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By N. J. Grant, C. F. Flo, F. B. Cuff

An investigation of the Ti-Cr system has shown the presence of a complete series of solid solutions in the ß phase, with a minimum in the solid us near 50 pct Cr. An intermetallic compound, TiCr2, forms during cooling from the ß solid solution. There is a eutectoid reaction at the low chromium side of the system. IN view of the recognition of the potentialities of titanium and its alloys as important structural materials there has arisen a need for a systematic investigation of various titanium binary diagrams. Of these, the Ti-Cr system was of particular interest because of the improved properties imparted to titanium by small chromium additions. A literature survey disclosed a partial constitution diagram that had been suggested by Vogel and Wenderott,¹ This diagram, shown in Fig. 1, is the result of work done on the Fe-Cr-Ti ternary system. Alloys containing less than 43 pct Cr were not investigated. In addition to this, a study of alloys in the Ti-Cr system was reported by McPherson and Fontana.² Adenstedt3 furnished a number of dilato-meter curves obtained from specimens containing 5, 10, and 15 pct Cr. Very recently, McQuillan4 submitted a proposed diagram covering the complete range of compositions between titanium and chromium. This diagram was in general agreement with the one described here. Experimental Procedure Sponge titanium (99.7 pct) and electrolytic chromium (Bureau of Mines analysis: 99.03 pct Cr, 0.40 pct Fe, 0.53 pct O2) were used for the initial determination of the system. Subsequent refinement of points, particularly for the low chromium side of the diagram, was accomplished by using iodide titanium and high purity chromium (National Research Corp. analysis: 0.050 pct C, 0.045 pct O2). The Ti-Cr alloys were prepared by melting 25 g charges in an enclosed, water-cooled copper crucible using a movable tungsten electrode. The atmosphere was helium, prepurified by first passing it through a drying agent and then through sponge titanium heated to 850°C. Particular care was taken to avoid any large scale segregation resulting from insufficient mixing of the components. Each charge was melted and kept molten for approximately 1 min, allowed to cool, inverted, remelted, and kept molten for an additional minute. In order to ascertain the amount of impurity pickup (oxygen and nitrogen) during the melting procedure, three iodide titanium specimens were melted in sequence and then checked for increased hardness. The specimens in the as-cast condition showed a relatively large hardness increase over the hardness of the as-received iodide titanium. The scattering on these readings was large. However, after the specimens had been homogenized at 840 °C for 2 hr and slowly cooled, the measured increase in hardness over the as-received titanium was small with a corresponding decrease in scatter. The reason for this hardness change is that in heat treating these specimens below the transformation temperature (885°C) there was a conversion from the as-cast structure to the more nearly equilibrium structure of the annealed specimen. The alloys were analyzed for chromium content and although the actual percentage was invariably low the deviation from the nominal composition never exceeded 0.6 pct Cr.

Jan 1, 1953

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

KNOWLEDGE of the isothermal transformation behavior and the TTT chart method of graphically summarizing such information has been of invaluable aid to the ferrous metallurgist in understanding and developing heat treatments intended to provide specific mechanical properties. It is to be expected that similar lines of study directed to titanium-base alloys will be as profitable. This paper summarizes, on conventional TTT charts, the isothermal transformation products and pertinent reaction rate data for binary alloys of titanium containing 1, 3, 5, 7, 9, and 11 pct Mo, respectively. The results so presented were derived from metal-lographic examination. Some X-ray diffraction work was done to clarify certain points of question. Ti-Mo System To the authors' k.nowledge, TTT charts have only been used to describe the reaction rates of eutectoidal decompositions. It would seem that the kinetics of decomposition of any unstable solid solution might be conveniently described in this manner. The equilibrium diagram of the Ti-Mo system' is shown in Fig. 1. The similarity with the Fe-Ni system will be recognized. Additions of molybdenum serve to stabilize the /3 phase to increasingly lower temperatures. The solubility of molybdenum in the a phase is restricted to less than 1 pct at 600°C. Under normal conditions. a homogeneous ,8 structure quenched to a, temperature in the a f & field will reject a of invariant composition. The rate at which this occurs depends on the degree of undercooling and the degree of supersaturation of /3. The structural character of the rejected phase may also be expected to be related to the undercooling. Materials and Experimental Methods A sponge titanium was used which has a nominal impurity content as reported in Table I. The nominal composition of the molybdenum used is also included. The alloys were prepared in 150 g melts by arc melting in an evacuated water-cooled copper crucible of the type reported in an earlier paper.' The pancake-type ingots were forged to 1/4x1/4 in. bars and homogenized for 24 hr at 1000°C in evacuated Vycor bulbs. Specimens Vi in. thick were cut from these bars for heat treatment. The heat treatment cycles followed an invariant procedure. The specimens were soaked at 1000°C for 20 min under a helium protective atmosphere prior to quenching into a lead bath held at a temperature corresponding to a chosen degree of undercooling. After a prescribed period of time at this temperature, the specimen was removed and water quenched. A series of specimens so treated for progressively longer periods served to establish the times for initiation and completion of the decomposition of the /3 phase at a particular temperature. Although heat treatment of unprotected specimens in a lead bath does permit surface contamination by lead diffusion, this method is necessary to insure sufficiently rapid quenching rates. As long as the bath treatments were of less than 1 hr duration. the contaminated surface was not unduly deep and could be removed without excessive grinding. Metal-lographically, the contaminated zone could be readily distinguished from the pure binary alloy. Transformation Characteristics of Ti-Mo Alloys Metallographic examination showed that a supersaturated p phase may decompose by one of two processes. Alloys containing 1 to 9 pct Mo, when quenched in water from the homogeneous /3 field,

