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By W. A. Hockings, D. W. Fuerstenau, A. L. Mular

This paper briefly describes a simple air pycno-meter and its use for rapid determination of the composition of mixtures of solid particles. Research on such problems as the pelletizing of solids, the mixing of solid particles, and the comminution of mixtures can be simplified by means of this analytical tool. THEORY OF OPERATION Liquid pycnometers1 are commonly employed to measure volumes. These devices are time consuming and sometimes give inconsistent results. The liquid used in the pycnometer may have an undesired influence on the material to be measured; moreover, complete displacement of air by the liquid is seldom

Jan 1, 1963

By H. P. Bucker, M. Felsenthal, F. R. Conley

INTRODUCTION In the intensive analysis of core samples from oil raservoirs, there is a recognized need for pore sizc distribution data. Such data, if collected with adequate precision and in sufficient quantity, should contribute to a better interpretation of fluid flow phenomena than is now possible from a knowledge of permeability and porosity data alone. It is hoped, for instance, that pore size distribution data may eventually provide a useful aid for predicting whether a water flood, or other secondary recovery methods. will he successful in a given reservoir.' Apparatus tor measurlng pore size distribution by mercury injection at pressures ranging from 0 to 2,000 psi have been described in the literature.2,3,4 All of these apparatus are somewhat complex and fairly expensive. Furthermore, the callbration of some of the apparatus is not always easy. Great difficulty, for instance, was experienced in obtaining reproducible pressure-volume correction data for the mercury pump shown in one of the references. An apparatus was therefore developed which was less complicated and less expensive than those of previously described designs. This apparatus is, in some respects, an improved version of a previously described low pressure apparatus' (maximum pressure 150 psi) which did not cmploy a mercury pump but instead used a precision bore glass tube for measuring the injected volumes. Tests were performed with the apparatus from vacuum to 2,000 psi and it was observed that the apparatus furnished reproducible pressure-volume correction data. In addition. it was noted that the maximum correction was small. precision of measurement was high. and operation of the entirc apparatus was relatively easy. Although the apparatus was designed exclusively for samples of 1 in. diameter and 1 in, length or smaller, it could be modified without much difficulty for larger samples, if desired. APPARATUS Arrangement of the pore six distribution apparatus is shown schematically in Fig. I. The heart of the apparatus is a steel sample chamber surmounted by a precision bore capillary glass tube. A mercury reservoir is connected to the lower half of the sample chamber. The top of the glass tube is in communication with a

Jan 1, 1957

THE strike and dip of bedded formations is readily determined by trigonometry if some marker horizon is intercepted by three holes. If no marker can be identified and if orientation of the cores is unknown, as is the usual case in diamond drilling, the determination still can be made readily by the use of a stereonet if the bearing, inclination, and angle the bedding makes with the core axis is known for each of the three holes. Such determination, valid only if the bedding orientation is fairly uniform within the area drilled, is considered simpler, faster, and more effective than any solution previously published. Method: The steps of this procedure are as follows: 1) Mark north and south poles on tracing paper placed over stereonet.* 2) Plot the three diamond drillholes by drawing a line from the center of the net in the direction of the bearings of the holes. Then rotate the paper until each line, in turn, lies along the equatorial diameter of the net; the end of each line is determined by the inclination of the hole measured in degrees from the periphery toward the center of the net along the equatorial diameter. Fig. 1 illustrates a vertical hole and a hole inclined at —23" due east. 3) With the projection of one diamond drillhole along the equatorial diameter, measure from the end of the hole, to the east and then to the west, a dis- tance in degrees equal to the core axis-bedding plane angle. Find two more points by measuring the same number of degrees north then south along the great circle from the end of the drillhole. Draw a circle, the center somewhere along the direction of the projection of the drillhole, to connect these four points. Draw circles for the other two diamond drillholes in the same manner. See Fig. 1 for two circles representing core axis-bedding plane angles of 35" and 23" and Fig. 2 for these plus a third circle representing a core axis-bedding angle of 42" in a hole bearing S 50 W inclined at —52". 4) Rotate the tracing paper until one great circle on the stereonet is found which is tangent to all three of the circles or parts of circles derived in the previous step. Trace this great circle on the paper and join its ends with a straight line passing through the center of the net. The bearing of this line is the strike of the bedding. In Fig. 2 the bedding strikes N 77 E. 5) Rotate the paper until the strike is along the polar diameter of the net. The dip of the bedding is determined by measuring along the equatorial diameter the distance in degrees from the periphery of the net to the great circle derived in step 4. The dip of plane illustrated in Fig. 2 is 55" to the N 13 W. Fig. 3 indicates the solution for three holes whose bearings and inclinations are N 20 W and —43o, due E and —30°, S 30 W and 23" with core axis-bedding angles of 30°, 50°, and 43" respectively. The bedding (stippled area) strikes N 44 W and dips 70" to the southwest.

