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By J. E. Hanlon, S. R. Butler, R. J. Wasilewski

It is known that stoichiometric NiTi transforms to a structure of lower symmetry near room temperature. The present investigation deals primarily with the changes in the electrical and magnetic properties which occur at the transformation. The effects of composition and various heat treatments on electrical properties are also discussed. In recent investigations by Purdy and Parr,' Wang et a1.,2 Dautovich and Purdy,~ Dautovich et a1.,4 and the authors, ~,' NiTi has been observed to undergo a martensitic phase transformation from the ordered CsCl (B2) structure to one of lower symmetry. The crystal structure of the low-temperature modification is still not completely worked out. This transformation occurs near room temperature for the stoichiometric composition. The thermodynamic, elastic, crystallographic, and microstructural characteristics of this transformation for some compositions have been previously reported.'-= In the present investigation, the changes in the electrical transport properties and magnetic susceptibility of NiTi when it undergoes the martensitic phase transformation have been measured. The approximate composition range covered is 48 to 52 pct Ti.* *All compositions are given in atomic percent._____________________ EXPERIMENTAL PROCEDURES AND RESULTS 1) Sample Preparation. The NiTi alloys were prepared from iodide titanium (>99.92 pct Ti) and vacuum-premelted carbonyl nickel (>99.95 pct Ni) by repeated arc melting under gettered argon and casting in a water-cooled copper mold. After the cast buttons were hot-forged at 800" to 950°C, the oxidized surface was removed by grinding and etching. Samples were cut from the worked polycrystalline buttons. After fabrication, the samples were annealed 1 hr at 900°C and water-quenched. The composition of the alloys was assumed to be the same as in the initial feed. This assumption was supported by material balance checks on 100-g arc-melted buttons which demonstrated quantitative recovery to within k0.02 pct. The oxygen content of the alloys was '150 ppma (weight) and the carbon content was 30 to 50 ppm. 2) Electrical Resistivity and Hall Effect. The electrical resistivity was measured over the composition range 48 to 52 pct Ti for temperatures varying from 4.2"K to 900°C. The high-temperature and many of the low-temperature experiments were carried out using conventional 4-probe dc techniques.7 The Hall coefficient and ac resistivity were measured at 20 cps using the apparatus shown schematically in Fig. 1. The equipment is basically an ac potentiometer: The resistive or Hall voltage of the sample is balanced by a comparison voltage provided by a dividing network across a standard series resistance. The off-balance signal is amplified by a Tektronix 122 amplifier and detected by a Princeton Applied Research (PAR) phase-sensitive detector. The precision of the resistivity and Hall coefficient measurements is i0.1 and i3 pct, respectively. The uncertainty in the data is increased by i2 pct from the precision limits because of uncertainty in dimensions and possible end effects. The temperature dependence of the electrical resistivity and Hall effect for a stoichiometric (50.0 pct Ti) NiTi sample are illustrated in Fig. 2. Above 75"C, this sample has essentially the B2 structure, while below about 0°C it is completely in the low-tempera-

Jan 1, 1968

By D. Silverman, A. R. Brown

EquipmENT and methods for locating the points of entry of salt water into oil wells are described. These techniques make it possible to delineate accurately the top and bottom boundaries of water zones whether bottom water or intermediate zones of production, Data are given on tests by this survey method on a number of producing wells, Complete results were obtained on wells shelving water percentages ranging from high values to as Little as 10 pct salt water. A number of the wells tested were plugged back and the results are reported in detail. While not all the work-overs were successful, evidence, including the results of reruns by this survey method, points to failure of the plugback operations. The data provided in the tests discussed show, contrary to general opinion, that a large percentage approaching 50 pct of the wells showed intermediate water instead of bottom water. Furthermore, approximately a third of the wells tested showed multiple zones of water production. The equipment comprises a long pipelike assembly carrying 10 pairs of electrodes spaced apart a distance of 4 ft. A surface-controlled solenoid-operated switch is provided to connect each of the individual pairs of electrodes in turn to a single-conductor steel-armored cable by means of which the conductivity of the fluid in the vicinity of each of the electrode pairs can be continuously recorded at the surface. Any number of electrode pairs and any spacing can be used. This assembly is lowered on tubing and placed in position opposite the section of the well to be studied. A conventional rod pump is used to produce the well for the survey. The pump inlet is placed below the lowest electrode pair. The well is conditioned by pumping Out the salt water normally standing in the well and introducing fresh water into the annulus at the surface. When the resistivity of the water standing in the well has been increased to a sufficiently high value, the inflowing fresh water is stopped and the drawdown operation of the survey is started. As the fluid head is lowered by pumping, fluids flow into the well and the entry Of salt water is indicated by the change in resistivity of the fresh water opposite the 'Ones Of water entry, The process can be repeated as Often as necessary with little effort and without moving any well equipment to be sure that the fluids produced from each zone are representative Of the true reservoir content. Introduction The oil industry has been concerned from its inception with the control of fluids entering its wells. In order to effect the greatest economy of operation and to get the greatest total production of petroleum liquids out of the ground, the flow of gas and water must be controlled and often extensive workovers are planned and carried Out for this purpose. This has become even more important in recent Years because of the need for the conservation of natural resources. Whereas producing operations concerned with the original completion of a well are assisted to a great extent by a wide variety of instruments developed and perfected for that purpose, workover operations on oil wells have been greatly hindered by a lack of suitable instrumentation. The industry has searched for many years for a satisfactory instrument and process that

