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By A. N. Diehl

IT is the object of this paper (1) to deal with the elements in blast-furnace gas from the standpoint of their importance, and the part they are to play in future consumption, and (2) to give detailed information about the construction and operation of a plant designed among the first in this country for washing gas on a large scale.

Jan 5, 1914

By A. McLean, D. W. Gomersall, R. G. Ward

An experimental study has been made of the solubility of nitrogen in liquid iron and liquid Fe-C alloys using levitation melting and a rapid quenching device. Iron alloy droplets were equilibrated with nitrogen gas at 1 atm pressure, quenched, and analyzed. Previous techniques for studying the Fe-C-N system have produced data which me in marked disagreement. This disagreement is due largely to errors caused by reaction between the molten alloy and the crucible material. With the levitation procedure, errors from this source have been eliminated and precise solubility data obtained for temperatures between 1450° and 1750°C. C-N interactions in molten iron have been expressed in terms of first- and second-order free energy, enthalpy, and entropy parameters. ALTHOUGH the solubility of nitrogen in iron base alloys is in general small, the effects of nitrogen on the properties of steel may be quite profound. For most purposes nitrogen in finished steels is undesirable, particularly in the low-carbon grades, since on cooling to room temperature the solubility limit of nitrogen in the steel may be exceeded and this can lead to embrittlement and loss of ductility on aging. On the other hand, nitrogen can improve the work-hardening properties and machinability of steels while in certain stainless grades nitrogen is important in order to stabilize the austenite phase. It is, therefore, desirable that one should be able to predict the solubility of nitrogen in liquid iron alloys. To do this, information is required concerning the interactions between nitrogen and the various alloying elements which may be present in liquid iron. There have been several investigations of these effects in recent years1"7 and the interactions between nitrogen and many elements dissolved in liquid iron are now known to a high degree of precision at steel-making temperatures. Unfortunately, a number of iron alloy systems which are of interest in steelmaking have been difficult to deal with by the experimental techniques generally used for this type of investigation. Among the most important of these are the Fe-C alloys. In the past, two methods have been widely used for determining nitrogen solubilities: the Sieverts' technique, in which the amount of nitrogen required to saturate a given mass of liquid metal at a particular temperature and pressure is measured volumetrically, and the sampled-bath technique in which liquid metal held in a crucible is equilibrated with a gas phase containing a known partial pressure of nitrogen, and samples drawn from the melt are quenched and analyzed. These two methods have been discussed in detail elsewhere.5,8 With the Sieverts' technique, errors may be introduced from the following sources: i) Gas adsorption on metal films which have condensed on the cooler parts of the reaction chamber. ii) Uncertainty in the determination of "hot volume" calibrations. iii) Crucible-melt interaction, particularly if a gaseous reaction product is formed or if the melt becomes contaminated with material from the crucible walls. The sampled-bath method may also suffer from errors due to reaction between the melt and the crucible material. In addition, there is the possibility that gas may be lost from the sample during solidification and cooling. In the present investigation, the solubility of nitrogen in liquid iron alloys has been studied by means of a new technique based on the use of levitation melting equipment and a rapid quenching device. In addition to the fact that problems of the type outlined above are avoided, this particular approach has the following advantages: i) The high-frequency current induces vigorous stirring within the levitated droplet so that gas-metal equilibration is rapidly attained. ii) The gas phase surrounding the melt can be changed very quickly and is easily controlled. For example, a droplet may be levitated in helium, deoxidized in hydrogen, equilibrated with nitrogen, and quenched, within a period of 15 min. ii) Melts can be readily under cooled or superheated, thus extending the effective temperature range of an investigation and allowing temperature-dependent data to be determined with a high degree of precision. Excellent reviews of levitation melting techniques and their application to physical-chemistry studies at high temperature have been published recently by Jenkins et al.,9 Peifer,10 and Rostron.11 In the present investigation a levitation melting technique has been used to obtain data for the solubility of nitrogen in pure liquid iron and liquid Fe-C alloys at temperatures between 1450° and 1750°C. The solution of nitrogen in liquid iron can be described by the reaction:

Jan 1, 1969

By P. D. Merica, H. Scott, R. G. Waltenberg

The remarkable phenomena exhibited by the aluminum alloy known as duralumin were discovered during the years 1903—1911 by A. Wilm1,2 and have been described by him and by others. 3, 4,5.6 The unusual feature of this alloy is the fact, as was shown by Wilm, that it can be hardened quite appreciably by quenching from tempera-

Jan 1, 1921

By Michael Poole, Joseph M. Chelini

Most earthmoving operations using off-road, rubber tired production equipment have abnormally high total tire costs. Achieving informational control over 7 direct and 2 indirect tire cost centers can reduce tire costs more than 50 percent; a 20 percent savings is often guaranteed. This is achieved by utilizing available computer software and implementing tire information management through the engineering deparatment.

