Search Documents

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By Oliver Bowles

Dimension stone is a term applied to stone sold in blocks or slabs of specified shapes and usually of specified sizes, contrasted with crushed, broken and pulverized stone covered in another chapter. Dimension stone includes cut stone, rough building stone, ashlar,* rubble, monumental stone, paving blocks, curbing, flagging, and many types of ornaments and novelties carved from stone. Riprap-large, irregular blocks used for shore protection-is classed with crushed and broken stone. Composition, Varieties, and Properties Dimension stones are of many kinds. The principal varieties are granites, trap rock (diabase, basalt, and gabbro), sandstone, limestone, and marble. Slate is covered in a separate chapter. Granite is a visibly granular crystalline rock consisting essentially of feldspar, quartz, and mica or hornblende. The basaltic rocks are darker in color than the granites. They contain little or no quartz and consist largely of plagioclase feldspar, augite, pyroxene, and hornblende. They are classed commercially as black granites. Limestone consists essentially of calcium carbonate. Dolomites and magnesian limestones used as dimension stone are classed with the high-calcium limestones. Marble is a crystalline form of limestone, but in the trade, any carbonate rock which will take a polish is called a marble. Many limestones which are fossiliferous but which will take a polish are sold as a decorative stone for lobbies of hotels and office buildings. Sandstone consists essentially of silica in the form of sand grains cemented into a coherent mass. Although rock occurrences are numerous and widespread, the exacting requirements of use condemn all but a small fraction of them for commercial use as dimension stone. No deposit that has closely spaced joints or planes of weakness can be used because sound blocks of moderate to large size are demanded. Uniform texture and grain size, constant and attractive colors or color pattern, and freedom from impurities that may cause stains or deterioration usually are demanded. Hardness is a variable property. Granites and diabases are as hard as or harder than steel, while limestones and marbles may be scratched with a knife. The hardness of sandstone depends upon the degree of cohesion of the grains. Workability depends to a considerable extent on hardness, but the degree of hardness has little influence on use except where stones are subjected to abrasion as on steps or floors. "Texture" as applied to stone relates to the arrangement, uniformity, and size of the constituent grains. Stones are of many colors and thus can satisfy a variety of tastes. For monumental stone, a marked contrast between polished and tooled surfaces is preferred in order that inscriptions may be read easily. Strength requirements usually may be disregarded because any sound structural stone suitable in other respects is almost invariably many times as strong as would be required for any ordinary use. The pressure on the base course of the Washington Monument, Washington, D. C., is less than 700 psi, and highgrade granites, limestones, sandstones, and marbles will sustain a crushing load of 10,000 to 25,000 psi. A structure made of stone with a crushing strength of 15,000 psi would have to be nearly 21h miles high before crushing of the lower courses would occur. However, stone disintegrates more readily under severe

Jan 1, 1960

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951

By M. C. Udy, C. H. Lorig

THROUGH the years much interest has been centered in attempting to develop a direct method of iron-ore reduction, to replace or supplement the present indirect blast-furnace process. It would not be difficult to produce a list of more than 500 patents dealing with the direct production of iron and steel, but the few of this type of process that have proved successful do not produce in competition with the blast furnace; they produce special products. A survey of the literature reveals that the equilibrium conditions for the reduction reactions (iron oxides with carbon monoxide and with hydrogen) have been fairly well established but that data on the rate of reaction are discordant, although the general effects of the variables are known. This dissertation deals with the rate of reduction of a magnetite concentrate with hydrogen. The following variables have been studied: bed depth, gas velocity, particle size and temperature. The behavior of a single particle was also studied. LITERATURE Two general factors should he considered in a study of reduction of iron oxide: (1) equilibrium relations, and (2) rate of reaction. The first factor, equilibrium, has received the attention of many investigators and the equilibria Fe3O4-FeO-H2-H2O, Fe304-FeO-CO-CO2, FeO-Fe-H2-H2O, FeO-Fe-CO-CO2 are fairly well established. Of the second factor, the rate of reaction, much less is known. Data are comparatively scarce and there is very little concordance. The discordance probably results from the large number of variables influencing the reactions. However, the general effect of the variables is known. Among these variables are temperature, gas velocity, particle size, porosity, gas composition (distance from equilibrium), presence of impurities, greater or less prevalence of side reactions, and even design of the apparatus itself. Wetherill and Furnas1 published an excellent paper in 1934. They point out that any one or more of five processes (the chemical reaction, diffusion of the reactant through the gas film, diffusion of the reactant through the solid phase, diffusion of the reaction product through the solid phase, or diffusion of the reaction product through the gas film) may be the slow process, and thus the rate-controlling process. It is regretted that the work of these authors was limited to experiments at one temperature, and that the range of gas compositions was limited. Langmuir2 has shown that heterogeneous reactions take place at phase boundaries.

