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By L. D. Mullins, W. R. Bartlett, R. H. Barham, W. L. Wahl

This paper describes an electrical model and its applicution to the analysis of four reservoirs in Saudi Arabia. The model has 2,501 mesh points and represents 35,000 sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of performance in matching reservoir history are discussed. The particular performance match achieved for the Arab-D rnember is presented. Details such as permeability barriers, aquifer depletion and iwerference between oil fields are given. The performance match realized in the Abqaiq pool is presented in detail. INTRODUCTION The resistor-capacitor network and associated control equipment described in this paper comprise an electrical analog of a reservoir system. Similar equipment has been used to study the transient response of reservoirs for many years. The unique feature of the model and application to be described is the extremely large size of the model and reservoir system, and the detail observed in simulating the reservoir with the model. The Arabian American Oil Co. first became interested in analog computers for simulation of oil reservoirs in 1949. Since that time, several models have been developed, each more elaborate and refined so that the reservoir system might be more closely simulated. The current model is the latest in a series designed, built and operated by the Field Research Laboratory of Socony Mobil Oil Co. in collaboration with Aramco. It has been and continues to be used to study the regional performance of the Arab-D member limestone reservoir. The Arab-D member is one of the Middle East's most prolific producing horizons.. THE MODEL The theory of simulating a reservoir system with an electrical system has been presented in the literature.1-5 Therefore, this paper will not discuss the theoretical aspect of the problem except to point out the correspondence between the fluid system and electrical system, as shown in Table 1. In general, the complete model is made up of input devices, output devices, central control and a resistance-capacitance (RC) network. At times, the RC network alone is referred to as the "model". However, it should be evident from the text which meaning is attached to the word "model". A discussion of the equipment follows. THE RESISTANCE-CAPACITANCE NETWORK The RC network consists of 2,501 capacitance decades interconnected through 4,900 resistance decades. The components are arranged to form a rectangular network of 2,501 mesh points in a 41- X 61-mesh array. Imposing the mesh grid system on the continuous reservoir system divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, the mesh size need not be uniform throughout the model. The RC network is fabricated in two sections which are connected at the top. An inside view of the "tunnel" formed by the two sections is shown in Fig. 1. The height and width of the tunnel are shown in the figure. Numerals appear along the bottom and along the back opening of the tunnel. These numbers denote the x and y co-ordinate positions of mesh points. Fig. 2 presents a rear view of one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown in this figure. The control dials used in adjusting the resistance and capacitance values on the model can be seen in the enlarged portion of the model shown in Fig. 3. The electrical capacity at any mesh point can range from 0 to 1.0 microfarads set to the nearest tenth of a microfarad. The electric resistance connecting any two mesh points can range from 0 to 9,990,000 ohms set to the nearest 1,000 ohms. External capacitors may be added to any or all mesh points if the need arises. The values of electrical resistance and capacitance are adjusted manually by manipulating the two types of decade units. INPUT EQUIPMENT A considerable quantity of equipment is used to control the input to the RC network. These input devices are