Jan 1, 1983

By T. F. Kassner

The dissolution kinetics of type 304 stainless steel in the Bi-Sn eutectic alloy have been investigated under the well-defined hydrodynamic conditions produced by the rotating-disc sample geometry. In addition, the mutual solubilities of iron, chromium, nickel, and manganese from 304 stainless steel in the eutectic alloy were determined over the temperature range 450" to 985°C. The convective -diffusion model for mass transport from a rotating disc was used to interpret the experinlental dissolution data. The dissolution process was found to be liquid-diffusion-controlled under specific conditions of temperature and Reynolds number. Liquid penetration into the 304 stainless steel resulted in a reduction of the di,ffusion-controlled mass flux and thus precluded the calculation of the diffusion coeficients of the four components from 304 stainless steel in the Bi-Sn eutectic alloy. The convective-diffusion model for diffusional limitations of electrode reactions and mass transport at the tationssurface of a rotating disc set forth by Levich 1,2 has found wide applicability in the investigation of electrochemical and dissolution phenomena in aqueous systems. Riddiford 3 and Rosner have reviewed the model and also include numerous references on work of this nature. More recently the rotating-disc system has been applied to the investigation of hetereogeneous reactions in liquid-metal systems. Shurygin and Kryuk 5 have measured the dissolution rates of carbon discs in molten Fe-C, Fe-Si, Fe-P, and Fe-Ni alloys. Shurygin and shantarin6 also studied the dissolution kinetics of iron, molybdenum, chromium, and tungsten, and the carbides of chromium and tungsten in Fe-C solutions with a rotating-disc sample geometry. In these systems it was possible to distinguish between diffusion and reaction control mainly through experimental confirmation of the velocity dependence of the dissolution rate predicted by the model. However in the absence of dependable solubility data and the virtual lack of diffusion data in these systems, a quantitative check of the magnitude and the temperature dependence of the rate was not possible. In many instances, estimates of the activation energy for solute diffusion and the diffusion coefficient based upon the experimental dissolution data are not credible. A recent study by this author7 has resulted in a critical test of the model in a liquid-metal system. The solution rates of tantalum discs in liquid tin were measured over a wide range of temperature and velocity conditions. In addition, the solubility and diffusion coefficient of tantalum in liquid tin were determined as a function of temperature. The latter data were used with the model to predict both the magnitude and the temperature dependence of the dissolution flux. In that work it was also deemed necessary to reevaluate the solution to the convective diffusion equation to incorporate the effect of the lower range of Schmidt numbers encountered in liquid-metal systems. Good agreement between the model and the experimental dissolution data in the region of diffusion control was obtained in the Ta-Sn system. The Bi-Sn eutectic alloy is used as a seal between the reactor head and the reactor vessel in the Experimental Breeder Reactor-11. The alloy is fused periodically prior to fuel-handling operations. In that connection, it was necessary to investigate the compatibility of the liquid alloy with the type 304 stainless-steel containment material. The results of a rotating-disc study in this multicomponent system are presented. EXPERIMENTAL METHOD The 5.08-cm-diam discs were machined from 0.317-cm-thick plate. Chemical analysis information for the type 304 SS material is given in Table I. The discs were ground flat on metallographic paper and given a final polish on Linde B abrasive. A thin support rod was threaded into the disc and the region around the threads was fused under an inert gas. The support rod was fitted with a quartz protection tube and then was attached to a supporting shaft which passed through a rotary push-pull vacuum seal. The disc and supporting shafts were dynamically balanced prior to insertion into the furnace tube. The apparatus is shown schematically in Fig. 1. The 58 pct Bi-42 pct Sn eutectic alloy melts were prepared from 99.995 pct pure Bi and Sn by fusing the components in a 7-cm-ID Pyrex crucible. The system in which the melts were made was evacuated to a pressure of 1 x 10-6 Torr and back-filled with purified argon several times before melting the charge. The ingot was reweighed and placed in a slightly larger-diameter Vycor crucible used in the dissolution runs. A run was started by lowering the disc into the liquid

Jan 1, 1968

By J. G. Richardson, J. W. Graham

The purpose of this paper is to present the results of theoretical and experimental studies of water imbibition. The imbibition processes are involved in recovery of oil from stratified and fractured-matrix formations in natural water drives and water flooding. An understanding of the role of inhibition in implementing the recovery of oil from such formations is deemed essential to proper control of these reservoirs to achieve maximum recovery. The theoretical studies involved development of the differential equations which describe the spontaneous imbibition of water by an oil-saturated rock. The dependence of the rate of water intake by the rock on the permeability, interfacial tension, contact angles, fluid viscosities and fluid saturatiorls is discussed. A few experiments were performed using core samples to determine the effects of core length and presence of a free gas suturation. The role of water imbibition in recovery of oil from a fractured-matrix reservoir by water flooding was investigated by use of a laboratory model. This model was scaled to represent one element of a frac-tured-matrix formation. Water floods were made at various rates with several fracture widths. Interpretations were made of the behavior expected in a system containing many matrix blocks. The presence of a free gas sntu.ration was found to reduce the rate of water imbibition. In the reservoir prototype of the fractured-matrix model, water imbibition rather than direct displacement by water was the dominant mechanism in the recovery of oil at low rates. INTRODUCTION Imbibition may be defined as the spontaneous taking up of a liquid by a porous solid. The spontaneous process of imbibition occurs when the fuid-filled solid is immersed or brought in contact with another fluid which preferentially wets the solid. In the process of wetting and flowing into the solid, the imbibing fluid displaces the non-wetting resident fluid. Common examples of this phenomenon are dry bricks soaking up water and expelling air, a blotter soaking up ink and expelling air and reservoir rock soaking up water and expelling oil. As increasingly better lithological descriptions have been made of the characteristics of petroleum-bearing formations, it has become obvious that imbibition phenomena which were once considered laboratory curiosities are of practical importance. For instance, in reservoirs composed of water-wet sand strata of different permeability in intimate contact, the tendency of water to channel through the more permeable stratum is offset by the tendency for water to imbibe into the tight sand and expel oil into the coarse sand. Also, in fractured-matrix formations the tendency of water to channel through the fractures is offset by water-wet matrix blocks. As some imbibition of the water into the of the largest fields in the world are fractured-matrix reservoirs, it has become increasingly important to understand all the factors involved in the imbibition process. Examples of fractured-matrix reservoirs are the Spraberry field in West Texas which produces from a fractured sandstone', the giant Kirkuk field in Iran', the Dukhan field in Qatar, Persian Gulf2, and the Masjid-I-Sula-main and the Haft-Kel fields in Southwestern Iran, which produce from fissured limestone3. Research into recovery of oil from fractured-matrix formations was stimulated by the rapid decline of oil productivity of wells in the Spraberry formation. One result of this research was the water imbibition process developed by the Atlantic Refining Co.4 Another idea was that much of the Spraberry oil could be recovered by conventional water-flooding procedures5. Subsequently, pilot floods were conducted in this field to test the feasibility of these ideas. It was felt that an understanding of the role played by imbibition processes in displacement of oil from a fractured-matrix reservoir could not be obtained from field data alone because of the many complicating factors and uncertainties involved. Therefore, theoretical and laboratory studies were undertaken to provide this understanding. Study of the equations which describe the linear, countercurrent imbibition process provided an insight into the role of various factors in the process, such as the permeability of rock and inter-facial tension. In addition to the theoretical studies, imbibition experiments were conducted with core samples to determine the effect on the rate of imbibition of such variables as core length and free gas saturation. The principal experimental studies were conducted by water flooding a scaled model of an clement of a frac-tu red-matrix reservoir to evaluate