Jan 1, 1948

By J. O. Lewis

The operation of gas-condensate fields is comparatively new and involves physical principles with which the industry was not prcviously familiar. It has been necessary to devise methods for testing gas-condensate wells and to correlate laboratory and field data. In this paper new methods are advanced for interpreting well G.P.M.† tests whereby dilution by dry gas can be estimated and information supplied on revaporization of condensates by dry gas. Inaccuracies in well test data are discussed. Changes in flow rates can cause changes in the G.P.M. of the effluent and it may take some time for a well to become stabilized after an important change in flow rate. Retrograde tests as usually conducted cannot be directly compared with field G.P.M. data, because the retrograde tests usually include solution gas in the condensates, which are reported On the cumulative basis whereas field data (G.P.M.) usually report pentaneS PlUS on a rate or instantaneous basis. Introduction Though long known to physicists, the phenomena Of retrograde condensation became known to the oil and gas industry Only in recent years, when deeper drilling disclosed that the behavior of vapors under changing pressures was different in high-pressure reservoirs than under the low-pressure operations with which the industry was familiar. These deep, high-pressure reservoirs in which condensation and vaporization behaved inversely to the accustomed manner became known as "gas-distillate," or preferably "gas-condensate" fields. Partly to prevent precipitation and retention of liquids in the reservoir, but still more to prevent the waste of residue gas, the operation known as "recycling," or preferably "cycling," was instituted, in which the residue gas is reinjected into the reservoir, thus maintaining pressure and driving the wet gas to the producing wells. For lack of field experience to serve as a guide, the industry had to assume that theory and laboratory experiments could accurately forecast retrograde behaviors in operating these gas-condensate fields, but it is obvious that these assumptions should be checked at the first opportunities against actual field experience. To make such checks, it is necessary to accumulate a large quantity of reliable field data, but experience has shown that it is difficult to obtain reliable field data and that the laboratory data as usually presented are not in directly comparable form. The problems of correlation involve the complex phase behavior on the one hand, and a knowledge of field data and a visualization of underground conditions on the other hand. This paper is an approach from field experience, The purposes of this article are to discuss the sources of uncertainty in the data and to present methods of analyzing, interpreting and correlating laboratory and field data. Data mostly from lower Gulf Coast fields are presented, from which some conclusions can be derived, but better data from more sources than those available to the writer will be required before satisfactory answers to many questions can be obtained. This paper is presented to stimulate the analysis and publication of data from other fields, the reexamination of field and laboratory methods, and the taking of more complete and reliable field tests. For these purposes, the writer presents some speculations that otherwise would not be appropriate.

Jan 1, 1947

By Roshan B. Bhappu, Raul A. Deju

A method is proposed by which the chemical reactions between water and a silicate bed can be related to equations of flow. First the reaction mechanism is studied both theoretically and experimentally. Once the reaction mechanism is established, the equations of flow are solved, and a solution (under physically reasonable side conditions) is obtained. Experiments to substantiate the solution are also presented. The knowledge of surface reactions at the water-solid interface is of critical importance in extractive metallurgy. This is especially true in regard to the froth-flotation process of mineral concentration and all phases of hydro metallurgical recovery of metals. Similarly, the problem of ground-water contamination is one of growing concern, not only because of the increasing demands on our sources of supply but also because of the increasing necessity to find vehicles of waste disposal. The hydrochemistry of waste waters must be understood to exploit and develop such resources properly. To understand these problems, it is necessary to obtain a better insight into the reactions that take place between water and a solid packed bed. To do this, we will develop here in a theoretical model that predicts the fate of a chemical species in solution as it reacts with a silicate bed through which the liquid percolates. The treatment will be one-dimensional in nature and will not include dispersion. Experiments will also be presented to substantiate the theoretical model, using the silicate minerals listed in Table 1. This paper is preliminary in nature and is part of a larger study of the surface chemistry of the silicate-water interface. Mechanism of Surface Reactions In a previous paper,' the authors discussed the properties of various silicate minerals from a mineralogical standpoint. Now efforts will be made to study the reactions that occur when these minerals are put in contact with water. The reactions occur almost entirely in the surface layer of the mineralsa and are termed sorp-tion reactions. In this study sorption denotes the composite of all physical adsorption and chemical adsorption occurring between the silicate surface and the water in contact with it. A model of sorption as seen from a chemical-bond standpoint is presented below. On the basis of this model, the surface reactions between deionized water and a silicate mineral can be studied. Sorption Model: It is known that as the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, the oxygen-to-metal bonding increases. Upon the fracturing of a silicate-mineral crystal, the oxygen-metal bond breaks more easily than the stronger oxygen-silicon bond, resulting in a negatively charged surface. Then, if the mineral is immersed in a liquid containing hydrogen ions, the negatively charged surface should tend to be neutralized by hydrogen ions from solution, resulting in a change of the solution pH. Thus, an increase in the degree of sorption of hydrogen ions must occur as the oxygen-silicon ratio in the crystal structure increases. Also in a previous paper,' the authors found that for a given silicate mineral the change of pH with time is given by

Jan 1, 1971

By D. T. Peterson, F. A. Schmidt, J. D. Verhoeven

The velocity of mig-ration of these solutes in thorium metal due to a high amperage dc current was measured at several temperatures. All three solutes migrated in the same direction as the electron flow. Diffusion coefficients were combined with the migration velocities to predict the steady-state concentration profile. Electrotransport was shown to be an effective method of removing carbon, oxygen, and nitrogen from thorium and resistance ratios several times larger than for crystal bar thorium were achieved. However, the maxirnum attained purification was well below the predicted values, apparently due to some form of contamination. THE migration of solutes in metals when a high current density dc current is passed has been known for many years. This phenomenon has been the subject of a number of reviews published in recent years.l~* Many of the earlier investigators of electromigration of interstitial solutes interpreted the direction and velocity of migration on the basis of a charge on the solute particle. This interpretation is unclear because, in a given experiment, one cannot separate the contributions to the force moving the solute which arise from the charge on the solute in an electric field gradient and the momentum transfer from the scattering of the electrons or holes. There have been only a few quantitative measurements of interstitial migration velocities and some of these have been characterized by poor accuracy or by errors in the analysis of the experiment. The electrotransport mobilities of carbon, nitrogen, and oxygen in thorium were determined by observing the rate of movement of a discontinuity in the concentration profile. This method was used by Carlson el a~.~ to determine the mobilities of interstitial solutes in yttrium and its advantages are discussed in that paper. The specimen is essentially a pair of semi-infinite, bar-type diffusion couples. The electro-transport velocity was measured by observing the displacement of the mean concentration point in a measured length of time. The diffusion coefficients were calculated by the Grube method from the concentration profile. The transport mobilities and diffusion coefficients can be used to predict the concentration profile in an electrotransport experiment of a given time, current density, and specimen length. At long times a steady state will be reached such that the natural logarithm of the concentration of each solute varies linearly along the bar with a slope which is equal to the velocity of the migrating solute divided by its diffusion coefficient. The estimation of the purification potential of electrotransport is discussed by ~erhoeven.' A comparison of the concentration profile and the purification which should be expected from known solute velocities and diffusion coefficients with that which is obtained in an experiment can be very useful in indicating whether the maximum possible purification has been achieved. EXPERIMENTAL METHOD The apparatus used in this study consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a high-vacuum system capable of obtaining pressure of 2 x lo-? Torr. The chamber was made of stainless steel and was 4 in. in diam and 6 in. long. The seal between the electrodes and the chamber was made with "0" rings and compression bushings. The thorium specimens were threaded and screwed into tantalum "U"-shaped adapters attached to the ends of the electrodes. This arrangement is shown in Fig. 1