By Michael Hoch, Walter C. Wyder

The isothermul section of the Nb-Ti-Zr-O system at 1500°C was investigated using X-ray dzffraction and metallographic techniques. UP to 66.7 at. pct 0, the system contains nine four-phase regions. Tsopleths at 10, 20, 30, 40, 50, and 55 at. pct 0 weye constructed. The purpose of this investigation was to determine the general shape of the quaternary equilibrium phase diagram of niobium, titanium, zirconium, and oxygen at 1500°C. The system was truncated at 66.7 at. pct. O., PREVIOUS INVESTIGATIONS The Ti-Zr-O system was investigated in this laboratory.' The binary systems of interest have been compiled and discussed by anssen2 and Levin, McMurdie, and Ha11. Elliott4 has determined the Nb-O system by metallographic and X-ray diffraction techniques. He shows the existence of three oxides, namely NbO, NbO2, and Nb2O5. At 1500°C the solubility of oxygen in niobium is about 4 at. pct. No solid solubility region is shown for either NbO or NbO2. EQUIPMENT The same equipment as that for the study of the Ti-Zr-O system was used. The X-ray diffraction patterns were analyzed with the help of the ASTM card set5 and NBS circulars.6 MATERIALS The niobium powder (99 pct pure), the titanium powder (99.6 pct pure), the niobium pentoxide, and the zirconium dioxide used in this study were purchased from the Fairmount Chemical Co., Newark, N.J. The zirconium powder (99.4 pct pure) was obtained from the Charles Hardy Co., Inc., N.Y. Reagent-grade titanium dioxide was purchased from the Matheson Co., Inc., Norwood, Ohio. The oxides were dried in air at 700°C for 24 hr before use. Though the materials used were not "hyper-pure," the impurities present do not affect the results (lattice parameters, phase boundaries), within the experimental accuracy. PROCEDURE Samples of the desired compositions were made up, in mole pct, from the materials listed above. In some cases the intermediate binary compounds, such as NbO and TiZrO4 were prepared beforehand and used in the preparation of the samples. This technique enabled equilibrium to be reached from two sides. The components of each sample were mechanically mixed in a mortar and pestle and pressed into 3/16-in. diam pellets. The pressures used in compacting were of the order of 50 to 100 x 103 psi. Sintering was accomplished by heating the samples in a tungsten crucible (3/4-in. high, %-in. diam, 1/8-in. wall, lid with XB-in. hole). The pellets were separated from each other and from the crucible by means of small spiral coils of tungsten wire placed between the stacked pellets and on the bottom of the crucible. The sintering time was from 4 to 12 hr at 1500°C under a vacuum of 6 x 101-5 to 1 x 10-6 mm of Hg. All samples were reground after the first or second heating repressed, and reheated. In most cases: equilibrium was obtained after the first heating, as the X-ray diffraction pictures after each heating remained unchanged. Quenching of the samples from 1500°C was at first only possible by allowing the crucible and its contents to lose heat by radiation. The temperature dropped from 1500° to 900°c in approximately 1 1/2 min, which was considered adequate when compared to the times used by other investigators to reach equilibrium in the temperature range of 1000°c and lower. Later, a new technique for faster quenching of the samples was cleveloped. This technique involved the removal of the samples from the crucible, whereupon they were quenched by coming in contact with the water-cooled copper base of the furnace. This manipulation was performed without breaking the vacuum. The sample pellets were placed on a tungsten wire rack inside the crucible. The wire rack passed through the hole in the crucible lid, where it was connected to a small nonmagnetic chain. The chain was fed to the side of the furnace by means of a brass rack which fitted between the body and lid of the furnace. Suspended at the end of the chain, near the furnace wall, were three magnetic washers. With the use of a strong

Jan 1, 1962

By Orrin Peterson

THE decision of the Supreme Court of the United States not to review the findings of the lower courts closes an interesting chapter in the mining litigation that has arisen as a result of the extralateral feature of the mining law. The time seems opportune to record some of the important geological features, and also some of the legal features, of the controversy, in the hope that these will be permanently accessible to members of the mining profession. After many rumors of litigation, the Utah Consolidated Mining Co. sued its neighbor for the ore that had been, it was alleged, wrongfully extracted from its so-called Yampa limestone lode. This ore lay beneath Utah-Apex surface and was claimed by virtue of the extralateral rights conferred on the Utah Consolidated Co. through the ownership of certain specific mining claims, one of the principal claims being the Yampa. Previous to bringing suit, the Utah Consolidated Co. had strengthened its position by purchasing the Old Yampa mine and by making an agreement with the Utah Metal & Tunnel Co., which gave it clearer title to the outcrop of the Highland Boy limestone. Access to the workings of the Utah-Apex Co. was secured and reciprocal privileges gave Utah-Apex representatives the right to enter the properties of the Utah Consolidated Co. This resulted in the Utah-Apex immediately bringing countersuit for ore alleged to have been wrongfully extracted from under its surface in the Leadville country, see Fig. 4. Six cases came up for consideration: five related to the original suit and the countersuit, and one related to the Dana extralateral claims of the Utah-Apex Co.

