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By Herbert E. Hawkes

“For his Pioneering leadership in the science and technology of mineral exploration, especially in the development and world-wide application of geochemical methods as major exploration tools, and for his lecture ‘Geothermal Hydrogen’.”

Jan 1, 1981

By E. A. Cisney

The formula for calculating the crystallographic angles of a tetragonal lattice is: C°S =where $ is the angle between planes (HKL) and (hkl). The angles in Table I have been calculated for indium

Jan 1, 1960

By C. C. Templeton, S. S. Rushing

Methods previously developed for the study of air-liquid displacements in microscopic capillaries (inner diameters of 3 to 40 microns) have been used to investigate oil-water displacements in capillaries initially filled with water. Displacement calculations assuming perfect displacement and no capillary pressure hysteresis yielded oil effective viscosities smaller than the macroscopic viscosities. For a given liquid pair, the oil effective viscosity decreased both with decreasing capillary size and with increasing oil-water viscosity ratio. This behavior can be explained by the existence of an annular water film (20 A to 260 A thick) on the capillary wall. When the capillary was first filled with oil, the ratio of the oil effective viscosity to the normal oil vircosity was highest for the first water displacement and decreased with subsequent displacements. Sometimes the oil effective viscosity ratio during the initial water displacement was greater than unity. INTRODUCTION In a previous paper1 a technique was described for studying air-liquid and liquid-liquid displacements in very small capillaries of uniform diameter, in the hope that such microscopic data would further the understanding of the nature of multiphase fluid flow through porous media. That paper contained comprehensive data for air-liquid displacements in Pyrex capillaries, with a few data for oil-water displacements in capillaries initially filled with water. The purpose of this paper is to present more complete results for oil-water displacements in capillaries initially filled with water, and to describe for the first time such observations in capillaries initially filled with oil. In this way the effect of the wetting history of the system upon the displacement process may be studied. METHODS The basic techniques employed were described in the previous paper.1 The measuring procedure and the working equations will be briefly summarized here and a few modilications will be pointed out. For the present study, temperature control within 0.l °C was obtained by placing the microscope and its immediate accessories in a thermostated air bath made of a steel frame covered with plexiglas. The water and oils used in this work were the same as in the previous paper,1 with the addition of "Medium Mineral Oil, U.S.P. supplied by the Harshaw Scientific Co. When the first liquid was introduced into the horizontal capillary, the air-liquid static capillary pressure Poc was measured along the observable length of the capillary. From the relation Poc = 4y cos 0/d, the capillary diameter d could be calculated from Poc if the "microscopic" air-liquid boundary tension, To = y cos On, was taken as equal to its known "macroscopic" value. This calculation involves assuming that cos 6 = 1 and that capillary size or the resulting high interfa-cial curvature has no effect on surface tension, or y cos 6, as was verified by our work, and also by that of Cohan and Meyers on air-liquid-solid systems. For several capillaries these calculated diameter values were compared with values measured visually with a filar micrometer eyepiece. For a given capillary the average values for the two methods agreed within 1 or 2 per cent, but the visual values were less reproducible than the calculated values. Further the calculated values were much less subject to personal bias and took into account any slight ellipticity that might be present. Hence diameters calculated from air-liquid Poc data were used throughout this paper. The second liquid was introduced in such a way that a single spherical interface separated the two liquids. Displacements were always made with a constant pressure, Pt, between the ends of the capillary. The times (t) at which the interface passed certain