Jan 1, 1956

By John J. McKetta. Jr., Louis B. Lesem, George H. Fancher

The proration of oil produced in the field frequently is based partially or entirely upon the gas-oil ratio of wells. The measurement of the gas-oil ratio is one of the more important field tests in regulatory and pro-ration work, and the test always should be conducted according to standardized methods and procedure. Obviously, the gas-oil ratio and the volume of gas produced by a well depend upon many factors but should be independent of the method of measurement and of the devices used to measure gas and oil. Consequently, the volume of gas accompanying a barrel of oil produced by a well may be measured by any reliable and accurate device or instrument. Frequently either a critical flow prover or an orifice well tester is used for this purpose, and for a particular well the same rate of flow of gas should be obtained regardless of whether a critical flow prover or an orifice well tester is employed in the test. In Texas, when using either instrument, either Capacity Table 1 or 5' is employed in making the necessary computations. If the tables are used, a discrepancy always is found whenever the two instruments are compared by extrapolation to the same conditions of flow. Clearly, Tables 1 and 5 must be at fault in some respects. The orifice well tester and the Bureau of Mines type of critical flow prover are essentially the same instrument; both devices utilize a square-edged orifice 1/8 in. in di-ameter as the primary element, and both freely discharge gas to the atmosphere. Tables for the orifice well tester' have been published in the ranges of 0 to 15 in, of water and 0 to 40 in. of mercury (Hg) differential in pressure. Coefficients for the critical flow prover have been published for differentials in pressure greater than 75 psia. An extrapolation of either differs from the other set of data as much as 18 per cent at some points. No immediately obvious reasons for the discrepancy was found, and data available from the literature were insufficient to effect reconciliation. Consequently, a series of experiments was performed to check the available data and to determine discharge coefficients for the two devices in an overlapping range of differential pressure. The correlating equation used in preparation of tables such as Tables 1 and 5' is the so-called hydraulic equation, Q = C1 vh .....(1) The tables cover orifice sizes from 1/8 through 1 1/4 in. A second set of tables, for use with greater differentials in pressure, apply only to the 3/4, 1, and 1 1/4-in. orifice plates over a pressure range of 0 to 40 in. of Hg. The correlating equation used in preparation of the tables is Q = C2 vH(29.32 + 0.3H)/G . (2) Each of these equations is valid only for the range to which it has been applied, and neither equation is valid for extrapolation. Theoretical equations for flow through an orifice are based upon assumptions of fractionless flow and an emergent jet the size of the orifice. A multiplier, C,, called the discharge coefficient, is inserted into the theoretical expression to compensate for both frictional losses and the contraction of the jet experienced in the plane of the orifice. Buckingham3 shows that C, should vary with the ratio of upstream to downstream pressure for flow of a compressible fluid at any average linear velocity through the orifice less than the velocity of sound. Work published by the National Advisory Committee for Aeronautics4 indicates that the variation continues into the so-called critical flow region until the vena contracta coincides with the plane of the orifice. The NACA work, however, does not indicate a leveling off of the coefficient. The work of the Bureau of Mines5 for the critical flow prover was based on differential pressures greater than 75 psi and indicates that the discharge coefficient, Cd, is constant in this region at a value of about 0.86.