Jan 6, 1924

By M. E. Shank, J. Wulff

At the present time, the designer of dies for metal powder pressing is handicapped by relative ignorance of stress distribution and frictional effects at the interior surface of the die. Unckell was the first to develop a method for the study of wall friction. He used three Brinell balls on which the die rested during pressing. The total frictional wall force was determined by the size of impression these balls left on a soft metal plate. Since the method does not give radial pressures, or distribution of such pressures, coefficients of friction could not be determined. Although Unckel measured density distribution, he was not able to determine radial or shear stresses. Shaler2 has proposed theoretical expressions for the stress and density distribution within cylindrical compacts during pressing, in accordance with the experimental results of Kamm, Steinberg, and Wulff.3 By application of Siebel's method,4 Kamm et a13 plotted stress trajectories for two compacts. From the stress trajectories they calculated coefficients of friction from point to point along the die wall. As pointed out by Shaler in the discussion of Ref. 3, these values are based on progressive point-to-point calculations on finite size grid squares across the compact. In the region of the die wall such calculated values may therefore have considerable cumulative error. The purpose of the present paper is to develop an experimental method by which the nonhydrostatic pressures and shears acting on the interior wall of a cylindrical die can be measured. Such measurements can then he correlated with existing data to aid in the explanation of the pressing process. The method used is based on the elastic: properties of the thick-walled tube used as the die. The principle of super-position of force systems on an elastic body is assumed to hold. Electric strain gauges were mounted in adjacent positions on the exterior die wall in order to get an exact measurement of the variation of tangential strain over the length of the die during pressing. While in this paper, measurements in terms of only tangential strains are considered, it is well to note that similar calculations may be set up for axial strains. The latter are not preferred, since they tend to be smaller than the tangential strains and therefore permit less sensitive measurements. Discussion in this work is restricted to compacts pressed from both ends, since the elastic deformation of the die is then more amenable to analysis. Before choosing the electric strain gauge method, a more direct line of attack was considered and discarded. The discarded idea was the insertion of a pressure gauge through a hole in the die wall.* The gauge would have been in the form of a small piston. If pressure were exerted against such a gauge, it would move outward along a radius of the die. One disadvantage of the scheme is its inability to measure shears along the die wall. Another more serious disadvantage is the disturbance caused by the device itself. It would serve to change the forces it was designed to measure. No matter how small the movement of the gauge, when pressure is applied a discontinuity would exist in the wall surface at that point. Due to the stress concentration caused by the hole, abnormal deflections of the die wall would occur around the gauge. During pressing, powder would be forced into the resulting depression. The depression would then become larger with increasing compacting pressure. Powder, not being a fluid, is capable of supporting shear. The ease with which it would flow into the die wall depression to further move the piston is an indication, not of the radial pressure at that point, but of the state of shear retarding the movement. Thus the "pressure" gauge is really a criterion of flowability, and of the capability of the powder to support shear. For these reasons, it was decided that the electric strain method, herein employed, was more reliable, if more indirect. The gauges and lead wires, mounted on the external die wall do not in any way affect the behavior of the metal powder or the die during pressing. Theory of the Method THE EFFECT OF RADIAL PRESSURE ON THE DIE WALL Effect of a Single Small Band of Hydrostatic Pressure Consider a die which is a thick-walled cylinder of outer radius R. and inner radius Ri. If over a small finite length L there is a normal pressure P, a tangential strain distribution at the outer wall results. This is shown schematically in Fig 1. The exact shape of the curve may he predicted by an extension of the theory of a semi-infinite beam on an elastic foundation.6 This