Jan 1, 1967

By W. C. Winegard, W. J. Bratina

Internal friction characteristics and temperature dependence of the torsion modulus for iodide zirconium containing 2.4 pct Hf were investigated, using a low frequency pendulum technique. The internal friction curve consists of a background which increases as the temperature increases, a maximum at 860°C apparently a background due to the al-lotropic transformation, a maximum due to grain boundary relaxation with an associated heat of activation of 58,000 cal per mol, and an anomaly below 350°C which may be associated with a precipitation perphenomenon, Oxygen in below small amounts reduces the grain boundary maximum substantially. The variation of the torsion modulus at 20°C was found to be 3450 Kg per mm2 for the zirconium used in the present work. IT is well known that small amounts of certain solutes materially affect the ductility of zirconium. Lely and Hamburger,&apos; as early as 1914, found that high purity zirconium exhibited a remarkable ductility, while Fast&apos; has shown that oxygen and nitrogen can cause substantia1 embrittlement. Treco" has recently demonstrated that the ductility decreases sharply with the oxygen content, and that 2 atomic pct O2 embrittles zirconium to such an extent that cold working is impossible. The marked decrease in ductility is difficult to understand in view of the fact that Domagala and McPherson4 report the solid solubility of oxygen in zirconium to be 29 atomic pct at 500 °C. Another metal which behaves much the same as zirconium in this respect is titanium. Pratt et al." investigated the internal friction characteristics of titanium and the effect of oxygen on the internal friction values. It is evident that internal friction measurements are of value for studying grain boundary segregation, as shown by Pratt et al. for oxygen in titanium, by Pearson for oxygen in copper, and by Maringer and Schwope for oxygen in molybdenum. With this in view, the internal friction characteristics of zirconium and the qualitative effect of oxygen on the grain boundary relaxation phenomenon were investigated. Materials and Experimental Procedure The zirconium used in the present work was supplied by the Foote Mineral Co. in the form of wire 0.05 in. diam. The analysis supplied by the manufacturer indicates the amount of hafnium as 2.4 pct, less than 0.01 pct O less than 0.01 pct N,, less than 0.02 pct H,, and less than 0.001 pct C. Additional spectro-graphic analysis indicates the other main impurities as follows: 0.01 pct Fe, 0.05 pct Si, 0.008 pct Cu, <0.005 pct W, <0.001 pct Al, <0.05 pct Mg, <0.001 pct Ni, <0.02 pct Ca, and <0.01 pct Ti. Microscopic examination of the material in the as received condition revealed very fine grains with numerous twins. Specimens were annealed either in situ in the internal friction apparatus or in evacuated silica tubes in an auxiliary furnace. When the specimens were annealed in the auxiliary furnace, they were wrapped in identical zirconium wire to prevent contamination by the container. Metallographic sections were taken in all cases. Some were taken from the specimens used for internal friction measurements after completion of the experiments, while others were taken from control specimens at intermediate stages of the experiments. lnternal friction values were obtained by measuring the free decay of a low frequency torsion pendulum (1 cycle per sec), the suspension of which was

Jan 1, 1957

By F. D. Rosi, C. A. Dube, B. H. Alexander

WHEN a deformed polpcrystalline metal is heated to a sufficiently high temperature, a recrystallized structure develops which consists of small, essentially stress-free grains. This transformation is referred to as primary recrystallization. Under certain conditions, on prolonged annealing of the specimens, a type of grain coarsening occurs in which a small number of grains commence to grow at various points by devouring the neighboring finegrained primary structure, which, in itself, exhibits a marked stability toward normal grain growth. This grain coarsening process has been referred to by Burgers&apos; as "secondary recrystallization" or "exaggerated grain growth." Although much work has been done on recrystallization and growth processes, present knowledge of the factors which determine the occurrence and growth of secondary grains is inadequate for the advancement of a theory which accounts for the observed characteristics of this recrystallization phenomenon. In this respect, it would be important to make measurements of the velocity of growth of these large secondary grains. The early work of Feitnecht2 on aluminum showed that the size of secondary grains increased with temperature and time, suggesting that such measurements would be possible. More recently, Burgers1 found that the growth velocity of these grains in aluminum was constant over a large time interval, as is generally found for the growth velocity of primary grains in a uniformly deformed test piece.3-5 It is reasonable to expect that the determination of the activation energy of the secondary growth process might lead to a better understanding of the underlying atomic mechanism. This investigation, therefore, is one of a series primarily designed to measure the growth velocity of secondary grains at various temperatures for silver, copper, and aluminum. It is hoped that these studies along with those of orientation relationships, will establish a sound basis for theorizing as to the origin and nature of the secondary transformation. Experimental Procedure The metal used in the present investigation was high-purity silver (999.9 fine), which was supplied in the form of cold-rolled plates 0.250 in. thick. These plates were annealed at 500°C for 1 hr and then straight-rolled to a thickness of 0.04 in. in three reductions of approximately 45 pct, followed in each case by an anneal at 450°C for 1/2 hr. The 0.04 in. sheets were given a final reduction of approximately 50 pct, which resulted in a thickness of 0.02 in., thereby insuring two-dimensional crystal growth. Individual specimens of this material about 1x3 cm were used for all heat treatments, unless otherwise noted. The annealing was carried out under an atmosphere of argon in an Inconel tube furnace whose temperature was controlled to within -+2°C. Metallographic examination of the secondary transformation was accomplished by mechanically polishing the specimens on one side to approximately one half their thickness through 2/0 metallographic emery paper, and then electrolytically polishing in a solution of potassium ferrocyanide and sodium cyanide. With a current density of approximately 20 amp per sq dm, the time required to obtain a satisfactory surface varied from 3 to 5 min. Standard potassium bichromate was used to etch the electrolytically polished surfaces. A heavy etch with this solution produced a sharp contrast between the secondary grains and the fine-grained primary structure, darkening the latter while leaving the large secondary grains bright. All area measurements of the secondary crystals were made with a planimeter on enlarged tracings of the grains.

