Search Documents

By H. J. McQueen, G. C. Kuczynski

ThE useful properties of k6-Alfenol and the thermenol alloys (summarized by J. E. Nachman and W. J. Buehler') have encouraged research into those alloys which, having compositions near 25 at. pct Al, 75 at. pct Fe, undergo an ordering transformation between 500° and 550°C. The equilibrium diagram of the iron-rich iron-aluminum alloys was first determined by Bradley and Jay.2,3 They distinguished three structures: the disordered, which is bcc; FeAl, which is simple cubic with one Fe atom and one Al atom per lattice site; and Fe3Al, which is fcc with three Fe atoms and one Al atom per lattice site. This last structure may be conceived as eight body-centered cubes with Al atoms at the centers of alternate ones, so that Al atoms have only Fe as first and second nearest neighbors. Later, Osawa and Murata4 determined the boundaries of the different superlattice regions in the iron-rich Fe-Al solid solution by dilatometric and X-ray methods. Two of the six phases, which they found between 0 and 50 at. pct Al, were never identified by other workers. A. Taylor and R. M. ones,' concurrently with and independently of this research, redetermined this diagram by measuring lattice parameters at temperature. Further reference will be made to their results. EQUILIBRIUM DIAGRAM A) Experimental Procedure—The alloys were prepared from NRC gas-free iron (99.9 pct Fe) and 99.99 pct Al. They were melted in alumina' crucubles under vacuum in an induction furnace. If the ingots were unsound or showed more than a 3 pct weight loss, they were rejected. The ingots were homogenized at 1100°C for 24 hr before hot-rolling at 700" to 900°C from 1 in. to 0.25 in. thick. It is interesting to note that alloys containing more than 28 at. pct Al were able to take an 80 pct reduction of area in the ordered FeAl region. The dilatometer specimens and specimens for chemical analysis were cut from these plates. A Leitz dilatometer was used to measure the coefficient of linear expansion as a function of temperature. The specimens were slowly cooled from 900" to 300°C where they were annealed for 10 hr before slowly cooling to room temperature. The expansion was recorded photographically as the alloys were heated and cooled at 1.5oC per min between 100" and 1000°C. The magnetic measurements determining the Curie points were performed on the dilatometer specimens in the dilatometer, by using direct current in the furnace windings both to heat the specimen at 1.5°C per min and to serve as the primary coil. The regular specimen holder was replaced by a thin alundum tube on which was wound, as a secondary, a closely spaced coil of fine copper wire. A reversal of current in the furnace windings produced, in the secondary, an emf which was proportional to the induction in the specimen, and which could be detected on a galvanometer. In this way, it was possible to determine the Curie points of alloys to within * 5°C. B) Results and Discussion—The coefficients of linear expansion, as obtained from the dilatometer curves, are plotted as a function of temperature and composition in Fig. 1. Since in many cases the heating and cooling curves were superimposed, it was decided to measure slopes of heating curves only. Definite high peaks, due to the transformations, were observed on each curve between 400" and 520°C, and, for alloys containing more than 23 at. pct Al, a second set of smaller peaks at temperatures above 660°C. The sharpness of the peaks indicates that ordering to Fe3Al is a first-order reaction. The compositions and the temperatures of these peaks are listed in Table I. When these temperatures are plotted as a function of the composition, the result is the constitution diagram presented in

Jan 1, 1960

By V. J. Berry, J. D. Pendergrass

Well pressure transient tests provide a means for directly obtaining information about formation pressure and reservoir flow capacity. Such tests have also been proposed for determining presence and location of faults or other reservoir closures and for measuring oil in place. For mathematical convenience, most theoretical studies have considered the reservoirs to be homogeneous. Definitive information is not yet available to show whether the actual presence of nonuniformities will make pressure transient behavior different from that of a uniform reservoir. The conclusions reached from actual transient tests are questionable, therefore, insofar as they rely on the original assumption of homogeneity. One type of nonuniformity commonly assumed to exist is that of stratification. In most reservoirs the strata are thought to be in vertical communication. Equations for the transient flow of a single-phase, compressible fluid in a one-well, bounded, circular reservoir have been solved for several situations involving crossflow between multiple strata of various thicknesses and permeabilities. The results show that except for the very early flow period, which usually is too short to be analyzed, the transient performance observed at the well is substantially identical with that of a homogeneous reservoir having the same dimensions and having the same steady-state flow capacity. Thus, stratification does not adversely affect interpretation of well transient tests. This conclusion holds for all commonly encountered combinations of reservoir thickness and external radius. Deviations are observed for unusually thick reservoirs whose outer radii are relatively small. The results of these studies also show that the presence and the amount of stratification cannot be simply diagnosed from reservoir pressure transient data when there is crossflow between strata. INTRODUCTION The last decade has brought wide acceptance of the transient well pressure test for determining reservoir parameters. Following the original work of Hurst and van Everdingen,1 the mathematical theory was thoroughly explored. Numerous authors have suggested how to determine static reservoir pressure, permeability-thickness product, original oil in place and reservoir limits for different reservoir geometry. The same mathematical techniques have been used to predict the transient performance of a reservoir over a long period of time. Most of the theoretical work has been for homogeneous, isotropic systems. Some results have also been presented for a homogeneous, anisotropic reservoir.2 Petroleum reservoirs are not homogeneous. The deposition process seems to favor creation of a stratified formation. This concept is sufficiently well accepted so that the most natural extension of the transient flow theory beyond the homogeneous case is to a stratified formation. Results for a stratified reservoir with no vertical communication between layers can be obtained from the results for a homogeneous reservoir. Lefkovitz, et a1,3 have given a thorough treatment of the two-layer case. Two recent papers4,5 have treated the case of a two-layered reservoir with vertical communication or crossflow, between layers. Russell and Prats4 find that, after a relatively short time, the two-layered reservoir with crossflow exhibits a simple exponential pressure decline. From this time forward, the behavior is not distinguishable from the behavior of a homogeneous reservoir having the same steady-state flow capacity. The results of Katz and Tek 5 are equivalent. Russell and Prats4 also speculate that a multi-layered reservoir with crossflow will behave as a homogeneous system after long enough production time "... providing the contrast in kh between layers is not too great". They also suggest that, at intermediate times, "... the relative positions of the layers with respect to each other will have a great influence on the production behavior and on the time at which the previously mentioned large-time approximation might be valid". Katz and Tek5 remark upon the mathematical difficulty of treating a reservoir having many layers or strata. If relative position of the layers is also