Jan 1, 1957

By David Cornell

Back pressure test data on natural gas wells are short time test data of unsteady state nature. Performance curves from which unsteady state effects have been eliminated, called stabilized performance curves, are necessary for understanding the behavior of gas wells and for scheduling gas fields for periods up to 20 years. A calculation procedure has been developed whereby three day, seven day, 30 day, or other duration stabilized performance curves may be calculated from back pressure test data. Such curves are essential for correct gas deliverability calculations and gas field scheduling. I NTRODUCTION The manner in which a back pressure test is made will affect the slope of the back pressure curve because the radius of drainage changes with the length of time that the well is allowed to flow. The reciprocal of the slope of the back pressure curve is defined as n in Equation 1 and varies from 0.5 to 1.0. If the flow is viscous and the radius of drainage constant, n will have a value of 1.0. Because of turbulence in the formation near the wellbore, the pressure drop is usually greater than the viscous flow pressure drop and the exponent n is frequently less than 1.0. In addition, since the radius of drainage moves away from the well-bore during the test, the gas flows a greater and greater distance as the test proceeds, with a resulting increased pressure drop at the high flow rates, and, again, n for the test tends to be less than 1.O. The effect of the changes in the radius of drainage may be calculated and the results used in preparing stabilized performance curves for fixed values of the radius of drainage. Such curves can be made for a defi- nite time period, such as three day, seven day, or 30 day stabilized performance curves. These cukes will show the effect of turbulence near the wellbore and can be used to predict the performance of the gas well at any flow rate or for any production period. In order to discuss the importance of the radius of drainage quantitatively, it should be defined. Muskat" defines the radius of drainage as follows: "... the radius of drainage gives the distance from the well to which the approximately steady state condition has been established ... it being assumed that no gas is removed from any point until the radius of drainage has passed that uoint." An eauivalent definition of the radius of drainage is that radius at which the extrapolated portion of the steady state portion of the pressure gradient gives a pressure equal to the shut-in reservoir pressure. This definition is also implied in the back pressure equation. The radius of drainage is, then, the distance into the reservoir from which the gas appears to originate at any time. It is, however, only a useful concept and does not actually exist. Fig. 1 illustrates the definition of the radius of drainage. At the end of each flow period the radius of drainage may depend on three factors: (1) the duration of each flow period; (2) the rate of gas production; and (3) the rate and duration of the previous flow periods. In general, back pressure tests are conducted with various lengths of production time and at various flow rates. Each individual back pressure test, therefore, requires an individual analysis. The calculations of the change in the radius of drainage have been made, however, for the case of equal flow periods for all four production rates and several sets of increasing flow rates. Fig. 2 illustrates the results of such calculations made by the method of Cornell and Katz2 for the case of 8, = 50,000 and the flow rate increasing in the ratio 1.0:2.0:3.0:4.0 for each flow period. The increase in the radius of drainage during the test is apparent.

Jan 1, 1956

By J. E. Miller, W. E. DeVaney, L. Stroud

During a recent phase study of a natural gas, two stable equilibrium liquid phases were observed at temperatures below —200°F and pressures above 200 psi. This paper reviews the published literature on the occurrence of multiple equilibrium liquid phases and presents analytical data for the vapor and two equilibrium liquid phases of the liquefied natural gas at five experimental conditions. In addition, data for 30 conditions of two-phase equilibria are included. INTRODUCTION The low-temperature phase behavior of gases, most of which contained helium, has been investigated in the laboratories of the Helium Activity for many years. Since 1952, experimental studies of these systems have been continuous as part of the research program at Amarillo, Tex. Because of their value to private industries interested in participating in the Helium Conservation Program, several "Open File" reports containing phase equilibria data for heliurn-bearing natural gases have already been released by the Helium Activity. A paper containing information on the general phase behavior, operating criteria and extensive vapor-liquid data for two helium-containing systems was recently published.2 Additional publications presenting experimental data on the phase relationships of various gas systems are now in process and will be available in the near future. PREVIOUS EXPERIMENTAL WORK Although the formation of multiple liquids has been reported for various systems, to our knowledge this paper is the only substantiated evidence of a vapor-liquid-liquid equilibria in a naturally occurring gas. In 1940, Vink, Ames, and others13 reported the presence of two liquid phases in a hydrocarbon system consisting of mixtures of crude oils, solvents and natural gas. Eilerts and co-workers; published data on the recombined fluids from a gas-condensate well. This condensed gas, containing approximately 76 per cent methane and 24 per cent ethane-plus, exhibited two distinct liquid phases. Weinaug and Bradley 14 observed "unusual" phase behavior in a reservoir mixture. These workers postulated that the anomalous phase behavior was due to the "imminent formation of a second liquid phase". Botkin, Reamer, Sage and Lacey 1 studied two California crude oils that exhibited multiple phases. Kohn and Kuratal0 recently reported two equilibrium liquid phases in the methane-hydrogen sulfide system. Roof and Crawfordl1 and Eakin, et a16 also have reported experiments with binary systems that formed two stable equilibrium liquid phases. APPARATUS AND PROCEDURE A U. S. Bureau of Mines Phase Equilibrium Apparatus was used in conducting this study. The apparatus and procedures employed in its operation have been previously described3 and will not be repeated in detail ill this report. Briefly, the apparatus consists of a windowed cell which can be maintained within ±0.5°F for temperatures between room temperature arid -320°F. Pressure within the cell can be maintained within 0.1 per cent of gauge reading up to 800 psig. Equilibrium vapor and liquid samples are obtained in special containers4 for analysis by a mass spectrometer. Although the accuracy of the analyzer is about ±0.1 mol per cent, the reproducibility of the phase-equilibrium apparatus is considered relatively poor. Values reported from methane and nitrogen are considered accurate to ±l.0 and ±0.6 mol per cent. Data for ethane-plus in the vapor are accurate within 0.2 mol per cent; liquid-phase data for this aggregate compolnent are accurate within 1.5 mol per cent. For helium in the vapor phase, the analytical data are accurate within 0.2 mol per cent; liquid-phase analyses for this component were obtained by the charcoal adsorption method described by Frost8 and are accurate within 0.006 mol per cent. All of these references to the accuracy of reported values are conservative estimates based upon a statistical treatment of reproducibility data obtained with the apparatus.

