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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 W. M. Reilly, Martin E. True, O&apos

A technique, equipment, and a compound have been developed and field tested for sealing tubing joint thread leaks without removing the tubing from the well. This eliminates the necessity of killing the well with possible damage to the producing formation, which could result if it were exposed to drilling mud. A thread sealing compound, developed and tested in the laboratory, is introduced into the tubing and squeezed into the joint to eliminate the leak. A high percentage of successful field applications have eflected an appreciable cost reduction in repairing leaking tubing strings in East Texas and in the Louisiana Gulf Coast area. INTRODUCTION In producing oil and gas wells the industry has been plagued with a never ending problem of tubing connection leakage. This situation is becoming increasingly more significant as more gas wells are placed on production and as higher pressures are encountered at greater depths of current drilling. Substantial progress has been made in minimizing thread leaks by careful handling and cleaning of joints and by the use of improved sealing compounds in combination with controlled makeup. But even with the use of the best known methods and sealing materials during initial makeup, occasional leaks through tubing joint threads appear inevitable. In some instances, tubing joints in high-pressure gas wells have been found to leak gas at relatively less pressure than that at which the tubing had been tested satisfactorily using liquid. Many expedients have been employed to prevent the physical replacement of tubing when leaks have developed. Perhaps the most commonly used is the sodium silicate treatment in which the solution is lubricated into the tubing to form a crystalline plug in the leak. Generally, any benefit realized is of a temporary nature. In addition to field studies on handling and makeup of tubing, extensive laboratory work has been undertaken on the development and testing of thread dopes.' Also, substantial effort has been devoted to testing tubing joints using high-pressure gas as a pressure medium.' The results of this work have emphasized that tubing joints are susceptible to occasional leaks, especially when subjected to relatively high differential pressures. To cope with the problem of leaking connections, an extensive investigation was undertaken to devise means of sealing leaks without removing the tubing from the well and without reducing the inside diameter of the tubing. The purpose of this paper is to present a technique, together with the associated equipment and compound, which have been developed for effecting a seal of leaking tubing in place. DISCUSSION Work was initiated simultaneously on two ventures: (1) to develop a satisfactory leak sealing compound and (2) to develop tools necessary to find the leak and place the compound. Leak Sealing Compound In the development of a sealing compound, tests were conducted on those compounds commercially available which include: (1) conventional thread lubricants, (2) thermo-setting resins and (3) other materials which held promise of effecting a seal. Although none proved completely satisfactory in their available form, two commercial compounds proved nearly equally effective in sealing leaks during laboratory tests after proportioned quantities of graded silica had been added. Field usage has indicated that the preferred compound is one prepared of an aluminum-stearate base thinned to the proper constituency and carrying a mixture of fine mesh graphite and graded silica. The compound developed by Humble Oil & Refining Co. is designated as Tubing Thread Leak Sealant 800. Placement Tools and Technique In developing tools to detect joint leaks and to place the sealing compound, work was done initially on wireline equipment. Preliminary designs were completed of a tool somewhat on the order of a pressure bomb to test individual joints with gas at high pressure to determine if the joint was leaking. An entirely different tool equipped with opposed packers was intended for placement of the sealing compound at high pressures in each leaking joint. The application of these tools