Jan 1, 1942

By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

By H. C. Chang, N. J. Grant, A. R. Chaudhuri

During the creep of coarse-grained polycrystalline magnesium at elevated temperatures, a nonbasal type of slip was found to play an important role in the deformation processes. The nonbasal slip traces were examined metallographically in eight specimens (13 grains) and the observed glide plane located stereographically for each grain. The tests were run at 500&apos; and 700°F at stresses of 148 to 786 psi. Based on these measurements and theoretical calculations, the crystallographic elements for nonbasal slip were determined. WHEN a metal deforms by slip, the conventional appearance of the slip bands on the surface of a specimen is that of straight lines. Such is the behavior of the face-centered-cubic metals, as for example, aluminum. The particular slip system on which slip occurs in these metals is governed by the criterion of resolved shear stress. Work on the body-centered-cubic metals a-iron,&apos;. &apos; molybdenum, and columbium4 has shown that the process of slip is somewhat more complicated than the simple gliding of one close-packed plane of atoms over another in a close-packed direction and that it results in the formation of wavy and irregular slip traces on the surface. The recent reviews and experiments of Vogel and Brick and Chen and Mad-din3 show that, for the body-centered-cubic metals, the resolved shear stresses along the planes and the degree of close-packing do not necessarily determine the slip system. Theirs and other investigations indicate that a complete understanding of the slip process in the body-centered-cubic metals is not yet possible. However, one behavior displayed by all these metals is that the slip direction is invariably one of the close-packed directions <11l>. The wavy nature of the slip-band traces has been explained on the basis of cooperative slip by planes sharing this same slip direction.1&apos;3l&apos; It is generally acknowledged that, when the hexagonal-close-packed metal magnesium (axial ratio c/a = 1.624) deforms by slip at room temperature, it does so by basal slip in the close-packed direction <1I%>. This type of slip has the conventional appearance of straight lines and is governed by the critical shear-stress law. Schmid and coworkers" showed that basal slip was operative in the temperature range of —185" to 300°C (—300" to 572°F). Work by Servi, Norton, and Grant6 has shown that, during the creep of coarse-grained aluminum at high temperatures, new slip systems come into operation. The existence of a new high temperature slip system at temperatures greater than 225 °C (437°F) for magnesium was suggested also by Schmid. This was later indicated by Bakarian and Mathewson&apos; to be slip along the pyramidal planes (10i1) in the close-packed direction <11%>.* They * Mention will be made in the text of pyramidal planes and prismatic planes. The pyramidal planes referred to are the type I. order 1 of the form {10il); and the prismatic planes of the type 1 of the form (10i0). For the sake of brevity, they are termed in the teat as pyramidal (10il: and prismatic (10i0) planes, respectively. Where reference is made to the pyramidal plane type 1, order 2 of the form {10i2), they are referred to as the pyramidal planes of the type (10i2:. observed that this kind of slip resulted in irregular markings on the specimen surface. According to them, a possible cause for the appearance of the markings was due to "limited accessory slip on the pyramidal {10i2) planes." Burke and Hibbard," on deforming a single crystal of magnesium at room temperature, found evidence of slip on a pyramidal plane {1011). They explained it as being due to the effect of grip restraints. It is pertinent to note at this point that, although basal slip has received a fair amount of attention, only two specimens have been investigated, that of Bakarian and Mathewson and of Burke and Hibbard, to establish the elements of nonbasal slip in magnesium. During the study of the deformation mechanisms

Jan 1, 1956

By E. G. Leonardon, C. Schlumberger, M. Schlumberger

Since the beginning of the year 1928 the senior authors and their associates have applied a series of procedures which makes possible the detailed study in situ of the formations traversed by a drill hole before the casing has been landed. They have given the name "electrical coring" to the ensemble of these processes, which now replace in a large measure the mechanical coring performed by the drillers, and permit the gathering of bottom-hole data hitherto unobtainable. Three years have elapsed since the technique and interpretation of these measurements emerged from the experimental stage and entered the field of industrial application on a large scale. The total length of drill holes so far surveyed by the authors and their associates, all over the world, amounts to several millions of feet. Practical and strongly built equipment has been evolved, which permits the examination in a short time of an open hole several thousand feet long. No comprehensive paper has yet been published discussing the essential principles of the processes applied and bringing into evidence their economic interest. This is the object of the present paper.&apos; Numerous examples of field work performed under varied geological conditions are given, constituting a concrete illustration of the services rendered by the new methods. The study in situ of the formations penetrated by a drill hole is based on the measurement of a given physical factor or parameter associated with these formations. Generally the measurements are made systematically along the whole length of the open hole. The physical factors , or parameters which are now utilized by us to this end are: (1) the resistivities of the rocks; (2) their porosity; (3) their electrical anisotropy; (4) their temperature; (5) the resistivity of the muds. In order to

Jan 1, 1934

By B. L. Averbach, M. Cohen

THE PROBLEM MANY hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or subatmospheric cooling.1,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1948

