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By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By J. J. Arps

n approach to the study of the electrical properlies of drilling muds, their cakes and their filtrates was made by treating the drilling fluid as a porous medium. Lluring this study it was found that the weight pararneter was omitted from previous investigations on electrical properties. Patnode in 1949 made a similar approach to ,his investigation. His work showed that there was a variation of resistivity relationships with per cent Puid present in a given suspension. This present study ex-tends Patnode's investigation to one in terms of the solids fraction of the drilling fluids. Previous investigations were made on low weight muds where the effect of the rolids fraction was obscured. The following equationr were fitted to data taken from 94 field muds and 47 laboratory muds (see Tables I and 2). The parameter, C, is a complex function of the solidr content, or mud weight, of a drilling fluid. It was also found that for all drilling muds examined. A nomograph is presented combining Eqs. I and 2. INTRODUCTION It is generally recognized that the materials present in drilling muds affect the relationship between mud filtrate and mud resistivities. However, most electric log interpretations proceed with the assumption that the mud resistivity and temperature are the only important parameters needed to obtain a filtrate resistivity or a mud cake resistivity. Lamont1 suggests that only average relationships exist between mud cake, mud filtrate and mud resistivities. He indicates that there is limited accuracy when these intercorrelated factors are used since no other measure-able variable is apparent. A previous paper by Patnode indicates that drilling fluids may be considered to be a system of fluids in solid particles which may be correlated electrically in a manner similar to rock solids. 1 he equation for the resistivity factor. F = (per cent fluid) is satisfied for a given clay type in water, but the value of m varies as different materials are used in the water. The resistivity factor is not constant for a given amount of clay. As is suspected it varies as the solids fraction conducts electrical current. Since both weighting material and clay solids are present in commonly used drilling fluids, it is expected that both materials contribute to the variation of the m factor in Eq. 3. An extension of Patnode's work is presented in this paper to show some of the interrelations which exist between the resistivities of mud cake, mud filtrate and mud. Use of these data enable a more accurate calculation of mud filtrate and mud cake resistivities if only the mud resistivity and weight are measured. EXPERIMENTAL The measurements of mud weight, fluid and solids resistivity, alkalinity, and chloride content of mud samples were made in this research. Mud samples representing drilling fluids from 94 Louisiana and Texas wells (Table 1) and 47 laboratory-constructed systems (Table 2) were used in the experimentation. The measurements of the mud properties were made both in the field and in the laboratory. The tests on the properties of weight, alkalinity and chloride ion were standard tests as described by API specifications. The resistivity measuring devices were constructed in the laboratory for this study. For details on the resistivity equipment see Fig. 1. The fluid cell