By J. Szekely, G. P. Martins

A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.' Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble's ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The ' 'anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at

Jan 1, 1970

By P. Shahinian, H. H. Smith, M. R. Achter

Crack growth rates are measured at elevated temperature in a resonant fatigue machine from vibration frequency decreases calibrated in terms of crack depth. Crack growth rates in Type 316 stainless steel at 500º and 800°C show a sharp increase with oxygen pressure in an intermediate pressure range and little or no change at high and low pressures. At 500°c, I torr of oxygen reduces the fatigue life by almost a factor of 100 in comparison to that in vacuum and raises the growth rate of shallow cracks by the same At At 800°C the effects are smaller. Changes in slope in the crack growth rate curves are discussed in terms of a model in which rates of surface production and of surface coverage by gas are compared. The use of a calculation method in which the surface exposure time is equal to X/v, where x is the interatomic spacing and v is the growth rate, makes it possible to obtain order of magnitude agreement at 500°C between the observed pressure and the predicted pressure at these slope changes. At 800°C oxidation becomes a .factor and the data cannot be treated by simple adsorption theory. THE decrease in the fatigue life of metals as a function of gas pressure usually follows a stepped curve with virtually all of the decrease concentrated in a sharp drop in a transition zone at intermediate pressures and little or no change at low and high ranges. A number of models, differing in the details of the mechanism, have been offered to explain the shape of the curve. Measurements of crack growth in aluminum as a function of gas pressure by Bradshaw and Wheeler' and Hordon2 demonstrated opportunities for quantitative comparison to evaluate the proposed models. Since comparable data were lacking at high temperatures, in the present work rates of crack propagation were measured in Type 316 stainless steel at 500" and 800°C as a function of oxygen pressure. Choice of this material was dictated by two considerations; it is stiff enough at these elevated temperatures to resonate with the regenerative drive on our fatigue machine and it is known to display a large effect of environment. A new method of calculation is described to predict the gas pressure at the critical point. EXPERIMENTAL PROCEDURE Because of the difficulty of measuring crack depths directly at high temperatures, an indirect method was developed based on the decrease in the resonant frequency with the growth of a crack. A reversed bending, constant amplitude fatigue machine, described previously,3 vibrates a specimen at its resonant frequency, automatically records any changes in it and shuts itself off after it has reached a preset value of frequency decrease. The record of frequency change is used to determine the rate of crack growth. Sheet type specimens of Type 316 stainless steel, Fig. 1, incorporated a sharp, shallow notch to localize the formation of a single crack. After machining, they were annealed in a vacuum of l0-6 torr either at 1066" (lot A) or 871°C (lot B) and then electropolished in an acetic-chromic acid solution. Bending strains were measured at 500" and 800°C by an optical technique4 and reported as total strain without correction for the notch. At 500°C, the 0.141 pct strain was 0.085 pct elastic and the remainder plastic. At 800°C the 0.062 pct strain was all elastic. To convert frequency decrease to crack length, calibration curves were obtained by interrupting the vibration at stated intervals of frequency decrease. The crack depth was measured microscopically at a magnification of X400 and reported as the average of the measurement on each edge. Some specimens were sectioned for crack measurement while others were returned to the machine and fatigued further. There was good agreement between the two methods. Before beginning the vibration, the vacuum chamber was first evacuated cold to 1 x 1O-6 torr, then heated to the operating temperature and held there until the pressure was again reduced to 1 x10-6 torr at which time oxygen was introduced to the desired pressure. In this investigation the vibration frequency was nominally 10 cps and a decrease of 0.6 cps was taken as the failure point. The choice of the frequency decrease to represent failure has no appreciable effect on the fatigue life because the crack is growing very fast at this point.

Jan 1, 1970

By Dan McLachlan

EXPERIMENTS on ionic solids,1 Cu-A1 alloys,2 and Fe-Si alloys3 have suggested that the ability of dislocations to cross-slip is one of the most important factors governing the nucleation and growth of fatigue cracks. These experiments necessarily had to be made on materials of different composition in order to vary the propensity for cross slip. However, re-