By Wilbur H. Somerton

In order to evaluate the quantitative determination of porosity by various neutron logging systems, four test wells were constructed to simulate some of the possible variab1e.r found in field logging conditions. All of the test holes contain sections of limestone with one section of sandstone included in one well. Each well has a representative section of high, medium, and low porosity. Three borehole sizes are represented by three of the test wells, all containing fresh water. One test well contains saturated brine. Statistical and tune constant checks are made for each system evaluated. Runs and repeat runs are made with the sonde centered and eccentric. Factors evaluated are the effect of borehole size, sonde position, salinity, chemical composition of rock, and statistical variation. A semi-quantitative method of evaluation of these effects is used giving the average maximum per cent error possible for each. Drift and calibration procedures are also discussed. The effect of the various factors appears to be largely a function of the phenomena detected as well as the means of detection. Graphic illustrations of some of these effects are presented. It is concluded, that for accurate log interpretation, the hole size and sonde position should be known. INTRODUCTION The use of neutron logs for the derivation of porosity has become an accepted practice in many areas. In recent years, many different neutron logging systems have been offered to the industry. The neutron sources presently available are of the radium-beryllium or polonium -beryllium type. Detector types used are ionization chambers, Geiger-Mueller-type counters, proportional counters, or scintillation detectors used to detect or measure gamma rays, thermal neutrons, epithermal neutrons, fast neutrons or combinations of these. It is well-known that all systems do not respond alike in all environments. As a result, testing facilities and an evaluation method were developed for use in evaluating the porosity discriminating ability of neutron logging systems using conditions simulating those normally encountered in the field. With such an evaluation, the suitability of a logging system can be determined lor selected field conditions. TEST FACILITIES The testing facilities consist of wells containing rocks of various porosities, constructed to include as many parameters as practicable. Three pits were drilled to a depth of 20 ft and the fourth to a depth of 9 ft, all having 48-in. diameters. Rat holes were dug to a depth of 6 ft in the center of each pit and fitted with sections of pipe having appropriate diameters. The top of this pipe was located approximately 8 in. above the pit bottom. A 6-in, layer of cement was then poured on the bottom and while still wet, 42-in. OD corrugated, galvanized culvert pipe was set on bottom and centered in place. This pipe extends approximately 1 ft above the surface of the ground. The annulus around the culvert pipe was then filled with cement to the top. A 1- or 2-in. layer of sand was placed on the cement bottom to provide an adjustable bed on which to place the series of rocks set in each hole. A cross section of a typical test well containing the porous rocks is shown in Fig. 1.

By H. S. Price, D. A. T. Donohue

The system of equations describing displacement of a hydrocarbon liquid by a hydrocarbon vapor in a porous medium where mass transfer takes place between the phases is solved numerically for a variety of gas injection processes. Even though the method of solution is quite general, only systems with three hydrocarbon components are considered. Computer simulations of displacement processes wherein mass transfer between phases is both considered and neglected are compared, and it is shown that neglecting mass transfer can give pessimistic displacement efficiencies. INTRODUCTION The role of the gas displacement process in the recovery of petroleum has been subjected to a series of detailed analyses; as a result, a number of predictive models have been published in the literature. However, because of major simplifying assumptions, most of these models do not completely represent the physical system. As a result, the effect of making the simplifying assumptions is unknown. Therefore, a complete representation of this process — one without major simplifying assumptions —should lead to a fuller understanding of the process, and perhaps to methods of improving it. The general method of developing a model for two-phase fluid flow in a porous medium is to solve simultaneously the continuity equation, the energy equations and the equation-of-state for each phase under the prescribed initial and boundary conditions. For an isothermal system, the energy equations reduce to the momentum equation. Darcy&apos;s law. However, since natural gas is the vapor state of the reservoir liquid, interphase mass transfer may take place with concomitant changes in both the intensive and extensive thermodynamic properties of each phase. It is this phenomenon that has often been omitted in previous mathematical models. An additional relation, then, which accounts for mass transfer between the phases, must be included with the other equations to specify a complete model. Completely formulating the equations to be solved is not a difficult task1 but obtaining their solution has been intractable up to now. Availability of large-memory, high-speed digital computers now makes an attack on this formidable problem possible. This paper presents a preliminary study of the problem. Since this investigation is intended to be exploratory, it is restricted to the linear, horizontal, isothermal, two-phase viscous flow of oil and gas in an oil reservoir. In the early development of predictive models of this process, the reservoir system was considered as a unit and various forms of the material balance equation were proposed.2-4 Pressure and saturation gradients were then added in the Buckley-Leverett model.5 The Buckley-Leverett formulation considered the fluids to be incompressible; thus, the mathematical model reduces to a steady-state system. In the 1950&apos;s, studies incorporating numerical techniques were being published.6-9 These mathematical models differed in the efficiency of finite difference techniques, the inclusion or exclusion of capillarity or the number of space dimensions considered. To solve these nonlinear, partial differential equations, each phase was considered to be homogeneous with time; therefore, mass transfer between phases was neglected. The effect of mass transfer on the gas displacement process was first reported by Attra. 10 He simulated the one-dimension flow system by a series of cells in each of which the fluids were equilibrated during a time step. In addition, the pressure throughout the system during each time step was predetermined and constant-phase velocities were calculated according to the Buckley-Leverett incompressible fluid flow model. Welge et al.11 developed a model for the displacement of oil by an enriched gas where composition is considered to be a dependent variable. Fluid