By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer's knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer's attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer' for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR'S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR'S have been quite high for the last several years of reported history.

Jan 1, 1952

By Nicholas J. Grant, Robert H. Kane, Bill C. Geissen

The platinum-rich section of the Ta-Pt Phase diagram was worked out by metallographic and X-ray techniques, using twenty alloys; solidus temperatures and solid solubilities were determined. Besides s phase, four intermediate stoi-chiometric phases were found: TaPt (high-temperatzrre phase, structure unknown); TaPt2 (ortho-rhomhic, new type); a TaPt3 (orthorhombic, TiCu3 type); ß TaPf3 (monoclinic, new type). TaPt2 and TaPt3 melt congmentlv; two eutectic, two beritec-tic, and one eutectoid reactions occur in the inuestigated range. THE Ta-Pt system was examined as part of a study of the phase diagrams and the intermediate phases of niobium and tantalum with Group VIII transition metals. Since the main scope of this work was the relation among the ordered close-packed phases occurring in the concentration range from AB to AB3 (A = Nb, Ta; B = Pd, Pt, and so forth), only the platinum-rich side of the diagram was worked out thoroughly, while spot checks were made to determine the approximate outline of the tantalum-rich portion. The system has not been thoroughly treated in the literature; Greenfield and Beck1 in their survey of refractory metal intermediate phases found a o phase between -18 and 37 at. pct Pt which coexists at higher platinum concentrations with an unidentified intermediate phase. Browning2 worked on the range between 55 and 100 at. pct Pt; however, this preliminary study did not cover temperatures >1500°C, and included no conclusive crystallo-graphic data. More recently, a study of the platinum-rich section of the Ta-Pt system has been carried out by Ray,3 while Hartley, Parsons, and steedly4 have studied the tantalum-rich section. The crystal structures of TaPt2, a TaPt3, ß TaPt3, and others have been reported in abstracted form by Giessen and Grant.5 EXPERIMENTAL METHODS The methods of alloy preparation and processing and of the metallographic and X-ray procedures follow very closely those described by Ritter, Giessen, and rant' for other refractory metal-noble metal systems, and will not be repeated except where significant differences exist. Starting materials were: tantalum rod of 99.95 pct purity, supplied by National Research Corp., and platinum sponge 99.9 pct, supplied by The International Nickel Co. An oxygen analysis of the tantalum rod showed 30 ppm O; other impurities were C, N, Si, Nb, Mo, none of these exceeding 50 ppm, and 100 ppm W. Homogeneous buttons were readily prepared as follows: ingots of 5 g were weighed and arc-melted under welding grade argon, followed by two remelts after inverting the button. Between 40 and 100 at. pct Pt, weight losses during the first melt rarely exceeded 0.1 pct, in which case the alloy was rejected, and were nil on subsequent remelts. Since the vapor pressure of platinum far exceeds that of tantalum, the small evaporation loss could be assumed to consist of platinum; therefore, a corresponding amount of platinum was added on the second melt. Since it was confirmed on pure tantalum samples that no weight gain through oxygen or impurity pickup occurs (see Ref. 71, it could be assumed that the uncertainty in the composition did not exceed ±0.1 at. pct for the range 40 to 100 at. pct Pt. For the four control melts from 0 to 40 at. pct Pt, an error of ±0.5 at. pct was calculated. Microscopic examination of the whole buttons after melting showed no inhomogeneity other than local coring. This was eliminated by a homogenization heat treatment. A total of twenty-three alloys were prepared. Heat treatments were carried out in a tantalum