Jan 1, 1950

By Emile Rector Abadie

The picturesque little mining town of Grass Valley, nestled in the foothills of the Sierra Nevada mountains, at an altitude of 2500 feet, has been for 43 years the scene of uninterrupted activity and prosperity, as the center of a mining district which was intimately associated with the pioneer days of California, and the discovery of gold by James W. Marshall, in El Dorado county, in January, 1848. Although placer-mining was inaugurated in Nevada county as early as 1848, the first quartz ledge was not located until the summer of 1850. Discoveries made on Gold Hill and Massachusetts Hill increased the excitement in quartz-mining, and hastened the erection (during the same year) of the first mill operated in the State. At the close of 1864, the district had produced $23,000,000 in gold, and all the well-known properties of to-day had been discovered and worked. The Eureka-Idaho, the North Star, and the Empire mines were in active operation ; and to-day we still find them equipped with large crushing-plants, operating 80 per cent. of all the stamps in the immediate Grass Valley district. Of the mines just named, the North Star possesses the most recently constructed mill, a description of which, the writer believes, may prove of interest to members of the Institute engaged in the milling of goldores. During the year 1386, operations at the North Star mine (the property of the North Star Mining Company) had reached such a stage of development that the necessity of a crushing-plant at the mine became imperative, and early in October the erection of a 30stamp mill was in progress. The building designed to contain 40 stamps was speedily erected ; and within sixty days the large structure was under cover. Plate A represents the appearance of the mill 40 days after work was commenced. Late in February, 1887, the mill was in readiness, and, upon the

Jan 1, 1895

By T. F. Witherbee

IT is proposed to give, first, a description of the works ; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

Jan 1, 1876

By Paul G. Shewmon

The migration of slightly solzrhle spherical particles through a solid under the infllrence of a temperature gradient is analylzed for the cases of various transport mechanisms. It is shown that the variation of the velocity of the particles with radius, r, depends on the dominant mechanism of matter transport around or through the inclusion. Thus the velocity varies as r-1 jor surface-dijf1~sion controlled migratzon. is independent of r for volume diffusion in either phase, and varies as if the rate is determined by an interfacial reaction (n is the order of the interfacia1 reaction). These same results hold tor the migration of a cvlinder of length much greater than its radius. and .for other types of potential gradients, e.g., an electrical field. These equations are combined with recent electron-microscopic ohservations to show that the rate of migratzolz of small helium-silled bubbles through copper is determined by surface diffusion of the metal atoms. With these equations and the temperature gradients attainahle in an electron-microscope joil, the dominant transpar/ mechanism (or any migrating pnrtzclos can he determined. AS a result of fission, rare-gas atoms are created in the hot fuel element of a nuclear reactor. These insoluble atoms precipitate to form bubbles of the gas in the fuel. The subsequent migration and coalescence of these bubbles is thought to play a dominant role in the swelling of fuel elements which in turn can limit the fuel-element life. As a result of this practical problem and because of the relative simplicity of the system, workers in several laboratories have imbedded rare-gas atoms in metals with the aid of an accelerator and studied the formation and behavior of the bubbles that form on annealing. Recently Barnes and Mazey have studied the migration of such helium-filled bubbles in copper foils using the electron microscope and the temperature gradient that can be induced in the foil by the electron beam. They found that the smaller bubbles moved faster than the larger ones. It is shown below that, if this is true, the rate-controlling step in their migration is surface diffusion of metal atoms instead of volume diffusion, vapor transport, or an interfacial reaction. The analysis given is in no way limited to gaseous inclusions so the variation of velocity with particle size for any relatively insoluble precipitate particles could be used to obtain information about the relative importance of surface diffusion, volume diffusion, and interfacial reaction in such two-phase systems. VOID MIGRATION IN A TEMPERATURE-GRADIENT ANALYSIS Barnes' studies indicate that helium does not dissolve or diffuse in metals to a measurable extent, so that when the voids move they must do so through the movement of metal atoms from the leading to the trailing sides of the void.' Thus voids might move by surface diffusion, diffusion of vacancies in the surrounding lattice, or vapor transport. We consider first the case of flow by surface diffusion alone. We assume that there is a force, in the sense of irreversible thermodynamics, tending to move the atoms around the bubble in a given direction. We designate this direction as the x axis and the force per atom as Fa. The net rate of flow of atoms from one side of the bubble to the other, under the influence of this force, is the surface flux, Js, times the cross-sectional area available for flow, A,. A, is taken as the circumference times the thickness of the high-diffusivity surface layer 6. Thus where 51 is the atomic volume. For bubbles to advance a distance dx, a volume equal to nr : dx must flow around the void so that The minus sign enters because the bubble moves in the direction opposite to that of the force on the atoms. Equations for volume diffusion and diffusion through the vapor can be obtained in the same manner. For vapor transport we have Ag = and the ratio of the densities of metal atoms in the gas and the solid (pg/pl) enters so that