Jan 1, 1958

By C. R. Fast

In order to evaluate the ability of a Hydrafrac treatment to effect a sustained increase in well production, data were accumulated on the first 65 wells in 26 fields treated by Stano-lind. Since these data were obtained from such a large number of fields, it is felt that individual well or reservoir characteristics do not affect the overall picture, as might be the case if the study were made in one field or one group of wells in a field. These data are tabulated in Table I and plotted on Figs. 1 and 2. An analysis of Fig. 1 shows that at the end of six months, 75 per cent, or 45, of 60 wells on which data were available showed a sustained production increase. At the end of two years, data were available on 25 wells. Of these, 15 wells, or 60 per cent, showed a sustained production increase. At the end of three years, 55 per cent, or 10, of 18 wells had a production rate greater at that time than before Hydrafrac treatment. The lack of information on additional wells at the end of the third year is primarily a result of the small number of treatments conducted in the early stages of field application

Jan 1, 1952

By R. C. Rumble

To /neet the need for a subsurface flowmeter capable of measuring low rates of flow, a new type flowmeter has been built and tested in the field. This instrument is self-contairzed, can be run on a wire measuritzg line, and may be run through 2-in tubing. It consists of a rotameter flow-measuring assembly used in conjuncfion with a conventional subsurface instrument clock and chart. Integral with the tool is an inflatable packer which, by effecting a seal between casing and tool, diverts all fluid through the metering assembly. Packers of different size adapt the tool to different sizes of casing or liner. The flowmeter is capable of measuring rates of flow as low as 4 BID. The flowmeter has been run experimentally in seven wells. It has yielded satisfactory resrrlts in five of the wells, and in the other two it failed to operate because of loose sand in the hole. INTRODUCTION One of the oldest problems facing the producing branch of the petroleum industry is the location of depths of entry of fluid into a wellbore and the determination of the amount of fluid entering at each depth. This problem is often encountered in oil and gas wells completed in single producing horizons as well as in multiple pays; it is a common problem in oil wells which produce excessive volumes of gas. Several subsurface instruments designed to detect and meter flow in the producing interval of wells have been described in the literature.1,2,3,4 Most of these, however, were apparently intended for use in wells producing at relatively high rates of flow, and consequently lack sensitivity to low flow rates. Because of this and of other possible disadvantages inherent in these instruments, development of the subsurface flowmeter described in this report was undertaken. DESIGN OF FLOWME'I'ER Design Requirements In considering the requirements for a flowmeter that would not be subject to the limitations of devices existing at the time work was started, attention was first given to the size of the tool. Such an instrument should be of sufficiently small diameter that it could be lowered readily in 2-in tubing in a producing well. The flowmeter should contain a recording unit so that it might be run on a wire measuring line with conventional reeling equipment. It should not be too long to be accommodated by a portable lubricator of the type used for running conventional subsurface instruments. The metering mechanism of the flowmeter should not be affected appreciably by the viscosity or density of the flowing fluid. Such an instrument should record flow rates in the range from less than 10 B/D to over 100 B/D. To achieve this, a packer should he provided to divert through the instrument all fluid flow in the wellbore. This packer should be of such nature that in the event of excessive flow the fluid would bypass the instrument instead of forcing it up the wellhore. General Description A flowmeter incorporating most of the desired features outlined above was developed and built. The instrument is an elongated tubular device terminated on

Jan 1, 1956

By D. W. Fuerstenau, L. M. Berlioz

In 1957, Charles1 first presented an analysis of a relationship between the energy expended in comminution and the extent of size reduction achieved. Subsequently, Schuhmann extended and interpreted Charles' approach to comminution. According to their analysis, the energy, E, expended in comminuting unit mass of fairly uniformly-sized material is related to the size modulus of the product, k, by where a is the distribution modulus (slope of the log-log cumulative size distribution plot) and C is a constant, which is primarily determined by properties of the solid. If there is any fundamental basis for the E vs k relationship, E must necessarily be concerned with the useful work for the size reduction process and not necessarily the work input, as discussed in detail by Harris.3 Charles and numerous other investigators tested this equation only by relating k to the grinding time, assuming expended energy to be directly proportional to time, but never directly measuring power. In our laboratories, we recently constructed a special batch ball mill with which the power could be accurately determined with torque measuring apparatus.4 With this device, a direct test of the Charles relationship could then be made for ball milling. 5 EXPERIMENTAL A stainless steel mill, 11.5 in. long and 10 in. in inside diam, lined with eight low-silhouette lifter bars, was used for these experiments. The grinding media consisted of 30 kg of single sized, 1-in. diam, stainless steel balls, which occupied about 50% of the total mill volume under static conditions. The void fraction of the static ball load was approximately 0.4, and for the dry grinding conditions used, the corresponding interstitial volume was filled when about 3300 g of the dolomite feed material was present. The 7x9 mesh dolomite used as feed was obtained as a natural, uncrushed product thus as- suring a random distribution of feed particle shapes. Charge weights of 660, 1320, 1980, 2480, 3300, 3960 and 5280 g, which correspond to 20%, 40%, 60%, 80%, l00%, 120%, and 160% of the interstitial load, respectively, were used. Grinding times of 20, 40, 60, 80, 100, 150, 200 and 300 revolutions were considered, with the mill operating at 54 rpm (approximately 60% of critical speed). The tests were made sequentially, in that the size distribution obtained after a certain grinding interval was utilized as the feed for the subsequent period of grinding. Agreement with control experiments where the mill ran continuously for the entire interval was excellent. Torque measurements were made utilizing a Baldwin-Lima-Hamilton SR-4 torque pickup in the manner that has been described previously.3 Standard wet (to obtain the -400 mesh material) and dry sieving procedures were followed using the Tyler full screen series. RESULTS The Gaudin-Schuhmann size distributions obtained in all of these experiments are characterized by distribution moduli (slopes), a, of about 0.66 and are representative of normal dry batch ball milling of a material like dolomite. As an illustration of typical