Jan 1, 1965

By N. H. Harrison, J. K. Rodgers, S. Regier

This paper presents comparisons of data obtained from a laboratory reservoir study and from a calculated behavior prediction with the actual production history of a condensate reservoir. A small non-commercial discovery was depleted under closely controlled conditions and the well fluids were sampled at frequent intervals. Data on the reservoir and production variables were accumulated on a fixed schedule. A laboratory reservoir study war made using the initial well fluid samples as charging stock. The production procedures and operating conditions were held constant throughout the study wherever possible and in general paralleled the field work. The well fluid compositions and the cumulative recoveries ar a function of the reservoir pressure were also calculated using conventional flash vaporization procedures and equilibrium constants. Comparisons based on the composition of the well fluid show good agreement, the laboratory study agreeing within experimental accuracy with the field work and the calculated data comparing equally well. The gas-oil ratios are also in good agreement, but with somewhat greater deviations at the higher pressures. In the overall picture, it is believed that a model st,~tiy can predict within experimental accuracy the production history of a condensate reservoir. Better equilibrium constants for the heavier hydrocarbons are needed in order to attain improved composition accuracy by calculation. INTRODUCTION In Aug., 1955, a gas condensate well was completed in San Juan County, Utah, that was initially thought capable of good commercial production. These conclusions were derived principally from core data and electric logs, which indicated good permeability, porosity and gas content. However, after the usual series of potential tests it was found that the reservoir pressure had declined some 22 per cent, and it was obvious that the zone tapped was but a small pocket or trap. It became apparent that, with a controlled depletion of a small reservoir, a unique opportunity was available to compare laboratory and calculated studies with an actual field depletion and to further the present knowledge of condensate reservoirs. FIELD WORK The Coalbed Canyon Well No. 1 was conventionally completed in the Paradox limestone formation to a total depth of 5,912 ft. The producing zone from 5,762 to 5,806 ft was perforated with four jet shots per ft. The wellhead and field equipment were also conventional, the major items consisting of a two-pass indirect fired line heater, a high- and a low-pressure separator with the necessary controls and accessories, gas meters, back-pressure regulators, flare stacks and condensate stock tanks. The initial testing of this well con-sisted of a series of flow potential and pressure build-up tests during which some 30 MMcf of gas was produced. The reservoir pressure declined from an estimated 2,300 to 1,782 psig during this period, from which it was concluded that the reservoir was very small. In order to approach steady-state conditions in the reservoir and so provide optimum conditions for making comparisons, the field depletion was programmed to approach, if possible, constant production conditions. Bi-hourly readings were taken of the tubing pressure, the pressure and temperature of the separators, oil and gas rates, and other pertinent operating data. The gas rate, as indicated by the orifice meter, was held constant by the adjustment of the choke in the line heater. The temperature of the first stage separator was held constant by adjustment of the line heater jacket temperature. Practical considerations of production made the maintenance oi a constant gas rate impossible. The test started with a gas rate of 4 MMcf/D and a separator pressure of 250 psig. This rate was maintained until the choke was fully opened. The gas rate then declined with the falling tubing pressure and production was continued until the rate was about 2

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By V. M. Dobrynin

Experimental data demonstrate that physical properties of porous rocks change under pressure. In this paper an assumption is made and proved that under pressure the changes of physical properties such as porosity, density, permeability, resistivity and velocity of elastic waves are controlled to a large extent by the pore compressibility of rocks. It is also shown that the pore compressibility of rocks can be determined, within the range of pressures from 0 to 20,000 psi, by knowing the maximum pore compressibility and the magnitude of the pressure. Mathematical equations were developed which permit one to define changes in physical properties of porous rocks under pressure. These equations were verified by experimental data obtained from the study of sandstones. INTRODUCTION In studying the behavior of porous rocks under pressure in the field of petroleum technology, the most interesting aspect is the observation of those properties which characterize the rocks as possible reservoirs — for example, porosity, permeability, resistivity, density and the velocity of elastic waves. The literature dealing with this problem mainly contains data concerning the study of only one or at most two of these parameters, but not of the group as a whole. An attempt is made in this paper to find general equations involving each of these parameters, which will permit the study of the behavior of rocks under pressure. All experimental data used here were obtained from the investigation of consolidated sandstones. EXPERIMENTAL In addition to the use of published experimental data, an experiment was carried out which studied the main physical properties of sandstones under pressure. Two homogeneous quartz sandstones were chosen for this purpose: (1) the Torpedo sandstone from Kansas, and (2) the Medina sandstone from Ohio. The porosity of the Torpedo sandstone was 20.2 per cent, and that of the Medina 8.7 per cent. Permeabilities were 45 md and less than 1 md, respectively. Each sandstone contained about 5 per cent clay minerals, consisting mostly of kaolinite and chlorite, which were distributed quite evenly throughout the samples. One cylindrical sample 2 in. in diameter and 5 in. in length was cut from each sandstone and then saturated in a vacuum with a 3N solution of NaC1. This high concentration was used in order to obtain true formation factors and to decrease the swelling of the clay minerals. The methods of mounting the samples and measuring the changes in porosity and resistivity were practically the same as those described by Fatt and Mann.1,2 Changes of resistivity under pressure were studied for sandstones with 100 per cent water saturation, and for sandstones with the irreducible water saturation. The irreducible saturation was obtained by enclosing the saturated rock samples in relatively fine silicate powder so as to remove the water by capillary action. This procedure is described by Orkin and Kuchinski.3 Changes of permeability with pressure were determined at room temperature using nitrogen as the flowing medium. In studying the effects of pressure, one series of measurements was made using an internal pore pressure Pi equal to the atmospheric pressure, while the overburden pressure Pe ranged from 0 to 20,000 psi. A second series of measurements was used over the same range of overburden pressure, but with an internal pore pressure of 1,800 psi. When the results were compared on the basis of net overburden pressure (Pe — 0.85 Pi ), there was practically no difference for these two sandstones. The origin of the factor 0.85 in the expression for net overburden pressure is given by Brandt,4 Fatt5 and Geertsma.6 The relatively large bulk volumes of the sample (about 15 cu in.) made it possible to observe a