Jan 1, 1964

By Robert E. Tally

CHAUNCEY L. BERRIEN, Butte, Mont. (written discussion).-Having had much actual experience with mine fires which have occurred or have been active in the mines of the Anaconda Copper Mining Co. during the past 4 years and having lately visited the fire zone of the United Verde mine with Mr. Tally, I wish to congratulate him for the success which he has had in controlling this fire and making the mine perfectly safe .for his miners. By this work he is not only keeping the property in operation but is reclaiming many lost orebodies. The ventilation system as described by him is practically the same as that used under my direction at the Mountain View mine fire in Butte in 1913 and at the Pennsylvania fire in 1916. This same system is at present being followed at the Leonard mine to extinguish a fire which has been active for 10 years although bulkheaded. The mining system in the Butte mine, at the origination of these fires was the same as that at the United Verde, namely, square setting .accompanied by the use of much timber bulkheading in the stopes owing to heavy ground. The pyritic content of the ore in Butte is not as high, but on the whole conditions have been the same, with the exception of actual location of the fire in the mine. I agree with Mr. Tally that flooding, the use of C02 or any gas, and the use of steam are all impracticable unless the fire zone can be absolutely sealed. His system of upcast escapement shafts in the fire zone, the use of bulkheads and fans to keep the gases away from the firemen, must be resorted to. By the method lie describes actual stoping may be carried on safely if started from the bottom of the fire and if the fire zone extends to the surface. In other words, the fire zone must be isolated from the rest of the mine by bulkheads and solid ground, with no ground above which can be damaged by spread of fire or caving. The serious fires in Butte have .occurred on or between levels in the mines where it was necessary to prevent their .extension upward, downward and laterally while the work of actually extinguishing them was in progress. This necessitated proper bulkheading should we lose control of the fire, the installation of ventilation similar to Mr. Tally's and the systematic drilling of holes with diamond drills for distributing water on the fire and around it.

Jan 12, 1916

By B. B. Rath, Hsun Hu, R. S. Cline

FOLLOWING the techniques used by Beck and co-worker~ "~ the characteristics of selective growth in the recrystallization of a zone-refined aluminum single crystal, rolled 80 pct at -78°C in the (110)[112] orientation, have been studied. The material was 99.999+ pct pure. The as-grown crystal had a resistance ratio, R(298°K) /R(4,2°K), of approximately 5000. The method of preparation of the single crystals and the necessary precautions in handling them during rolling in order to avoid recrystallization in locally distorted regions were described in an earlier paper.3 The rolling texture of this zone-refined aluminum crystal is practically identical with that of less pure aluminum crystals rolle! in the same orientation, i.e., a very sharp (110)[112]. Random nuclei were provided by artificial nuclea-tion by abrading one face of the rolled crystal on 600-grit emery paper in a random fashion. The thin layer of disturbed metal recrystallized at room temperature into fine grains almost immediately. An X-ray diffraction pattern was taken from the abraded surface of the crystal, and the relative intensities of the various reflection peaks were compared with those obtained from a powder specimen. As shown in Fig. 1, the relative intensities of the various peaks from the recrystallized layer varied somewhat from experiment to experiment, depending presumably on the abrading technique. However, the texture of the recrystallized layer produced by this method is nearly as random as that of a powder specimen. Fig. 2 shows the texture determined from the "growth side" (face opposite the abraded surface) of the crystal after it was kept at room temperature for 100 hr. The specimen was only partially recrystallized, as shown by the remaining deformation texture. The new orientations are derived from the recrystallized grains grown through the thickness of the crystal from the "nucleation side" (the abraded surface). Fig. 3 shows the texture after complete recrystallization produced by annealing at 60°C for 1 hr. The arrows indicate 40-deg rotation around the (111) axes of the deformation texture. The microstructure of a completely recrystallized specimen is shown in Fig. 4. As shown in Figs. 2 and 3, the texture of the re-crystallized grains grown from the nucleation side to the growth side is essentially the same as that observed in less pure aluminum' (99.994 pct) and dilute alloyz crystals rolled in the same orientation. How-