By Robert G. Nisle

In conducting a pressure build-up test on an oil well, it is often necessary to shut-in the well for a short time prior to initiation of the test. The effect of such a short tern shut-in on the resulting pressure build-up curve is derived. The derivation is based on the Kelvin point-source solution and is a straight forward extension of the fundarnental theory. The magnitude of the effect is evaluatecl and illustrated by an example. It is shown that if the production subsequent to the short term shut-in is at least 10 times the duration of the shrct-in, the effect will he less than 10 per cent. INTRODUCTION It often happens that before a pressure build-up test can be made an additional valve must be mounted on the wellhead, or on arrival at the well, it might be learned that the well had been shut-in several hours the previous day because of a shortage of tankage. In such cases the question is How will such an interruption of production affect the results of a pressure buildup test This work explains how to take account of such a short term shut-in in order that the test can proceed without further delay. The solution presented here makes use of the Kelvin point-source solution used by Horne1 in his treatment of the pressure build-up in wells. Use is also made of the super-position theorem. MATHEMATICAL DERIVATION The well is assumed to have been in production at a constant rate for a relatively long time (several days or more). It is then shut-in for a short time, after which it is again placed in production at the previous constant rate. It continues to produce at this rate until shut-in for a pressure build-up test. The Kelvin point-source solution is expressed by Eq. 1. The sequence of production rates is listed in Table I. TABLE 1 — SEQUENCE OF PRODUCTION RATES Time interval Production Rate At time AT the pressure will be the resultant of the sequence of production rates shown in Table 1. An expression for the super-posed effects may be derived from this table. (Effect of + q for T + ? T) + (Effect of - q for T + ?T-t,) + (Effect of + q for T + ? T - t,) + (Effect of - q for ? T) = Resultant........(2) The desired result is obtained by substituting the effect defined by Eq. 1 for the terms in Eq. 2. The result is Eq. 3. When the logarithmic approximation is made for the exponential integrals and the terms collected the result is Eq. 4. Let T — t2 = T = flowing time following short term shut-in t2 — t1 = 6 = duration of short term shut-in Then T - t1 = r + 6 Substitution of these quantities in Eq. 4 gives p(rw ?T) = P,, -When d<<t - AT then d—&apos;-, T— approaches 1. r + AT In this case the effect of the short term shut-in may be ignored. In order to get some idea of the numerical magnitudes involved take the worst possible case, when AT = 0, that is at shut-in. If the error is made less than some maximum acceptable value at this time, it will be less than the maximum for all subsequent times. d + r Let the difference between the value of y-— and 1 be less than 0.1. Then —6+r — 1 < 0.1 S < O.l T Therefore, if the flowing time following a short term shut-in is at least 10 times the duration of the short term shut-in, the error introduced by ignoring the short term shut-in will not exceed 10 per cent of T+AT A T