Jan 1, 1968

By T. P. Meloy

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,

Jan 1, 1963

By Strathmore R. B. Cooke, Iwao Iwasaki

RECENTLY spectrophotometry has been reported to provide a convenient technique for the rapid and reproducible determination of xanthate concentration in pulp solutions,12 and for a kinetic study of xanthate decomposition in acid solutions." Since the application of this analytical technique is feasible for those compounds showing pronounced light absorption maxima in the near ultraviolet region, it was deemed advisable to investigate the absorption spectra of some of the organic compounds that are used in flotation. It is known empirically that certain groups of atoms in an organic compound cause characteristic light absorption in the ultraviolet and near ultraviolet range, and the wavelengths and intensities of the corresponding absorption maxima are relatively independent of the nature of the remainder of the compound. The characteristic values of such groups, which are known as chromophores, are given in the literature.4,5 According to this information, many of the sulphydryl compounds are expected to show absorption maxima in the near or long wavelength ultraviolet region, whereas the saturated fatty acids and the saturated alkylamines do not. This article reports the absorption spectra of the six following types of sulphydryl compounds; mono-, di-(xanthate), and trithiocarbonates, dithiocarba-mate, dithiophosphate (aerofloat), and mercaptan. A Beckman DU quartz spectrophotometer was used to investigate the spectra in the wavelength region of 215 to 350mp. Materials: All the mono-, di-, and trithiocarbonates used in this investigation were prepared in the usual manner" from appropriate compounds obtained from Eastman Distillation Product Industries. The dithiocarbonates included the normal alkyl compounds from methyl to octyl inclusive, as well as the isopropyl, isobutyl, and isoamyl xanthates. Iodo-metric titration gave 99.7 and 99.5 pct purity for

Jan 1, 1958

By Frederick C. Langenberg

IT has been shown1 that copper can be removed from iron-base alloys by solvent extraction with molten lead and sodium sulfide slags. In these processes copper removal is favored by a positive deviation of copper in iron from ideal behavior. Chou' determined the distribution of copper between liquid silver and iron and obtained a value for the activity coefficient of copper in iron at 1600°C, y°, of 9.12. Chipman" calculated the activity coefficient from the Fe-Cu phase diagram to be 12 at 1600°C. More recent work by Koros and Chipman" yields a value at 1600°C for y V equal to 8.0. In this latter work, the distribution of copper between silver and iron was measured at 1600°C, while the activity of copper in the silver phase was determined from calculations based on the Ag-Cu phase diagram. The present work presents another value of based on calculations from the Cu-Pb phase diagram, on the heat of mixing data for the Cu-Pb system, and on an experimental study of the distribution of copper between iron and lead at 1600°C. These experiments were part of a larger research on the removal of copper from iron-base alloys conducted at The Pennsylvania State University. Experimental Procedure—The distribution of copper between pure iron and lead at 1600°C was made in the furnace assembly shown in Fig. 1. The melts were made in high purity alumina crucibles under an atmosphere of prepurified argon. Temperatures were read with an optical pyrometer sighted into a %-in. hole drilled in the inductor. Extensive calibration of the optical readings with immersion readings had been carried out previously. The initial charges consisted of 100 g of electrolytic iron and varying weights of copper. The melts were brought rapidly to 1600°C and 75 g of lead added. The temperature was quickly readjusted to 1600°C, and the melts were held for 10 min at this temperature. A sample was then drawn from the iron layer in a fused silica tube. This sample was analyzed to determine the copper content of the iron layer at equilibrium, while the copper content of the lead layer was determined from a material balance. The validity of the material balance was confirmed by a chemical analysis of the entire lead layer for one heat in which the crucible was removed and quenched after the iron sample was taken. The calculated copper content of the lead-rich phase was 1.18 pct; while the entire lead layer analyzed 1.20 pct Cu. The distribution results are shown in Fig. 2. The distribution constant, N,.'r'"/N, is equal to 3.95. Discussion—From the Cu-Pb phase diagram' it can be seen that lead-rich liquid Pb-Cu solutions