Jan 1, 1968

By C. S. Matthews, H. C. Lefkovits

Drilling progress is often delayed by sticking of the drill string. The development of preventive and remedial methods has been hampered by incomplete understanding of the sticking mechanism. A recent lahorntory investigation hns indicated that one type of sticking may be attributed to the difference in pressure between the borehole and formation. This paper shows, by means of soil mechanics, that the primary cause for differential pressure sticking is cessation of pipe movement, whereas diflerential pressre and stanrtding time determine the severity of the sticking. The analysis stresses the importance of using low-weight muds with low solids content and low water loss to alleviate diflerential pressure sticking and describes why packed hole drilling, long strings of drill collars, and a large deviation from the vertical are conducive to sticking. Finally, preventrve and remedial methods ore evaluated, and a theory is presented on the release of stuck pipe by spotting oil. INTRODUCTION Since drilling with long strings of oversize drill collars has become standard practice in many areas, the incidence and severity of the stuck pipe problem has increased. It has been noticed that in the majority of these cases the sticking could not possibly be attributed to key seating or caving of shales. It appeared that, due to the differential pressure between the mud column and the formation fluid, the collars were pressed into the wall and so became "wall stuck". Points to note about differential pressure sticking are: (1) sticking is restricted to the drill collars, (2) the collars become stuck opposite a permeable formation, (3) the sticking occurs after an interruption of pipe movement, (4) circulation, if interrupted, can be restarted after the sticking is noticed, and (5) no large amounts of cuttings are circulated out after restarting circulation. Helmick and Longleyl investigated pipe sticking by differential pressure in the laboratory and found an empirical relationship between the differential pressure, the sticking time and the required pull-out force. In this paper an explanation of the mechanism is given based on Terzaghi's theory of clay consolidation. A qualitative description is given in the following paragraphs while the derivation of fonnulas is given in Appendices. This paper is a first attempt to explain pressure differential sticking and many points will require additional theoretical and practical investigation before the problem can be fully understood. PRESSURE DIFFERENTIAL STICKING AS A CONSOLIDATION PROBLEM In any borehole, where the mud pressure is higher than that exerted by the formation fluids, a mud cake is formed opposite the permeable sections of the hole and a continuous flow of filtrate takes place from the mud, through the cake and into the formation. This radial flow pattern requires a certain distribution of the hydraulic and the effective (grain-to-grain) stresses inside the mud cake. Any quantitative or qualitative change in the external pressure conditions will produce a change in the flow pattern and, consequently, also in the internal stress distribution inside the cake. In view of the low permeability and the high compressibility of a clay mud cake, the adjustment of the internal stress distribution is slow and is accompanied by a change in volume. Time dependent stresses are thus created which gradually diminish as the new state of equilibrium between internal and external pressures is approached. Some 30 years ago, Terzaghi developed his "Theory of Consolidation" to account for the time-dependent stresses and settling of clay formations under the influence of external loads. He derived a differential equation by which the time-dependent hydraulic stress and the consolidation can be computed for any point inside the layer during the consolidation process. His theory is based on the assumption that the change in stress is solely due to a change in water content and it may only be applied to one-dimensional consolidation phenomena. Other investiga-tors5,10 have expanded his theory to include processes of more than one dimension. The difference between the external pressures on the mud cake before and after sticking is a qualitative one (isolation of part of the cake by the static contact with the drill collars after pipe movement has been stopped)', and the time-dependent stresses thus created may be investigated by means of Terzaghi's theory. By this analysis the changes in the nature of the contact surface between the drill collars and the mud cake during the sticking can be explained; and the friction force between the two may be computed as a function of the sticking time, the borehole dimensions and the mud cake characteristics.