Jan 1, 1953

By J. Geertsma

In order to obtain a better insight into the pressure-volume relationship of reservoir rocks a theory of pore and rock bulk volume variations is presented. The theory is independent of the shape of the pores but is restricted to isotropic porous media built up of continuous homogeneous matrix material. The main conclusion obtained from this theory is that only three elastic constants and three viscous constants are required for describing pore and rock bulk volume variations if the porosity is explicitly introduced into the treatment. In addition, reasonable approximations are introduced for various types of reservoir rock, e.g., sandstones, limestones, and shales, which lead to further simplifications of the basic formulas. In consequence there is then a further reduction in the number of deformation constants which have to be determined experimentally. It is shown how measurements of these remaining deformation constants can be performed most conveniently. Finally the application of the theory to reservoir studies is discussed and the translation of experimental results obtained in the laboratory into reservoir behavior is considered. INTRODUCTION The decline of fluid pressure in connection with the withdrawal of fluid from an underground reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock results in a decrease of both the pore volume and the total volume of the fluid-filled formation. Whereas the variation in volume of the reservoir fluids with pressure is usually known from PVT analysis, that in the volume of the porous medium is rarely measured, as it is considered of minor importance in reservoir engineering. Nevertheless, certain experimental results' suggest that in a number of cases the neglection of the variation in pore volume may introduce errors into material balance calculations of reservoirs producing above the bubble point. Only a few experimental results on the compressibility of porous rocks have been published. The compressibility of pure quartz and of calcite can be found in a paper by Adams and Williamson'. Botset and Reed' carried out some experiments on the compressibility of loose sands, while Carpenter and Spencer' measured the compressibility of a number of consolidated sandstones, which data were supplemented by Hughes and Cooke5. Hall' finally reported a number of experiments designed to study the influence of the porosity on the compressibility of oil-bearing formations, from which it appeared that, particularly in the low porosity range, the compressibility of the pore volume is important enough to be taken into account. Difficulties, however, arise in applying these experimental results to field cases. This is partly due to the fragmentary nature of the published data. Yet even if more complete data were available, the need for a theoretical background would be strongly felt. Such a background can be partially found in studies carried out by Biot,6,7 who published a theory of elastic deformations of porous materials and their influence on fluid displacement within the pores, by Lubinski8, who studied the stress distribution in an elastic porous medium neglecting pore compressibility, and by Gass-mann" who mathematically analysed the elasticity of packings of spheres. The contributions of Biot intro-duce a number of deformation constants which are impractical for reservoir rocks from an aspect of experi-mental determination. The theory developed by dass-mann is correct but difficult to read. It appeared, how-

Jan 1, 1958

By Kefton H. Teague

Olivine is a mineral containing a mixture of forsterite (Mg2SiO4) and fayalite (Fe2SiO4) in solid solution. The name olivine was first applied by Werner in 1790 (Hunter, 1941) because of the olive-green color of the mineral. Olivine is the principal component of the rock dunite, which itself is a member of the peridotite group of ultrabasic igneous rocks. European uses of the terms olivine and dunite are somewhat different than US usage. In commerce European usage defines dunite as containing 36 to 42% MgO, 36 to 39% SiO2, and loss on ignition of approximately 10%. The term olivine is used to designate a material containing approximately 85% forsterite, with a chemical composition of approximately 45 to 50% MgO, 40 to 43% Si02, 5 to 8% Fe2O3, and ignition loss of 1 to 2%. Uses The principal use of olivine is in various applications involving hot metal. Table I shows the best estimate available as to the amount of olivine consumed by various industries worldwide. In excess of 90% of world uses involve hot metal, with approximately 75% as a slag conditioner in the blast furnace production of pig iron. Approximately 15% of total olivine usage is as a special foundry sand in mold making for the brass, aluminum, magnesium, and manganese steel foundries (Schaller, 1957, 1958; Snyder, 1957; Anon., 1977). Olivine was first used as an industrial mineral in the early 1930s for a refractory material (Anon., 1970; Hunter, 1941). As a refractory raw material, olivine was first introduced in the United States as hand-cobbed, selected, shaped blocks of crude olivine. This use met with limited success. More recently, finely ground olivine blended with MgO and pressed into bricks, which are then fired, has found use in glass tank furnaces and open-hearth furnaces. Ramming or gunning mixes for basic furnace linings also utilize olivine. Olivine has been used in ladle linings with varied success. In Europe, substantial tonnages of olivine are utilized in refractory brick for night storage heaters (Anon., 1970). A limited amount of olivine has been used in the past as a fertilizer (magnesium source) and has been fused with rock phosphate to produce a magnesium phosphate as a plant food. The relatively high magnesia (MgO) content of olivine also attracted attention to it as a potential source of both magnesium compounds and as a source of metallic magnesium (Bengston, 1956; Hunter, 1941). The use of olivine as an additive in the blast furnace is relatively new, having been developed during the last decade. J.W. Currier (Private communication, 1978) describes the behavior of olivine in the blast furnace as follows: Olivine (Mg, Fe2, Si04) represents a unique lime-free source of magnesia and silica as a blast furnace charge component. Only recently has the magnesia-rich mineral been recognized as beneficial cleaner for blast furnace experiencing the problems associated with excessive alkali inputs and/or low coke stabilities. For some time it has been known that alkalis tend to recycle and accumulate in blast furnaces. In the high temperature region of volatilization the elemental alkalis formed attack the integrity of the graphite structure. This alkali attachment is enhanced when poor coke is used. Higher in the furnace stack volatile alkali cyanides condense and oxidize. This accumulation of alkalis tends to agglomerate the burden materials, producing scabs and scaffolds. These structures not only inhibit the downward movement of burden materials and the upward passage of wind, but also lead to erratic furnace performance