Jan 1, 1957

By C. E. Birchenall, H. M. Schadel, G. Derge

EXISTING distribution data' for silicon between liquid iron and silver at steelmaking temperatures, 1500" to 1600°C, has made activity relationships in liquid silver-silicon alloys desirable as a method of determining the silicon activity in molten iron. To this end, through the use of radioactive Ag110 and the molecular beam technique described in a previous paper,' the vapor pressure of silver as a function of temperature has been measured over three silver-silicon alloys containing 3.9, 9.3, and 15.4 atomic pct (eutectic composition) silicon. The technique was that described for pure silver with the exception that a porcelain liner was used inside

Jan 1, 1951

By L. F. Stutzman, George Thodos

The friction factor plot presented by Cornell and Katz4 and developed for the flow of fluids through consolidated formations has been directly adapted for handling fluid flow problems involvitrg both linear and radial flow. In this adaptation the friction factor plot is used directly for the solution of problems and thereby eliminates the use of conventional equations which are specific to laminar (Darcy) or turbutent flow. This upproach overcomes the disadvantages inherent in the use of these conventional equations. It eliminates the necessity of checking the type of flow occurring in order to identify the specific equation which must be used. In radial flow problems, because of the increasing mass velocity of the fluids as they approach the wellbore. the type of flow may no longer remain laminar. Consequently, it is necessary to use more than one equation in a problem and to identify the range over which each equation should be applied. Finally, in practice it has been found that much of the flow of gases through consolidated media occurs in a range that is neither laminar or turbulent. For this transitional region, no convenient equations are available. The method and presented friction factor plot are appficahle to both liquids and gases. INTRODUCTION The flow of fluids through unconsolidated media in packed beds has been treated extensively by a number of investigatorsl,2,3,5,7,8 Most of these studies present friction factors as a function of modified Reynolds number similar to those developed for conventional fluid flow through pipes. These friction factor plots are presented for linear flow; however, Elenbaas and Katz have extended these concepts to apply to radial flow. All of these studies on unconsolidated materials require a knowledge of packing properties such as sphericity. porosity, and particle diameter. Sphericity and particle diameter cannot be defined at the present time for consolidated formations such as those commonly found in gas or oil reservoirs. As a result many investigators have not utilized friction factors and Reynolds number in the study of fluid flow through consolidated media. However, Cornell and Katz4 present a plot (Fig. 1) for the flow of fluids through consolidated porous media, in which the friction factor defined as: The turbulence coefficient, P, is related to the formation permeability, K, as presented in Fig. 2. Three different types of flow may exist in the flow ot

Jan 1, 1957

By P. A. Toynbee

An experimental air-slide classifier1 has been applied to the de-dusting of ground dolomite in an attempt to produce a grade of -30 +150 mesh (B. S. Sieves) material from a raw material containing 30-35% of the -150 mesh fraction. Air flows varying between 1.5 and 2.5 cu ft/sec sq ft of screen area were used. The throughput of dolomite was between 80 and 100 lbs/h. inch of screen width. The size analyses of the de-dusted material and of the original dolomite are shown in table at right. The proportions of the +100 mesh material in the feed and in the de-dusted products have been used to calculate materials balances, on the assumption that there is no loss, as dust, of this +100 mesh fraction. By interpolation, it can be shown that a de-dusted product recovery of 68.5% will be obtained at an air flow of 2.13 cu ft/sec sq ft of screen area. The feed material contains 68.5% of +150 mesh material, so that if the de-dusting gave a perfectly sharp cut, the product would contain no material less than 150 mesh. Further calculations based on the size analyses, show that, at an air flow of 2.13 cu ft/sec sq ft of screen air, the -150 mesh fraction in the de-dusted product will fall just below the specified maximum limit of 5%.