Jan 1, 1953

By C. S. Matthews, M. J. Fischer

Distortions caused by dip on five-spot sweep pattern were determined by visual experiments on a model composed of parallel plates of glass with holes drilled at the well positions. This model war designed to simulate a reservoir depleted of its primary oil and containing a gas phase. Prior to interference, it was found that the injected fluid took a nearly circular shape about the injection well for the cases studied. However, these circles moved down-dip considerably under the influence of gravity. It was concluded that pattern flooding should be practical for many dipping reservoirs. A quantitative measure is given of how much the well position should be altered to allow for dip. Experimental deternzinarions of injectivity showed this to be about the same in a dipping reservoir as in a horizontal one. INTRODUCTION This investigation was undertaken at the suggestion of the Pacific Coast area, Shell Oil Co., where a pilot water flood in a dipping reservoir was being carried out at the time this paper was in preparation. Prior to the undertaking of this flood there had been considerable speculation as to how gravity would distort a flood pattern in a dipping reservoir. The thought was expressed in some quarters that a five-spot flood would not be applicable to a dipping reservoir because the flood pattern would elongate in the direction of dip and would never form a "seal" around each five-spot. If the flood pattern elongated sufficiently, both the oil and the water might flow largely downdip rather than into the pattern producers. In view of the importance of the California water floods, it was deemed important to determine the effects of gravity on a five-spot pattern in a dipping reservoir. Previous work had also been carried out in this laboratory,1 but only for the single-fluid case. The present investigation extends these results to multifluid cases. Several sets of pictures of flood fronts are presented so that the process can be visualized. From these pictures, curves are obtained which show the correct drilling position for achieving equal times of oil-bank breakthrough. Several injectivity curves are also presented which may aid in prediction of injection rate. ASSUMPTIONS The present results were obtained with a model composed of two parallel plates of glass spaced about 1 mm apart. When the inertial forces are small, as in these experiments, the flow between the plates follows Darcy&apos;s law and is analogous to flow through porous media. In using these plates, it is not possible to scale effects of capillarity correctly as regards a transition zone between injected and displaced fluid. Calculations show, however, that effects of such capillarity should not be important in determining the gross flooding pattern in the field. In fact, in this model the capillary forces tend to circularize the pattern to a greater degree than in the field. To preserve a large ratio between the viscous forces and the circularizing capillary forces in the laboratory model, viswus glycerine was used as the flooding liquid and the rate of flooding was very high. The circularizing force is believed negligible in these experiments. In addition to the effect of the surface tension y, which tends to circularize the pattern, another capillary force must be considered. This is the adhesion tension y cos, which acts at right angles to the circularizing term y. If the plates in the model are "wetted" the same all around the periphery, then the adhesion tension,

Jan 1, 1957

By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By E. I. Organick, B. H. Golding

A simple correlation is presented for the prediction of saturation pressures in condensate-gas and volatile-oil mixtures. Saturation pressure is related directly to the composition of the mixture with the aid of two generalized composition characteristics, B, the molal average boiling point, and W, the modified weight average equivalent molecular weight. The need for hydrocarbon equilibrium constants is entirely eliminated. Only the values of the two conlposition parameters need be obtained, and these are calculated in a simple and reproducible manner from the stream analysis of the mixture and the ASTM distillation for the heavy ends. The correlation is given .in the form of a set of 14 working charts in which saturation pressures, either retrograde dew points or bubble points, are plotted cs temperature, forming partial phase envelopes for mixtures having discrete values of the composition parameters, B and Wul. A locus of critical states on each chart intersects the partial phase envelopes, distinguishing retrograde dew point pressures from bubble pressures. A comparison Between experimental and predicted saturation pressures reveals that: the probable error of the predicted values, when considering the data as a whole (214 experimental points), is five per cent; for high gasjoil ratio condensate fluids (approximately 40.000 or more cu ft/bbl) the probable error is about 8 per cent. In either case, however, the probable error is comparable with the overall uncertainty of the data from which the correlation is derived. INTRODUCTION There is a present need for a simplified, yet reasonably accurate method for predicting upper phase boundaries of reservoir fluids. In the case of high gas/oil ratio fluids, namely the so-called highly volatile oils and the condensate gases, no simple method, accurate within 5 to 10 per cent, is now available by which bubble point and retrograde dew point pressures may be predicted. In order to calculate the upper phase boundary of a volatile reservoir fluid, using correlations now available, it is necessary to find and employ the proper K-values (equilibrium volatility ratios of the hydrocarbons in that fluid). This process of finding the Proper K-values usually involves a double trial and error computation. Since the K-values are in themselves dependent upon the composition of the fluid, their use in the calculation of a saturation pressure actually represents an unnecessary complication. The correlation described in this paper relates saturation pressure directly to the stream composition, entirely eliminating the need for K-values. The only data required to calculate the Stream composition are obtained from the customary low temperature fractional analyses of separator gas and liquidt and from the ASTM distillation of the c,+ fraction of the separator liquid. A considerable simplification in the procedure for predicting saturation pressures is thereby effected without significant loss in accuracy. BASIS FOR A CORRELATION Empirical relationships between the saturation pressure and the composition of the fluid in question have already been partially explored by one of the authors.V n particular, a relationship between the critical pressure for a hydrocarbon mixture and its composition was developed. The critical pressure is in reality a saturation pressure, as it repregents a limiting case either of a dew point or of a buhhle point pressure for any given mixture. It was found that the critical pressure may be correlated as a function of two generalized composition characteristics or variables. One characteristic expressed a molal average prop-erty, the other a weight average property of the mixture. Specifically, the molal average boiling point (MABP, or B as it