By R. G. Davies, R. H. Richman

Several techniques, X-ray diffraction, transmission electron microscopy, conventional, metallography, and mechanical property measurements are combined to investigate decomposition in the suPersaturated solid solution Fe-27 at. pct Be. The following sequence of structures for aging temperatures below 400°C is established: massive short-range order, pseudo-FeBe (L2o) order, Fe3Be (DU3) order, sinusoidal modulation of composition, general or continuous precipitation, and discontinuous or cellular precipitation. In addition to this sequence itself, several features of the individual stages are noteworthy; for example, when coherent modulations occur, their development is parallel to (100) everywhere in the specimen apparently without incubation, and both the wavelength and the composition amplitude of the modulations increase with aging time. Two types of discontinuous reaction are observed, depending upon the aging temperature. At low temperatures (<550°C) the boundary-nucleated variety of discontinuous precipitate predominates; but at higher temperatures (>600°C) the crystallographic variety occurs instead. Hardness and flow-stress measurements clearly reflect the quoted structure sequence. Some qualitative aspects of the structure changes and of the relationship between mechanical properties and structure are discussed. BERYLLIUM in solid solution markedly strengthens iron.&apos;" A recent study demonstrated that not only were supersaturated single crystals of Fe-27 at. pct Be very strong, but they deformed primarily by mechanical twinning.3 Such behavior, coupled with the decrease in solid solubility of beryllium in a Fe from about 33 at. pct at 1165°C to about 10 at. pct at 500°C4 as shown in Fig. 1, leads naturally to questions about property changes with aging in this system. In 1929 roll,1 and later Seljesater and Rogers,5 reported that useful increases in strength could be obtained by aging quenched Fe-Be alloys, but it was not until quite recently that any of the details of precipitation in these alloys were studied. Richman6 observed that both an Fe3Be superlattice (with a DO3 crystal structure the same as Fe3A1, illustrated in Fig. 2) and a modulated structure preceded the appearance of a discrete second phase in the 20 at. pct Be composition. Here, a modulated structure refers to a periodic composition fluctuation within one crystal, while its lattice remains coherent. Subsequent work on a Fe-Be alloys by Heubner7 and von Heimendahl and Heubner8 confirmed the existence of the modulated structure, although only an FeBe (L20) ordered structure was detected (also shown in Fig. 2). Both Rich-man and Heubner corroborated the large increases in hardness during aging reported earlier, but other mechanical properties were not examined. Since modulated systems are encountered relatively infrequently, the influence of coherent modulation upon mechanical properties is not well-known. With the accumulation of information about age-hardening systems, it has become clear that many precipitation reactions cannot always be described by the concept of heterogeneous nucleation at some lattice discontinuity followed by diffusional growth. Rather, complex sequences involving prior "preparation" of the matrix are quite common; that is, a transition structure occurs in the parent phase, instead of in some "nucleus" form. Delineation of such subtle sequences appears to be a worthwhile step toward the understanding of solid-state precipitation. Since not many structural progressions of comparable nature have been reported, the objectives of the present survey are to identify and elucidate the various

Jan 1, 1967

By Frederic L. Kadey

Diatomite is a siliceous, sedimentary rock consisting principally of the fossilized skeletal remains of the diatom, a unicellular aquatic plant related to the algae. Thus, it has been formed by the induration of diatomaceous ooze, and consists mainly of diatomaceous silica, a form or variety of opal which is first formed in the cell walls of the living diatom. Diatomaceous silica is not generally regarded as a synonym or the equivalent for diatomite, although it has been so used at various times. Accurately, diatomaceous silica is the preferred name for the principal mineral component of which the rock, diatomite, is composed. The terms diatomaceous earth and kieselguhr are used as synonymous with diatomite. The designations tripoli, tripolite, infusorial earth, etc., were used at one time but are now obsolete. With the changing nomenclature, these terms that were at one time correct when proposed and used for generations would be considered incorrect if used today in the light of current knowledge. The designation diatomite is reserved for those accumulations of diatomaceous silica that are of sufficient quality, size, and minability to be considered of potential commercial value. Processed diatomite possesses an unusual particulate structure and chemical stability that lends itself to applications not filled by any other form of silica. Foremost among these applications is its use as a filter aid, which accounts for over half of its current consumption. Its unique diatom structure, low bulk density, high absorptive capacity, high surface area, and relatively low abrasion are attributes responsible for its utility as a functional filler and as an extender in paint, paper, rubber, and in plastics; and as an anti-caking agent; thermal insulating material; catalyst carrier; and chromatographic support; polish, abrasive, and pesticide extender to name a few representative applications. The United States is the principal producing country, although diatomite is found in numerous other locations. Geology Composition and Morphology Diatomaceous silica qualifies as a. mineral of organic origin in much the same way that aragonite and collophane do. The silica of the fossilized diatom skeleton closely resembles opal or hydrous silica in composition (SiO2 • nH2O) .4, 12, 203 The silica is of acute biological significance, not only for the cell wall component, but also for the basic life process.45, 51 Without silica, cell development ceases .31 In addition to bound water, varying between 3.5 and 8%, the siliceous skeleton may also contain, in solid solution, or as part of the Si02 complex, small amounts of associated inorganic components-alumina, principally-and lesser amounts of iron, 46, 49, 55 alkaline earths, alkali metals, and other minor constituents.59, 63, 67 Boron is reported to be an essential element for diatom growth .52, 58 Since diatomaceous silica is not pure hydrous silica but contains other intimately associated elements, there is good reason to consider it a distinct type or variety.4 Associated with the diatomaceous silica, and integrated as part of the diatomite, may be variable amounts of organic matter, soluble salts, and particles of rock-forming minerals that were syngenetically deposited or precipitated with the diatom frustules. Sand, clay, carbonate, and volcanic ash are typical common contaminants. Other contaminating minerals may be present, such as feldspar, mica, amphiboles, pyroxenes, rutile, zircon-the result of weathering, then transporting, and subsequent redeposition of surrounding land masses. Commercial diatomite may also contain fragments and particles of