By R. E. Hobart

THE development of the Hauto power plant and the claims made by various engineers that electricity was more economical than steam for power purposes in and about the mines; led the Lehigh Coal and Navigation Co., in 1911, to conduct a test to ascertain the consumption of power used by a large steam hoisting engine. The question being one on which no reliable information could be found, and the opinion of various engineers differing to such an extent, it was decided that a test under actual operating conditions was necessary. This was arranged for at one of the collieries. The engine selected was a 30 by 60-in. (76.2 by 152.4-cm.) piston-valve engine of modern type, and comparatively new. The boiler plant from which the hoist received its power was about 600 ft. (182 m.) from the engine, the latter being fed by a 10-in. (25.4-cm.) steam line insulated with magnesia pipe covering. Two batteries of the boiler plant, aggregating 1200 hp., were cut off and fed into a separate steam line leading direct to the hoist engine. Steam auxiliaries, consisting of feed-water pump and blowers, were fed by the boilers in test, and their consumption charged against the hoist. A barrel weighing device was installed, as it was felt that this would be the most accurate way of determining the consumption of water. The fuel, No. 3 buckwheat, was carefully weighed, and every precaution was taken to make the test accurate in every particular. The test was run for 1 week, or a total of 168 hr. A record was kept of the number of trips hoisted or lowered, and continuous indicator cards were taken. One particular set of cards was taken with the hoist operating balanced, and also with the hoist operating with no counterweight other than the empty cage, the coal in the car being weighed. The speed of the hoist was taken by means, of a graphic recording instrument which registered the number of revolutions every 5 sec. From this record, speed-time curves were plotted.

Jan 2, 1918

By James K. Stanley

WHEN a plastically deformed metal is heated to a certain temperature, it undergoes a complete change in microstructure, the consequence of which is a marked alteration of mechanical properties such as hardness, strength and ductility. This change in microstructure occurs by recrystallization and is a process involving the formation and growth of strain-free nuclei in the deformed matrix. These nuclei continue to form with time and grow until a new grain structure replaces the cold-worked structure. The formation of the nuclei in the deformed sheet of 1 per cent silicon ferrite is illustrated in Fig. 1. If a recrystallization is conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time leads to an isothermal recrystallization curve, first established in 1942.1 Such recrystallization curves are shown in Fig. 4. These curves show that the recrystallization of a cold-worked metal is best considered as a rate process rather than a time independent process such as is suggested by the improperly named and misleading recrystallization diagrams involving deformation, temperature, and grain size. 2-5 Any study of the rate of recrystallization resolves itself into a study of the component rates of nucleation and growth. The previous paper&apos; provided an account of the determination of the rates of nucleation; N, the number of nuclei formed per unit time per unit of unrecrystallized area, and growth, G, the radial growth in unit time, in the recrystallization of silicon ferrite (1 per cent Si). A method was developed to furnish experimental data for evaluating the effect of the recrystallization variables on N and G. The mathematical analysis for the derivation of the isothermal recrystallization curve was developed for a two-dimensional case (in thin sheets where the diameter of the recrystallized grain is greater than the sheet thickness). The present paper is a continuation of the study of recrystallization of 1 per cent silicon ferrite begun in 1942.1 In this work the effect of the factors deformation, temperature, grain size, composition, and recovery is studied with respect to the rates of nucleation and growth. At the same time it is shown how the cooperation of N and G affects the isothermal recrystallization curve. The study of these variables on N and G has a definite bearing on the mechanism of recrystallization and should lay a foundation for a rational theory on the subject. PROCEDURE The procedure used in these experiments was essentially the same as that described previously but in certain details some changes were made in the interests of speed. With few exceptions, the procedure is the same for the study of all the variables. Where the procedure is different from standard manipulations attention is called to this fact.