Jan 1, 1952

By H. W. Weart, S. Sarian

The effect of temperature, impurities, and capillarity on the morphology of solid particles in a liquid matrix is investigated. For the NbC-liquid iron system, at least, it is found that those particles which are dissolving will assume a spherical shape; all others will take the equilibrium shape. An aniso-tropic-isotropic transition in the interfacial tension is observed at about 1725°C and is believed to be due to cooperative roughening of the interface on an atomic scale. The presence of boron as an impurity lowers the transition temperature. It is the purpose of this paper to present some observations on the shape of particles in a system consisting of solid particles of nonuniform size in a liquid matrix and to propose an explanation for these observations. Although qualitative only, these observations, which were made largely in the course of a study of particle-growth kinetics,&apos; are presented separately to draw attention to them. They reveal the effect of particle size, temperature, and surface-active impurities on particle shape in the solid NbC-liquid iron system, and are unique in demonstrating for the first time the reversible effect of temperature and impurity concentration on the anisotropy of the energy of the solid-liquid interfaces involved. Some of the changes are readily demonstrated with the few particles whose shapes can be clearly shown in a single photomicrograph, but others are more subtle, and their recognition depends upon some experience and the study of a much larger sample. For this reason, a certain amount of judgment must be acknowledged to underlie their detection, but every effort was made to maintain proper scientific objectivity in evaluating the observations. The observations will be presented first, and then an explanation rationalizing them will be offered. Brief reminders of the relevant theories will be inserted into the discussion at the appropriate points. EXPERIMENTAL The observations were made of the shape of NbC particles dispersed in liquid iron. All specimens were prepared by pressing NbC powder and car- bony1 iron powder treated according to standard powder-metallurgical procedures. Except as noted, all specimens were heated to 1900°C for 1/2 hr. In investigating the effect of temperature, specimens were quenched from 1900°C to various lower temperatures, and held long enough (48 hr) to allow shape changes to be completed. Boron, in the form of amorphous powder, and oxygen, in the form of niobium oxide powder, were added as impurities to some specimens. Nitrogen was introduced into some specimens as an impurity by heat treating the samples under a partial pressure of nitrogen gas. Effect of Temperature. It was first observed that increasing temperature had a marked effect in rounding the corners and edges of the particles. At 1900°C the particles are all very nearly spherical and remain so even when the holding time is extended to 48 hr. As can be seen from Fig. 1, there is virtually no evidence of the presence of low-index planes. At 1300°C, however, most of the particles are prismatic with very slightly rounded edges and corners, Fig. 2. (In making these shape comparisons, attention should be focused on the larger particles, even though the smaller ones would be expected to be the first to change shape, owing to the shorter diffusion distances involved. The cause of the mixed particle shape will be explored later.) It was established that these structures are re-

Jan 1, 1965

By L. R. Page, J. J. Norton

EFFECTIVE methods for determining grade and reserves of pegmatites in advance of mining have been developed in recent years. When intensive work began on the economic geology of pegmatites during the early years of World War 11, it was widely believed that grade and reserves could be estimated only in a most general way. The literature indicated that not all pegmatite deposits are unpredictable, but statements emphasizing unpredictability and irregularity seem to have been more widely accepted. Many standard references reflect the prevailing opinion that minerals: are unsystematic in their occurrence in pegmatites. Pegmatites have been described as "notorious for their irregular structure," and minerals within pegmatites as "irregularly distributed." "irregularly disseminated," of "erratic occurrence," "proverbially erratic in distribution," "characterized by extreme irregularity in ... size and distribution of the essential minerals, and variety and proportion of the accessory minerals," and "spotty.&apos;"" Over many years, however, geologic techniques have been applied with increasing success to economic analysis of pegmatites. Investigations, chiefly since 1939, have shown that mineral distribution and structure of pegmatites are largely systematic and that detailed geologic study can be used to predict the size and shape of mineral deposits in pegmatites. Because the writers are most familiar with the pegmatites of the Black Hills, S. D., examples cited are from that area." Pegmatites mined in other dis- * All examples are described more cornpletely elsewhere.: tricts are similar to those in the Black Hills," and the techniques described here have been applied by geologists and engineers working in other districts. In actual practice few pegmatite mine operators attempt to make accurate estimates of grade and reserves in advance of mining. Many deposits are too small for mining except on a very small scale; few pegmatite mines have more than ten employes. Hence there is little systematic preparation for mining, and the capital outlay may be so small that only a general knowledge of reserves is necessary. Technical personnel are rarely employed by pegmatite mine operators to make such estimates. In the future, however, as capital outlay becomes larger, estimates of grade and reserves will have to be more accurate. Geologic Aspects of Determining Grade and Reserves Estimating grade and reserves requires that the type of pegmatite, the size and shape, and the internal structure be determined by detailed geologic mapping and careful mineralogic study. The wide variations in the texture and distribution of minerals within many pegmatite deposits make a thorough geologic study of this kind necessary before it is possible to decide what sampling methods should be used to determine mineral content or grade. Types of Pegmatites: The first step in economic appraisal of a pegmatite is to determine the min-eralogical and structural type. In general, pegmatites may be classified into two groups: 1) those in which component minerals are more or less evenly distributed throughout the entire body and show relatively minor variations in texture, and 2) those in which component minerals have been segregated into units with recognizable differences in texture, mineralogy. or both. Johnston" has classified these types of pegmatites as homogeneous and heterogeneous, respectively. Cameron et al.10 have used the terms ~inzoned and zoned for similar types. The difference between the homogeneous and heterogeneous types is of great commercial importance. Homogeneous pegmatites can seldom be mined where the products are concentrated by the hand methods now commonly used, but they have been mined in a few places where a milling process has