Jan 1, 1983

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, &apos; the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

By L. V. Pirela, S. M. Farouq Ali

Some interest has been expressed recently in the application of solvents in conjunction with a thermal drive, such as a steamflood. At least one field project of this type has been reported. This paper makes the first attempt to provide some of the basic information necessary for choosing a solvent for such an application. Results of displacements conducted at elevated temperatures are also discussed. This paper shows that, in the case of alcohol-hydrocarbon-water or brine ternary systems, the system miscibility may increase, decrease, or both increase and decrease within the same system when the temperature increases. The distribution coefficient was consistently found to increase in favor of the oleic phase with an increase in temperature, which is advantageous from the standpoint of oil recovery. Results of solvent displacements in a sandstone core showed that even a relatively small temperature effect in the favorable direction (increase in miscibility and distribution coefficient) can lead to a 50 percent increase in oil recovery. On the other hand, if the system miscibility decreases with the temperature, even though the distribution coefficient increases, the oil recovery at the higher temperature may not increase. INTRODUCTION Miscible displacement has been the subject of many investigations. Miscible-phase solvent flooding, employing solvents such as alcohols that are miscible with both oil and water, has received considerable attention. Investigations conducted by Gatlin and Slobod,l Taber, Kamath and Reed,2 Holm and Csaszar,3 and Farouq Ali and Stah14 have helped in understanding the mechanism of solvent flooding. While the use of alcohols and similar solvents as oil recovery agents is economically unattractive, these solvents nevertheless provide a means of understanding the mechanistic aspects of important miscible-phase oil recovery processes such as the Maraflood process (discussed by Gogarty5). As shown by Taber et a1.,2 the phase behavior of a solvent-oil-water system is of .utmost importance in determining the efficiency of the oil displacement. This paper makes the first attempt to obtain the ternary phase behavior data for nine alcohol-hydrocarbon-water/brine systems at elevated temperatures. Results of core tests at elevated temperatures are also presented which corroborate the effect of temperature on oil recovery, as judged on the basis of phase-behavior data. The use of solvents at elevated temperatures has been suggested earlier by Farouq Ali.6 At least one field test of this type has been reportedO7 With the widespread use of thermal recovery techniques, it is possible in some situations (especially in steamflooding) that the use of a suitable solvent in conjunction with the heat carrier may be economically feasible. This paper attempts to provide some of the basic information needed for judging such feasibility. LOCATION OF THE PLAIT POINT The phase behavior of a typical ternary system consisting of a solvent, hydrocarbon and brine (or water) can be represented by a triangular diagram such as the one shown in Fig. 1 (for temperature TI). Point Pon the binodal curve represents the plait point, being the limit of tie lines such as Y1 Y2 The compositions of the coexisting oleic and aqueous phases are given by points Y2 and Y1, respectively, for any mixture composition along Y1Y2. The characteristics of ternary diagrams have been discussed by Findlay8 and others. Taber et aL3 have shown that the position of the plait point in a particular ternary system plays the decisive role in determining whether or not theoleic phase would be displaced in a continuous manner during an alcohol displacement. The area above the binodal curve also is important, since it represents

Jan 1, 1969

By A. N. Crownover, H. T. Kennedy, E. P. Miesch, C. H. Bowman

The paper presents correlations of (l) molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C,-plus fraction; (2) shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and (3) bubble-point pressure with temperature, composition and characteristics of C, plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sul-fide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psis, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. he equations resented are all explicit in the dependent variable, and require no iteration on the digital cow puter. INTRODUCTION The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer arc useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy The van der Waals equation is modified to make a and b functions of temperature instead of being constants for each material.This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between a,,, and b,,, for mixtures and the a, and b, for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. For normal mixtures, however, the area may be added to any of the bounding areas without substantial error. The new relationships employed are