Jan 1, 1945

By H. M. Cyr, T. F. Steele, C. W. Siller

The development of a new metallurgical roasting device is described. It consists of a refractory column into which air is injected at various levels, forming several superimposed fluidized beds with no supporting grates. When pelleted zinc sulphide concentrates are charged, the roasted product needs no further sintering before reduction to metal. WHEN a gas such as air is blown upward with increasing velocities through a loose mass of solid particles, marked changes in the physical behavior of the particles are noted. At first, when the velocity of the gas is insufficient to support any of the solid, the mass constitutes a "fixed bed." As the gas velocity increases until the pressure drop through the bed approaches the effective weight of the bed per unit area, the bed expands until the solid particles are supported by the air rather than by the lower particles. Some vibration of the particles becomes apparent, but little mixing occurs. This condition is called a "quiescent fluid bed." A further increase in gas velocity imparts more separation and more motion to the individual particles until a condition of turbulence is reached. This "turbulent fluid bed" resembles a rapidly boiling liquid with the characteristic highly agitated diffuse surface and many small eruptions of the boiling mass. Different degrees of turbulence can be generated and all produce excellent mixing. The final stage occurs when the gas velocity becomes so great as to create a "dispersed suspension." Here no surface of the mass is defined and the gas carries solid particles out of their original positions. These changing conditions of fluidization have been studied carefully and pertinent nomenclature standardized by a committee of the American Institute of Chemical Engineers.&apos; Many mathematical analyses2-3 have been made of the forces acting in a fluid bed. These analyses are invaluable, especially for the design of column sizes and selection of equipment. However, in a metallurgical process involving solids of many sizes with changing densities, varying temperatures, and changing gas compositions within the bed, calculations based on theory become approximate. Optimum operating conditions then are best determined experimentally. Many applications have been made of the principles of fluid-bed action by mechanical, chemical, and metallurgical engineers. Especially when good con- tact between reacting solids and gases is desired, very effective results are obtained from fluid beds. They permit excellent temperature control and uniformity throughout a mass of solids in fluid action. Heat transfer to walls and any coolers is high, and fast reaction rates are attained because the solid surfaces are continuously swept clean. The main disadvantages of fluid-bed operations are the danger of short-circuiting in a single bed, danger of incipient sintering which stops action, the necessity of avoiding large changes in particle size or density during roasting, and dust losses when particles of the charge are carried out with exit gases. In the metallurgical field the roasting of sulphide ores to form oxides and sulphur dioxide appears to combine several operating conditions which can be achieved to advantage in a fluid bed. Roasting involves a solid-gas reaction where a high reaction rate is necessary for high capacity, where good temperature control is important in order to prevent sintering, where good heat transfer is needed, and where the density of the solids, when changing from sulphides to oxides, is not largely changed. Short-circuiting, however, constitutes a major problem when a single fluid bed is used. Because of the turbulence of the bed, an entering particle may be in the region of the discharge before it is roasted. Hence, to attain a satisfactorily low sulphur in the calcine, a long average residence time with correspondingly low capacity is required. The solution to this difficulty is the use of multiple stages, which in the conventional fluid-bed design requires separate hearths with feed and discharge mechanisms for each stage. A further practical difficulty in fluid-bed roasting of flotation zinc concentrates is their fine particle size which makes a true fluid action without excessive carry-over of dust very difficult to attain, especially when the large air volumes necessary for high capacity are used. A New Design After considerable experimentation in the laboratory and on a semipilot-plant scale, a new method and equipment for roasting were devised which provided a unique solution to these problems. A detailed account of this development appears in the patent literature," and many of the variations of this development reported herein are the subject of

Jan 1, 1955

By W. N. Lacey, R. H. Olds, B. H. Sage

Samules of liquid and gas were obtained from the primary separator of a well in the Paloma field. The volumetric properties of the samples and of six systematically chosen mixtures of the samples were experimentally determined at 100°, 190°, and 250°F. at pressures up to 5000 lb. per sq. inch. From these data the influence ,of pressure and temperature upon the composition and specific volume of the bubble-point liquid and of the retrograde dew-point gas was established, The formation volumes and gas-oil ratios of the rnixtures investigated were calculated on the basis of the plant-product oil, which is defined as the isobutane and less volatile portion of each mixture. The results are presented in graphical and tabular form. The volumetric behavior of the mixture corresponding to that produced by the well at the time of sampling was determined for 235ºF., the reported reservoir temperature, by graphical interpolation of the experimental data with respect to composition and temperature. The results indicate that the well-production mixture probably existed as a gas at its retrograde dew point under the conditions of temperature and pressure believed to prevail in the producing zone at the time of sampling. The effect upon the phase behavim occasioned by the omission from the well-production mixture of certain components of intermediate molecular weight was investigated. In the first case, all of the isobutane and 11-butane, and substantially all of the iso-pentane, were removed from the mixture of trap samples corresponding to the well production. In the second case, all the propane, isobutane and n-butane, and substantially all of the isopentane, were removed. Both modifications led to considerable increases in the retrograde dew-point Pressure at 235ºF.; an increase of 558 lb. Per sq. in. above that of the unmodified well-production mixture in the first case, and an increase of 1208 lb. Per sq. in. in the second. It was concluded that the material? remaining after the removal of certain components of intermediate molecular weight could not be injected back into the reservoir in the saqe proportion in which they were produced without entailing appreciable loss of liquid material through condensation within the formation. Introduction Under the usual conditions of production practice, petroleum arrives at the surface of the earth in a physical state considerably different from that in which it existed in the underground reservoir. The relative rates of production and the properties of oil and gas measured at surface conditions do not constitute, in general, even a qualitative description of the fluids existing in the reservoir. The estimation of reserves and the attainment of optimum efficiency with regard to rate, quantity, and cost of production require accurate data concerning the physical properties of petroleum throughout large changes in pressure and temperature. Many schemes have been devised for predicting the behavior of propane, as it is encountered in nature? but the experimental work upon which these predictions are based has not, for the most part, been extended to the higher pressures that occur in practice, nor do these methods permit, as yet, the estima-