Jan 1, 1958

By D. L. Martin

THAT small amounts of impurities have a harm-J- ful effect on the malleability of metals and alloys is well-known. One common type of em-brittlement involves the formation of a small quantity of eutectic at the grain boundaries, and is typified by sulfur embrittlement of nickel. Another example of eutectic embrittlement—sulfur embrittlement of cobalt—is described in this report. In the preparation of specimens for a study of Co-Pt alloys, it was observed that the hot swagabil-ity of the alloys appeared to be influenced by the grade of cobalt used as melting stock. The cause of the hot-shortness was not traced to any particular impurity, although sulfur was suspected.' The damaging action of sulfur on the malleability of cobalt has not been generally recognized,'; in spite of the fact that the Co-S phase diagram8 eveals the same basic conditions—low solubility and eutectic formation—responsible for sulfur embrittlement of iron and nickel.7, 8 Apparently sulfur embrittlement has not been a serious problem in the fabrication of cobalt alloys. One related factor is likely the limited commercial experience with high cobalt alloys, since the predominant use of cobalt has been in alloys containing less than 75 pet Co. A series of Co-S alloys was prepared and studied to establish the effect of sulfur on the hot working characteristics of cobalt. Specimens, 5/8 in. diam by 4 in. long, were prepared by vacuum melting in magnesium oxide crucibles and casting in a copper mold. Two grades of low sulfur electrolytic cobalt were used as the basic material for the study, one from Johnson, Matthey and Co. and the other from the International Nickel Co. Each contained about 99.5 pet Co and had a nominal sulfur content under 0.005 pet. The sulfur was added initially as cobalt sulfide powder. Later, some low sulfur alloys were prepared by diluting the high sulfur alloys with cobalt. Trouble was experienced in controlling the sulfur content. Apparently much of the cobalt sulfide powder was lost during melting, as most of the samples contained a lower sulfur content than was added. The alloys were evaluated for hot brittleness by heating to 1000°C in a hydrogen furnace and swaging in air. The results of these tests are summarized in Table I. All the alloys containing less than 0.008 pet S were successfully hot swaged to 1/4 in. diam. The bars containing more than 0.015 pet S could not be swaged because of the formation of intercrystal-line cracks similar to those illustrated in Fig. 1. Examination of the microstructure of the cast bars revealed cobalt sulfide eutectic at the grain boundaries, Fig. 2. The sulfide was not always continuous at grain boundaries in bars that were hot embrittled but, in general, the particles did form a network that could account for the brittleness above the eutectic temperature, 880°C. There is no question about the brittle nature of a specimen exhibiting a continuous sulfide network such as is shown in Fig. 2b, though a sulfide distribution similar to that in Fig. 2a is marginal. This particular bar cracked when hot-swaged. However, other bars with lower sulfur content but with some sulfide phase at grain boundaries were successfully worked. The reduction of area of a hot tensile test specimen was also found to be a sensitive indicator of sulfur embrittlement. The variation of reduction of area with sulfur content is shown in Fig. 3 for specimens fractured at 900°C in an evacuated capsule. The ductility of cobalt is greatly reduced when the sulfur content exceeds 0.005 pet. Similar results were obtained for alloys tested at 800°C, below the eutectic temperature. The upper sulfur embrittlement limit of 0.015 pet, Table I, agrees with the observation of Kalmus8 hat

Jan 1, 1957

By P. Schwed

IN determining the mechanism responsible for sintering, the most direct procedure available is the comparison of the observed time and temperature dependence of the process with the dependence to be expected upon the basis of each conceivable mechanism. This was done by Kuczynskil who, in treating the mechanism of surface diffusion, postulated, in effect, that the concentration gradient of vacancies is different from zero only within the neck. This procedure was recently questioned by Cabrera' who assumed, on the contrary, that diffusion occurs only in the region outside the neck. In the present note, the calculations are performed without restriction on the region of diffusion. To carry out this objective it is first necessary to