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by

By B. L. Averbach, M. Cohen, C. H. Shih

The isothermal formation of martensite is studied in Fe-Ni-Mn and Fe-Mn-C alloys under conditions where the athermal transformation is completely avoided, there being no martensite present at the beginning of the isothermal reaction. The initial rate of martensite formation is extremely low under these conditions, but it increases greatly as soon as some martensite is formed. It appears that true initial characteristics of the isothermal reaction can be studied only in samples wherein the formation of martensite on cooling is completely eliminated. THE phenomenon of isothermal martensite formation is well established1 -" but the observations have been made in the presence of varying quantities of athermal martensite. Complete avoidance of athermal martensite and the formation of martensite under pure isothermal conditions have been reported by Kurdjumov and Maksimova2 in an Fe-Ni-Mn alloy (23 pct Ni, 3.4 pct Mn, and the balance Fe) and have been confirmed by recent experiments of Cech and Hollomon in a similar alloy. In each case, the isothermal transformation rate was a maximum at the beginning of the transformation and decreased as the reaction proceeded. These initial transformation rates were used by Fisher7 for the confirmation of calculated nucleation rates based on classical nucleation theory extended to include the effect of elastic strain energy. Cech and Hollomon have admitted, however, that up to 3 pct martensite formed on cooling in their samples and thus was present at the initiation of their isothermal runs. In this paper, experiments on similar alloys are described, except that care was taken to remove the incidental martensite developed at the surface prior to the isothermal reaction. It is shown here that the reaction rate at the beginning of the strictly isothermal reaction is very low. As soon as some detectable amount of martensite is produced, the transformation rate increases rapidly but ultimately decreases as the reaction proceeds. When martensite is allowed to form isothermally in the presence of about 2 pct of prior martensite, the apparent initial reaction rate is a maximum and corresponds to the observations of Kurdjumov and Maksimova and Cech and Hollomon. It is evident that the cooperative nature of the martensitic reaction results in a significant stimulating or autocatalytic effect on the isothermal reaction rate. Experimental Procedure The chemical compositions of the alloys used in this investigation are listed in Table I. The Fe-Ni-Mn alloys A and B were melted in an induction furnace, cast into ingots 2 in. diam by 4 in. long, and forged into % in. diam rods. The manganese steel (alloy C) was melted in an arc furnace and cast into ceramic molds 1/4 in. diam by 5 in. long. The rods were sealed in evacuated Vycor tubes and homogenized at 1175" to 1200°C for 50 hr. The long homogenization resulted in some manganese loss from the surface, producing a thin layer of transformed material. This surface layer was removed by grinding and the specimens were then swaged to 0.050 in. diam wire. Measurements of electrical resistance were made with a Kelvin double bridge to follow the course of the martensitic transformation. A small permanent magnet was also useful in scanning an entire specimen for small localized quantities of martensite. This test is almost as sensitive as the electrical resistance method in detecting the presence of martensite (which is ferromagnetic in these alloys) and it was especially useful in deciding whether a specimen was completely free of martensite. The wire specimens (0.050 in. diam by 2.5 in. long) were sealed in evacuated tubes and austenitized for 5 min at 1150°C. The specimens were quenched into water and, unless otherwise stated, stress-relieved for 1 hr at 650 °C in order to induce greater uniformity in the subsequent martensitic transformation. As dem-

Jan 1, 1956

By V. Kondic, W. M. Rumball

HUNT and Jackson' have recently suggested that binary eutectics might be classified according to the entropy of fusion of the component phases. Such a classification was in fact proposed2 some time ago by the authors and the purpose of this communication is to present some supporting evidence. As pointed out by Hunt and Jackson' typical metals of low entropy of fusion, ?S, tend to form normal eutectics (using Scheil's terminology3). Where one phase is metallic (low ?S) and the other nonmetallic (high AS) then anomalous structures are formed. These anomalous structures may either be regular (e.g., Bi-Sn)or irregular (e.g., A1-Si). Finally Hunt and Jackson suggest that where both phases are of high ?S regular faceted structures are formed. In the proposed classification2 the ratio of the entropies of fusion is taken as the quantitative parameter, i.e., ?Sa/?SB = E, where e > 1.0. An extensive literature survey has been carried out2,4 for reliable photomicrographs of eutectic structures. The structures, numbering 151, have been classified into two classes, viz., normal (i.e., lamellar and rodlike) and anomalous. The latter group has been arbitrarily subdivided into regular and irregular anomalous eutectics. Details and sources of the structures are given elsewhere.2,4 In the absence of better thermodynamic data the value of E has been determined for each of the systems making the following assumptions and approximations: l) The entropy of fusion of solid solutions may be calculated additively;5 ii) Inter metallic compounds are treated similarly but with the addition of the following term for fully ordered structures.5 -4.573(Ni lOg10 Nl + N2 log10 N2) where Nl and N2 are the atomic fractions. It might be argued that the entropies of fusion are meaningless as the eutectic phases form at some temperature (T,°K) below their true melting point (Ta or Tb). As AS, = Lo/To if La the latent heat of fusion of a, is assumed independent of temperature, the actual entropy change AS& is given by La/Te. The ratio of entropies of fusion then becomes Fig. 1 shows E' plotted against cumulative totals for normal and anomalous systems from which it is seen that normal eutectics predominate at low values of E'; e.g., some 90 pct of normal systems lie below E' = 1.5 with 65 pct of anomalous systems above this value. Fig. 1 also shows that the regular anomalous structures occur mostly at low values of c' possibly suggesting growth more akin to normal than anomalous growth. The choice of c as a classification parameter was based on nucleation concepts, it being observed that metals widely separated in Sundquist and Mondolfo's8 nucleation series were anomalous and those close together normal. The basis of these classification views is really outside the intended scope of this communication but it is hoped to explain them fully in the near future.7 Having arrived at this entropy of fusion classification by nucleation considerations it is interesting to note that Hunt and Jackson's ideas are based on growth considerations. Elsewhere one of the authors4 has shown that an even better classification of the metallographic structures reviewed is obtained from purely conventional heterogeneous nucleation concepts. It has been found that systems having a value of the parameter +b less than 0.28 are almost certainly normal and above this anomalous: V, is the gram atomic volume. This parameter is nevertheless closely related to c and c', these being an approximation of p. The parameter is also related to the other classification3,8,9 which have met with any success in the past. All these classifications are to be reviewed shortly by the authorsU7 A significant thing about the classifications based on