Jan 1, 1957

By R. Schuhmann, E. J. Michal

Experimental measurements are reported for the oxygen pressures of iron-silicate slags in equilibrium with solid silica. CO2-CO mixtures were bubbled through the slags in silica crucibles to find equilibrium values of p co2/p co over the entire composition range of silica-saturated slags at 1250°, 1300°, and 1350°C. From the data, the activity vs. composition relationships were calculated for O, FeO, and Fe. SLAGS composed primarily of silica and iron oxides have particular practical importance in copper smelting,&apos; in acid steelmaking, and in accounting for the service behavior of silica refractories. These slags all contain both ferrous and ferric iron, so that, strictly speaking, they are ternary or three-component liquid solutions. For convenience, the components may be taken as the three oxides, FeO, Fe2O3, and SiO2. The constitution of the FeO-Fe,O,-SiO, system at slagmaking temperatures has been studied in a recent investigation described in a separate paper.&apos; This work showed the compositional ranges of iron-silicate melts at temperatures up to 1450°C and also the temperature-composition relationships for melts in equilibrium with various solid phases, including iron, wüstite, magnetite, and silica. Broadly speaking, the compositions of iron-silicate melts at a given temperature should be thought of as varying over a two-dimensional field. In the first place, the silica/total iron oxide relationship varies from maximum silica for silica-saturated melts to minimum silica for wüstite-saturated melts or, at higher temperatures, to zero silica for straight iron oxide melts. In copper smelting, for example, the converter slags approach the low silica limits while the reverberatory-furnace slags have intermediate silica contents, perhaps approaching silica saturation in some circumstances. Liquids formed in the pores of silica refractories presumably are close to silica saturation. The second type of composition variation is in the ferric/ferrous relationship, which depends on how oxidizing or how reducing the process conditions are. Relatively reducing slags, such as acid-steelmaking slags, are lower in ferric oxide and ap- proach saturation with metallic iron. Oxidized slags, such as copper-smelting slags, contain larger percentages of ferric oxides and approach or reach saturation with magnetite. Since these two kinds of compositional variations are closely related to two general properties of interest for all metallurgical slags, basicity, and oxidizing power, it is hoped that the thermodynamic study of iron-silicate slags eventually will throw further light on the significance and nature of these long-recognized but as yet poorly understood slag properties. Measurements of oxygen activity as a function of slag composition, using CO-CO2 gas mixture to fix oxygen activities, afford an experimentally convenient approach to the study of the thermodynamic properties of iron-silicate slags. In a preceding investigation,³ his approach was used in a systematic study of iron-silicate slags in equilibrium with solid iron. The present paper gives the results of a similar study of the iron-silicate slags in equilibrium with solid silica. The experimental work consisted in the determination of CO2: CO ratios in gas mixtures at equilibrium in the system: gas: liquid slag: silica Determinations were made at temperatures from 1250° to 1350°C for slags ranging in composition from iron saturation to magnetite saturation. Also, equilibrium CO,: CO ratios and slag compositions were determined for the univariant systems: gas: liquid slag: silica: iron gas: liquid slag: silica: magnetite Experimental Methods The experimental procedure was essentially the same as that used in the previous study of iron-silicate slags saturated with solid iron," but in order to work with the silica-saturated slags an all-silica crucible assembly was used. A liquid slag was prepared from pure prefused stock materials and brought to equilibrium with the silica crucible at the desired temperature. Then a mixture of CO2 and CO was continuously bubbled through the melt

Jan 1, 1953

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy&apos;s law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy&apos;s law as a premise and other papers4-7,16-10 which recognize that Darcy&apos;s law may not hold for flow into gas wells. Miller8 compared theory based on Darcy&apos;s law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy&apos;s law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy&apos;s law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy&apos;s law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy&apos;s law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy&apos;s law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy&apos;s law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas&apos;-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller&apos;s results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By Robert E. Green, Edmund G. Henneke