Jan 1, 1983

By F. F. Craig

A series of both welter and gas puttern Hoods was made in the laboratory to study the oil recovery performances of .such operations. These tests were contlrrctt~tl on consolidated sandstone models, using oil. water, and gas. The model floods were scaled to reprotlrrce field performance under gas arid water five-spot injection. X-ray shadowgraphs permitted observation of the gross fluid movement within the models. A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The area1 sweep efficiency. tit breakthrough for dispersed gas drives is much higher than previorsly expected, Iying in the range of 50 to 100 per cent. A method is presented for predictitig the water-oil ratio performance of five-spot pattern water flood., in uniform sands. This method is verified experimentally for the cotidition of 120 free gas initially present and for va1ues of gas saturation normally encountered in fields following depletion operations. Prodrrction perfort?zut~cc for pattern gas injection is also predictable by this method. INTRODUCTION In field pattern hater flooding or dispersed gas injection operations, the displacing fluid (water or gas) is injected and oil is produced through wells which are, area-wise. small openings in a large container or rescrwir of oil. As a result, not all of the area between the injection and producing wells is necessarily contacted by the injected fluid by the time it first reaches the producing wells. The question arises in predicting oil recovery. as to what traction of the pattern area involved is contacted by either the injected water or gas due to the relative position of the injection and producing wells. This is the areal sweep efficiency. It is also desirable to know how well arrangement affects the oil production performance. A solution to this problem has been attempted by many means. Mathematical analysis¹,²,³, and electrolytic models', have been used to establish a breakthrough areal sweep efficiency of 73 per cent for a five-spot pattern in which the ability of the oil to flow ahead of the invading fluid is equal to the ability of the invading fluid to flow in the invaded zone. All of these studies simulate only one of many field conditions. Improved studies of areal sweep efficiency at breakthrough were made using the fluid mapper5, poten-tiometric models" and X-ray shadowgraph techniques. In these it was possible to study the effect of variations in mobility of the injected and displaced fluids, and so to cover a wide range of field conditions. The limitation of these studies is that, with these models, it was not possible to simulate the saturation gradient behind the flood front when oil is displaced by gas or water. In the most recent published technical paperS on the subject, a method was presented for predicting the oil recovery performance after breakthrough in a five-spot pattern water flood. The method involved correlations which were obtained experimentally using miscible fluids. One limitation of this work was that a saturation gradient, usually found in immiscible fluid displacement, was absent in these studies. Also the laboratory studies did not cover the situation of a water flood following oil recovery by depletion drive. as is the situation in most field water floods. The tests reported in this paper were made using oil. water, and gas, thus eliminating the simplifications of former studies. Also reported are laboratory studies on

Jan 1, 1956

By H. D. Yoo, M. R. Tek, D. L. Katz

The behavior of gas-storage reservoirs subject to water drive is investigated through analog simulation on an electronic differential analyzer. The simulation technique developed on an LM-10 computer permits the prediction of reservoir volume or pressure resulting from the movement of water in the surrounding aquifer. The method developed on the analog computer consists of setting up an appropriate transfer-function circuit and feeding the arbitrary time-varying boundary conditions as an input signal. The input may be specified as gas reservoir pressure, pore volume or the water flux. Several cases studied include an isolated gas reservoir on a limited aquifer, interference among three reservoirs adjacent to a common aquifer and the growth of gas-storage volume on an aquifer. It is concluded that the method developed on an electronic differential analyzer provides an excellent technique to simulate and investigate the behavior of gas reservoirs subject to water drive. The agreement between the reservoir performance as predicted from the simulation technique and as measured from actual field data is found to be better than the range usually encountered in predicting water-drive behavior. INTRODUCTION It is generally known that some gas-storage reservoirs are located on top of blanket sands of large extent, saturated with brine called aquifers. Because the volume of the body of water associated with aquifers is usually very large and water is compressible, the cyclic pressure variations encountered in normal storage service inevitably cause unsteady, compressible flow conditions in the adjacent aquifers. The solution to radial diffusivity equation for a limited aquifer for constant terminal conditions has been know111 since the early 1930's. The solution for the constant terminal conditions for an infinite aquifer was puhlished in 1949.2 The proldem of handling the unsteady flow of water through a porous medium with time-varying boundary conditions has been studied by many investigators through the use of graphical,3 digital4 computing techniques or on an R-C type of electrical analog called a reservoir analyzer.5 The digital computer performs a series of arithmetic calculations to superimpose the solutions of constant terminal conditions, while the R-C type of analyzer permits the simulation of the continuous medium by means of "lumped-cell" electrical resistance and capacitance elements based on finite-difference approximations. The graphical method is based on the convolution integral solution of the partial differential equalion. The purpose of the present study was to simulate the behavior of an aquifer on a general-purpose, electronic differential analyzer to obtain the influx of water or the change in pressure at the reservoir continuous1r and quickly. The use of the electronic differential analyzer was based on well known solutions for the constant terminal conditions already available in the literature.2,6-8 THEORETICAL DEVELOPMENT MODEL. The gas reservoir (R) is described in relation to an aquifer in Fig. 1. The permeability and porosity of an aquifer sand, the viscosity of the brine, and the compressibility of the brine and the formation are assumed to be constant. It further is assumed that the blanket sand is not thick enough to give appreciable vertical pressure distribution. The model in consideration is circular with radial geometry. The aquifer radius can be of limited or infinite extent. The gas-water interface is assumed to be fully segregated, and the displacement of the gas by