Jan 1, 1966

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954&apos;and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,&apos; and Bond,&apos; respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By William C. Hagel

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a PL-IORh chamber, and splzeres of a Fe2O3 containing three or less grains was determined from 9000 to 1250°C. Isotope equilibrum on crystal surfaces appears to be quickly established, and the rate-determining factor is self-difiusion confbvrning to the relation D = 2.04 esp(- 77,900/RT) sq cin sec-&apos;. Changing sphere diameters caused no detectable variation in diffusion coefficients. Oxygen ions diffuse faster than cations at low temperatures, but a crossover may occur at about 1150°C. INVESTIGATIONS by Davies et al.&apos; and Himmel et al2 have suggested that the mechanism of iron oxidation above 600°C involves a predominance of cation migration in the wüstite (FeO) and magnetite (Fe301) layers and oxygen-ion migration in the hematite (a Fe2O3) layer. Evidence for little cation migration during hematite growth consists of: 1) the disappearance of radioactive-silver markers, presumed to vaporize from the oxide-gas interface, and 2) a large discrepancy between parabolic rate constants for magnetite oxidation and those calculated from Lindner&apos;s3 data for cation self-diffusion, D:, using Wagner&apos;s theory.4 Reversing the calculations gave anticipated self-diffusion coefficients, D:, for oxygen ions of 3.6 x 10-9 sq cm sec-1 at 1100°C and 5.9 x 10-10 sq cm sec-1 at 1000°C. Since then Kingery et a1.5 reported three values for oxygen-ion diffusion in polycrystalline, sintered hematite. These were obtained near 1200°C, at an oxygen pressure of approximately 150 mm Hg, and could be represented by the Arrhenius expression, Dg = 1 x 10 11 exp(-146,000/RT) sq cm sec-1. Extrapolation to temperatures below 1100°C infers that oxygen ions are less mobile than cations. This contradicts the aforementioned oxidation evidence and also coble7s study of the initial sintering of hematite. From the latter, apparent diffusion coefficients for the slowest rate-controlling species could be calculated, and fair agreement was found with an extension of Lindner&apos;s data for cation diffusion. Fig. 1 depicts such comparisons graphically. Three points have been included for the determinations of Himmel et al. on cation diffusion in large, natural hematite crystals surrounded by pure oxygen at atmospheric pressure. No dependence on crystal log raphic direction was noted. Since the value of 10-l4 sq cm sec-&apos; at 1000°C actually represents an upper limit, one might interpret that there is a small decrease in D: when single crystals are employed. On the whole, however, cation diffusion appears relatively well-defined,* while the few results tension to lower temperatures. After having gained experience measuring oxygen-ion diffusion in certain glasses7 and in the corundum oxide, a Cr2O3, the purpose of this work was to determine D; values for hematite and thus possibly assist a mechanistic understanding of the kinetics of the oxidation and reduction of solid iron oxides. I) EXPERIMENTAL PROCEDURE A) Material. Hematite powder of moderately high purity was received from the Columbian Carbon Co. An accompanying lot analysis listed 0.03 H2O, 0.008 weight percents, with the remainder Fe2O3. Subsequent treatments were ball milling, drying, prepressing, and hot-pressing for 60 min at 1350°C under 5000 psi. Since graphite dies coated with a slurry of alumina were used for hot-pressing, the surrounding atmosphere at temperature was sufficiently reducing to form some magnetite on the outer surface of each cylinder. After removing any attached alumina, a stabilizing anneal of 50 hr at 1300°C in oxygen was added. The final product was nonmagnetic and exceeded 97 pct of the density (5.24 g cm-3) usually given for FezO3. On polishing cylindrical ends, counts were made of the number of grain boundary intercepts per