Jan 1, 1952

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 F. D. Rosi

IN the production of single crystals by the Bridg-man method of solidification from the melt in vacuum at a crucible lowering rate of 0.25 in. per hr, a cellular structure was frequently observed in copper and copper-base alloys at the terminal surface of the as-cast crystals (i.e., the surface representing the last portion of the crystal to solidify). The geometrical form of this structure varied from crystal to crystal, but, in general, could be classified as either hexagonal or quadrilateral. Fig. 1 shows examples of this cellular structure, which is similar to that reported by Buergerl and, more recently, by Pond and Kessler&apos; and Rutter and Chalmers. In the micrographs of Figs. lb and c, the cubic structure in the alloy crystals is obscured somewhat by excessive surface evaporation in the final stages of solidification. X-ray orientation studies indicate that the traces outlining the various geometrical forms correspond to octahedral planes, which are the planes of greatest reticular density in the face-centered cubic lattice. It would appear from this that the view first propounded by Bravais,4 that the surface energies and normal growth velocities of the different crystal planes are inversely proportional to their reticular densities, applies to this cellular structure, since those surviving are the planes of greatest atomic density. Thus, the observed variation in the geometrical form of this structure in crystals of different orientation is readily understandable from the distribution of the (111) planes in the standard {111}, (1101, and (1001 stereographic projections. Depending upon whether the crystal axis (i.e., the direction of crystallization) coincides with a <111>, <111>, or <100> direction, the cellular structure viewed from a surface perpendicular to the crystal axis will consist of a network of regular hexagons, skewed hexagons (with interfacial angles of 110" and 125"), or cubes, respectively. It follows, moreover, that off-orientations from these principal directions will yield modifications of these three basic geometric configurations. In this connection, it is interesting to note that the bounding planes of the hexagonal structure observed in tin by Rutter and Chalmers3 showed no preferred orientation.

Jan 1, 1954

By L. D. Jaffe

IN 1945-1946, the author measured temper brittle-ness in ingots of varying composition prepared by remelting SAE 3135 bar stock under vacuum. Since other investigators1-" have been referring to this hitherto unpublished work, belated publication seems worthwhile. Steel in 7 lb batches&apos; was induction melted with nickel additions in a magnesia crucible under a pressure of 10 microns of Hg or less and cast into a 2 in. diam chill mold. The compositions of ingots A, B, and C prepared in this way are shown in Table I; the vacuum melting lowered carbon, manganese, sulphur, and nitrogen content. Ingot B was homogenized 24 hr at 1095°C; ingots A and C were not homogenized. Blanks, M in. square, were cut from each ingot, austenitized 1 hr at 870°C, water quenched, tempered 1 hr at 595"C, and water quenched. Half the blanks from each ingot were given an embrittling treatment of 50 hr at 455°C and water quenched. A few specimens, embrittled and unembrittled, were finally heated 1 hr at 580°C and water quenched. Charpy specimens machined from the blanks were V-notched on the side closest to ingot mid-radius and paired as to radial position in the ingot, one of each pair having received the embrittling treatment and the other not. Specimens were broken in a standard impact machine at various temperatures, the same temperature, in general, being used for both bars of a pair. Fig. 1 shows the results. It is evident that temper brittleness, as measured by the increase in temperature of transition from brittle to tough failure introduced by the 455°C treatment, was decreased but not eliminated by reducing carbon to 0.006 pct, manganese to < 0.004 pct, and nitrogen to 0.001 pct. In another study," temper brittleness was apparently eliminated by -reducing carbon to 0.003 pct, with 0.80 pct Mn and 0.0015 pct N (ingot D)." • Analyses given for carbon below 0.02 pct were made by Jensen method; for nitrogen, by Kjehldahl method. Values quoted else-where&apos;-&apos;." for carbon content of ingot C and for nitrogen content of ingot D were obtained by conventional combustlon and by vacuum fusion methods, respectively, and are considered much less accurate. The 580°C final treatment removed previous em-brittlement (ingot B particularly), indicating that this was "reversible embrittlement."" Metallographic examination of ingot C with 1 pct nital etch revealed only ferrite; ingot A had carbide spheroids uniformly distributed in a ferrite matrix. With ethereal picric acid plus zephiran chloride etchant.&apos; no differences between embrittled and un- embrittled specimens of ingots A, B, or C were noted. Fracture of C and D below the transition temperature was predominantly transcrystalline, with traces of intercrystalline, in both embrittled and unembrittled conditions. The corresponding fracture of unembrittled B was mixed transcrystalline and intercrystalline; of embrittled B, predominantly intercrystalline with some transcrystalline areas. . . . Acknowledgment The efforts of J. C. Leschen, formerly of National Research CO~P., in preparing the ingots are acknowledged with thanks.