By H. R. Brannon, R. J. Robinson, G. W. Kattawar

Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and .98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gulf water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. INTRODUCTION Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydro-dynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. l-3 One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice5.6 in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker 7 have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire,8 among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii,10 establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other areas as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents (1) a practical approach to computing wave profiles hat depict shapes of waves for use in force calculations, (2) a summary of relations for predicting probabilities of wave crest elevations, (3) correlations of parameters needed to apply these methods in the Gulf of Mexico and (4) examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities. These relations also identify quantities that must be related to storm

By R. E. Carter, C. Wagner, F. D. Richardson

By means of inert markers of radio-platinum, it has been shown that cobalt metal oxidizes by out-ward diffusion of cobalt atoms through the oxide. Oxidation rates have been measured at various temperatures and oxygen pressures and have been found to agree with the rates calculated from the Wagner equation and the authors' values for the diffusion coefficient of cobalt in the oxide. The distribution of radio-cobalt in growing oxide loyers has been accurately measured and found to be different from that predicted from the Wagner oxidation theory. Attempts have been made to measure the change of lattice parameter of the oxide with composition. SEVERAL investigators have shown that cobalt metal oxidizes according to the parabolic law,1-3 but no detailed study has been made of the oxidation mechanism. Cobaltous oxide has a metal-deficient lattice, but the defect concentration which is dependent on the oxygen pressure is only approximately known.' From the similarities in the structures of "CoO" and "FeO" and the rate laws governing the oxidation of cobalt and iron, Gulbransen- as suggested that cobalt, like iron," oxidizes by diffusion of cobaltous ions through the oxide layer. To substantiate this hypothesis, he has attempted to measure the oxidation rate of cobalt as a function of the oxygen pressure but has been able to report only that the rate depends on a "small" power of the pressure. On the other hand, Preece," Valensi,' and Arkharov' all have suggested from indirect evidence that oxygen diffuses through the COO to the metal-oxide interface. The present authors, in a previous paper,' have shown that the rate of diffusion of cobalt in cobaltous oxide is dependent on the oxygen pressure. In that investigation, they also found that cobaltous oxide disks made by complete oxidation of cobalt metal were porous at their centers (Fig. 5L, ref. 4). Both these facts strongly suggest that oxidation of the metal proceeds via outward diffusion of cations. In order to establish the mechanism unequivocally, oxidation experiments were made with inert radioactive platinum markers, and the dependence of oxidation rate on oxygen pressure was measured. In addition, an attempt was made to determine the form of the cation vacancy gradient, which the marker experiment showed must exist across a growing oxide layer. This was done by depositing radioactive Co on the surface of a cobalt disk and then measuring the tracer distribution across the oxide layer produced by partial oxidation of the metal. Finally, an X-ray examination was made in an attempt to find the expected change of lattice parameter of COO with oxygen pressure. Experimental The apparatus and materials used were substantially the same as those previously described by the authors.4 Marker Studies: The use of inert markers to follow oxidation reactions was first attempted by Pfeil" in 1929, and radioactive markers have recently been used by Davies et al.' In the investigation reported here, the markers were applied as an (NH4)2PtCI6 slurry in several thin streaks across both faces of four disks of cobalt metal 1 mm thick and 14 mm in diameter. The disks were then oxidized almost to completion at 1200°C in pure oxygen. After oxidation, they were mounted and sectioned and auto-radiographs were taken to locate the markers. Oxidation Rate: The oxidation rate of cobalt was measured at 1148°C at oxygen pressures ranging from 0.0055 to 1.0 atm and at 1000°, 1148", and 1350°C under 1 atm of oxygen. The rate was deter-

Jan 1, 1956

By C. R. Claus, G. A. Standish

Since March. 1945, the Magnolia Petroleum CO. has drilled 39 wells in Southwest Coastal Louisiana. All wells were drilled within a comparatively small radius, but the area provides a large variety of problems. The deepest well drilled was 13,518 ft, and the total depth averaged 10,977 ft. Throughout this period drilling mud control and types of mud handled were: (I) phosphate, (2) red lime (late conversion), (3) red lime starch (early conversion), (4) red lime starch oil emulsion, (5) precision controlled low alkalinity-low lime content. and (6) gel muds for completion purposes. Improvement has been obtained in effecting some or all of the following: (I) more rapid penetration, (2) reduction in drilling hazards, (3) better evaluation of cores and logs, and (4) better completions. The geological sequence of zones penetrated range from recent sediments at the grass roots through the Frio section. Anticipation of high-pressure zones and incompetent formations entails precision control of drilling mud weights, and the unconsolidated nature of the various zones requires constant attention to the filtrate, viscosity, and gel strength values. In the Chalkley field, particularly, this combination of problems exists, where the formation pressures and overburden weight density values are in very close proximity. Design of casing and drilling mud programs must be modified to fit each well. INTRODUCTION Field and research work on drilling fluids has made constant progress, enabling operators to prospect progressively deeper horizons. Numerous papers have been written on the theoretical aspects of drilling fluid devel- opment, but in the field engineers have found it difficult to evaluate the role of specific mud constitutents when dealing in terms of thousand barrel mud systems. For that reason field data is somewhat lagging in technical report writing. However, applications of new techniques in the field have usually paralleled, and in numerous instances preceded, research work. The information obtained by Magnolia Petroleum Co. in the course of drilling 39 wells within a comparatively small area in Southwest Coastal Louisiana provides an excellent opportunity of reviewing a specific example of drilling mud evolution. A large variety of problems has been coped with, the most important result being that every well was successfully drilled to its projected total depth. The discussion begins with the advent of deep drilling in this area in March, 1945, and is concluded with a resume of recent drilling operations in the Chalkley field. The primary purpose of this paper is to describe the evolution in types of drilling fluids as it occurred and its application in the solution of various drilling problems. All of this information and experience resulted in the successful drilling of the three wells in the Chalkley field, where a combination of the most sound techniques was necessary in carrying drilling operations to the projected total depths. Other operators along with service company engineers have contributed considerably through the interchange of ideas and information to this paper, but the data and conclusions which are contained are based on first-hand observation of Magnolia Petroleum Company's drilling operations. The 39 wells drilled by Magnolia Petroleum Co. average in depth 10,977 ft per well, while the maximum depth penetrated was 13,518 ft. The cost of drilling fluids have varied from $8,700 to $165,000, with the over-all drilling costs ranging from $74,000 to $543,000 per well. This wide variance illustrates the unpredictable nature of each well and the effects on over-all cost when high density muds are required to control