Jan 1, 1967

By R. C. Ku, A. J. McEvily, T. L. Johnston

The microplastic response of a series ofas-quenched Fe-Ni-C martensites has been measured at 77°K. At strains less than JO'3 the flow stress is governed primarily by the transformation-induced dislocation structure of the martensite. Only at strains in excess of 10-3 is the influence of carbon manifested in the flow stress. At these macroscopic strains, typically 10-2, the solid-solution hardening is proportional to (wt pct C)1/3, and, in an alloy containing 0.39 wt pct C, amounts to 50 pct of the flow stress. THE technological significance of high-strength ferrous martensite has stimulated many investigations of its structure and properties. Although our knowledge of the characteristics of martensite has increased immensely, especially with the advent of high-resolution techniques, an understanding of the basic strengthening mechanism still remains elusive. The purpose of the present paper is to consider certain aspects of micro-plastic behavior of Fe-Ni-C martensite which we feel can help to resolve this important problem. Such alloys are particularly suitable for experimental investigation because their compositions can be adjusted to reduce the M, to a temperature low enough essentially to eliminate the diffusion of carbon in the freshly formed martensite.1 The mechanical properties in this condition are of interest inasmuch as they reflect a state that is free of the important but complicating influence of precipitation processes. In this virgin martensite the carbon is distributed as it was inherited from the parent austenite; i.e., it is present interstitially, and gives rise to tetragonality through strain-induced ordering.' In order to determine the source of strength of such alloys, Winchell and Cohen1 investigated the low-temperature macroscopic stress-strain behavior of a series of virgin martensites of increasing carbon content but of common M, temperature (-35°C). They found that the flow stress increased rapidly with carbon content up to 0.4 wt pct; beyond this point the flow stress increased at a much slower rate. It was concluded that martensite is inherently strong. To account quantitatively for the strength of virgin or as- quenched martensite in terms of the role of carbon, Winchell and cohen3 suggested that the carbon atoms, trapped in their original positions by the diffusionless martensite transformation, interfere with dislocation motion according to a model akin to that of Mott and Nabarro. 4 In this treatment, individual carbon atoms are considered to constitute centers of elastic strain and thereby generate an average stress resisting the motion of dislocations throughout the lattice. The additional stress necessary to move dislocations, over and above that necessary for motion in a carbon-free martensite, is given by where L is an effective length of dislocation capable of motion. L was assumed to be limited to the spacing between the twins that are an essential structural element of Fe-Ni-C martensites. They assumtd the spacing to be invariant and of the order of 100A. However, recent work5 has shown that L is variable and can be in excess of 1000Å, so that the assignment of an appropriate value of L is not straightforward. In contrast to the above conclusion that there is an intrinsically high resistance to plastic flow, it has been suggested by Polakowski6 that freshly quenched martensite is in fact "soft" in the sense that dislocations are initially free to move upon application of stress. The high indentation hardness and macroscopic yield stress of ferrous martensites are then a consequence of rapid strain hardening that depends upon carbon in solution. Consistent with this point of view are the results of Beau lieu and Dubé who measured the rate of recovery of internal friction as a function of aging (tempering) temperature in a freshly quenched steel containing 0.90 wt pct C, 0.37 wt pct Mn, 0.1 wt pct Cr, and 0.07 wt pct Ni. The kinetics were clearly consistent with the idea that many dislocations are unpinned in the as-quenched state and that during aging they become progressively pinned by carbon at a rate controlled by carbon diffusion in the body-centered martensite lattice. In order to provide a basis upon which to distinguish between the "hard" and "soft" interpretations indicated above, we have made studies of the initial stages of plastic deformation in Fe-Ni-C martensites similar to those'used by Winchell and Cohen. It will be shown that the results support the contention that dislocation segments in as-quenched material are indeed

Jan 1, 1967

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.'a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.' However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By W. C. Maurer

A study of bit-tooth penetration, or crater forniation. under simulated borehole condirions has been made. Pressure conditions existing when drilling with air, water and mud have been sirnulated for depths of 0 to 20.000 ft. These crater tests showed that a threshold bit-tooth force must he exceeded before a crater is .formed. This thresh old force increased with both tooth dullness and diflerenrial pressure between the borehole and formalion fluids. At low differential pressures, the craters formed in a brittle manner and the cuttings were easily removed. At high differenlial pressures, the cunings were firmly held in the craters and the craters were formed by a pseudoplas-tic mechanism. With constant farce of 6,500 16 applied to the bit reeth, an increase in differential pressure (sitnulated mud drilling) from 0 to 5,000 psi reduced the crater volumes by 90 per cent. A comparable increase in hydrostatic fluid pressure (simulated water drilling) produced only a 50 per cent decrease in volutne while changes in overburden pressure (simulated air drilling) had no detectable effect on crater volume. Crater tests in unconsolidated sand subjected to differential pressure showed that high friction was present in the sand at high pressures. Similar friction belween the cuttings in craters produces the transition from brittle to pseudo plastic craters. INTRODUCTION The number of wells drilled below 15,000 ft increased from 5 in 1950 to 308 in 1964. Associated with these deep wells are low drilling rates and high costs. High bottom-hole pressures produce low drilling rates by increasing rock strength and by creating bottom-hole cleaning problems. This paper describes an experimental investigation of crater formation under bottom-hole conditions simulating air, water and mud drilling. Although numerous investigators have studied bit-tooth penetration (cratering) at atmospheric pressure conditions, only limited work has been done on cratering in rocks subjected to pressures existing in oil wells. Payne and Chippendale2 have studied cratering in rocks subjected to hydrostatic pressure using spherical penetrators. Garner et aLJ conducted crater tests in dry limestone by varying overburden pressure and borehole fluid pressure independently and using atmospheric formation-fluid pressure Gnirk and Cheathem4,5 have studied crater formation in several dry rocks subjected to equal overburden and borehole pressure and atmospheric formotion pressure. Podio and Gray studied the effect of pore fluid viscosity on crater formation using atmospheric borehole and formation-fluid pressurc and varying overburden pressure. Although these studies have provided useful information on crater formation under pressure, they were limited in that the three bottom-hole pressures could not be varied independently and, therefore, that many drilling conditions could not be simulated. The prersure chamber used in this study allowed visual observation of the cratering mechanism and independent control of the borehole, formation and confining pressures. By using different fluids in the chamber, pressure conditions existing in air, water and mud drilling to depths of 20,000 ft were simulated. The mechanisms involved in cratering at these different pressure conditions were studied for teeth of varying dullness and at different loadins rates. High-speed movies (8,000 frames/sec) and closed-circuit television were used to visually study the crater mechanism under pressure. EXPERIMENTAT PROCEDURE PRESSURE CHAMBER The Pressure chamber in Fig. I was used to simulate bottom-hole pressure conditions. This chamber has been pressure-tested to 22,500 psi and is normally operated at pressures up to 15,000 psi. The chamber contains four lucite windows' used for illuminating and observing the crater mechanism under pressurc. A closed-circuit television and a Fastax camera (8,000 frames/sec) have been used in these studies. Cylindrical rock specimens (8-in. diameter X 6-in. long) were subjected to three independently controlled pressures simulating overburden, borehole fluid and formation-fluid pressures. Overburden pressure, which corresponds to the stress induced by the overlying earth mass, was applied by exerting fluid pressure against a rubber sleeve surrounding the rock. Borehole pressure, which is the pressure exerted by the column of mud in the wellbore, was simulated by applying pressure to the fluid overlying the rock in the chamber. Formation pressure was simulated by applying pressure to the water saturating the rock. The borehole and formation pressures were equal except when mud was used in the chamber, in which case the differential pressure between these fluids acted across the mud filter cake.