Jan 1, 1968

By S. R. Maloof, W. R. Mitchell, J. A. Mullendore

Preliminary experimental evidence is presented to show that the metallic impurities aluminum, iron, and silicon, and beryllium oxide as found in commercially pure hot-pressed beryllium powder can be reduced to lower Concentrations by Zone -Purification techniques. The reduction in the concentration of aluminum to extremely low levels (10 PPm) is noteworthy, since earlier work demonstrated that aluminum is a major factor contributing to the hot-tearing of beryllium during fusion welding. On the basis of present findings, a method is suggested for producing beryllium metal of improved weldability. EXPERIMENTAL research now being conducted on the purification of beryllium indicates that several of the metallic impurities and beryllium oxide can be reduced to lower concentrations by employing standard horizontal zone-refining techniques. For the preliminary work, commercially-pure hot-pressed beryllium having a purity of 97.84 pct was used. The chemical composition is given in Table I. The hot-pressed beryllium was machined into bars 5/8 by 5/8 by 4 to 6 in. in length. Beryllium-oxide boats which had been conditioned by prior heating in a vacuum of 10"5 mm of Hg at 1100°C for 3 hr were used to hold the beryllium while it was zone melted. The boat with its charge, along with a smaller beryllium-oxide boat containing scrap beryllium to be used for gettering purposes, was loaded into a quartz tube and evacuated to 10-6 mm of Hg. Alter alternately evacuating and flushing three times with purified argon, the furnace tube was backfilled to a pressure of 1/6 atm of A and sealed off by means of a vacuum-tight stopcock. It was then removed from the pumping equipment and mounted on the traveling carriage of the zone-refining apparatus. Heating was accomplished with a 10 kw 450 kc induc- tion heating unit using an induction coil consisting of two turns of 3/16-in. diam copper tubing. Before starting to zone melt, the atmosphere in the furnace tube was gettered by heating the scrap beryllium in the smaller boat to above its melting point and holding at temperature for several minutes. The carriage was then shifted so as to locate one end of the beryllium ingot in the large boat within the induction coil. A molten zone approximately 3/4 to 1 in. was established by loading directly into the ingot. The molten zone was moved very slowly along the length of the ingot. Before each pass was made the procedure for evacuating, flushing, and backfilling, and so forth was repeatedI' Speeds of 1 1/2 and 3 in- per hr were used with up to twelve zone passes. The appearance of a typical zone-refined ingot is shown in Fig. 1. After zone refining, the grains in the ingot appear to be elongated in the direction of zone travel, whilst before, they are essentially equi-axed. A microexamination revealed the presence of a network in the beryllium grains as seen in Fig. 2. Laue spots in back reflection pictures taken of the sample were not sharp, indicating the presence of subgrains in the structure. As can be seen, however, many of the network boundaries cross beryllium grain boundaries. It has been shown by Martin and Moore1 that beryllium solidifies as a bcc structure which then transforms to the hexagonal structure at about 1250oC.It is believed that the observed network is merely the outline of the bcc structure which formed from the melt and are not subgrain boundaries. In order to eliminate surface contaminants, approximately 1/16 of an inch of material was removed from the outer skin of each ingot after zone refining.

Jan 1, 1962

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By R. I. Jaffee, C. M. Craighead, G. A. Lenning

THERE has been considerable discussion among A metallurgists and others interested in the development of titanium alloys as to the nature of the fine line markings which appear in the microstruc-tures of unalloyed titanium and a titanium alloys. These markings have been variously called x phase, etching pits, and twins. Figs. 1 to 3 show typical examples of the line markings as they appear, respectively, in high purity iodide titanium, commercial purity titanium rod, and a high purity a alloy containing 0.2 pct N. The commercial purity titanium sample, shown in Fig. 2, contains both line markings and some spheroidal retained-ß phase. The ß phase seen in this micrograph should not be confused with the line marking, since it originates from the iron present as an impurity in the sponge metal. It will be noted that the line markings seem to have a definite orientation pattern with respect to the grains and in titanium noticeably resemble the precipitation occurring in artificially aged high purity Al-Cu alloys. This similarity led to the hypothesis that the line markings observed in titanium and a titanium alloys resulted from precipitation of some unknown phase. With the work of Hägg1 and McQuillan2 as background, there was little reason to suspect hydrogen of being responsible for the line markings. Hagg reported that up to 33 atomic pct H was soluble in a titanium, and McQuillan reported an a solubility of up to 8 atomic pct. Furthermore, McQuillan examined metallographically a 5.1 atomic pct H alloy quenched from 300°C and stated that the structure appeared to be a single-phase a solid solution. Line markings have been observed frequently and were first noted by Jaffee and Campbell3 in 1949. They did not observe them in vacuum-annealed titanium and a Ti-O and Ti-N alloys, but did observe them in Ti-H alloys containing 0.25, 0.5, and 1 atomic pct H. They stated that it was doubtful that the markings were a second phase based on hydrogen, because 1 atomic pct was far from the accepted solid solubility of hydrogen in titanium. Finlay, Resketo, and Vordahl,4 in 1950, concluded that the markings were a true second phase as a result of observations on their etching characteristics. Anderson5 Commenting on these markings in titanium was inclined to associate them with hydrogen, but was loath to call them titanium hydride, because of the reported high solubility of hydrogen. Work at Battelle Memorial Institute for the Navy Bureau of Aeronautics," done concurrently with the work described in this paper, provided information on the experiment converse to that described by Jaffee and Campbell in 1949. This work showed that the amount of line markings in unalloyed titanium could be decreased by vacuum annealing at elevated temperature. It was suggested that this was the result of removal of hydrogen; previously, the data of Jaffee and Campbell9 howed that the markings appeared when hydrogen was added. Recent work at Battelle for the Ordnance Corps, Department of the Army, which is described here, now establishes the identity of the markings as a titanium hydride phase. A sample of high-purity titanium rod 1/4 in. diam, 0.009±0.001 wt pct H (0.43 atomic pct), Fig. 1, was resistance heated in a 0.05 micron vacuum for 41/2 hr at 1500°C. During the early states of heating, the pressure increased to 150 microns, indicating that gases were being evolved. After cooling in vacuum, the iodide titanium rod was analyzed for hydrogen. Vacuum-fusion analysis showed 0.0006 ±0.0003 wt pct H (0.03 atomic pct) to be present.* Metallographic examination of the vacuum-annealed rod showed only a transformed ß structure. There was no evidence of fine line markings, Fig. 4. A section of this vacuum-annealed rod was cold rolled to 0.040 in. thick sheet and annealed for 1 hr