Jan 1, 1957

By A. R. Brown, D. Silverman

EquipmENT and methods for locating the points of entry of salt water into oil wells are described. These techniques make it possible to delineate accurately the top and bottom boundaries of water zones whether bottom water or intermediate zones of production, Data are given on tests by this survey method on a number of producing wells, Complete results were obtained on wells shelving water percentages ranging from high values to as Little as 10 pct salt water. A number of the wells tested were plugged back and the results are reported in detail. While not all the work-overs were successful, evidence, including the results of reruns by this survey method, points to failure of the plugback operations. The data provided in the tests discussed show, contrary to general opinion, that a large percentage approaching 50 pct of the wells showed intermediate water instead of bottom water. Furthermore, approximately a third of the wells tested showed multiple zones of water production. The equipment comprises a long pipelike assembly carrying 10 pairs of electrodes spaced apart a distance of 4 ft. A surface-controlled solenoid-operated switch is provided to connect each of the individual pairs of electrodes in turn to a single-conductor steel-armored cable by means of which the conductivity of the fluid in the vicinity of each of the electrode pairs can be continuously recorded at the surface. Any number of electrode pairs and any spacing can be used. This assembly is lowered on tubing and placed in position opposite the section of the well to be studied. A conventional rod pump is used to produce the well for the survey. The pump inlet is placed below the lowest electrode pair. The well is conditioned by pumping Out the salt water normally standing in the well and introducing fresh water into the annulus at the surface. When the resistivity of the water standing in the well has been increased to a sufficiently high value, the inflowing fresh water is stopped and the drawdown operation of the survey is started. As the fluid head is lowered by pumping, fluids flow into the well and the entry Of salt water is indicated by the change in resistivity of the fresh water opposite the &apos;Ones Of water entry, The process can be repeated as Often as necessary with little effort and without moving any well equipment to be sure that the fluids produced from each zone are representative Of the true reservoir content. Introduction The oil industry has been concerned from its inception with the control of fluids entering its wells. In order to effect the greatest economy of operation and to get the greatest total production of petroleum liquids out of the ground, the flow of gas and water must be controlled and often extensive workovers are planned and carried Out for this purpose. This has become even more important in recent Years because of the need for the conservation of natural resources. Whereas producing operations concerned with the original completion of a well are assisted to a great extent by a wide variety of instruments developed and perfected for that purpose, workover operations on oil wells have been greatly hindered by a lack of suitable instrumentation. The industry has searched for many years for a satisfactory instrument and process that

Jan 1, 1948

By Bengt Helmerson

A new tankhouse was started in January 1959 at the Copper Refinery of the Boliden Co., Skelleftehamn, Sweden. In early 1961 a semiautomatic machine for looping and straightening of starting sheets was introduced to substitute previous manual operations. The machine as well as consequent, racking and handling is described. Finally, economic benefits achieved and new constructions for the future are discussed. HISTORY Tankhouse operations at the Boliden Co. &apos;s Smelter in Skelleftehamn started in 1932 on a scale that since then has been gradually increasing. In order to rationalize the operations, a new tankhouse was erected. It went into production in January 1959 and was designed for a yearly production of 35,000 metric tons at a current density of 16 amps per sq ft. Already from the beginning, however, the tankhouse has been run with a current density of 21.5 amps per sq ft, corresponding to a maximum capacity of 50,000 tons a year. During the time of planning of the new tankhouse, due consideration was given to the possibilities of mechanizing the operations. New ideas could be and were actually tested on full or pilot plant scale in the old tankhouse. In that way we developed a system for the cathode handling including washing, weighing, and transportation. A system using forklift trucks in combination with trailers and overhead cranes has been developed for transportation and racking of anodes and also for handling of anode scrap. With respect to the electrolyte, circulation and temperature control are partly automatic. Special attention was paid to the production of starting sheets, which operation normally requires a great number of man hours, and it was made the object of a particular survey as to the best ways of straightening starting sheets, attaching loops to the sheets, and so forth. As a result, a machine was designed during 1957-58 and built in our own shops. After a period of tests, the new equipment was put in operation commercially on the 10th of April, 1961. Since this date the machine has produced about 2 million starting sheets without interruption and has been the only source of looped starting sheets for the tankhouse. GENERAL DESCRIPTION Fig. 1 shows all the major parts of the system. These parts are: slitting machine with feeding table (I), standard roller leveler, type Ungerer (2), tilting roller table (3), conveyors for sheets and suspension bars (4, 7), storage of suspension bars (51, punching and stitching machine (6), two lift-turn-tilt tables (8) for discharging the starting sheets, two rack conveyors (9) for sheet assemblies. Included are a hy-daulic pump station and panels for pneumatic and electric controls. SLITTING AND STRAIGHTENING The machine is fed by hand by a man sitting in front of the slitting-machine table, Fig. 2. This operator inserts one sheet at a time into the slitter. After being trimmed, the sheet is automatically conveyed to the following step of handling, straightening. The slitting machine cuts away about 8 mm of the upper and lower parts of the sheet (in relation to its original position in the stripper section) for two reasons. The first one is to give the machine sheets of uniform dimensions; the second one is a matter of quality. Normally the starting sheets as stripped have a thick edge at the bottom end. This part would collect anode slimes and might also cause short circuits when inserted in the cells without trimming. The straightener used is of German construction

Jan 1, 1967

By T. E. Schmieman, J. E. Miller, M. L. Rizzone

Both centrifugal and reciprocating-type pumps have been widely used in the transport of slurries. Although with some limitations, centrifugal pumps may be used, especially for short-haul systems, however, for the long pipelines the reciprocating pumps are better suited. A state-of-the-art review is presented in which a discussion of applications is made and some of the problems associated with meeting the proper design conditions for satisfactory service are discussed. Several developments underway give considerable promise of better pumps in the future, although the current level of development provides for an economical means to move slurries. The movement of liquids in pipelines necessarily occasions the use of pumps. The petroleum industry is familiar with the transport of solids through mud pumps and cementing and fracturing pumps where the movement of slurries is an everyday matter. In the drilling of an oil well, the circulating fluid utilized to remove drill cuttings is called drilling mud. This substance is usually a fairly sophisticated material designed to develop certain characteristics desirable in the drilling process. The cuttings are suspended in a moving column of this fluid and brought to the surface. The separation of the cuttings from the drilling fluids is accomplished by the use of shaker screens and settling pits; however, it is impractical to remove the cuttings completely and as a result they are pumped through the mud pumps back into the circulating stream. Over the years, mud pumps have been improved so that rather long life can be obtained from liquid end parts subject to the attritional effects of the abrasive-laden fluid. It is from this background that reciprocating-type slurry pumps have been developed. Centrifugal Pumps Centrifugal pumps have also been used to transport solids, where low heads are required, typically up to 200 ft or so, and for short hauls. The centrifugal pump is a hydrokinetic device wherein the increase in velocity of a fluid stream is converted to head, and to achieve high heads a large change in velocity is necessary. Abrasive laden fluids cause wear on impellers and casings as a result of erosion by the fluid and the suspended particles. Centrifugal pumps, therefore, can only be used where the internal velocity of flow is rela- tively low. The advantage of centrifugal pumps is their high capacity at relatively low capital cost and usually relatively small space requirement. One of the disadvantages of the centrifugal pump when used in slurry pipelining can be seen in its typical pressure-volume performance relationship, which tends to work against the application (see Fig. I). If an increase in pressure (head) is occasioned by flow restrictions in the pipeline, say by the dropping out of solids, a desirable characteristic of a slurry pump would be that it develop increased pressure to overcome the restriction. The centrifugal pump provides the increased pressure only at the expense of considerably reduced volume which then results in a lower flow velocity. With the reduced flow rate, adequate velocity to hold the material in suspension and keep it flowing in the line might not be achieved. If centrifugal pumps are considerd for the movement of solids in a long line, a series of pumps must be staged in order to provide the necessary motivating force. A large number of pumps in the line would be required, since each of the pumps could provide only a small pressure increment. An equal number of standby pumps