Expressions are derived for the orientation factors associated with dislocation damping due to dislocation motion in the basal slip plane. The results of the calculation of these factors for zinc crystals aye pvesepzted and the relevance of these results to ultvasonic-attenuation measuvements is discussed. In this paper expressions are derived for the orientation factors associated with damping of sound waves due to dislocation motion in the basal slip plane of hexagonal crystals. For zinc crystals, the orientation factors for dislocation motion in one slip direction only, as well as for simultaneous motion in all three basal slip directions, have been calculated at 1-deg intervals. The results of these calculations are presented in the form of contour diagrams in a sector of a standard polar coordinate graph. The calculations have been carried out for both the traveling- and the standing-wave conditions. The relevance of these results to ultra sonic-attenuation measurements is discussed. Associated with the calculation of the orientation factors, the modes of elastic-wave calculation were also evaluated, according to the procedure previously employed by Hinton and Green.&apos; The results of these calculations are not presented here since similar results have been reported earlier by Mus-grave.2 However, it should be mentioned that, although the qualitative features of Musgrave&apos;s results are preserved, the quantitative values are somewhat altered since different values for the elastic constants of zinc were used. ORIENTATION FACTORS It is convenient to refer to three different sets of coordinate axes, Fig. 1, in the following calculations. First, there are the Miller-Bravais axes which are used in describing the Miller-Bravais indices of planes and directions in a hexagonal crystal. These axes are denoted in the conventional manner by a,, a,, a,, and c. The second set of axes used is a rectangular Cartesian coordinate system located as shown in Fig. 1. Note that the x axis coincides with the close-packed direction al [2110], the z axis coincides with the c axis [0001], and the y axis is orthogonal to these two lying in the [0110 ] direction. Finally, a form of Eulerian angles is used to locate the position of the specimen axis. The angle between the specimen axis and the c axis is denoted by 0 and the angle between the projection of the specimen axis on the basal plane and the a, direction is denoted by ø. The majority of observations on plastic deformation of metal crystals indicates that such deformation is caused by the motion of dislocations on a limited number of crystalline planes and in a close-packed direction. In crystals with hexagonal symmetry the most prominent slip plane is the basal plane (0001) and the slip directiops- are one of the close-packed directions, [2110], [ 12101, or [ 1120]. To properly set the stage for the following work, several points must be clarified. First, we want to consider the contribution to the attenuation of elastic waves by dislocations only. While the Granato-Lucke, model for dislocation damping is presently the one most quoted, it is not necessary to refer the present work to it. The only assumption that need be made is that the motion of dislocations absorbs energy from the elastic wave and therefore attenuates it. It is immaterial here how this energy absorption occurs. However, because dislocations have been observed to move most freely on the (0001) plane for hexagonal crystals undergoing plastic deformation, it will be assumed that it is the dislocation motion on this plane which attributes to the observed attenuation. The basic orientation factor, Ok, is essentially the same as that used by Green and Hinton for fee crystals,4 defined by the equation

Jan 1, 1968

By N. Jaffe, J. E. Dorn

This investigation is concerned with the possibility that the creep resistance of metals might be reduced as a result of recovery at the creep temperature when the applied stress is reduced. For this purpose the effect of stress on the recovery of the creep behavior of pure polycrys talline aluminum was investigated in the cross-slip temperature range where the activation energy for creep is 28.000 cal per mole. Before recovery all specimens were given the same substructure by creeping them under a stress of 7800psi to a strain of 0.218. Recovery was then accomplished by holding the specimens at the creep temperatures of 327" and 337°K under a series of reduced stresses for various periods of time. When the original stress was reapplied the specimens crept more rapidly than when the original stress was first removed, illustrating that recovery did take place. The extent of recovery could be indexed in terms of the UNDER certain conditions of test, the creep rate decreases over the primary stage of creep often by as much as a factor of 10~B. Since the external variables of stress and temperature are held constant, such pronounced and significant changes in the creep rate must be attributed to various substructural modifications that are introduced as a result of creep itself. At the secondary stage of creep, over which the creep rate remains constant and the substructure no longer changes, a balance must be achieved between the rate of increase in creep resistance due to creep straining and the rate of recovery of the substructural modifications. The general validity of these concepts on substructural changes has already been shown,&apos; including the corollary that a more creep-resistant substructure is introduced under a more rapid creep rate arising from a higher applied stress.&apos; In spite of these well-documented facts, very little progress has been additional strain undertaken by the recovered specimen to achieve the same strain rate as the unrecovered specimen. It is significant that the higher recovery stresses gave the most rapid rates of recovery. Over the high range of reduced stresses, where some creq took place during recovery, the activation energy for recovery equaled that for creep, namely 28,000 cal per mole. But for stresses during recovery below 0.80 of the original creep stress, no creep was detected during recovery and an activation energy for recovery of about 72,000 cal per mole was obtained. Whereas the activation energy of 28,000 cal per mole suggests that cross-slip of dislocations is responsible for this recovery, the mechanism for the 72,000 cal per mole process is not known. This activation energy, however, is about twice that for self-difhsion. made in determining, in satisfactory detail, precisely what substructural changes so effectively modify the creep rate.&apos; Up to the present, electron microscopy has failed to uncover, in a satisfactory quantitative manner, the mechanistic processes involved. Since, however, creep, at least at moderate and high temperatures, arises from one or more types of dynamic recovery processes, it should be possible to shed additional light on the total problem by investigating the recovery of creep resistance. The importance of such an investigation becomes apparent when the fact is recognized that there has yet been no direct experimental proof that the rate of softening due to substructural changes as a result of recovery equals the rate of hardening due to creep-induced substructural strengthening over the secondary stages of creep. Furthermore the problem of what happens to the creep-strain induced strengthening when the material recovers either at zero or some reduced operating stress has significant engineering consequences. It was for these reasons that the present investigation on the recovery of creep behavior was initiated. Inasmuch as a substantial background has now developed on the creep of high-purity aluminum, this material was again selected for the current investigation. Furthermore extensive evidence is now