Jan 1, 1966

By W. H. Class

The embrittling effects of oxygen, ozone, nitrogen, air, and surface residues, on NaCl has been investigated. The embrittlement by ozone and oxygen was found to be associated with the formation of a NaClO3 surface compound. In these cases the initial crack that was responsible for fracture (in a bend test) always nucleated at the corners between the tension and side faces. The behavior of air was very erratic and on certain days did not produce enzbrittlement. During these periods, crystals that had become embrittled by the ozone treatment completely recovered their ductility after a short exposure to the ambient atmosphere, It was established many years ago1 that considerable ductility could be obtained in NaCl single-crystal specimens if the crystal surfaces were dissolved in water either during or immediately prior to the test. The original interpretation of this effect by Joffe attributed the enhanced ductility to the removal of surface microcracks by dissolution. Later investigations2'3 have suggested that the exclusion of air from the specimen surface is the criterion for extensive plastic flow prior to fracture. The air em-brittlement in this later work was attributed to the diffusion of gaseous atoms into the surface layers of the crystal, thereby impeding the movement of dislocations. This model satisfactorily accounts for the reembrittlement observed after further air exposure subsequent to the water dissolution treatment. However, the situation has recently become more complex by the observations in several laboratories4-t that under certain conditions air exposure does not impair the ductility of NaC1. It has also been recognized5 that improper drying operations after water dissolution can leave surface precipitates that lead to embrittlement. Cleavage defects on as-cleaved crystals can often be another source of embrittlement. In the present work the effect of the gaseous atmospheres nitrogen, argon, air, oxygen, and ozone, on the ductility of rock salt was studied extensively. The embrittlement resulting from oxygen and ozone exposures was found to be associated with the formation of a NaC1O3 surface film. It is suggested that certain atmospheres, one of which often can be ambient air, which inhibit the formation or favor the decomposition of this compound, can promote ductility. Thus one aspect of the Joffe effect is certainly related to the removal of surface compounds or complexes by water dissolution. The effect of surface precipitates that remain after drying operations and of cleavage defects were also studied. In neither of the latter cases was the embrittlement as severe as that found with a NaClO3 surface layer. PROCEDURE AND SPECIMEN PREPARATION The nature of the embrittlement produced by the agents mentioned above was studied by means of microscopy, mechanical testing, and X-ray diffraction. Specimens were cleaved from large crystals of optical quality sodium chloride obtained from the Harshaw Chemical Co., and, except for those tested in the as-cleaved condition, were given a 15- to 20-sec immersion in distilled water followed by a rinse in absolute methyl alcohol. The specimens were then blotted on a soft, absorbent paper, and dried by a few seconds exposure to a stream of warm, dry air. Such a procedure was found to give a control surface which was microscopically free of residues. (A few crystals were intentionally painted with a concentrated NaCl solution in order to investigate the effect of surface residues). All specimens were of 0.140 sq in. cross-section. Crystals prepared in the above manner were immediately placed in a gas train where they could be exposed to the desired gases for preselected periods of time. For the oxygen and nitrogen exposures, pure reagent-grade gases were employed. The ozone was provided in the form of an ozone-oxygen mixture (approximately 10 pct ozone) prepared by passing commercial grade oxygen over a strong ultraviolet light source. All gases were dried prior to their introduction into the train. Since argon was found to be completely inert in its behavior (i.e., residue-free specimens that were exposed to argon were not embrittled), it was periodically utilized to check the control specimen surfaces as well as the condition of the gas train used for aging the specimens. After exposure to the gaseous media in question, the crystals to be used for the measurement of the strain to fracture were transferred from the gas train to a protective oil bath (without further exposure to the atmosphere) where the tests were conducted in three-point bending. The apparatus was so adjusted that the load could be applied at a constant, continuous rate. Other Snecimens from the gas train were deformed