Jan 1, 1956

By Jack Parker

The White Pine mine site lies five miles south of Lake Superior in Ontonagon County, Mich. Copper sulfide, mixed with some native copper, is mined by a room-and-pillar system from gently dipping Upper Kewee-nawan sediments. Depth of mining now varies from 700 to 1800 ft and the ore body continues to a depth of at least 3400 ft. An area roughly 21/2 miles square has already been mined. Mining height has varied from 61/2 to 22 ft. A rock mechanics program was set up in late 1963 to promote safety and mining efficiency. This note reports some of the findings. Rock Strength Compressive strength of small, dry specimens of sandstones, siltstones, and shales from the ore zone varies from 20,000 to 30,000 psi. This is intermediate between the softer coal mine sediments and the meta-morphic and igneous rocks of hard rock mines. Annual Cycle of Rock Failure Since 1963, every roof and pillar failure involving more than a few tons of rock has been examined and documented. Some 1500 stations have been installed for measuring convergence, -c1/1000 in., with Invar extensometers. At first it was thought that there was some kind of a cycle of roof failures; perhaps annual, perhaps even elated to the moon or to earth tides, but records (see

Jan 1, 1971

By J. W. Pugh

VANADIUM has only recently received consideration with respect to structural applications. It would appear likely to find service where its high electrical resistance and constact temperature

Jan 1, 1958

By W. R. Hibbard

T has been proposed1 on the basis of slip and flow I- that the ideal deformation texture of cold rolled face-centered cubic metals is (110) [112]. As pointed out recently by Brick,&apos; this theory does not account for the difference between the pole figures for cold rolled copper and 70-30 alpha brass, which develop strikingly different spreads from the ideal orientations. It does suggest that the pole figures might be similar for these two metals if they are rolled sufficiently. This has been found to be the case for cold drawn wire.&apos; Experimental Procedure: Four inch sections of cast cakes of copper and 70-30 alpha brass were obtained through the courtesy of the Bridgeport Brass Co. Pieces from these cakes were cold straight rolled 99.993 pct reduction in thickness with the assistance of the Remington Arms Co., Bridgeport, Conn., and by the use of pack rolling. Pole figures were made using the X ray camera and techniques described by Brick.&apos; These pole figures were not significantly different from those previously published for the same materials rolled 98 pct. Eight thicknesses of this strip were then pack rolled. This material failed completely and extensively in tension as shown in fig. 1, developing wavy transverse fractures and bulges. No further work could be done on these samples. Summary: Within the range of this experiment, no attainable amount of cold rolling would cause the pole figures of cold rolled copper and 70-30 brass to become similar, in spite of the fact that such a similarity is predicted by theory.&apos; References W. R. Hibbard. Jr. and M. K. Yen: Trans. AIME (1948) 175, 126. Met. Tech. Feb. 1948. TP 2334. ²R. M. Brick: Trans. ASM (1949) 41A, 99. 3W. R. Hibbard, Jr.: Trans. AIME (1949) 185, 598, Jnl. of Metals, Sept. 1949. "R. M. Brick: Trans. AIME (1940) 137, 193. &apos;R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675.

Jan 1, 1951

By Knut L. Sandvik, Aage Solbakken

it is an established fact that the collecting properties of xanthates and anionic collectors are dependent on the hydrocarbon chain length. This is ascribed to the greater adsorption densities caused by increasing the xanthate chain length. As batch flotation tests showed similar trends for amines, an investigation of the adsorbing properties of amines was undertaken. Because earlier investigations showed adsorption densities for dodecylamine salts on quartz varying as much as 20 times under apparently similar conditions,1-4 it was decided to make a survey of the changes in adsorption density due to the drying conditions of the quartz. EXPERIMENTAL PROCEDURE The quartz, handpicked in the pegmatite quarries of Iveland, Setesdal, had the following composition: SiO2 99.81, A12O3 0.01, Fe2O3 0.05 and loss by ig-

