingly, that relatively little work has been done on this property for all types of cast iron. Insufficient data are available on thermal and electrical conductivities to develop the Weidemann-Franz ratio, or the Lorentz relationship, for estimation purposes. There are no data on nodular irons and the published data on malleable irons are quite sketchy. For these reasons the conductivity of the group of nodular irons listed in Table I were measured. Irons I to IV were made in such a fashion as to maintain the carbon and alloy content essentially the same while varying the silicon content. Test specimens were cut from the mid-section of 4-in. keel castings. Iron V is a commercial casting of nodular iron. The test specimen of this iron was cut from the center of a large cast billet 3x10x26 in. All alloys were tested in the as-cast condition. A microstructural examination showed that each iron had spheroidal graphite but the size and distribution varied with the silicon content of the iron. The spheroid size decreased while the number of graphite nodules increased as the silicon content of the iron was increased. The matrix structures of each iron consisted of pearlite and ferrite with the proportions varying from predominantly pearlite in the low-silicon iron to mostly ferrite in the high-silicon iron. The commercial heat, iron V, was predominantly pearlite probably because of its higher manganese and phosphorus content. Two methods for measuring the thermal conductivity were used. The first was a modification of the techniques described by Powell and Hickman and Van Dusen and Shelton,² the second method was a simpler technique described by Jakob and Hawkins." Since the agreement of both methods as tested on two sets of duplicate samples was excellent, the simpler experimental technique was used. The results of the measurements are given in Table II along with a summary of the microstructural constituents. These conductivity data indicate that as the percentage of silicon increases there is a corresponding decrease in the thermal conductivity even though the structure is changing from pearlitic to ferritic. Such a change in microstructure is usually accompanied by an increase in conductivity. A third factor involved in the behavior of these irons is the size and distribution of the graphite nodules. The relative amounts of graphite do not change greatly but the size and distribution do. Generally graphite improves the conductivity but in the present case such an effect is probably masked by the alloying effect from the silicon and its dispersion through the matrix. The thermal conductivity of the nodular irons studied is less than that of regular foundry irons by some 10 to 30 pct and is less than that of regular malleable irons.' The cause of the decreased conductivity is probably the more highly alloyed fer-rites obtained in these irons and the changed mode of distribution of the graphite as compared to the regular foundry irons. References R. W. Powell and M. J. Hickman: Journal Iron and Steel Inst. (1946) 154, No. 2, p. 99. 'M. S. Van Dusen and S. M. Shelton: U. S. Bur. Standards Journal of Research, RP668 (1934) 12, p. 429. ³M. Jakob and G. A. Hawkins: Elements of Heat Transfer and Insulation. 2nd Ed. (1950) New York. John Wiley and Sons. ' J. W. Donaldson: Journal Iron and Steel Inst. (1933) 128, No. 2, p. 255.

Jan 1, 1954