Jan 1, 1962

By W. B. Braden

This paper presents a suitable method for predicting gas-free oil viscosities at temperatures up to 500F knowing only the API gravity of the oil at 60F and the viscosity of the oil measured at any relatively low temperature. The API pravity and the one viscosity value are used as parameters to determine the slope of a straight line on the ASTM slanaord viscosity-temperature chart. Then, knowing the slope of the line and one point on the line, the vrscosities at higher temperatures can be determined. The line slope correlations were developed at I00 and 210F since viscosity data are frequently measured at these temperatures. A procedure is given for predicting line slopes from measurements at other tetnperatures. A nomogram is furnished for solving the relationship. The correlation has been evaluated at temperatures up to 5OOF for oils varyzng in gravity from 10 to 33 " API. The correiution is applicable only to Newtonian fluids. Comparison at 500F of true viscosities and those predicted from values at 100F shows an average deviation of 3.0 per cent (maximum deviation of 6.0 per cent). Predictions from the values at 21 0F for the same oils how an average deviation of 1.5 per cent (maximum deviation of 3.4 per cent). INTRODUCTION Correlations have been developed by Beal' and by Chew and Connally' for predicting viscosities of gas-saturated oils at reservoir conditions. Each of these correlations requires a knowledge of the solution gas-oil ratio and the viscosity of the gas-free oil at the reservoir temperature. For temperatures below 350F, measurements of the gas-free oil viscosities can be made easily using commercially available equipment. In thermal recovery processes, however, reservoir temperatures well in excess of 350F are encountered. Viscosity measurements at such conditions are more difficult and time consuming and require modification of existing equipment or the construction of new equipment. Measurements are further complicated by the difficulty of handling highly viscous oils associated with thermal recovery processes. Therefore, it is desirable to have a correlation which allows accurate prediction of viscosities at high temperatures. A commonly used technique for predicting viscosities at high temperatures is to measure the viscosities at two lower temperatures, plot the values on ASTM standard viscosity-temperature charts and extrapolate to the temperatures desired. If either of the values is slightly in error, the extrapolated value can be significantly in error. To justify an extrapolation, three points are actually necessary. This procedure can consume much time, particularly with heavy oils. Considering the cost of viscosity measurements, it would be desirable to eliminate the need for direct measurements by having correlations which would allow viscosity predictions from other physical or chemical properties. Beal1 investigated the possibility of correlating viscosity with oil gravity at temperatures from 100 to 220F. While showing that a general relationship exists, he also found significant deviations. It is possible that correlations will be developed based on oil composition as more information becomes available. While not eliminating the need for viscosity rneasurements, the method presented herein requires that only one viscosity measurement be made. The API gravity must also be known. The theory is based on the fact that the viscosity of paraffins (high gravity) changes less with temperature than does the viscosity of naph-thenes or aromatics (low gravity). The gravity. therefore, is used as a parameter to determine the slope of a straight line on the ASTM standard viscosity-temperature charts. The correlation is applicable only to Newtonian oils, and deviations due to thermal decomposition and nonhomo-geneity cannot be predicted. Oils containing additives have not been evaluated. PROCEDURE Fifteen oils were used in developing the correlation; eight were crudes and seven were processed oils. Oil gravities varied from 9.9" API (naphthene base) to 32.7' API (paraffin base). The temperature range studied was 81 to 516F. Each oil used had a minimum of three viscosity measurements and each plotted essentially as a straight line on the ASTM charts. In all, 91 viscosity measurements were used in the correlation. Saybolt, rolling ball and capillary tube viscometers were used for the measurements. Viscosity data for Samples 1, 2, 4, 7, 10, 11 and 14 were obtained in Texaco, Inc. laboratories. The data for Samples 3, 5, 6, 8, 9, 12 and 15 were from Fortsch and Wilson,3 and data for Sample 13 were from Dean and Lane.' All data points used in the correlation are plotted in Fig. 1. It is seen that some of the viscosity values deviated slightly from the straight-line plots at the higher temperatures. Properties of the oils after exposure to the

Jan 1, 1967

By D. B. Robinson, C. A. Macrygeorgos, G. W. Govier

Experimental data have been obtained on the volurrletric behavior of ternary mixtures of methane, hydrogen sulfide and carbon dioxide at temperalures of 40°, 100" and 160°F up to pressures of 3,000 psia. The results indicate that the compressibility factors for this system do not agree with compressibility factors for sweet natural gases at the same pseudo-reduced conditions. The deviation increases as the temperature and methane content decrease. Discrepancies of up to 35 per cent were observed. A careful analysis has been made of the existing pUrblished data on compressibility factors for binary systems containing light hydrocnrbons and hydrogen sulfide or carbon dioxide. It has been found that the deviation of actual from predicted compressibility factors for methane-acid gas mixtures is a function of the methane content and the pseudo-critical properties,.v of the mixture. The ratio between actual compressibility factors for methane-acid gas mixtures and compressibility factors for sweet natrlral gases at the same pseudo-reduced conditions has been currelated over a range of pP,, from 0 to at least 7 arid a range of pT, from about 1.15 to at 1east 2 0 with an error not exceeding 3 per cent and over most of the range within I per cent. The validity of the correlation for mixtures containing appreciable hearvier hydrocorbons has not been fully established, but it is shown to be preferable than the use of a corretation based only on hydrocarbons. INTRODUCTION Although a relatively accurate method for predicting compressibility factors of pure materials is provided by charts based on reduced properties and the assumption that the compressibility factor is a unique function of T P and z the determination of the correct values of compressibility factors for gas mixtures is somewhat difficult. Two general methods of dealing with gaseous mixtures have been proposed. The first assumes a direct or modified additivity of certain properties of the mixture in terms of the properties of the individual components. Examples of this method are based on the familiar laws of Dalton and Amagat. The second method averages the constants of an equation of state applicable to the pure components. Both of these methods are of limited value in engineering calculations because the first usually provides reliable answers only over narrow ranges of pressure and temperature and the second is cumbersome to handle. In petroleum engineering practice accurate estimations of the volumetric behavior of natural gases arc frequently required. To fulfill this need, several generalized compressibility charts have been developed.' ' Of these, the one prepared by Standing, el al is widely used at present. In the construction of charts of this type a third method for dealing with mixtures has been followed. It is based on correlation of pseudo-critical properties as outlined by Kay and calculated from the critical properties of the individual components in a mixture. Although these charts provide relatively accurate information on the compressibility of dry or wet sweet natural gases, they are less reliable when used for gases containing high concentrations of hydrogen sulfide or carbon dioxide or both. Thus, an experimental program, although time consuming, is the best means now available for the determination of the volumetric behavior of sour or acid gas mixtures. An increased interest in the behavior of these gas mixtures, particularly in connection with some of the fields in Western Canada where the acid gas concentration of the reservoirs may be as high as 55 per cent and where hydrogen sulfide alone may be as high as 36 per cent, provided the incentive for this study. It was the purpose of the investigation to determine the volumetric behavior of selected mixtures of methane, hydrogen sulfide and carbon dioxide over a range of temperature from 40" to 160°F and at pressures up to 3,000 psi. EXPERIMENTAL METHOD The apparatus used in this investigation was basically the same as that described by Lorenzo.'" The amount of each pure component used in preparing the gas mixtures was measured over mercury in a glass-windowed pressure vessel. The pure components were then transferred individually in the desired amounts to a second glass-windowed pressure vessel where the volumetric behavior of the mixture was determined. Volume was varied by mercury injection or withdrawal. The capacity of the cell was about 125 cc. Temperatures in the cells were measured with copper-constantan thermocouples and a Leeds Northrup semi-