Jan 1, 1964

By A. G. Metcalfe

THE failure to detect any change in the thermal properties of cobalt at the Curie point would appear to indicate that the apparatus may have a limited sensitivity. The Curie temperature has been determined by direct methods to be 1121+3°CP and 1131°C.3 The specific heat has been determined many times'.' and weighted values are given in Table I. The allotropic transformations in iron and titanium, used by the authors to test the experiment method, involved a volume change of the order of 3 pct on going from the close-packed to the body-centered-cubic lattice. These energy changes are likely to be much larger than those involved in a diffusionless transformation from a hexagonal to a cubic-close-packed lattice. However, it has been pointed out that thermal observations are unreliable in the detection of phase changes when these are near a Curie point.' James 0. McCaldin and Pol Duwez (authors' reply)—The sensitivity of the present technique is limited to first-order transformations, so that gradual changes in specific heat, e.g., in the vicinity of Curie points, are not detected. Furthermore, the existence of first-order transformations with latent heats much smaller than those occurring in the known allotropic transformations of iron and titanium is, we agree, still pending.

Jan 1, 1956

By J. O. McCaldin, P. Duwez

ALLOTROPIC transformations between 1000° and 1900°C have recently been reported for several metallic elements. Since the proposed transformations are based on limited evidence, it was decided to examine the elements in question as well as some refractory metals by thermal analysis with a photoelectric technique similar to that described by Hug-gins, Roll, and Udin.1 In this method, a lead sulphide cell was used to detect thermal radiation from an electric-resistance heated strip specimen. A thermocouple spot welded to the specimen was used to calibrate the temperature of the system under steady temperature conditions, and recording was accomplished with a cathode ray oscilloscope. In the method used by the present authors, the temperature calibration was omitted and the cathode ray oscilloscope was replaced by a recording galvanometer. This technique, in which electric current passing through the specimen heats it, will be referred to henceforth as Method 1. Another arrangement was required for those cases where the specimen could not be formed into a wire or strip suitable for resistance heating. In such cases the specimen was a sintered compact heated by thermal radiation from a hot tungsten strip, Fig. 1. The specimen was insulated from the heating strip with a thin layer of thoria powder or suspended on 0.004 in. tungsten wires. The take-up spring had just sufficient tension to prevent buckling of the heating strip due to thermal expansion. This technique will be called Method 2. Both methods were tested with specimens of iron and titanium and the well known allotropic transformations, a toy and ? to 8 in iron and a to in titanium, were very clearly detected. Fig. 2 shows one of the records obtained for titanium. For this particular experiment, the iodide titanium specimen was a square rod 0.080 in. on an edge and 3 in. long.

Jan 1, 1955

By Austin E. Dwight

IT has been shown by Oelsen and Wever' that the effect of a solute element on the allotropic transformation in iron is dependent upon the quantity

Jan 1, 1957

By W. Rostoker

IN the course of the development of the phase equilibrium diagram for the system Zr-Cr,' the structure of an as-cast allov having the composition ZrCr2 was analyzed and established to be isomorphous with MgZn2 (C14, hexagonal lattice, 12 atoms per unit cell). In a recent paper on the same system, Hayes, Roberson, and Davies' report for the ZrCr2 phase an isomorphy with MgCu2 (C15, cubic lattice, 24 atoms per unit cell). It appeared that this conflict might be resolved by assuming a high and low temperature modification for ZrCr2. That this was the case with the phase TiCr2 has recently been demonstrated by Levinger." Specimens of ZrCr2 annealed at 1200°, 1100°, 994", 900°, 834", 800°, and 700°C, respectively, and subsequently quenched were examined by X-ray diffraction analysis. It was successfully demonstrated that a transition from the MgZn, structure at lower temperatures to the MgCu, structure did occur at some temperature between 900" and 994°C. Table I lists the observed structures at the various annealing temperatures. In Table II, a summary of line spacings and intensities is given for each of the allotropic modifications. The first six lines of the MgCu2 structures have been located in the table to illustrate the close similarity between the patterns. Lattice parameters of the two modifications were calculated by a least squares solution of equations for interplanar spacings for a series of high angle lines. The results are as follows: MgZn2 type - c = 8.262 kX, A = 5.079 kX. MgCu2 type — a = 7.195 kX. It is interesting to note that TiCr2 behaves in reverse fashion yn that the MgCu, structure is the low temperature modification and the MgZn2 structure is the high temperature modification. References lR. F. Domagala, D. J. McPherson, and M. Hansen: This issue p. 279. 'E. T. Hayes, A. H. Roberson, M. H. Davies: Trans. AIME (1952) 194, p. 304; Journal of Metals (March 1952). 3B. W. Levinger: Trans. AIME (1953) 197, pp. 195-196; Journal of Metals (February 1953).