Jan 1, 1967

By A. S. Odeh

ABSTRACT A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs fram pressure build-up and/or drawdown plots. INTRODUCTION The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard,l Freeman and Natanson,2 and Samara.3 The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results,4 Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a fractured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. TO understand the behavior of the pressure buildup and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions: 1. The matrix blocks act like sources which feed the fractures with fluid; 2. The net fluid movement toward the wellbore obtains only in the fractures; and 3. The fractures&apos; flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures&apos; bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady -state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. la this paper, the fundamental equation of flow

Jan 1, 1966

By Sidney A. Swensrud

MUCH discussion has occurred as to the use or uses which might be made after the war of either or both .of the large diameter (24 inch and 20 inch) War Emergency pipe lines built by y the United States Government during the war, to move crude petroleum and refined products such as gasoline and light distillate fuels. Indeed, the disposition and future use of these lines constitutes, in the minds of many people, one of the most important problems of postwar readjustment in the Oil Industry. The two lines, running from points in Texas to the New York-New Jersey-Philadelphia area, were constructed only because of the inability during the war to continue normal ocean tanker movements from the Gulf Coast to the East Coast. Physically they could continue after the war to move crude or refined products, and it appears that lines of such large diameter as these, if operated at or near capacity, could move these liquids at costs per barrel which might be considered in the same general cost range as for tanker movements.1 If, therefore, we were to look forward at the end of the war to a shortage of tankers, it is probable that the continued use of these pipe lines for petroleum movements to the East Coast would be worth considering, as against building new tankers to take over the movement, provided there were no other economic or national defense reasons for restoring tanker fleets and no other better use for the pipe lines. Because of the extensive tanker construction program which has been and still is in progress, and because of our Navy&apos;s marked success in combating the submarine problem, it appears to be quite possible, however, that instead of a shortage of tankers at the end of the war, we may have a surplus instead. If this should turn out to be the case, then there would seem to be considerable doubt that these lines would continue to be used for moving petroleum or products to the East Coast at the expense of tying up tankers. It would hardly seem probable that the owner of any such tankers would ship via one of the large lines at the expense of tying up one of its own tankers, unless the pipe line tariff rate charged was lower than the out-of-pocket cost of operating a tanker as against the out-of-pocket cost of keeping it tied up. And considering that a substantial part of the cost of operating a tanker goes on even when it is tied up, it is very difficult to figure out how any pipeline tariff could be established that would be low enough to compete with individually owned tankers that otherwise would be idle. Certainly a pipe line tariff rate high enough to cover direct costs plus even a low rate of depreciation and return on the investment would be far above the out-of-pocket tanker operating costs. In view of these considerations, it has seemed desirable to examine with some care some of the various alternatives that have been suggested as to other possible uses to which these lines might be put. One of these is for transportation of natural gas to the New York-New Jersey Philadelphia area. This Eastern area, located at the destination of these lines, contains the heaviest concentration of population in the United States, and is not now served with natural gas. At the other end of the lines lie the greatest discovered natural gas reserves in the United States, if not in the world, and many

Jan 1, 1944

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR&apos;s are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By E. S. Machlin, Morris Cohen