Jan 1, 1955

By N. S. Stoloff, R. G. Davies

The annealing behavior of a heavily cold-worked FeCo-V alloy has been studied at temperatures both above and below Tc, the critical temperature for ordering. It was found that re crystallization and grain growth can take place below Tc in the ordered state and that, in agreement with results for fcc alloys, order retards grain growth. The activation energy for pain growth is -55 kcal per mole in the disordered condition; it was not possible to assign a value to the activation energy for grain growth below Tc because the degree of order is changing rapidly over the temperature interval investigated. Precipitation of an fcc y phase was observed upon annealing the cold-worked alloy at temperatures of 675°C and below. SINCE it is known that diffusion constants are greatly affected by long-range order,' it is not unreasonable to anticipate that order will influence the diffusion-controlled phenomena of recrystallization and grain growth. In the course of a study of strain aging of ordering alloys around the composition Ni3Fe Vidoz, Lazarevic, and cahn2 noted that a disordered cold-worked alloy annealed at a temperature T1 just below Tc will order but not recrystallize; Tc is the critical temperature for order. The same alloy annealed at a temperature T2 just above Tc, or an alloy of different (nonordering) composition annealed at either T1 or T2, will recrystallize after equivalent amounts of cold work. Initially Selisskii and coworkers,3,4 who examined a series of cold-worked and annealed bcc Fe- Co alloys, reported that alloys forming the B2 FeCo super lattice could not be recrystallized below Tc. However in a later paper5 it was shown that FeCo ordered alloys could be recrystallized below Tc. Thus the first question to be answered by the present investigation was whether or not a heavily cold-worked Fe-Co-V alloy could be recrystallized below Tc. When it was found that the alloy would indeed re-crystallize below Tc, the influence of long-range order upon subsequent grain growth was studied. EXPERIMENTAL PROCEDURE The grain-growth measurements were made upon FeCo-2 pct V wire of 0.031 in. diam; the alloy was the same as that used in an earlier study of the mechanical properties of FeCO-v.6 The wire was produced by cold swageing and drawing a rod 0.125 in. diam that had been quenched into iced brine from 850°C to disorder the alloy; the initial grain size was 0.05 mm. Rates of grain browth were measured after isother-mally annealing the wire in the temperature range 675° to 825°C; T, is -720°C. Grain diameters were measured on the transverse cross section of the wires. The line-intercept method of determining the grain diameter was used; conventional light photomicrographs were taken when the grain size was greater than 10 . Carbon replicas were produced and examined in the electron microscope if the grain size was less than Dislocation configurations after recrystallization anneals were studied by electron transmission microscopy of foils produced by cold rolling a 0.125-in.-thick strip of the quenched material to 0.012 in. The foils, after heat treatments similar to the wire samples, were thinned by electropolishing in a chromic-

Jan 1, 1967

By W. R. Wilcox

The camphor-anthracene system was chosen as a transparent low-melting analog of the zirconium carbide -graphite system. Camphor and zirconium car -bide both grow nonfaceted, while casting of mixtures yields platelets of both anthracene and graphite. Zone melting of thin layers of organic was observed under the microscope. Irregular lamellar structures were produced at high values of the ratio of the temperature gradient G to the zoning rate V. The anthracene invariably led the camphor, indicating lower kinetic undercooling for the anthracene. The lamellar spacing was an order of magnitude greater than typical spacings for metal eutectic systems. Exact behavior depended on orientation of the anthracene. Oriented dendritic structures were produced at low values of G/V. Transient and oscillatory behavior were also observed—much of it unexpected. A.RC-CAST refractory carbide-graphite mixtures are promising thermal-shock resistant materials. Oriented structures of these materials would be superior to arc-cast materials for many applications. Mollard and Flemings1 and Cline2 have shown that aligned structures can be obtained for a wide range of Pb-Sn alloys. However, these metals both solidify in a nonfaceted manner while graphite yields platelets or flakes. In addition only small diameter samples of Pb-Sn alloys were produced because it was necessary to avoid free convection and to have high temperature gradients. The purpose of the present work was twofold: 1) To observe the solidification of a transparent low-melting analog of carbide-graphite systems and 2) to see if larger diameter samples can be produced. EXPERIMENTAL PROCEDURE When zirconium carbide-graphite mixtures are cast, the resulting structure naturally depends on composition. Carbide-rich mixtures yield metal-like nonfaceted carbide dendrites in a eutectic matrix. Graphite-rich alloys have graphite platelets in a eutectic matrix. Empirically it was found that camphor-anthracene mixtures produce similar structures with camphor being nonfaceted and anthracene forming plates. The organic eutectic melted at 116°C and was composed of 78 wt pet camphor.3 The camphor used was U.S.P. grade from Fisher Scientific Company; the anthracene was 98+ pet fro Aldrich Chemical Co. The impurity content is judged to be on the order of 1 pet. Mixtures ranging from 50 to 88 wt pet camphor were employed for the experiments. All but one of the experiments were performed on the microscope-stage zone melting apparatus described in detail elsewhere.4 The organic mixtures were contained in horizontal cells made of microscope slides or cover glasses. In most of the cells the organic was present as a very thin layer, thus giving almost two-dimensional growth behavior. The cells were moved slowly under a heated wire, which caused a molten zone to move through the solid at rates ranging from 0.01 to 5.4 cm per hr. The temperature gradient was estimated before moving the zone by measuring the distance between the line where all solid was melted (freezing point) and that where solid first began to melt (eutectic temperature). The temperature gradient was found to be 465°C per cm in the thinnest cells used, which were made by pressing together two microscope cover slips in the organic melt and then rapidly withdrawing them. RESULTS The experimental results are described in four parts: simultaneous growth, dendritic growth, irregular growth, and transients and erratic phenomena. Steady state data are summarized in Fig. 1. Except where noted all comments are for the cells containing a thin layer of organic. A) Simultaneous Growth. Simultaneous and roughly parallel growth of anthracene and camphor was obtained over the full range of compositions investi-