Jan 1, 1953

By R. A. Graham, R. W. Rohde, J. R. Holland

In a shock wave compression study of a martensitic Fe-30 pct Ni alloy, Graham, Anderson, and Holland' found a region of unusual compressibility extending from a few kilobars up to about 20 kbars. This region was characterized by a continuously decreasing shock wave velocity with increasing stress. In this note, we report the results of a study initiated to determine the source of this unusual compressibility. In earlier shock-loading experiments on martensitic Fe-30 pct Ni, Loree et a1.' determined that a phase change occurred at about 80 kbars. Subsequently, Bowden and elly found that samples of a similar material shock-loaded at about 100 kbars experienced a martensite-to-austenite transition. Their crystal-lographic analysis showed the transition was a direct reversal of the established martensite system to the austenite phase. The shock loading in the present experiments was accomplished by precisely controlled plane impact between two discs of the sample material. This configuration created a state of uniaxial strain in the two the front of a projectile which was accelerated to various velocities. Planarity between the impacting discs was controlled to 5 x 10-4 rad, and impact velocities were measured to 0.5 pct. From a knowledge of the Hugoniot relationships of the material and the impact velocity, the shock-wave stress can be calculated. Samples were shocked at 18, 50, 70, and 100 kbars. The specimen discs shocked at 18 and 50 kbars were instrumented with quartz gages to observe the stress time profile. A more detailed description of the experiment has been given previously.4 The shock-loaded specimens were recovered intact by decelerating them in a catcher filled with soft wood. Discs of Fe-30 pct Ni nominally 12.7 mm thick and 64 mm in diam were cut from bar stock. Chemical analysis of the material provided the following composition in weight percents: 29.5 Ni, 0.50 Mn, 0.21 Si, and 0.10 C, with traces of Cr, Cu, Mo, Al, and Co. The discs were austenitized at 650° C for 2 hr at a pressure of less than l0-' torr, and furnace-cooled. Martensite was then produced by quenching the discs at -196" and holding 168 hr. The initial martensitic structure formed is shown in Fig. l(a). Typical microstructures of samples shock-loaded at 18 and 100 kbars are shown in Figs. l(b) and l(c). The banded structure with the austenite regions running parallel to the shock propagation direction was characteristic of samples shock-loaded at all stresses. No such banding was found in samples that were not shock-loaded. Comparison of Figs. l(b) and l(c) shows that, although under the optical microscope the two microstructures are quite similar, the martensite plates of the specimen shocked at 100 kbars etched in a distinctly different manner. This unique etching behavior of martensite in samples shock-loaded above the 80 kbar transition point has also been observed by Leslie el al.' These investigators determined from X-ray and electron microscope studies that fcc martensite, similar in appearance to normal bcc martensite, had been formed under shock loading. A quantitative determination of the amount of austenite present after shock loading was made by X-ray techniques. Both the methods of Lindren' and Miller' were utilized. The results are shown in Table I. The error limits are those experimentally observed from two independent analyses of each sample and represent the precision of the experiment. The absolute error, which should be similar for each sample, is believed to be about 10 pct. It is seen that as the shock stress increases the amount of austenite present also increases. On the basis of the X-ray and microscopic observations, we conclude that shock loading below the 80 kbar ersal will initiate a martensitic reversal: the amount of reversal that occurs increases with in-

Jan 1, 1969

By H. A. Fisch, A. J. Opinsky, J. L. Bartos

Fort?-six- two-grain bounduries were studied in doped tungsten 1amp wire that had been heated to 3450°K very vapidly. Back-reflection Laue photograms were taken of the grain boundary partners and solved, using a computer. The resulting distribution of large-grain orientations was analyzed. Rotational axes were calculatedfor each grain boundary pair. The axes of least rotation show an anisotropy of rolalional angle. WhILE the orientations of large grains in straight doped tungsten wire have been studied extensively, little has been done to characterize the boundary that separates them. Rosi.1 upon seeing the jagged interlocking boundary in doped tungsten wire. inferred that the grains should have a preferred orientation, and proved it. He interprets his data as indicative of a single ideal orientation—(531)— being parallel to the wire axis. Rieck2, 3 and Mannerkoski' have essentially confirmed this finding. Opinsky, Orehotsky, and Siegle argue that the data suggest that (211)—a plane-is parallel to the wire axis instead. This (211 ) contains the (531). and hence would appear to be a more general case.5 Ahlborn and wasserman6 report that their orientation data stretch from (110) through (531) to (311). This path is the locus of {211 Recently. Opinsky has suggested that the data can be interpreted as a series of ideal orientations that can be related by coincidence relationships to the (110) fiber texture. All these investigators have determined the orientations of the large grains by the back-reflection Laue technique, and they have all obtained similar results. Only Rieck5 as methodically looked at the large grains along a wire. He was apparently not concerned with the relationships of the large grains across their common boundary, but only with their individual orientations. This research was undertaken to fill this gap in the under standing of the mechanical properties of tungsten wire. Only the crystallographic aspects of the problem will be reported here. In addition, the large number of large-grain orientations, which was accumulated in this study. will also be analyzed. EXPERIMENTAL MATERIAL AND TECHNIQUES All of the data were obtained from four pieces of the same 7-mil-diam General Electric tungsten lamp wire. Twelve-inch lengths of the cleaned wire were heated in vacuum by the flick of a switch to 90 pct of the amperes necessary for fusion (a temperature of approximately 3450°K) and held for 1 min. On the basis of other data. it is estimated that the rise time is of the order of 0.5 sec. The four pieces of wire could have come from anywhere within about 18 ft of wire. Consecutive segments of each piece of wire were mounted in bakelite and polished metallographically The polishing procedure followed that described by woods. "nly boundaries between two grains that each occupied the entire cross section of the wire were photographed and X-rayed. The metallographic sample was mounted accurately with respect to the X-ray unit. Steps were taken to read the films as accurately as possible with the conventional Greninger net. The data were then entered into computer programs that solve the Laue film by precisely the same techniques that are used in the solution of the film by means of the stereographic projection. The use of the computer has probably shifted the main source of error from the stereographic plot to the reading of the film. On the basis of several experiments, it is thought that the error associated with the entire process, from mounting the sample through the computer solution, is of the order of about one-half degree. The output of the computer is the direction cosines of the fiducial direction (the wire axis) and the locations of the three cube axes. The former data were used to calculate the differences in orientation between the two grain boundary partners, and the latter were used in the calculation of the rotational axes that could bring the two grains