By Kwong Yung Kwang

This mine, which is sometimes called Tong colliery, from its director, Tong King Sing, is about 80 miles northeast of Tientsin (see map, Fig. 1). Fig. 2 shows a vertical transverse section through the coal-beds. These beds have a dip to the south of about 45' and are interstratified with sandstone, shale, indurated clay and fire-clay. Of the

Jan 1, 1888

By W. E. Bonini, E. A. Hickok

IN the course of an investigation directed toward expanding ground-water facilities in Essex and Morris counties, New Jersey, the Board of Water Commissioners of the city of East Orange authorized a seismic-refraction survey' for the purpose of de-lineating bedrock topography below unconsolidated overburden. Results of the survey were highly satisfactory and led to the preparation of a comparatively detailed bedrock contour map. Knowledge of the bedrock depth and configuration was an important aid in selection of sites for test drilling. The portion of the East Orange Water Reserve under consideration is in the flood plain of the Pas-saic River about 10 miles west of Newark, N. J. The flood plain is about 175 ft above mean sea level and is bordered by low hills rising to elevations of approximately 250 ft. The bedrock underlying the Water Reserve consists of sandstone and shale of the Triassic Brunswick formation and is covered everywhere by deposits of unconsolidated glacial outwash sand and gravel, lacustrine clay, and recent river silt as much as 150 ft thick. Yield of wells in the sandstone and shale averages 100 to 200 gpm. Since production wells constructed in the sand and gravel aquifer in the buried river valley shown on the contour map (Fig. 1) yield 300 to 1400 gpm, it was proposed to locate additional production wells in this buried valley, where the yields per well would be maximum. In 1939 and 1946 the East Orange Water Dept. had electrical-resistivity surveys made to determine depths to bedrock. From the resistivity data the exploration company prepared a bedrock contour map. A well field expansion program begun in 1955 utilized this information to locate sites for test wells along a predicted northward extension of the buried valley in which existing production wells are located. After several test wells (wells 201-205) had been drilled, it became apparent that the resistivity information was unreliable." For example, test well 201 recorded bedrock at a depth of 72 ft, whereas the resistivity depth determination was 130 ft. As a consequence, the test drilling program was temporarily suspended and a seismic survey was under- taken to determine the topography and extent of the buried valley known from well records to underlie the existing well field. In the first phase of this study, several seismic shot point locations were placed at sites where well logs had been obtained previously. This procedure is necessary in a new area to determine whether the seismic method is applicable and what degree of accuracy is to be expected. At the East Orange Water Reserve, depths obtained from the shot points near test wells 202, 203, and 204 were within 8 to 11 pct of the depths logged (Table I). With this assurance that accurate results could be obtained, additional seismic spreads were located on the Water Reserve. Using a portable refraction seismograph, in the fall of 1955 a crew of four men shot a total of 29 reversed seismic spreads in a period equivalent to six field days. Charges as heavy as 3 1b of 40 pct dynamite were necessary at a few places to overcome ground vibrations caused by traffic on nearby highways. At most other sites, a 1-1b charge was sufficient. Travel-time plots were made for all spreads, and depths and true velocities were calculated according to formulas for multiple sloping layers by Ewing, Woollard, and Vine.' The plot of spread 7 (Fig. 2) is typical of the short spreads in which bedrock was shallow—about 50 ft in this case. Where there were not enough arrivals through the bedrock to define the high velocity bedrock line, the spreads were lengthened. This was done by placing shots on line several hundred feet away from each end of the line of geophones. It was then possible to construct complete reverse plots for both short and extended shot points (see spread 27, Fig. 3). Four individual depths were calculated from each extended spread. Three and in some cases four seismic layers were observed. The surficial layer had a velocity range of 900 to 1200 fps, the lowest velocity recorded. This seismic layer is above the water table and is interpreted as recent river silt. The bedrock had the highest velocities, which ranged from 10,600 to 16,400 fps. Intermediate velocities ranged from 4500 to 6800 fps. In every case the intermediate layer was within