Jan 1, 1954

By J. B. Clark, F. N. Rhines

THE A1-Mg phase diagram in the composition range from 30 to 60 pct Mg remains uncertain. Four intermetallic compounds are reported in this composition range. All of the published diagrams are in agreement as to the existence of intermediate phases near 37 and 52 pct Mg (Mgl,A1,). Confusion exists, however, as to the number and identity of the intermetallic phases present in the intervening composition range from 37 to 52 pct Mg. Mikheeva and Kurnakovl denote the existence of a phase e near 42 pct Mg. Kawakami," Reiderer? and Laves report a phase near 48 pct Mg. Eickhoff and Vosskuhler, from a critical survey of the literature, composed the diagram shown in Fig. 1, with the exception of the eutectoid horizontal of the e-phase shown at 210°C. RaynorV n a similar survey discounts the existence of the phase proposed by Ka-wakami et al.' at 48 pct Mg and reports a composite diagram similar to that of Eickhoff and Vosskuhler." This uncertainty as to the number of intermetallic phases in the A1-Mg system may be eliminated by annealing a diffusion couple of pure aluminum and

Jan 1, 1958

By P. H. Scott, Walter Rose

Recent papers by S. T. Yuster have called attention to the largely ignored concept that there will be a transfer of viscous forces across fluid-fluid interfaces during the flow of immiscible fluid phases through porous media. This leads to the implication that the relative permeability us saturation function, as applied to each of the fluid phases of the system, will in some way be dependent on the viscosities of all the other fluid phases which are contiguous to the flowing fluid of interest. In fact, Yuster has selected and analyzed the properties of a capillary-tube model of the reservoir-prototype flow systems and concludes from his studies that relative permeability values will be very markedly influenced by the viscosity ratio in two-phase systems. On the other hand, relative permeability data have been reported in the literature for more than 20 years; and where these data are consistent at all, they consistently how no dependence on viscosity ratio (cf. chapter 7 of Muskat3 for a resume of past experiniental work). This paradoxical situation has prompted us to re-evaluate Yuster's work. The major flaw we find has to do with the properties of the model Yuster employed to give qualitative support to his predictions. This model is defective in that important surface area parameters characteristic of the prototype-reservoir flow system have not been propertly scaled. Fig. 1 shows how we believe Yuster's model should be modified to circumvent this difficulty. It depicts the capillary tube of radius R and length L, comprised of two elements in series. The first part of length, L has the nonwetting phase flowing centrally out to a radius distance r, where an interfacial boundary exists with the wetting phase which flows in the concentric annular pace of the tube. The second part of length, L-L,. has the

Jan 1, 1953

By A. G. Allten

EXAMINATION by metallographic and X-ray diffraction means of an austenitic steel containing 0.06 pct C, 1.26 pct Mn, 0.38 pct Si, 21.15 pct Ni, 18.72 pct Cr, 3.07 pet W, and 9.14 pet Mo indicated that a - phase, which had not been reported in the literature, existed in this steel. Both the s and car-bides of the M6 C type were present in the as-forged steel. The carbides dissolved completely in the aus-tenite at approximately 2200°F (1205°C). The s, however, was present at all temperatures up to the solidus temperature of the steel at approximately 2375°F (1300°C). Ferrite was not found in any condition of the steel. The faintness of some of the s lines in X-ray patterns obtained from samples of the steel made it desirable to isolate the s prior to verification of its entire pattern. It was found that the s phase could be separated from samples of the steel which had been water quenched from 2250°F (1230°C) by dis-

Jan 1, 1955