Jan 1, 1970

By R. D. Mollison, C. F. Fogarty

Sulfur is widely distributed in nature. It is present in the earth's crust, the ocean, the meteorites that come to us from cosmic space and in practically all animal and plant life. According to Clarke,9 the earth's crust contains 0.06 pct sulfur. Large quantities of free or combined sulfur are found in coal, natural gas and petroleum. Mineral waters contain sulfates and hydrogen sulfide. Sulfur is rather plentiful in the crust of the earth; however, only under special circumstances can it be produced profitably. Sulfur is one of the cheapest raw materials used by industry; and, therefore, the economic feasibility of a given deposit is strongly dictated by the law of supply and demand on local as well as world-wide levels. The forms which are commercially important are elemental sulfur or brimstone, and the sulfides such as pyrite (FeS2), pyrrhotite (FenSn+1), chalcocite (Cu2S), sphalerite (ZnS), and galena (PbS); the sulfates such as gypsum (CaSO4,2H2O), anhydrite (CaSO4), and kieserite (MgSO4,H2O). Elemental Sulfur Elemental sulfur is found in many localities, generally in solfataras and gypsum type deposits. The solfatara deposits are found commonly in the neighborhood of active or extinct volcanoes as in Italy, Japan and Chile, or fumaroles associated with mineral springs such as the Mammoth Hot Springs in Yellowstone Park. Here the sulfur is deposited in tufas or other porous host rocks. This type of sulfur deposit probably results from the oxidation of hydrogen sulfide or the reaction of hydrogen sulfide with sulfur dioxide. Most of the world's supply of elemental sulfur comes from the gypsum-type deposits. Here the mineral occurs as either crystalline or amorphous sulfur in sedimentary rocks in close association with gypsum and limestone. This association is characteristic and occurs in almost all the great gypsum beds of the world, although sulfur is not always present in quantities of economic importance. Various theories have been advanced to account for this association. Bischof5 suggested that the sulfur came from hydrogen sulfide which resulted from the reduction of calcium sulfate by carbon or methane in accordance with the following reactions: CaSO4 + 2C= CaS + 2CO2 CaS + C02+ H2O = CaCO3 + H2S CaSO4 + CH4= CaS + C02+ 2H20 2H2S + 02= 2H20 + 2S All of the sulfur-bearing domes on the Gulf Coast have calcium sulfate in great quantity in the cap. They all show the presence of hydrocarbons. The oxygen for the final reaction could have been supplied by circulating ground waters. The principal objection to this theory is that temperatures of 700° to 1000°C are needed to reduce the sulfate to sulfide with carbon compounds. The geologic evidence is that the temperature of the sulfur-bearing domes of Texas did not exceed 100°C. Proponents of the theory say that geologic time or a catalyst replaced temperature. According to another theory the sulfur in the salt domes is the result of bacterial action. Sulfate reducing bacteria have been detected in sulfur cores and in the formation water issuing from salt domes. It has, therefore, been suggested that these bacteria converted the sulfate to sulfide which subsequently was converted to elemental sulfur.