Jan 1, 1970

By N. Jaffee, J. E. Dorn

An activation energy of 27,400 5 1000 cal per mole was obtained for the creep of poly crystaLline aluminum over the temperature range of 273° to 350°K, at strains varying from 0.003 to 0.230. Stresses varied fronz 2250 to 6000 psi, strain rates from 0.1145 x 10-5 to 29.5 x 10~s min.-1. A strain temperature-compensated time correlatzon was oblained indicating that the structure was depedent solely upon the strain at a given stress; X-ray diffraction analyses and tensile tests on precrept specimens verified this. PREVIOUS investigations1 have revealed that the apparent activation energies for creep of high-purity polycrystalline aluminum are insensitive to the applied stress, strain, and strain rate. On the other hand, the apparent activation energy is dependent on the temperature1,2 as shown by the data reproduced in Fig. 1. Each plateau of this curve is associated with a unique rate-controlling dislocation mechanism for thermally activated creep. It is now very well-established that over the high-temperature range, where the activation energy is about 35,500 cal per mole, the creep rate is controlled by the dislocation climb mechanism. 3 Over the intermediate range of temperatures, from about 260° to 370°K, another unique activation energy, namely 28,000 cal per mole, is obtained. Current evidence strongly supports the contention that cross slip is the rate controlling mechanism for creep in this case: 1) Crystal recovery can occur by a number of mechanisms prominent among which are climb and cross slip. Astrom,4 using the Borelius micro-calorimeter, reported rapid crystal recovery of cold-worked polycrystalline A1 at 340° to 370°K giving an activation energy of 28,000 cal per mole and additional recovery at 455° to 478°K giving an activation energy of 3 6,000 cal per mole. Whereas the latter recovery process was clearly associated with the dislocation climb mechanism, the former, 28,000 cal per mole process could have arisen as a result of the cross-slip mechanism. 2) Single crystals of high-purity A1 favorably oriented for octahedral glide exhibit an activation energy for creep of about 3400 cal per mole over the range from 0° to 400°K and that of about 28,O:O cal per mole over the range from 600° to 775°K . Whereas the lower activation energy process is accompanied by the development of sharp slip-band traces, the 28,000 cal per mole process was uniquely characterized by extensive cross slip. 3) Theoretical calculations by Seeger and schoeck6 suggest an apparent activation energy for cross slip in A1 of about 24,000 cal per mole and another theoretical estimate by Friedel 7 gives the observed 28,000 cal per mole as the theoretical activation energy. It is therefore consistent with this evidence to, at least tentatively, ascribe the 28,000 cal per mole creep process in A1 to the operation of cross slip as the rate controlling mechanism. Although creep has been rather well-explored in the dislocation climb range, very little, excepting perhaps the activation energy, is known about creep in the cross slip range. This investigation was undertaken, therefore, to reconfirm the activation energy for creep in polycrystalline A1 in the intermediate temperature range and to study the strain-time relationship for creep at a constant stress in the cross slip region. EXPERIMENTAL PROCEDURE AND TECHNIQUE The three types of high-purity A1 alloy specimens described in Table I were used in this investigation. Specimens were milled from 0.100 in. thick cold-rolled sheets with their tensile axes in the rolling direction following which they were given a recrys-tallization and grain growth heat treatment at temperatures well above those which were subsequently employed in the creep tests.