Jan 1, 1945

By C. G. Dunn, J. L. Walter

Secondary recrystallization to the (110) [001] texture in high-purity silicon iron occurs if low-oxygen material is annealed in a nonoxidizing atmosphere. Any departure from these conditions results in a growth of (100) oriented grains. The nature of the matrix and secondary recrystallization structures and textures and the nature of grain boundary interactions during growth show that the low gas-metal interfacial energy of the (110) surfaces provides the driving force for growth of these grains. A type of grain growth, characterized by a driving force which derives from energy differences of {hkl} surfaces at the gas-metal interface, has been treated in recent papers.&apos;-7 Secondary recrystallization to the cube text!:: in high-purity silicon iron provides one example. The present paper also deals with a surface energy driving force but the texture that results by secondary recrystallization is not the cube texture; it is a texture in which the (110) plane is in the plane of rolling and the [001] direction is in the direction of rolling. The phenomenon described in this paper is different from the impurity (dispersed phase)-controlled secondary recrystallization process in which the (110) [001] oriented grains grow under the action of grain boundary driving forces.8-12 It is also different from tertiary recrystallization,2 which also produces the (110) [001] texture in high-purity silicon iron, since the matrix textures and grain sizes are different. Finally, it is unlike any other form of secondary recrystallization reported in the literature. The possibility of obtaining the (110) [001] texture in high-purity silicon iron became clear in a study of the effect of impurity atoms on the energy relationships of (100) and (110) surfaces. In this study Walter and Dunn6 observed the migration of (100)/(110) boundaries, i.e., boundaries between two grains, one of which has a (100) plane and the other a (110) plane, respectively, parallel to the plane of the sheet specimen. At 1200°C the (100)/(110) boundaries advanced into (100) grains in a vacuum anneal, then reversed their direction and migrated into (110) grains in a subsequent anneal in impure argon. Finally, the direction of migration reversed once again with (110) grains growing into (100) grains in a second vacuum anneal. These results were explained in terms of a change in concentration of oxygen atoms at the gas-metal interface during the anneals. Thus, oxygen atoms were added to the surface during the anneals in impure argon to the point where ?100, the specific surface energy of the (100) oriented grains, was lower than ?110, the surface energy of (110) oriented grains. In vacuum, however, the oxygen concentration at the surface was lowered to the point where ?110 < ?100. Concerning the possibility of secondary recrystallization in high-purity silicon iron with a low initial oxygen concentration, the observed effect of adsorbed oxygen atoms has indicated6 that a good vacuum anneal would favor the rapid growth of matrix grains with the (110) plane in the plane of the sheet much more than grains in the (100) orientation. The growth of only (110) oriented grains of course would depend upon y110 being less than ?hkl, where hkl refers to any plane different from (110). The present paper is concerned with the application of the above ideas to secondary recrystallization to the (110) [001] texture in high-purity silicon iron. The matrix and secondary recrystallization textures and structures are defined and discussed. Observations of growth of nuclei for secondary recrystallization and of boundary interactions are included to provide direct information on the surface energy relationships between (110) and other (hkl) surfaces. EXPERIMENTAL PROCEDURE As before, 2,4-6 high-purity iron and silicon were melted and cast in vacuum to provide an alloy containing 3 pct Si with less than 0.005 wt pct impurities. The oxygen content of the ingot was lower than in previous ingots, being approximately 3 ppm (by weight). The carbon content of this ingot may have been slightly higher than was found for previous ingots. The same rolling and annealing schedule used previously2 was followed in this study to obtain samples 0.012 in. (0.3 mm) thick. These samples were electropolished prior to annealing. After rolling and polishing, the oxygen content of the material was approximately 6 ppm; material used in the previous studies contained about twice this amount of oxygen.

Jan 1, 1961

By Robert E. Hoffman, John B. Hudson

The self-diffusion coefficient of pure lead has been measured at five pressures between atmospheric and 40 kb. over a temperature range of about 150°C near the melting point at each pressure. Measurements were made using a radiotracer technique, samples being sectioned electrochemically after the diffusion anneal to determine the diffusion penetration curve. Pressure was applied in a "belt" type pressure device similar to that used by Hall et al., in the diamond synthesis. The self-diffusion coefficient, D, can be represented by an equation of the form at constant pressure, and an equation of the format constant temperature. An apparent correlation between the effects of pressure on self-diffusion and on the melting point of the material observed by Nachtrieb et al., at pressures below 10 kb. was found to be only approximate as measurements are carried to higher pressures. OVER the course of the past 30 years a large number of studies1-&apos; of the rate of atom movements in solid metals have been carried out. These studies have in general been aimed at increasing the understanding of the detailed atomic process by which atom movements in metals can take place. The largest portion of these studies consisted of measurements of the self-diffusion coefficient, D, as a function of temperature. From such studies con- siderable information regarding the energetics of the motive process has been deduced. Recently such measurements have been extended to the pressure dimension. However, the existing work in this area is scanty and has in the past been limited to the pressures attainable in oil or gas bombs—i.e., up to about 10 kilobars (kb). In the present work, the self-diffusion behavior of pure lead has been investigated using the "belt" type high-pressure apparatus designed by Hall7 over a pressure range from atmospheric to 40 kb at temperatures extending over about a 150°C range close to the melting point at each pressure.