Jan 1, 1960

By Paul A. Flinn, Jean-Marie Robert Genin

The MCssbauer effect was used to study the distribution of carbon in Fe-C alloys of high carbon content during room-temperature aging. In freshly formed rnartensite the carbon distribution is approximately random; carbon clustering occurs dun'ng aging. In the retained austete the carbon atoms are isolated, suggesting an efiective repulsion; and no rearrangement during room-temperature aging is evident. The kinetics of the carbon clustering in martensite has been studied in detail at 0" . 10". and 20°C. The time and temperature dependence observed is sinzilar to that reported for a variety of other aging effects, such as resistance change, hardness increase, and recovery of internal friction. The stabilization of the martensite kransformation also appears to be related to the clustering effect. DESPITE extensive efforts since the early days of Reaumur, the mechanism which provides the strengthening of steel remains controversial in many cases for several reasons: 1) The structure of as-quenched martensite is not well-determined. 2) Experimental methods capable of distinguishing between various hardening mechanisms are not well-developed. 3) The temperature of formation of many low-alloy martensites is so high that the martensite formed during quenching may be already tempered to some extent before any observation. Among all the hardening phenomena, the most puzzling one occurs at room temperature, where no structural changes have been detected by the usual methods of X-ray diffraction or electron microscopy. However, a new and more sensitive technique became available with the discovery of the MBssbauer effect. This effect makes possible the detection of changes in the local environment of iron atoms in solid solution. It has been extensively used in the study of substitutional alloy systems, for example, Fe-Al,1 Fe-Si,2,3 Fe-Rh,4 and Fe-Ni.5 Making use of the possibility of obtaining new structural information, we undertook an investigation of the aging of high-carbon Fe-C martensite to follow the structural changes involved in the aging at room temperature. Preliminary results6 showed that a clustering of the carbon atoms occurs with time. A systematic study of the kinetics of the process showed a striking similarity to the kinetics of stabilization of the marten-sitic transformation, thus suggesting further investigation of the relationship. EXPERIMENTAL TECHNIQUE To eliminate difficulties with the aging of martensite prior to the first experimental measurements, we needed an alloy with an M, temperature not above room temperature. Other investigators7 were misled by results obtained on alloys which transformed above room temperature and underwent structural changes prior to the first Mossbauer measurements. Winchell and cohen8 dealt with this difficulty by using a third element, nickel, to depress the MS below room temperature. The presence of nickel did not seriously interfere with hardness or resistivity measurements, but it would complicate the interpretation of the Mossbauer data by increasing the variety of iron environments. We chose, therefore, to obtain the necessary lowering of the M, simply by increasing the carbon content. After the first quench to room temperature, our specimens are retained austenite, which we later quench into liquid nitrogen. The martensitic transformation takes place suddenly, so that the as-quenched condition of the samples is retained, since the temperature is low enough to prevent any carbon diffusion. A Massbauer spectrum at 77°K can be taken and analyzed; after an appropriate up-quenching to the aging temperature, a new Mossbauer measurement at 77°K can be made. Fig. 1 shows a typical cycle of experiments. The samples were foils 25 p thick of high-purity

Jan 1, 1969

By H. A. Lequear, J. D. Lubahn

A sudden change from one constant strain rate to another during a tensile test causes an unusual transient in aluminum alloy 61ST. A sudden change from one constant stress to another during a creep test does not produce an unusual transient in this material. A specially devised test shows that the nature of the previous steady-state conditions, which the sudden change disturbs, is one of the factors affecting the transient behavior. Some of the observations may be explained in terms of strain aging. USUALLY a sudden change during a tensile test from one constant strain rate to another causes a small, abrupt vertical shift from one stress-strain curve to another, parallel one. This behavior is apparently characteristic of all metals at very low temperatures and of many metals for wide ranges of temperature. It is illustrated in Fig. 1 for some early data on 61ST tested at — 195oC, and in Fig. 2 for some recent data on copper at room temperature. The greater accuracy of the results of Fig. 2 over previous ones' is due to the equipment shown in Fig. 3. Three levers apply the bulk of the load, while the changes in the small remainder load are indicated sensitively by a low capacity load scale. Refs. 2 and 3 describe the recording equipment. A test like those in Figs. 1 and 2 provides the information necessary to determine the rate sensitizrity, n,4 of the metal. ( a log s ) ? log s n = ------------------------ ----------------------------= ( a logs e, ? log e logS2-logS1 log S2/S1 log i2 — log e1 log e2/e1 where S equals stress: e is logarithmic strain or natural logarithm of (final gage length/initial gage length);" i is strain rate or de/dt: and n is rate sensitivity, rate of change of log stress with log strain rate at a given strain, or (a log S/a log i),. Normally, the rate sensitivity, n, is positive, which means that an increase in stress causes an increase in rate. However, certain exceptions, attributed to strain aging,5 have been observed. Fig. 2 indicates how rate sensitivity values are derived from the measurements. Table I summarizes the rate sensitivity values derivable from Fig. 1. In contrast to the behavior of copper in Fig. 2, the aluminum alloy 61ST, which strain ages when tested near room temperature, exhibits an unusual transient when the strain rate is suddenly changed,' as shown in Fig. 4. Initially, there is a comparatively sudden vertical shift of the stress-strain curve in a direction corresponding to the rate change, but then the curve gradually shifts back again. The initial shift is not as sudden as might be expected, because the testing machine is unable to achieve the impressed rate change instantaneously, as illustrated in Fig. 2. The behavior shown in Fig. 4 will be referred to as a tensile transient, the word tensile implying that the behavior was observed in a tension type of test. The corresponding test, where the strain rate is maintained constant except for the sudden change, will be called a tensile transient test. A creep transient, by contrast, will be defined as a temporarily abnormal behavior in a creep transient test, where there is a sudden change from one constant load to another.' In Fig. 4, a naive look at the gradually decreasing and then increasing load after a sudden rate incre-

Jan 1, 1957

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 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. '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 Jun-Yan Chen, Stefan H. Boshkov