Jan 1, 1962

By F. D. Patchen

Changes in the properties of partland cement upon the addition of fine-ground silica are discussed. Data were collected from formulations cured for periods up to 60 days at temperatures varying from 180" to 350°F. Compressive strengths, permeabilities and thickening times are compared. It is demonstrated that addition of find-ground silica in proper proportion results in a hydrated cement with superior properties above 230°F; i.e., early compressive strengths are higher and increase with additional curing, permeabilities are significantly lnrver and thickening times are increased. X-ray analysis of hydrated cement samples have been used to determine more fully the complex chemistry of these systems. Dicalcium silicate alpha-hydrate was found in all neat cements cured above 260°F. A 10 weight per cent silica addition produced a maximum amount of this phase. Xonotlite and tobermorite have been identified as hydration products at 320°F in systems containing 35 or more weight per cent silica. Formation of these components appears to be primarily responsible for the gain in strength and reduction of permeability observed after the addition of silica. INTRODUCTION For several years it has been recognized that loss of compressive strength occurs when portland cement is cured at a temperature above 250°F. This phenomenon has been called "strength retrogression". More recently it has been recognized that increased permeability usually is associated with decreased compressive strength at these temperatures. At curing temperatures above 300°F, these factors reach serious proportions. A compressive strength loss of 50 per cent between curing times of 24 hours and 14 days has been reported,' and permeabilities as high as 10 md have been measured in neat cements cured at 320°F for seven days.' Earlier investigators,' although unsuccessful in eliminating strength retrogression, stated ". . . .it appears possible that by the proper selection of additives for cement, strength loss with age at high temperatures can be either eliminated or considerably lessened". One solution suggested was the use of a pozzolanic material, hydrated lime, and a retarder. Menze15 in 1934 discovered that portland cement containing finely divided silica possessed high compressive strengths when the curing temperature was 350°F. The use of such a composition is now an established practice in the manufacture of steam-cured cement blocks. It is reasonable to assume that the same beneficial effect can be used advantageously in high-temperature oilwell cementing operations. Ludwig first mentioned the use of sand for this purpose. Later, a portland cement containing moderate additions of silica flour and retarded with CMHEC, a cellulose derivative. was recommended for high-temperature application." These formulations have been successfully employed in the field."'" This paper presents the results of a research program to test the efficacy of finely ground silica in increasing the compressive strength and reducing the permeability of oilwell cement compositions containing portland cement. Included also are X-ray diffraction patterns of powdered samples which have been used to determine some of the important chemical reactions occurring in these systems. LABORATORY PROCEDURES AND MATERIALS All compressive-strength test specimens were prepared and cured from a slurry in accordance with API RP 10B, with two modifications. A final curing pressure of 5,000 psi was maintained for a one- or three-day period; but, for further curing, pressures were reduced to the vapor pressure of water at the curing temperature. Also, the water content was varied in samples containing silica to maintain the slurry viscosity within a range of 5 to 15 poise as measured on a consistometer. Test specimens at 180°T were cured in a water bath at atmospheric pressure. At higher temperatures the specimens were cured in a steam-jacketed high-pressure curing vessel at 5,000 psi for a one- or three-day period. cubes cured for longer periods were removed from the pressure-curing vessel after 24 hours, sealed in small bombs containing water and placed in an aging oven.

By C. R. Simcoe, T. J. Koppenaal

The effect of direct and alternating currents on the quench aging behavior in an Al-4 pct Cu alloy has been investigated by use of resistivity measurements. The reaction rate increases with direct current density in the investigated range of 1000 to 3000 amps per sq cm. Alternating current of a specific frequency is observed to decrease the reaction rate by a factor of about two. ErDMANN-JESNITZER et al.,1,2 investigated the effect of direct and alternating current on the quench and strain aging behavior of low-carbon iron. In both cases they observed that direct current accelerates the aging reaction and that an alternating current can completely inhibit the aging process. The purpose of the present research was to investigate these phenomena in the quench aging behavior of an Al-4 pct Cu alloy and to determine the correlation, if any, between the increase in the observed reaction rate and possible heating effects accompanying the aging with direct current. EXPERIMENTAL PROCEDURE The aluminum-base alloy used in this investigation contained 3.98 wt pct Cu (1.72 at. pct) with impurities of 0.003 pct Si, 0.002 pct Fe, and 0.001 pct Mg. The alloy was rolled into a ribbon about 0.36 mm thick and 3.7 mm wide. The ribbon was split end from end with the ends being used as electrical contacts and the central unsplit section, about 5.3 cm in length, serving as the specimen. Solution treatment was accomplished by quenching from a salt bath at 520° ± 2°C into water at 25° ±0.5°C; the specimen was immediately transferred to a liquid nitrogen bath. All aging was done at 75° ± 0.2°C in a rapidly stirred ethylene glycol bath. Resistivity measurements were made by the double potentio-metric method employing a standard resistor; for purposes of convenience, the resistance measurements were made at 77°K. The transfer of the specimen from the aging bath to a liquid nitrogen dewar was accomplished in less than 1 sec. The aging kinteics were studied with the specimen being aged under the influence of direct current, alternating current, and without any type of current. The amount of heating caused by direct currents was investigated by soldering a thermocouple on the specimen surface and measuring the temperature change after applying various current densities. The temperature was observed to increase (from 75°C, the aging temperature) about 0.8°, 3.0°, and 8.5°C with direct currents of 1000, 2000, and 3000 amp per sq cm, respectively. When employing alternating current, the circuit was monitored with an oscilloscope and adjustments made to produce a normal sine-wave pattern. RESULTS Prior investigations3'4 in the aging characteristics of A1-4 wt pct Cu have shown that the resistivity initially increases, reaches a maximum, and then decreases to values significantly lower than the as-quenched resistivity. This type of behavior is seen in Fig. 1 which shows the resistivity at 77°K as a function of aging time at 75°C observed in this investigation. At this aging temperature, the resistivity maximum is seen to occur in about 1 to 1-1/2 min and it further decreases to the as-quenched value in about 24 min. The behavior observed with the application of direct currents of 1000, 2000, and 3000 amp per sq cm during aging is shown in Fig. 2. With increasing current densities, (+) ?pmax decreases and the rate of the aging process increases. The time necessary to reach the as-quenched resistivity value decreases from 24 min for aging without current to about 16, 10, and 7 min for aging with 1000, 2000, and 3000 amp per sq cm direct current, respectively. Fig. 3 shows the results obtained when two changes were made during the aging with 2000 amp per sq cm

Jan 1, 1963