Jan 1, 1962

By P. Hazebroek, C. S. Mathews, E. E. Allen, H. C. Lefkovits

A rigorous study was made of the behavior of reservoirs composed of horizontal layers, unconnected except at the well and filled with a compressible fluid. The report is presented in two parts. Part I deals with the practical implications of the results obtained; Part 11 contains the mathematical derivation of the solution. The main portion of Part I is concerned with application of the results to reservoirs composed of two layers. Relative rates of depletion of the layers are studied, and it is shown that differential depletion between layers exists in the transient stage of the reservoir, which generally is of an order of magnitude longer than the transient stage in a single-layer reservoir. In the transient stage, the more permeable layer is depleted faster than the less permeable. However, the reservoir approaches a steady-state situation where both layers contribute equally to production. Theoretical build-up curves from such reservoirs are presented, and the influence of a skin effect and flow into casing and tubing are also evaluated. The build-up curves are predicted to have, first, the familiar logarithmic straight-line section and, subsequently, a rising and flattened section. The results found are compared with an extension of an approximate theory, and it is found that this simplified theory is applicable over most of the life of the reservoir. Extensions to reservoirs containing more than two layers are indicated, and examples of the performance and build-up curves for three-layered reservoirs are presented. The theoretical results on build-up curves were applied to field examples of such reservoirs, and satisfactory results were obtained. From the build-up curve, the pemeability-thickness product, the wellbore damage and the static pressure are obtained. However, it apparently is not possible to determine the properties of the individual layers from the combined build-up curve. A large number of reservoirs have been found where the producing formation is composed of two or more layers of differing physical characteristics, such as permeability and porosity, and where also the thicknesses of the layers differ. Since in general a differential depletion should exist between the layers of such reservoirs, it would be advantageous to know the amount of the differential depletion under a given production history. It also would be valuable to know the pressure behavior, because it could be undesirable to produce a reservoir in such a manner that the pressure in one of the layers would have fallen below the bubble point of the oil at a time when another layer might still be virtually undepleted. The determination of static pressures in shut-in wells with slow build-up is another feature of importance in layered reservoirs. If the behavior of the reservoir differs appreciably from the predicted behavior of a single-layer reservoir, the type of analysis for build-up curves suggested for single-layer reservoirs is not applicable. Several authors have treated the problem of finding the pressure and production characteristics of multilayer reservoirs. Horner treated the problem of n layers in an infinite field, the layers being connected only at the well. Tempelaar-Lietz2 has presented an approximate treatment of the characteristics of a bounded reservoir composed of two layers of different permeabilities and equal thicknesses. Homer gave no information on differential depletion between layers, and the treatment of Tempelaar-Lietz was not applicable for prediction of pressure build-up behavior. In addition, it was thought that a more rigorous treatment than the one by Tempelaar-Lietz would be valuable in determining the range of validity of this solution. The present study, therefore, was made of a bounded reservoir composed of two or more layers,

By N. F. Foster

The use of piezoelectric semiconducting materials for the fahrication of ultrasonic transducers has raised the upper fundamental frequency limit for transducers from about 200 mc to above 10 kmc, Several types of semiconductor transducer configurations have been proposed and examined experimentally. Depletion-layer transducers have been made and operated at frequencies below 1 kmc hut they appear to he better suited for operation at considerably higher frequencies around 10 knzc. Diffusion-layer transducers have been made and operated in the range 50 to 1000 mc and have exhihited considerably improved conversion losses and bandwidths compared with other transducers available in the frequency range. A variety of novel structures are possible using these new types of transducers, some of which could lead to substantial advances both in research and in the fabrication of ultrasonic delay lines and memory elements. THE field of ultrasonics today spans some five decades of the frequency spectrum from the audible to the kmc range and finds applications ranging from fundamental research into the atomic structure of matter to the degreasing of machine parts. To cover this wide range it has been necessary to develop a great many types of ultrasonic trandsucers utilizing a variety of materials and physical phenomena. The first ultrasonic transducers were made during World War I for a submarine-detection system. They consisted of plates of single-crystal quartz bonded between metal plates and were one of the first applications of the phenomenon of piezoelectricity discovered nearly 30 years previously. Despite the many advances which have been made in transducer technology, piezoelectric transducers using single-crystal quartz are still used almost exclusively for application above about 30 mc. Transducers at these frequencies are normally made in the form of thin quartz plates which are then bonded onto the medium in which the ultrasonic wave is to be propagated. The crystallographic orientation and geometry of these plates determines the type of wave generated and the way in which the efficiency of the electromechanical conversion varies with frequency. Analysis of the design parameters shows1 that the frequency of maximum efficiency (the fundamental or resonant frequency) is that frequency at which the transducer is approximately half the wavelength of the ultrasonic wave in the material. As the frequency increases, the ultrasonic wavelength, and therefore the optimum transducer thickness, decreases and in practice the fabrication of quartz transducers with fundamental freauencies above 100 mc becomes extremely difficult due to the extreme thinness required. For frequencies above 100 mc quartz transducers can be used in overtone-mode operation, and for very high frequencies (500 to 24,000 me) a technique using a quartz rod inserted in a high-Q microwave cavity4 is available. These techniques, however, exhibit comparatively low fractional bandwidths and rather poor conversion efficiencies. The present trend in ultrasonics is towards high frequencies and greater bandwidth to allow the use of shorter pulses which can give increased discrimination in radar-system delay lines and greater storage capacity in computer applications. The increasing demand for more efficient transducers with greater bandwidth