The isothermal formation of martensite in a 71 pct Fe, 29 pct Ni alloy is found to take place mainly by the nucleation of new plates rather than by the growth of existing ones, and is dependent on the temperature and time of the isothermal hold, the amount of atherrnal martensite present, the state of internal strain, and the application of tensile stress. The conclusion is reached that the isothermal nucleation is activated by thermal fluctuations superimposed on localized regions of very high strain. The reaction-path concept, involving martensite nucleation at strain embryos by athermal activation on cooling, or by thermal fluctuations on holding, reconciles the athermal and isothermal modes of transformation, and offers a unified picture of the kinetics of martensite formation. THE phenomenon of isothermal martensite formation has been the subject of considerable study lately,&apos;-&apos; and its reality has been thoroughly established. The existence of such isothermal transformation has been claimed to confirm the nucleation and growth hypothesis as applied to the martensitic reaction.1 " However, the isothermal formation of a martensitic phase is also compatible with the reaction-pathw escription of the transformation. The purpose of this investigation is to examine the isothermal mode of the martensitic reaction, both theoretically and experimentally, in order to test the likelihood of the above two mechanisms. Material and Methods The alloy used in this study contained about 71 pct Fe and 29 pct Ni. The complete analysis was 29.5 ± 0.2 pct Ni, 0.036 pct C, 0.02 pct N, 0.19 pct Mn, 0.09 pct Si, 0.008 pct P, and 0.006 pct S. The amount of isothermal transformation was determined by electrical resistance measurements using a Kelvin double bridge. The specimens were in the form of rods 1/16 in. diam x 4 in. long. Aus-tenitizing was performed at 1095°C for % hr either in a pre-purified nitrogen atmosphere or in an evacuated Vycor tube, followed by oil quenching to room temperature. After this treatment, the samples were completely austenitic, and the transformation studies were conducted at subatmospheric tempera- tures. Lineal analysis and X-ray determinations of retained austenite were used to calibrate the electrical resistance changes in terms of the percentage of martensite. The martensite range curve for this alloy is given in Fig. 9 of ref. 6. The M, temperature occurs at about -18°C (255°K). Reaction-Path Theory The nucleation and growth description of the martensitic transformation that occurs isothermally has already been given by Kurdjumow.&apos;,&apos;2 However, no comparable treatment exists using the reaction-path concept." Consequently this section presents the reaction-path description of the isothermal mode of the martensitic transformation. According to the latter theory, there is a reaction path (a strain) which describes the relative motion of the atoms during their transference from the austenitic to the martensitic state. The possibility exists, therefore, that the nucleation of a martensitic plate is accomplished by an embryo that comprises a state intermediate between that of austenite and martensite. This state may be attained within a finite volume by means of a homogeneous strain of the austenitic matrix. There is a free-energy barrier (F.) along the reaction path, corresponding to a critical strain in a critical volume. When activation is achieved, a spontaneous increase in strain and volume of the embryo takes place to generate the full-size martensitic plate. This mode of nucleation is to be distinguished from the more conventional mode involving embryos of the martensitic phase that merely grow in size by an interface motion. There are two ways whereby embryos in the austenitic phase can achieve the critical state of strain for isothermal nucleation: 1—through the formation of internal strains by plastic deformation or by stress; and 2—through thermal fluctuations, preferably superimposed upon existing internal strains. The activation free energy F,, must be supplied either mechanically by internal strains or thermally by energy fluctuations, or by a combination of both.

Jan 1, 1953

By Charles Stein

The effects of several different prior treatments an the creep behavior of 99.9995 pct aluminum at 260°C and 1000 psi canstant stress are compared with annealed specimens. Quenching from 538oC, irradiation with 2 mev electrons, and tension-compression room temperature fatigue damage were used to change the substructure of the specimens prior to their creep testing. The quenched and the irradiated specimens showed a larger primary and transient stage contribution to the creep curve than those specimens which were only annealed prim to creep testing. The specimen receiving prior fatigue damage at room temperature showed no first stage or transient creep when tested under identical conditions as the above specimens and had an average creep rate seven orders of magnitude lower than that of either the annealed, the quenched or the irradiated creep specimens. In a previous electron transmission microscopy investigationl of the substructure developed during the creep of pure aluminum at 0.57 Tm, it was noted that a large concentration of vacancy loops and dislocation loops were present in and near the subboundaries while the interior of the subgrains contained few of these defects and had a low dislocation density, see Fig. 1. Yim and Grant2 and Hazlett3 have shown that the presence in nickel of a substructure developed by prior cold work effectively reduces the primary and transient contributions to the creep curve. Hultgren,4 McLean,5 Gervais, Norton, and Grant,6 Chang and Grant,7 and others have shown the same effect with the higher stacking fault energy material, aluminum. However, the specific defect responsible for the change in the creep behavior developed by the prior cold work was not established. Specifically, what effectively interfered with dislocation motion in these materials at elevated temperatures? Was it jogs on dislocations produced by their interaction with other dislocations or with vacancy or dipole loops, see Fig. 1, or did the subgrain walls determine the mean free path for glissile dislocations? This would be a realistic possibility only if subgrain boundaries are effective barriers to dislocation motion. The ability of a subgrain boundary to act effectively against glissile dislocations depends on the number and the arrangement of dislocations in the subboundary,8 which in turn is a function of the creep strain.&apos; This paper compares the creep rate of specimens possessing a large vacancy concentration to that of annealed specimens and with specimens having a stable subboundary wall containing Lomer locks produced by prior fatigue damage. EXPERIMENTAL PROCEDURE Vacancy Loops. Aluminum creep specimens, 99.9995 pct pure, were machined from zone refined rod to a 2-in. gage length and a cross-sectional area of 0.025 in. These specimens were annealed at 538oC, 1000°F, for 10 min and quenched into ice water. They were then reheated to the creep test temperature of 260°C, 500°F, and held at this temperature for 18 min to al-low for vacancy condensation and loop formation. The specimens were subsequently creep tested at 1000 psi constant stress at 260°C. The temperature along the gage length was monitored by three Pt-Pt, 13 pct Rh thermocouples, two embedded in the upper and lower shoulders of the specimen and one attached to the mid-point of the gage length- The temperature gradient was held to ± l°C or less throughout the Creep test. Elongations were measured by two LVDT&apos;s &apos;connected in an averaging &apos;On-figuration, with quartz extension arms placed against the specimen at the extremes of the 2-in. gage length. i K 3J?--&apos; * *H - >^> - &apos; ^L r 77 . *y J OJL, J Fig. 1—Transmission electron micrograph of pure aluminum strained 8.2 pct at 260°C and 1000 psi constant stress. Note the presence of numerous loops near the light dislocation tangle