Jan 1, 1969

By Walter J. Karplus, Otto J. M. Smith

The transient response of earth formations may be tlcter.171ined by means of four electrodes mounted coli-rienrly on n sonde. Exponentially decaying current pules are applied to one pair of electrodes and the re.rrrlting voltage transient at the other pair is recorded. It is shown by theoreticol analysis and verified by laboratory experiments that this arrangement readily yields the direct resistivity of the formation and provides valrrable additional information as well. INTRODUCTION Although electrical transients have been employed with moderate success in geophysical prospecting, their application to well logging has received virtually no attention in technical literature. In the conventional direct resistivity logging methods only the zero frequency impedance of the formation under study is measured, and no information is obtained regarding its reactive characteristics. Since the use of certain transients appears to offer some advantages in this respect, experiments were performed on a laboratory scale to investigate this possibility. This investigation was limited to a study of a four-electrode array where both the receiving and transmitting electrode pairs are mounted on a logging sonde, and decaying exponential pulses are applied to the transmitting electrodes. THEORY Given an electrode configuration as shown in Fig. I, located in a homogenous medium of resistivity p, if each electrode has an effective radius, r, which is small compared to the spacing, s and a, it is easy to show by integrating the volume resistivity that the input resistance, Rrw, of the transmitting electrodes is Rxw=p/2pr If a capacitor of capacity C, charged to a voltage Em, is suddenly connected to these electrodes, the resulting current, I(t), will then be The voltage transient, E(t), at the receiving electrodes may then be found by substracting the resulting potential at electrode Y from that appearing at electrode Z. and by inserting Eqs. 1 and 2 Integrating Eq. 4 with respect to tim

Jan 1, 1957

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat&apos;s&apos; The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K&apos;(tn), related by K(m) = K&apos;(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K&apos;(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K&apos; (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K&apos; (m)] is a streamline of value $[K(m), K&apos; (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K&apos; (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

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. G. Richardson

The performance of laboratory water floods is compared with the flooding behavior calculated by the Buckley-Leverett techniques from steady-state relative permeability-saturation relations. Both the steady-state and unsteady-state experiments were conducted on the same sand-packed column. Relative permeabilities were calculated by the Welge technique from the unsteady-state waterflooding displacement experiments and compared with those measured by steady-state techniques. An evaluation of the various calculation procedures was made. It was demonstrated that steady-state relative permeabilities could be used to calczcJate waterflood performance. INTRODUCTION To calculate the waterflooding behavior of a given reservoir, relative permeability-saturation relations of the reservoir rock are required. These relative permeabilities are commonly measured on core samples by steady-state experiments such as the Penn State technique.&apos; The relative permeabilities obtained in steady-state experiments are calculated from oil and gas flow rates and pressure drops measured under conditions of equilibrium distribution of oil and water in the pore spaces with slow approach to equilibrium. On the other hand, in water floods the water saturation at a given point changes rapidly with time as the flood front passes. Extensive research2 has shown that the steady-state relative permeabilities to oil and water are independent of the rate of flow and the fluid viscosities. Research has also demonstrated that the waterflooding performance of homogeneous sands uniformly contacted by water is independent of rate when capillary pressure gradients, which are important in short laboratory columns, are made negligible. However, there is little experimental data in the literature comparing relative permeabilities calculated from steady-state flow experiments with those calculated from flooding experiments. In this paper, the production data of two water floods and the relative permeabilities calculated from a series of steady-state experiments on an unconsolidated sand column are presented along with the comparisons calculated by the Buckley-Leverett and by the Welge techniques. The purpose of this study was to determine if steady-state relative permeabilities could be used to predict the waterflooding performance. This study also permitted an evaluation of the Buckley-Leverett and Welge calculation procedures and allowed an insight into the nature of microscopic displacement of oil by water. EXPERIMENTAL APPARATUS AND PROCEDURE The apparatus used in this investigation was a Lucite column 1 ft long and 11/2 in. in diameter. A drawing of the apparatus is shown in Fig. 1. Six pressure taps were evenly spaced along the top of the column to measure the oil pressures. Three pressure taps fitted with small porous disks were spaced along the side of the column to measure water pressure. Water was admitted to the inflow face of the sand through a porous disk while oil was admitted through a hole in the porous disk and distributed to the face of the sand by grooves machined in the porous disk. Retainer screens of 325-mesh stainless steel were cemented over the inlet and outlet ports and the pressure taps to prevent loss of sand. The column was packed with a clean dry sand all of which was finer than 200 mesh. Next, the sand was saturated with a solution of 150,000 ppm sodium chloride solution. The column was weighed dry and water-saturated to obtain data for the calculation of the pore volume. A 151-cp oil was then injected into