Jan 1, 1971

By Nicholas J. Grant, Rolf Nordheim, Bill C. Gissen

The system Cb-Re was examined in detail utilizing pure metals, careful melting techniques, and heat treatments. Metallographic and X-my methods were utilized for phase identification. In addition to soli-dus determinations, the composition limits and mode of formation of the intermetallic compounds 0 and X were determined. The binary constitution diagram Cb-Re has been the subject of a number of investigations.&apos;-7 Two intermetallic phases have been described and tentative diagrams have been proposed. It was the aim of this investigation to obtain a complete and more accurate diagram through the use of purer alloys and improved techniques. The diagram worked out by Knapton7 was published after our experiments were concluded. EXPERIMENTAL METHODS The starting materials were Re powder of 99.95 pct purity, supplied by the Chase Brass and Copper Co., and Cb rondelles of 99.6 pct purity, supplied by the Electro Metallurgical Co. Typical analyses are given in Table I. The alloys were prepared from compacted Re powder and Cb rondelles; for critical compositions master alloys were used. The melts varied from 5 to 50 g and were melted nonconsumably in an Heraeus arc furnace, under ti-tanium-gettered laboratory grade argon. It was necessary to invert the buttons and remelt, followed by crushing and further remeltings, the number of which depended on the nature of the fracture of the alloy. The weight of each alloy was carefully checked after each melting operation. It was found that significant weight losses occurred only when loose Re powder was used. These losses amounted to a maximum of 3 wt pct in such instances, but did not occur after the charge was once molten, regardless of the composition. Typical loss of weight after 4 remelts, including crushing, amounted to 0.2 wt pct. Oxygen pickup during successive melting cycles did not appear to be significant, since the weight gain values never exceeded 0.01 wt pct. Control of the composition of the alloys was not too difficult; however, the problem of homogenization was a far greater one. Optimum alloying conditions were finally achieved by a combination of master alloy production and repeated crushing and remelting cycles. The compositions of the alloys utilized to determine the constitution diagram are listed in Table 11. The weight balance method was used ultimately as the sole analytical method, since repeated checks indicated that it was accurate to 0.2 pct, if the weight losses were small. The results were double-checked by a metallographic study of the homogeneity of the samples, since this was presumed to be the more serious factor. Heat treatments at 1200°C or lower were accomplished by sealing the specimens in Vycor tubes, heating in a Globar furnace, followed by air cooling. This was considered to be an adequate quench because of the very low temperatures involved. For temperatures of 1200" to 1900°, alloys were homogenized and heat treated in a tungsten-filament resistance vacuum furnace. From 1900" to 2750" a tantalum-tube resistance furnace was utilized, operating under a vacuum of 105 mm Hg. The temperature measurements up to 1200" were made by means of platinum-platinum 10 pct Rh thermocouples, with an accuracy of 5°C. For temperature measurements greater than 1200°C, optical pyrometers were used. They were calibrated against a standardized instru-

Jan 1, 1962

By J. N. Anderson

Developments in reverberatory furnace practice at Noranda over the period 1928 to 1953 are described. Features of interest are increasing furnace tonnage from 700 to 2000 tons per furnace day, the use of the suspended basic roof, and improvements in furnace fuel ratio. Points of comparison and contrast between Canadian and American furnace practice are given. OPERATIONS at the Noranda smelter have been described in a series of papers published between 1930 and 1945.1-4 In the present paper the development of reverberatory furnace practice over the 25 year period from the beginning of operations up to the present time will be reviewed and current furnace practice will be described in some detail. Particular attention will be given to those features which are characteristic of Canadian practice: first, the use of the suspended basic roof; second, the deliberate driving of furnaces to give tonnages in the range of 1400 to 2000 tons of solid charge per furnace day; and third, the continuous operation of furnaces at high tonnage for many years without any extended shutdown for repairs or rebuilding. Finally, points of comparison and contrast between reverberatory furnace practice in Canada and the United States will be discussed. The Noranda smelter, which started in December 1927, was built for the reduction of ore from the Horne mine where early development had shown a comparatively small tonnage of rich cop-per-gold ore of a grade and character which would require direct smelting. The smelter was designed for a capacity of 1000 tons of ore a day and originally consisted of eight roasters, two reverberatory furnaces, and two converters, together with necessary auxiliaries. The discovery of a large new body of ore in 1928 made it necessary to increase both the size and the scope of the reduction plant. A mill which was ultimately brought to a capacity of 3000 tons a day was built for concentrating low grade ore and in addition the capacity of the smelting plant had to be greatly expanded, so that for the next fifteen years every effort in the smelter was directed toward achieving maximum tonnage. Because the layout and design of the smelter made it impracticable to add a third furnace, it was necessary to increase the tonnage on the two original furnaces by improvements in furnace design and operation, roasting and converting equipment being added as required to meet the demands of increased furnace capacity. The smelter tonnage, which reached a peak in 1941, was curtailed in 1944 when it became necessary to operate on a one-furnace basis because of a reduction in the output of the Horne mine due to a shortage of labor. Two-furnace operation at a moderate tonnage was resumed in 1949. In the early years the smelter tonnage was made up almost entirely of Noranda ores and concentrates. However, since 1937 an increasing tonnage of ores and concentrates from other mines has been treated in the smelter. In recent years, with decreased production from the Horne mine, copper concentrates from several mines in the district, treated on a custom basis, have formed an important part of the smelter tonnage. A review of developments in reverberatory furnace practice at Noranda falls naturally into the following four periods: 1—1928 to 1935, the early years; 2—1935 to 1944, the period of greatest change and development; 3—1944 to 1949, one-furnace op-