Jan 1, 1964

By A. H. Daane, J. J. Hanak, F. H. Spedding

IN the study of the rare earths at the authors&apos; laboratory, methods have been devised for preparing pure rare earths and many of their properties&apos;- have been determined. Very little information is found in the literature on the properties of europium metal, which is the scarcest of the naturally occurring rare earths. Since we have recently prepared europium in appreciable quantities, we are in a position to describe the method of preparation and some of the properties of this metal. Metallic europium was first prepared by Klemm and Bommera who heated a mixture of potassium and EuC1, in vacuo, and obtained a mixture of europium metal and KC1. Trombe4 electrolyzed a molten salt bath containing NaC1, KC1 and EuC1, and collected the europium in a molten cadmium electrode as a cadmium alloy. The cadmium was subsequently removed by distillation but the properties of the residue indicate that pure europium was not obtained. McCoy attempted to prepare europium by distilling mercury from europium amalgam, but the stability of the Eu-Hg intermetallic compounds prevented a complete separation of the two elements. The preparation of very pure europium was suggested by previous work in this laboratory1,4 in which ytterbium and samarium were prepared by heating the respective sesquioxides with lanthanum metal turnings to 1450°C in vacuo and distilling ytterbium and samarium from the mixtures. Subsequently, small test experiments showed that europium also could be prepared by this method. A more detailed version of this method was used in the work described in this paper. Klemm and Bommer3 found by X-ray analysis that the metal had a body-centered cubic (bcc) structure with a lattice constant a, = 4.582 ± 0.00A (converted from kX units), with a bulk density of 5.30 g per cu cm. They found europium to be weakly ferromagnetic. Spedding, et al,7 found a,, to be 4.606 ± 0.001A. Barrett&apos; showed that the bcc structure persists throughout the temperature range 5 to 3000K with a, at 5, 78, and 300°K being 4.551 ± 0.003, 4.551 ± 0.004 and 4.577 ± 0.001A, respectively. Trombe1 described europium as being iron gray, malleable, about as hard as neodymium and not attacked by cold water. He estimated the melting point to be between 1100 and 1200°C. Previous work in this laboratory indicated that the pure metal corrodes rapidly in air and reacts with cold

Jan 1, 1959

By W. N. Hiatt

The mathematical theory of the flow of two-phase, incompressible fluid through porous media is clarified, and the development of a general fluid displacement equation for two-phase, incompressible vertical flow through porous media is outlined. The relationship between the three components of the equation — the "fluid drive effect", the "gravity effect", and the "capillary effect&apos;&apos; — is discussed, as well as implications of the analysis in connection with the study of certain types of petroleum reservoirs. INTRODUCTION The purpose of this paper is to clarify and summarize the mathematical basis of the theory of two-phase incompressible fluid flow through porous media, particularly as it pertains to vertical flow, and to present a qualitative* exposition of the controlling factors involved in circumstances where this type of flow may exist. Although the generally accepted theory of heterogeneous fluid flow through porous media was developed a number of years ago by Muskat,1 and Buckley and Leverett2, 3 using the basic premise of Darcy, (and since then expounded upon by many others) there is a need for an over-all summary and clarification of this theory, especially regarding certain types of applications in connection with so-called "gravity-drainage-type reservoirs". The source and derivation is outlined for what is referred to here as the "General Fluid Displacement Equation for Incompressible Vertical Two-Phase Flow through Porous Media&apos;&apos;. This equation would apply under the condition where the pressure drop along the path of flow is negligible in comparison with the pressure level on the system, or where compressibility and solubility effects are negligible. These conditions exist ordinarily in gravity-drainage-type reservoirs. Specifically, it will be shown that this general equation may be developed directly from the basic equations, which, according to present theory, govern the general case of viscous heterogeneous flow through porous media. This general equation has appeared in the literature previously, but in most cases its development from basic theory is not indicated clearly, or the equation is presented in terms of groups of constants and variables involving reduced or dimensionless quantities. This presentation is expedient in cases of experimental or computer applications; but it may make it difficult for the practicing petroleum engineer to identify all the factors involved or to understand the relationships between them. Therefore, in the following development, only ordinary mathematical parlance will be used, and no terms involving groups of other equations or reduced or dimensionless quantities will be used. DERIVATION The following equations for two-phase oil and gas flow result from analogy with Muskat&apos;s general equations,** if solubility and compressibility effects are neglected, and if all volumes are considered in terms of reservoir conditions, and the water phase, if present, is considered to be immobile (or effectively a part of the porous medium.) In this case, the sum of the oil and gas saturations may be taken as unity, and the saturation of each phase is in terms of the total hydrocarbon saturation. Note that in Eqs. 1 and 2, and in the derivation following, z is taken as positive in the vertically downward direction,

Jan 1, 1969