Jan 1, 1958

By G. J. Harmsen

is shown that in any isotropic porous medium there is a fixed ratio, : , between the numerical valrles of the total pore perimeter per unit of cross-section and the specific surface area per unit of bulk volume. The consequences of this fact on the use of the concept "hydraulic radius" in the case of porous media are examined. The validity for consolidated sands of Kozeny&apos;s rela- tionship and of the formula derived by Carman for capillary rise are discussed. INTRODUCTION In the course of time several quantities and relations have been put forward in order to describe the texture of a porous medium and the flow of fluid through it. Among these relations the so-called Kozeny formula and a formula for capillary rise, for both of which Carman&apos;,&apos; has given a derivation, will be specially considered here. These relations are of a semi-empirical nature and the derivations must be considered to have a heuristic significance only. For unconsolidated mate-

Jan 1, 1956

By Frank G. Miller, Ralph A. Seban

Problems relating to thermal methods of oil recovery have been given increasing attention during the past year. The nature of the physical and chemical processes underlying thermal recovery are not yet well understood. The need for pertinent basic information is recognized generally. One of the processes involved is the transfer of heat by conduction in oil reservoir rocks containing moving reservoir fluids. This technical note deals with heat conduction in a laboratory sand column filled with a moving hydrocarbon and therefore should be contributory to the presently inadequate fund of knowledge on thc over-all subject. In an analysis of the flow of vaporiziny propane through a horizontal column of sand, one of the present author9 demonstrated correspondence between thc measured values of pressure along the length of the column and those predicted by a theory which postulated that the enthalpy of the propane was invariable along the length of the column. This postulate way implied as a deduction from the principle of conservation of energy but the details of the deduction were not given. The specific purpose of this technical note is the presentation of these details both as an adjunct to the earlier analysis and to supply some additional details on the processes involved in this type of flow. Results disclose that rates of heat transfer by conduction, in the direction of fluid motion, generally would be small for systems of the type studied. FUNDARIENrAI. ENERGY EiQUAI-[ON The principle of conservation of energy may be applied to a section of the porous material on the basis that heat transfer, like fluid flow, is possible in the x direction only. Transfer of heat in the y and z di&apos;rections is prevented by suitable insulation or by taking the medium as infinite in directions perpendicular to the x axis. For steady state heat conduction and conditions of steady fluid flow the principle of conservation of energy specifies that any reduction in the enthalpy rate increases the flow of heat in the same proportion. Stated mathematically, dH KA 87 —- = - — - — U) * dx W dx........ Lvhere is the flow of heat in the positive x W dx direction. TEMPERATURE DISTRIBUTION IN DIRECTION OF FLOW The column of sand used in the previoi~sly described research is divisible into three different flow regimes. each of which may be analyzed independently. In the entrance region the liquid approaches the saturation state. A transition region is postulated following the transverse section at which the saturation state of the liquid is attained. In this transition region gas and liquid phases are both envisioned as present, with no vaporization occurring and with fluid movement restricted to the liquid. The upstream end of the exit region is at the transverse section of the column where the fraction of the pore space occupied by gas first becomes great enough for gas flow and where vaporization of the liquid begins. Fig. 1 indicates schematicaHy the thermodynamic processes undergone hv the fluid in the three flow regimes.