Metal mining in the People's Republic of China has shown great growth during the last three decades. Over 150 new iron ore mines and nonferrous base metal mines have been opened since 1949, althouc.11 most of them of medium and small size. Concurrently, many old mines were enlarged and reconstructed. The production of iron ore has grown from less than 1.5 million tons per year in 1949 to almost 76 million tons in 1978. A corresponding increase in the total annual output in the nonferrous metal mineral industry has also been noted. It is well known that the PRC is very rich in metal mineral resources. The reserves of tungsten, tin, antimony, molybdenum and iron ore are ranked in the top three in the world. Recently, some copper porphyry ore deposits were discovered in Jianxi and Anhui provinces. Some large nickel-copper sulfide deposits were discovered and have been developed in North- West China. Huge iron ore deposits have been found in Liaoning, Hebei and Szechwan provinces. However, the bulk of the iron ores are low grade. The growing metal mineral production has met basic domestic needs since 1949; it has also proven China's big resource potential. Mining methods have also undergone development in the past 30 years. About 80% of the annual output of iron ore comes from open pits, whereas about 58% of nonferrous metal ores come from underground mines. Blasthole open stoping, sublevel caving and induced block caving are widely used in Chinese underground metal mines (table 1). This paper summarizes in detail the planning for and application of these three bulk mining methods in the nonferrous and iron ore mines in China. CLASSIFICATION OF UNDERGROUND MINING METHODS The main principle of the classification of underground mining methods in PRC is ground support in the stoping cycles of the mining blocks or stopes. Table 2 lists this classification. It is essentially the same as that given in the SME Mining Engineering Handbook. Be- cause pillar removal is a secondary mining operation, using a variety of methods, they are not included in this classification. As is the case with most classifications in science and technology, there is no precise division between the classes of mining methods. Because of the rapid development of consolidated filling techniques in the past twenty years, some types of open stoping methods use fill in order to improve the ground conditions for the secondary recovery stage. Thus, these mining methods have features of both methods using no artificial support and those using artificial support. In this classification, this type of mining method is placed in the latter category. The shrinkage stoping method has been employed extensively to mine steeply dipping narrow veins of tungsten and tin in the Jiangxi, Hunan, Guangdong and Guangxi provinces. Shrink- age stoping is placed under the class of mining methods without artificial support be- cause this reflects the nature of the Chinese experience. The function of the broken ore serving to support the footwall and/or hanging wall is limited, because the expectation is for the host rocks to remain unsupported until the stope is drawn empty. APPLICATION OF BULK MINING METHODS Bulk mining methods consist of blasthole open stoping, sublevel caving and block caving. These stoping methods have much in common, such as: bulk ore materials blasted by long holes; higher production rates of stopes or blocks and higher production efficiencies of the whole mining systems.

Jan 1, 1981

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By L. Yarborough, L. R. Smith

This paper presents results of a laboratory study of retrograde condensate recovery by revaporization into dry injection gas. Flow tests were performed in 10.6-ft long sand packs at 100F and 1,500 psi. In three runs methane revaporized the liquid from a n-pentane-methane mixture in the presence of immobile water. TWO of these tests were water-wet, and the third was totally oil-wet. In the three runs n-pentane recovery was complete after 2.5 hydrocarbon PV of injection. There was no significant performance difference between the two wettability extremes. In a fourth experiment, a methane-hydrogen sulfide mixture revaporized a synthetic light, sour condensate. No water saturation was present. Equilibrium compositions and volumetric data were obtained for the four-component condensate. The heavy component, n-beptane, was removed after 6 PV production. Comparison of the effluent fluid compositions with known equilibrium data shows that the flowing fluid was equilibrium vapor and that the mixing zone between equilibrium vapor and dry injection gas was short. Data indicated that complete recovery of retrograde liquid occurred after it was contacted by a sufficient quantity of dry gas. INTRODUCTION When pressure declines below the fluid dew point in a gas condensate reservoir, a liquid phase forms. In this process, referred to as retrograde condensation, the quantity of liquid formed is frequently small enough that the liquid is not a flowing phase. To prevent loss of valuable retrograde liquids, the process of dry gas cycling has been employed for several years as a more or less standard practice. In this procedure the reservoir pressure is maintained above the fluid dew point so that the liquid components may be produced as vapor and then separated at the surface. Although full pressure maintenance by gas cycling seems ideal in terms of preventing liquids loss, several factors can reduce the atuactiveness of such an operation. From a study of a condensate reservoir in Alberta, Canada, Havlena et a1.1 con-cluded that cycling under conditions of declining pressure leads to economic advantages and to a high recovery of hydrocarbon liquids. This study considered effects of volumetric sweep efficiency, retrograde behavior of the original wet gas and revaporization characteristics of the retrograde liquid when contacted by dry gas. The first major work concerning revaporization of liquid in a gas condensate system is that of Standing et a1.2 Calculations based upon the PVT behavior of a recombined gas condensate fluid indicated that all retrograde liquid can be recovered if it is contacted by a sufficient quantity of dry gas. The paper considered the effect of variable permeability upon the recovery of retrograde liquid. Standing et al. concluded that recovery of heavier components in the retrograde liquid is greatest if reservoir pressure is allowed to decline below the dew point prior to dry gas injection. Since the work of Standing et al., several laboratory studies have been reported which show that recovery of hydrocarbon liquids by vaporization into dry injected gas can contribute to increased recovery above that obtained by ordinary production practices. Vaporization from retrograde condensate,3 conventional oil4-7 and volatile oil8 reservoirs has been considered. There is little work that deals with revaporization recovery from condensate reservoirs. This study demonstrates that vapor-liquid equilibrium exists when a dry gas is injected into a porous medium containing retrograde condensate; investigates the effect of wettability on revaporization of retrograde condensate; and provides an indication of the amount of dry gas necessary to

Jan 1, 1969

By C. S. Land

Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water - wet rocks for both two- and three - phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. INTRODUCTION Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. 1 and by Osaba et a1.2 Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems.3 Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by snel14 as 11, ID, DI and DD. I and D refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis5 published three-phase curves for unconsolidated sand, and Snell4 reported results of several English authors for both drairrage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et a1.3 for increasing water and gas saturations (ID). Corey et a1.6 reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean7 and Sarem8 calculated three-phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three-phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (11) are those of Naar and Wygal.9 These curves are based on a theoretical study of the model of Wyllie and Gardner 10 as modified by Naar and Henderson.11 Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids.12 Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term.13 The works of Purcell and Burdine were combined by Corey14 into a form that has

Jan 1, 1969