Jan 1, 1963

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,&apos; at 0.6 to 0.9 of included to see whether Mullins&apos; theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for spectroscopically pure silver, and for o series of solid solutions of silver with cadmium, indium, and tin, using a Ke-type torsion pendulum apparatus. Some experiments have also been made to investigate the effect of nonmetallic impurity on grain boundary relaxation in silver. The effect of the alloying elements is to increase the grain boundary viscosity, and to raise the activation energy for grain boundary relaxation from 22,000 cal per mol for pure silver to 43,000 cal per mol for the solid solutions; the same value being obtained, within the limits of experimental error, for all the alloying elements and solute concentrations investigated. Results of the experiments show exactly the same trend as those obtained previously for a similar series of copper solid solutions. They are in agreement with the general theory of grain boundary relaxation developed by Zener and Ke, but do not seem to be in agreement with either of the mechanisms so far put forward to explain grain boundary slip. EXPERIMENTS described in this paper were made as part of an investigation into the effect of alloying elements in substitutional solid solution on grain boundary viscosity, measured by the internal friction method developed by Ke.&apos; The apparatus and experimental procedure have already been described.&apos; Preliminary work was done with spectro-scopically pure silver. Experimental Work Materials Used—All the materials were supplied in the form of % mm diam wire by Messrs. Johnson Matthey and Co. Ltd. The silver and all the alloying elements used were spectroscopically pure. Composition of the alloys is given in Table I. They were all melted and chill cast under the same conditions as the copper alloys. The ingots were rolled to 1/4 in. sq rod with intermediate annealing at 600°C in an atmosphere of cracked ammonia when necessary. These rods were then drawn to wire by standard procedure with intermediate bright anneals at suitable steps in the drawing operations. Specimens from the annealed wires were sectioned longitudinally. mechanically polished, and examined under the microscope. They were then etched and reexamined. Grain sizes were reasonably uniform for all wires, and no traces of a second constituent were observed. The wires were weighed before and after testing so as to measure any loss of the alloying element due to evaporation. The loss was less than the accuracy of measurement—< 0.1 pct of the total weight— for the Ag-In and Ag-Sn alloys, but appreciable loss of weight occurred in the case of the Ag-Cd alloys. The percentage loss is given in Table 11. X-ray diffraction photographs were taken of all thc wires after test to determine whether there was any marked preferred orientation. Results of the examination are given in Table 111. Experiments on Spectroscopically Pure Silver-— Experiments were made on specimens in which the grain diameter was small relative to that of the wire, and on one specimen in which the grains were grown by the usual strain-anneal method to extend across the full diameter of the wire. These large grained specimens will be referred to as single crystal specimens. The wires were annealed for 11/2 hr at 700°C, and experiments were made at two frequencies of vibration, 1.5 and 0.4 vibrations per sec. The variation of internal friction with temperature is shown in Fig. 1. Experiments on a second small grain specimen gave approximately the same results as for the first wire. It will be seen from Fig. 1 that the peak in the curve for the small grained wire, which is presum-