Jan 1, 1959

By J. E. Powell, F. H. Spedding

WHILE rare earths are reported to be widely distributed in nature and are not really rare," in practice, there are only a few minerals which are sufficiently rich in rare earths to serve as practical sources. Perhaps the best known of these is monazite which is a phosphate mineral containing rare earths and thorium. This mineral occurs as a dense brown sand in gravel beds and is particularly rich in the light rare earths of the cerium subgroup. This mineral is processed commercially for its thorium, cerium, and lanthanum content, and, consequently, furnishes rich concentrates from which neodymium, praseodymium, samarium, europium, and gadolinium may be obtained. Unfortunately, monazite is rather lean in rare earths heavier than gadolinium. A second mineral which is rich in the light rare earths is bastnasite, a fluoro-carbonate. Extensive deposits of this ore have been discovered in the western United States and have received considerable newspaper publicity in recent years. While bastnasite is very rich with respect to cerium, lanthanum, and neodymium, it contains even less heavy rare earths than does monazite. One of the better sources of heavy rare earths of the yttrium subgroup is gadolinite, a black silicate rock from which the rare-earth content can be extracted readily by acid leaching. It is obtained chiefly from Norway at the present time, although there are known deposits in the United States. Other sources of heavy rare earths include fergu-sonite, euxenite, and samarskite which are refractory tantalo-columbate ores. These minerals require caustic fusion or reduction to carbides with carbon before the rare-earth content can be extracted. All of the minerals which are rich in the heavy rare earths contain yttrium as a major constituent. After the rare earths have been extracted as a group from an ore by chemical means, it is generally convenient to precipitate them from acid media with oxalic acid in order to eliminate certain non-rare-earth impurities such as iron, beryllium, etc., which are usually present. The oxalate can then be readily ignited to R2O3. The oxide can be dissolved in acid and is the starting point for subsequent separation into the pure components. Perhaps the principal reason why the rare earths have not been studied as extensively as other elements of the periodic table, whose natural abundances are comparable, is that they are extremely difficult to separate from each other by the usual chemical means. Prior to 1945, the separation of one trivalent rare earth from another was a laborious process. All separations were based on repeated fractionation processes, i.e., fractional precipitation, fractional decomposition, fractional crystallization, etc. These processes were repeated from a few hundred to many thousands of times in order to obtain individual rare-earth salts of reasonable purity. Of course, mention should be made that, in the few cases where a rare earth could be oxidized or reduced to a valence state other than three, more conventional chemical means could be utilized to separate the oxidized or reduced ion from the other normally trivalent rare earths. The ionic states which deserve special mention are CeIV, SmII, Eu11, and Yb11. When it is possible to remove an element of the series efficiently, due to an optional valence state, its immediate neighbors also become easier to isolate. For example, binary mixtures of lanthanum and cerium, and praseodymium and cerium can be obtained by a relatively small number of fractional operations. The tetravalent state of cerium then allows the complete resolution of the binary mixtures by ordinary chemical means. Although the tetravalent state of cerium has been known for a long time, the divalent states of samarium, europium, and ytterbium were not used extensively in separations prior to 1930 because they are relatively unstable in aqueous media.'-" No attempt will be made to give a comprehensive review of the extensive literature dealing with the separation of rare earths. Rather, this paper will be confined to a review of those methods which have been developed at Iowa State College during recent years, and which have proved extraordinarily successful for the isolation of highly pure rare earths in quantity. It was obvious that, if pure rare earths were to become generally available, methods would have to be developed wherein the thousands of fractional operations made necessary by the similarity of rare-earth properties could be performed automatically. The development of chromatographic techniques and ion-exchange resins appeared to offer a mechanism by which this objective could be accomplished. A number of early attempts were made to separate rare earths by these means; for example, Russell and Pearce12 passed a mixture of rare earths through a cation-exchange column and reported

Jan 1, 1955

By D. L. Creighton, S. A. Hoenig

The field-emission microscope has been adapted for the study of microcrack growth during the early stages of fracture in metal wires. Cracks as small as 6 1 in length can be detected and their growth can be followed to specimen failure. The system is quite useful in searching for microcracks since only sharp-edged surface defects will emit electrons under the experimental conditions. THE conditions leading to brittle fracture were discussed a number of years ago by Griffith1 and the term Griffith Cracks is often used for the small surface cracks which are responsible for brittle fracture. Griffith's theory has been modified by stroh2 and more recent results on metals are discussed by Allen,3 pp. 123-40. At present the phenomenon is not completely understood but there is general agreement that at least in certain materials the sequence leading to brittle fracture involves several stages. The initial microcracks are present because of cooling or working stresses, Hahn et al.,3 p. 95. When a stress is applied to the specimen the cracks grow slowly until the release of stored elastic energy is large enough to accelerate the crack and provide the necessary surface energy for crack growth. At this point the growth rate appears to increase rapidly to some new equilibrium velocity, and failure occurs. Since the microcracks are usually about the size of a single metallic grain (Ref. 3, p. 99) it is not easy to find them and it is very difficult to follow their growth under stress. This paper will report on the use of a cylindrical field-emission microscope for observation of the formation and growth of microcracks. I) THE FIELD-EMISSION MICROSCOPE The field-emission microscope (FEM) has a high magnification and resolution and is almost uniquely suited for observations of microcracks. Since the FEM is relatively new as a metallurgical instrument, a short description will be given here. Normally metals at room temperature do not emit electrons; however in the presence of a strong electric-field gradient, electrons can tunnel out through the reduced potential barrier. Since this tunneling is a function of the local field gradient and the local work function, the emitted electrons can be used to produce a highly magnified image of the surface by allowing them to strike a phosphor screen. Because the electron emission is dependent upon the local field gradient, smooth surfaces emit few electrons except at very high fields. On the other hand cracks, extrusions, or other surface defects, having sharp edges, emit strongly since the field gradient is very high in the vicinity of these defects. This indicates that the FEM should be most useful for detection of microcracks on otherwise smooth surfaces. A field-emission microscope was first used by Muller4 in 1936 for observation of metal surfaces, and recent reviews have been given by Muller5 and Gomer.6 The instrument has been used for metallurgical studies in the area of surface diffusion,= recrystallization,7 and grain growth 8 (Ref. 8 is directed specifically at metallurgists). In the work of Muller4,5 and Gomer 6 the specimen was in the form of a sharp metal point at the center of a phosphor-coated glais sphere. The impact of the emitted electrons on the phosphor produced a highly magnified image of the specimens. Such a system is not practical for applying a controlled stress to the specimen and a cylindrical geometry has been used in this investigation. This allowed the application of a controlled tensile stress to the wire specimen. Normally a cylindrical FEM geometry produces magnification only in the radial direction. This is the case because a smooth wire at the center of a cylinder produces a purely radial electrical field. However, if there is a break in the smooth surface of the inner cylinder, the field near the break becomes three-dimensional and the area of the break is highly magnified. The reason for this is clear if it is recalled that the field gradient depends on the relative radii of the inner and outer cylinders; if a crack forms, its edge radii are of atomic dimensions and a very high field gradient is formed near these crack edges. Since the electrons receive most of their acceleration near the crack edge and are always traveling perpendicular to the field lines, they tend to spread out and produce the magnified image observed in the cylindrical field-emission microscope. 11) BRITTLE-FRACTURE STUDIES A) Experimental Apparatus. The geometrical arrangement chosen was that used earlier by Gifford

Jan 1, 1965

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.' Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.'.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949