By George Sachs, S. M. Clark, George Espey

he tendency of a commercially drawn cartridge case to crack in the mercury test and the relation of cracking tendency to residual stress retained after drawing were studied. The fourth drawpiece (next to the final) of caliber 0.30 cartridge cases produced by Frankford Arsenal were selected as test pieces. These exhibited an exceptionally high cracking tendency, making a detailed study possible. To obtain fast cracking in the mercury test, about 0.0015 to 0.003 in. must be removed from the wall thickness of the drawpiece by pickling, and it must be subjected to the mercury test immediately after washing. Removal of the adhering mercury by annealing and subsequent squeezing of the case in a vise was used to reveal definitely the presence or absence of cracks. Various lots of apparently identically fabricated cases were shown to possess a different cracking tendency. Machining off or boring a hole in the base gradually reduced and eventually eliminated the cracking tendency. On the contrary, shortening of the wall (body) reduced the cracking tendency only if the wall became so short that the cracking zone was directly affected. By boring out the base and pickling from the outside and then splitting the resulting rings, it was possible to determine the approximate stress distribution in the base and in the adjacent part of the wall. Small compression stresses were present in the core and the major part of the base, while the surface of the base and the adjacent wall contained high circumferential tensile stresses. On the contrary, the wall when parted from the base contained only insignificant residual stress. The conception is advanced, that the stress distribution in a drawn cartridge case corresponds fundamentally to that of a tube (wall) shrunk on a disk (base). Such a stress distribution results from the tendency of the base to recover elastically by an increase in diameter from the biaxial compression during drawing while the wall exhibits little tendency to change its diameter after progressing through the die. This is confirmed by measurements which show the base diameter to be slightly larger than the wall diameter.

Jan 1, 1945

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By B. B. Wood, M. J. Rzasa, E. W. Hough

An apparatus for the determination of fluid-fluid interfacial tension by the pendant drop method has been constructed. The apparatus is refined beyond those previously described in that the samples are introduced into an evacuated windowed cell without contacting air or mercury. Interfacial tension data are reported for the water-methane system between 74 and 280°F and 15 and 15,000 psi. The variation of wettability of the stainless-steel dropper tip with pressure and temperature was observed incidentally to the measurements. INTRODUCTION The most refined previous apparatus --for the determination of fluid-fluid interfacial tension at reservoir conditions was built by Hauser and Michaels.' These authors used the pendant drop method, previously investigated by Andreas, Hauser, and Tucker.' Recently, Fordham3 has made the pendant drop method an absolute one by numerical integration of the differential equation of drop shape. It is necessary to know the difference in density of the two fluids and the acceleration due to gravity in order to evaluate the interfacial tension from measurements of drop dimensions. Contact angle is not involved in the measurements by this method. Some precise tests of the method have been made at atmospheric pressure and 77°F by Douglas," who found agreement with established values to within about 0.1 per cent for water and air, cyclohexane and air, benzene and air, and benzene and water. No values of interfacial tension from the recent pendant drop apparatusJ have been published by Hauser and Michaels. However, values for the water-benzene and water-decane systems are given in Michaels' thesis5 or Dressures from 15 .to 10,000 psi and temperatures from 73 to 268ºF. Some determinations on gas-oil and gas-water systems in the range of 15 to 4,000 psi and 78 to 178°F have been made by Hozott,' by the drop-volume method. The capillary rise method has been used to investigate the interfacial tension in gas-oil systems at 88°F to several thousand psi by Swartz.7 Other determinations in gas-oil systems at pressures under 1,000 psia have been made by Jones: and Beecher and Parkhurst.9 The scarcity of data for pressures above 5.000 psi is apparent. APPARATUS An assembly drawing of the working section of the interfacial tenqion apparatus is given in Fig. 2. 'The endanant drop (A) is housed in a pressure chamber having glass windows (B). An agitator (6) is provided. The metal parts of the apparatus coming into contact with the sample are made of AISI: Type 316 steel. Drain grooves are provided around the whdows so that the sample in contact with the O-rings is not returned to the working section when the pressure is reduced. A schematic arrangement of the apparatus is given in Fig. 3. The working section containing the pendant drop (A) is filled by samples from bombs (B) with the aid of the vacuum system (C). The O-ring sealed pistons (D) used to separate the sample from the hydraulic fluid are shown together with the pressure production and measurement system (E). A front view of the apparatus is shown in Fig. 1. Most of the hydraulic system is at the top of the panel. The pump and displacement piston are at the lower right. The Variacs for the air bath heaters. the camera. and the vacuum gauge are a1so visible on the panel. The working section together with a window closure and a drop-forming tip closure are shown in Fig. 9. The carbon arc light source with filter is visible in the upper part of the picture. Two sides of the air bath with the impeller and a part of the convection shield can also be seen. The assembled air bath is shown in Fig. 10.