Jan 1, 1957

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"&apos; and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

LEAD and tin mixed together make an alloy through an attachment of natural affinity which they have with each other, so that when they are mixed it is difficult to recognize by the sight which one it is, if the essences of their qualities are not surpassed by more than half. If, indeed, one can be recognized, it is the tin which gives off a certain sharp odor to the sense of smell, besides having a greater hardness and whiteness. The best of these is the one that is the purest in its kind. In the alloy of tin it is the one that is the whitest and hardest, or, when it is bent or some thin end of it is held tightly by the teeth, is heard to crackle as frozen water does. Because this happens more with this than with other metals, I do not wish now to inquire into it. It is enough that it be a sign for recognizing when tin is pure or mixed. Pewterers say that it should be joined in alloy with lead and that it is better for working when it contains four or six pounds to the hundred because it makes it softer to the hammer and more fluid in casting. But I do not like to hear this, even if all they say is true, for I see that the tin that comes from England, when worked as well as in cakes that show it to be pure, is much more beautiful and better in all works than is that made in Venice. And I believe that it is not better for any work when mixed than when pure, except for the advantage of the master who, if he does nothing else, sells lead that is worth little for tin that is worth much. I find that when mixed it serves in only two things. One is when it is wished to make a solder for copper, for use when it is not worth while to solder the bottoms and large pieces of vessels with low-grade silver as should be done. The other is when master potters calcine it in order to make glazes and to apply white to their vases. I consider lead to be useless in all other works of any kind of metal, since it unites with none of the other metals of good company except tin.

Jan 1, 1942

By J. T. Norton, A. L. Mowry

S. J. SINDEBAND*—(1) Discussing the properties of the powders used, Mr. Rostoker mentioned a silicon powder as being between 150 and 325 mesh. We always had much difficulty in measuring particle size of silicon powder by screen analysis, because of its tendency to agglomerate. I would be interested in the method used to measure these particle sizes. (2) Mr. Rostoker maintains that the measurement of magnetic properties is more accurate in determining complete homogenization of an alloy, than is the X ray diffraction technique. I wonder whether this is really true. Even when diffusion is complete, magnetic properties will change during continuation of the heat treatment, due to change in density and pore shapes, as has been demonstrated by Mr. Rostoker himself. Which effect is faster, the diffusion of the alloy components or the attainment of final density, will, in my opinion, depend very much on initial material and sintering conditions used. For magnetic applications, of course, the magnetic measurements are most suited for determining the point at which equilibrium conditions are reached. (3) I was glad to see that Mr. Rostoker had used sample sizes which are similar to those I had used previously, and I believe that ring samples of about 2 in. od will become more or less standard samples for the determination of magnetic properties of powder metallurgy products. I should like to ask how the density was changed for the samples on which the effect of porosity was investi- gated, and, further, why the sintering temperature used for this series of experiments was so low. It is somewhat surprising that a 24-hr treatment at 850°C acts so much more to spheroidize the pores than a treatment for 1 hr at 1100°C. But the effect seems to be indisputable. I have made an investigation of the influence of sintering temperature for longer times on the maximum permeabilities of iron powder compacts which was presented at the International Powder Metallurgy Conference in Graz, in 1948, and I hope that these results will be published here within a short time. The results of this investigation are confirmed by Mr. Rostoker&apos;s findings that the change of time from 1 to 24 hr changes the permeability behavior considerably in the direction as indicated by Polder and Van Santen for spheroidiza-tion of pores. I do not quite understand Mr. Rostoker&apos;s explanation of the influ-