Jan 1, 1955

By C. F. Cockrell, H. E. Shafer, J. W. Leonard

A significant technological development is discussed for the processing of certain power plant flyashes that are a problem because they contain a high water-soluble mineral content and yield inferior flyash-based brick. This development is based on the addition of hydrochloric acid to the flyash-bottom ash-sodium silicate blends used for the production of flyash-based structures. Favorable changes are evi-dent in sodium silicate consumption, where about half the amount used for making brick from normal flyash is required, processing costs, and strength and appearance of the resulting freshly formed green and fired structural products. In some high cost in-stances (above the $30 or less per thousand brick estimated for normal flyash), hydrochloric acid additions can replace or reduce other costly additives normally required for problem flyashes. This results in savings of as much as $9 per thousand brick. These developments offer promising possibilities for utilizing problem flyashes as well as flyashes which may come into contact with water soluble sulfur as a result of the eventual application of certain experimental air pollution control processes. Much of the research datal-6 accrued through work by the Coal Research Bureau of West Virginia University for the Department of Interior&apos;s Office of Coal Research on converting waste power coal ash to valuable brick and other structural products, can be categorized as follows: (1) general ash-to-brick tech- nology; (2) specific ash-to-brick optimization; (3) pilot plant progress; (4) production cost estimates. A summary of the progress on bench-scale experiments indicates that coal ash can yield two types of brick. An acceptable brick is obtained by mixing 73.6% fly-ash, 23.5% bottom ash and 2.9% sodium silicate solution (dry basis). Depending on the flyash and bottom ash used, optimum brick can be manufactured by mixing 72-77% flyash, 20-25% bottom ash and 2.3-3.0% sodium silicate (dry basis) with Na2O : SiO2 ratio varied according to the composition of the flyash used. These blends are thoroughly mixed and mechanically formed into green brick shapes at pressures ranging from 1000 to the more usual 3000 lb per sq in. The green shapes then are dried and fired at temperatures ranging from 1975-2150°F using clay brick cycles that are shorter than standard. Other findings reported to date indicate that when making optimum brick, it is necessary to carefully control the top size of the moisture-releasing bottom ash so that it falls between 8 and 30 mesh, depending on the flyash used. Moreover, the chemical composition of bottom ash and flyash have been found to be of little significance with the exception of a few problem flyashes which are the subject of this paper. Finally, the pilot plant, which was previously reported under construction, is now in operation. This will indicate, among other things, the cost of brick production, which was earlier estimated for non-problem flyashes at $30 or less per thousand brick. The foregoing bench-scale technology is applicable to all the initially tested ashes as well as to the majority of ashes examined during the course of research. However, a few of the ashes yield green and fired products that may be structurally inferior or unacceptable, necessitating excessive and diverse reagent addition, and/or may be coated with unsightly surface deposits. These problem ashes generally originate in certain areas of Illinois, western Ken-

Jan 1, 1969

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,&apos; but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation&apos; and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a&apos;c&apos; and c&apos;b are equal to a&apos;b cos +, and a&apos;b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m&apos;c&apos; and c&apos;b are projected as lengths from point a, rather than from point a&apos;. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

By D. R. McCord

Data of a known statistical quality has been successfully used in a system of conventional fluid mechanics equations essentially free of empirical "conformance factors to prediet early detailed field 03 in a reservoir where gravity drainage is important and oil and rock properties vary con. siderably. The system is useful where comparative recovery predictions for one or more cases of natural depletion and gas cap pressure maintenance are needed and the reservoir is not too heterogeneous. INTRODUCTION Many authors, have examined various facet* of the gravity drainage-gas cap pressure maintenance problem over the last several years. Two of them. Burtchaell and Elkins, have published practical studies. In the case described in the present paper the best development and operating plan for one of the important reservoirs of the Bolivar Coastal Field in Western Venezuela was urgently needed. It was requested that sound comparative economics be presented along with an engineering evaluation of no additional drilling, maximum drilling. several cases of gas pressure maintenance, of water flooding and combination cases. A rapid analysis of the effect on recovery of the range of crude and rock properties indicated that none of the published methods using average properties would yield adequate comparative predictions. This paper covers the predictive system developed to deal with natural depletion and gas cap pressure maintenance. The large amount of data available for this field permitted statistically reliable correlations to be made of most rock and oil properties, and the evident smooth areal variations of these properties encouraged the construction of a lineal mathematical model of material balance and fluid flow equations, which could be manipulated by a modified iterative procedure. The manipulation is much more adaptable to computing machines than manually operated calculators and subsequent studies have been prepared for the IBM Card Program Calculator. A matrix as opposed to linear model has been tentatively worked out by other members of our group to deal with more heterogeneous reservoirs. It is more adaptable to computers such as IBM-701 or the Remington-Rand Univac. In 1950, when the system reported below was developed, no rapid computing machines were available to the author. Their existence and promise encouraged an initial approach by hand. Some details of oil and rock Property correlation are included because there are a surprisingly large number of medium-sized reservoirs in the world that show systematic property variations which are significant for a rigorous analycon. All large reservoirs (over half a billion barrels recovery) with which the author is familiar contain at minimum a significant temperature variation. Using the rock and oil property correlations, past pressure and production, the gas-oil ratio history of the reservoir was computed and found to be in close agreement with field measurements. The future performance under cases of natural depletion, gas injection of 100 MMcf/day, and of 130 MMcf/day, was then computed; a 70 MMcf/day case was also carried far enough to provide data for comparative economics. The 130 MMcf/day case proved to be the most attractive. A 50,000 horsepower gas turbine driven centrifugal compressor plant to take this quantity of adjacent field gas from 30 to 1,950 psia and inject it into the reservoir is under construction. The total cost of the project will exceed 20 million dollars.

Jan 1, 1953