Jan 1, 1970

By A. H. Geisler, F. Keller

Some of the important changes that take lace in the structure of aluminum alloys are largely submicroscopic in character. This is especially true of the changes that accompany age-hardening and recrys-tallization. Although improved metal-lographic practices have been helpful in indicating some of these changes indirectly, results are limited by the resolving power of optical microscope lenses. The electron microscope, however, provides a new and important means for investigating the fine structure of metals in a range not possible heretofore. It is anticipated that this microscope will yield new and useful information to metallurgists when suitable techniques are developed to utilize its very high resolving power. Several unique methods have been devised to permit the examination of the structure of opaque samples by the electron microscope. These are all based 011 the principle of producing a very thin film that represents the prepared surface of the opaque metal sample, which can be examined in the transmission microscope; however, the available methods fall into three categories, depending on the manner in which the film is obtained. With the oxide-film method developed by Mah13-l7 a very thin surface layer of the metallographic sample is converted into oxide by a thermal, chcmical or anodic treatment. .After removal from the metal sample by one of the special techniques described by Evans,l9 this oxide film is examined in the electron microscope, and is found to portray the structure of the original metal surface. Films formed on aluminum,8,l7 nicke1,7 iron3,8,9 and a nickel-beryllium alloyl1 by heating; films formed on iron8,9 by chemical action; and films formed on aluminum3-&apos;" by anodic oxidation, have been examined. The other two are more recent methods developed principally in this country; they consist in making the thin film in the form of a mold or replica of the surface contour of an etched sample. With the negative replica method the thin film is made directly on the sample; with the positive replica method it is made on a negative reproduction of the sample. With both methods, variations in the contour of the metal sample, caused mainly by etching, produce variations in the thickness of the surface replica. Because of the direct dependence of the amount of scattering of the illuminating electrons upon the thickness of the film penetrated, only the variations in thickness of the replica are responsible for tones in the electron image. Negative replicas are made by forming a thin film of some suitable material directly on the polished and etched metal sample, and derive their name from the fact that after removal from the sample they have the high and low points in the sample reversed, as shown in Fig. I. Nega-