Jan 1, 1950

By John Henry Harden

THIS shaft, located in the northern anthracite coal-field about 2300 feet southwest from the court-house at Wilkes-Barre, in the County of Luzerne, Pa., is the property of the Lehigh & Wilkes¬Barre Coal Company. The sinking and cribbing to the solid rock (see isometrical view on Plate IX) was conducted by Mr. W. W. Kenrick. Dimensions of the earthwork to the foundation of the cribbing, 51&apos; 1/2" long, 17&apos; 4" wide, 31&apos; deep. Total amount of excavation in cubic yards, 998.5. Dimensions within the permanent cribbing, 45&apos; 4" long, 11&apos; 16" wide, 31&apos; deep, divided into six parts by buttons 8" x 12", each division, 7&apos; x 11’ 16". Permanent cribbing 12" x 12"; temporary cribbing 8" x 10"; backing, 3" thick ; clay puddle to ex¬clude surface water, 12" thick; conductors, 8" x 5"; lining, 1" thick from top to bottom of the shaft. In the latter part of the year 1871, Mr. H. Murray & Son contracted with the company for the continuation of the work at the rate of four hundred dollars per yard in depth, to a point 100 feet below the Hillman seam of coal ; for the succeeding 100 feet the price to be increased twenty-five dollars per yard, and so on until the bottom rock of the Baltimore seam of coal was found. The size of the shaft within the cribbing timbers is 45 feet 4 inches by 11 feet 6 inches, having six divisions of equal dimensions, 7 feet by 11 feet 6 inches, giving room for what is known as the" standard diamond" car, whose capacity when level full is 100 cubic feet, but when loaded by the miner 4 inches above the top contains 112 cubic feet.* Two divisions of this shaft are intended for hoisting coal from the Hillman seam, two from the Baltimore seam, one for ventilation, and one for pumps. The works were planned for two pairs of direct-acting, high-pres¬sure engines, twenty-four boilers, and for an estimated output of 2500 tons of coal per day from the two seams. * Size of the "standard diamond" car, 8&apos; 10” x 4&apos; 3" x 2’ 8” = 100.1.4; loaded 4 inches above the top, 8&apos; 10” x 4’ 3” x 3’ “0"= 112.7.6.

Jan 1, 1877

By N. A. Gokcen, S. Fujishiro

THE pressures of Mn(g) in equilibrium with Mn7C3 and graphite have been measured by McCabe and Hudson&apos; and Butler, McCabe, and paxton2 by means of graphite, zirconia, and Ta-Mo Knudsen cells. The details of corrections in their measurements were somewhat different from those of the authors;3&apos;4 hence, further independent results at higher temperatures seemed to be warranted. The stoichiom-etry of Mn7C3 in equilibrium with graphite and its stability up to the vicinity of 1373 °K have been satisfactorily established by Kuo and persson5 (See also Hansen and Anderko).&apos; The method of investigation has been described elsewhere in detail.3&apos;4 The carbide was prepared in the manner described by McCabe and Hudson. In order to avoid possible reactions with refractory oxides, only graphite cells were used for the effusion experiments. The authors&apos; results are the runs M-1, M-2 and M-3 listed in Table I, together with those of McCabe and co-workers. The heat capacity, c;, of Mn7C3 is not known; therefore McCable et al. plotted their data as log P vs 1/T and the results were only expressed first&apos; as, and later2 as logP=- -14220+6.06 without further thermodynamic calculations. However, it is possible to estimate closely the necessary heat capacity as follows: When H; - &98 of CrC, or MnO, is plotted vs x, corresponding to various compounds, with temperature as the parameter, it is seen that the relationship is represented by a line of very small curvature. This relationship is also followed by other compounds which do not exhibit solid state phase transformations. In view of the fact that chromium and manganese have the atomic numbers of 24 and 25 respectively, it is reasonable to assume that H; - H;ae vs x for MnC, follows the same type of lines as those for CrC, for which adequate data are available.7 Similar correlations appear to be valid for oxides of two neighboring metals for which reliable data are available. The procedure is thus to move the lines for CrC, vertically (parallel to the axis of HT - H298) until they coincide with the points for MnC1/3, the only carbide of manganese whose H; - HO298 has been

Jan 1, 1963

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 R. J. Wygal, J. Naar

An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by 1/pc2 = CS*. The evolution of an oil-gas system imbibing water from Swi to(Sw,imb )max is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturation. When the gas satuation cannot be reduced further, the system evolves along a line of constant Sg with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. INTRODUCTION Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper,1 a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model: (1) an analytical expression of oil isoperms; (2) oil isoperrns as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by 1/PC = CS*; and (3) evaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson1 for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid. The following expressions were derived from the model. 1. The amount of oil blocked by the invading water is