Jan 1, 1956

By Pol Duwez

IN the course of an investigation of the V-CO system, two intermediate phases were found. One of these phases corresponds approximately to the stoichiometric composition VCo and is isomorphous with the sigma phase in the Fe-Cr system.&apos; The second phase has the composition V3Co; its crystal structure is described in the present note. The alloys were prepared by mixing the two metals in the powder form, pressing a small disk weighing about 5 g at 80,000 psi, and arc melting this disk on a water-cooled copper plate in an atmosphere of pure helium. The details of this technique have been described.&apos; The vanadium powder was obtained from Westinghouse Electric Corp., Bloomfield, N. J. This powder is probably of very high purity, since when it is properly sintered or melted in the above-mentioned arc furnace, ductile specimens are obtained. The cobalt powder, from Charles Hardy, Inc., New York, contained 0.5 pct Ni, 0.1 pct Cr, and traces of Si and Fe. After melting, the V,Co samples were sealed in evacuated quartz tubes and homogenized for ten days at 800°C. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using Ka copper radiation. The patterns were readily indexed on the basis of a primitive cubic lattice with a parameter equal to 4.675A. The density, determined by the immersion method, was 6.71 g per cu cm; hence the number of molecules per unit cell is approximately 1.95; i.e., 2. At this point, the possibility that the structure might be that of beta tungstena became apparent. The beta tungsten structure is described as follows: Space group 03,, — Pm3n 2 Co in (a) : 000; ?4lhYZ (hhl) reflection present only if 1 = 2n. Assuming this structure to be the correct one, intensities were computed by means of the usual eauation: 1 + cos220 I oc p F sin 0 cos 6 where F is the structure factor, 0 the Bragg angle, and p the multiplicity factor. The observed and calculated values of sin 0 and the intensities are given in Table I. The agreement between the observed and the calculated sin 0 is good and there are no flagrant discrepancies between the calculated intensities and those estimated visually. The (hhl) reflections for which 1 is odd are not observed, as required by the space group. In addition, the (410), (430), and (531) reflections are missing as expected, because of the special (a) and (c) positions in0%. However, six reflections—(llo), (220), (310), (411), (422), and (510)—which have very weak computed intensities were not observed. For these reflections, the structure factor is proportional to the difference between the scattering factors of the two atoms in the structure. Since the scattering factors of vanadium and cobalt are not very different, these reflections are weak. However, by using Ka chromium radiation, whose wavelength is just above the absorption edge of vanadium, the effective scattering factor of vanadium may be decreased by one or two units; consequently the difference between the cobalt and vanadium scattering factors is increased. It was, indeed, found that in a powder pattern taken with chromium Ka radiation, the three reflections (110), (220), and (310) were actually present. The three other reflections (411), (422), and (510), with spacings smaller than half the wavelength of chromium Ka, were obviously not obtainable with chromium radiation. All the experimental results appear to confirm the beta tungsten structure for V,Co. In this structure, each cobalt atom is surrounded by twelve vanadium atoms at 2.61A; each vanadium atom is surrounded by two vanadium atoms at 2.34A, four cobalt atoms at 2.61 A, and eight vanadium atoms at 2.86A. Acknowledgment This work was done at the Jet Propulsion Laboratory, California Institute of Technology, under contract number W-04-200-ORD-455 with the Army Ordnance Department, Washington, D. C. The author wishes to thank this agency for the permission to publish the results of this investigation. References &apos;P. Duwez and S. R. Baen: X-Ray Study of the Sigma Phase in Various Alloy Systems. Symposium on the Nature, Occurrence, and Effect of Sigma Phase. ASTM Special Tech. Pub. No. 110, pp. 48-54. Philadelphia, 1951. 2 C. H. Schramm, P. Gordon, and A. R. Kaufmann: The Alloy Systems Uranium-Tungsten, Uranium-Tantalum, and Tungsten-Tantalum. Trans. AIME (1950) 188, pp. 195-204; Journal of Metals (January 1950). 3 M. C. Neuburger: The Crystal Structure and Lattice Constants of Alpha and Beta Tungsten. Ztsch. fiir Krist. (1933) 85, pp. 232-237.

Jan 1, 1952

By J. E. Dorn

A STUDY of the increase in density of copper powder as as a function of the time and temperature of sintering has been previously reported.&apos; The present note will describe the results of a series of experiments under conditions similar in all respects to those of the first series, except that

Jan 1, 1951