Jan 1, 1944

By C. E. Cottrell, G. W. Preckshot, N. D. Delisle, D. L. Katz

Most crude oils contain asphaltic substances that may be naturally or artificially precipitated. In the Greeley field, California, this asphaltic bitumen is precipitated during the flow of the oil from the reservoir to the stock tank The mechanism of such precipitation is not well understood. This paper presents the progress that has been made by using the electron microscope as a new tool and by observing the effects of the streaming potential on the formation of bitumen particles. Crude oils at atmospheric pressure viewed in the electron microscope in very thin films under a vacuum showed no asphaltic particles. A technique of preparing slides of thin films by dilution of the oil with benzene and washing in petroleum ether was used at first, and these observations showed that the solvents caused the formation of the particles, varying from 0.01 to 0.2 micron in diameter. The electrical effects of fluids flowing through porous solid were studied, with emphasis on the formation of colloidal particles by the streaming potential. The streaming potential of crude oil flowing through sand was measured and was shown to be responsible for the formation of bitumen particles. These results bring out a new phenomenon, which may occur when crude oil flows through the porous oil reservoir. mechanisms. Asphalt has been the subject of widespread investigation but, owing to the complexity of the substances being considered, progress has been slow. Investigators working primarily with the asphaltic substances have treated the subject from the colloidal standpoint and have developed theories that picture the asphaltic particles as surrounded by adsorbed materia1s.14,15,17,24 The deasphaltization of lubricating oil by the use of solvents treats the subject primarily from the standpoint of liquid-liquid equilibria.&apos;&apos; A complete understanding of asphaltic substances would make possible the following of the material from its initial state in the crude oil through precipitation processes to the final plastic stage, the most common form of which is used in asphaltic pavements. Since these asphaltic particles are very small, it appears &apos;hat the electron microscope4 might be a useful tool in studying the precipitation processes. Specimens are examined by the electron microscope in a vacuum and as very thin films, requiring special techniques in preparation of samples. A brief description of the electron microscope and its operation will bring out the difficulties and advantages of its use for this problem. The first work was done with crude oils that had been diluted with solvents for the preparation of the film to be examined. Later a technique was developed by which the undiluted oil film could be made thin enough for direct examination. These two techniques show vastly different results Asphaltic particles have been precipitated from crude oils by a variety of

Jan 1, 1943

By G. W. Preckshot, C. E. Cottrell, D. L. Katz, N. D. Delisle

Most crude oils contain asphaltic substances that may be naturally or artificially precipitated. In the Greeley field, California, this asphaltic bitumen is precipitated during the flow of the oil from the reservoir to the stock tank The mechanism of such precipitation is not well understood. This paper presents the progress that has been made by using the electron microscope as a new tool and by observing the effects of the streaming potential on the formation of bitumen particles. Crude oils at atmospheric pressure viewed in the electron microscope in very thin films under a vacuum showed no asphaltic particles. A technique of preparing slides of thin films by dilution of the oil with benzene and washing in petroleum ether was used at first, and these observations showed that the solvents caused the formation of the particles, varying from 0.01 to 0.2 micron in diameter. The electrical effects of fluids flowing through porous solid were studied, with emphasis on the formation of colloidal particles by the streaming potential. The streaming potential of crude oil flowing through sand was measured and was shown to be responsible for the formation of bitumen particles. These results bring out a new phenomenon, which may occur when crude oil flows through the porous oil reservoir. mechanisms. Asphalt has been the subject of widespread investigation but, owing to the complexity of the substances being considered, progress has been slow. Investigators working primarily with the asphaltic substances have treated the subject from the colloidal standpoint and have developed theories that picture the asphaltic particles as surrounded by adsorbed materia1s.14,15,17,24 The deasphaltization of lubricating oil by the use of solvents treats the subject primarily from the standpoint of liquid-liquid equilibria.&apos;&apos; A complete understanding of asphaltic substances would make possible the following of the material from its initial state in the crude oil through precipitation processes to the final plastic stage, the most common form of which is used in asphaltic pavements. Since these asphaltic particles are very small, it appears &apos;hat the electron microscope4 might be a useful tool in studying the precipitation processes. Specimens are examined by the electron microscope in a vacuum and as very thin films, requiring special techniques in preparation of samples. A brief description of the electron microscope and its operation will bring out the difficulties and advantages of its use for this problem. The first work was done with crude oils that had been diluted with solvents for the preparation of the film to be examined. Later a technique was developed by which the undiluted oil film could be made thin enough for direct examination. These two techniques show vastly different results Asphaltic particles have been precipitated from crude oils by a variety of

Jan 1, 1943