Jan 1, 1951

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

The compositions of coexisting phases in the methane-propane-n-pentane system were determined at 160° and -2 20°F. throughout the two-phase region, at pressures above 500 lb. per sq. in. The experimental results permitted the calculation of gas-liquid equilibrium constants as well as the establishment of the critical behavior of this ternary system. Although many binary paraffin hydrocarbon systems have been investigated, the experimental work relating to the phase behavior of ternary paraffin hydrocarbon mixtures at elevated pressures is relatively scarce, being limited to a study of the meth-ane-propane-PL-pentane system at 100°F.l,2 However, Guter and co-workers have studied the phase behavior of the methane-ethane-ethylene system at relatively low temperatures. Information concerning the phase behavior of ternary systems is of value in predicting the behavior of the components in multicomponent systems, since the influence of pressure, temperature, and concentration may be individually ascertained. In the light of the importance of such information, the study of this ternary system was extended to higher temperatures in order to increase the field of temperature in which the data could be applied. Since all states encountered in this investigation are above the critical temperature of methane, the details of its phase behavior are not of direct significance. The properties of propane in the heterogeneous region were taken from a correlation3 based upon recently published data. The corresponding information for n-pentane was taken from experimentally measured vapor pressures and volumetric data.4 The rnethane-propane system has been studied throughout the two-phase region at temperatures above 70°F.,5 while the phase behavior of the propane-n-pentane system has been established for temperatures above 160°F.6 The volumetric and phase behavior of the methane-72-pentane system has been studied in detai1.7,8 The experimental measurements serve to establish with adequate accuracy the phase behavior of the components and of the constituent binary systems for this ternary system. It is believed that, with the exception of the measurements for the methane-propane system, the uncertainties in the earlier data relating to the pure substances and the binary mixtures are probably less than those associated with the values reported here. Method The methods and apparatus employed in this investigation have been described.137 In principle, the method involved the withdrawal of samples of the coexisting gas and liquid phases from a vessel containing a heterogeneous mixture of methane, propane and n-pentane. Provision was made so that

Jan 1, 1943

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

The compositions of coexisting phases in the methane-propane-n-pentane system were determined at 160° and -2 20°F. throughout the two-phase region, at pressures above 500 lb. per sq. in. The experimental results permitted the calculation of gas-liquid equilibrium constants as well as the establishment of the critical behavior of this ternary system. Although many binary paraffin hydrocarbon systems have been investigated, the experimental work relating to the phase behavior of ternary paraffin hydrocarbon mixtures at elevated pressures is relatively scarce, being limited to a study of the meth-ane-propane-PL-pentane system at 100°F.l,2 However, Guter and co-workers have studied the phase behavior of the methane-ethane-ethylene system at relatively low temperatures. Information concerning the phase behavior of ternary systems is of value in predicting the behavior of the components in multicomponent systems, since the influence of pressure, temperature, and concentration may be individually ascertained. In the light of the importance of such information, the study of this ternary system was extended to higher temperatures in order to increase the field of temperature in which the data could be applied. Since all states encountered in this investigation are above the critical temperature of methane, the details of its phase behavior are not of direct significance. The properties of propane in the heterogeneous region were taken from a correlation3 based upon recently published data. The corresponding information for n-pentane was taken from experimentally measured vapor pressures and volumetric data.4 The rnethane-propane system has been studied throughout the two-phase region at temperatures above 70°F.,5 while the phase behavior of the propane-n-pentane system has been established for temperatures above 160°F.6 The volumetric and phase behavior of the methane-72-pentane system has been studied in detai1.7,8 The experimental measurements serve to establish with adequate accuracy the phase behavior of the components and of the constituent binary systems for this ternary system. It is believed that, with the exception of the measurements for the methane-propane system, the uncertainties in the earlier data relating to the pure substances and the binary mixtures are probably less than those associated with the values reported here. Method The methods and apparatus employed in this investigation have been described.137 In principle, the method involved the withdrawal of samples of the coexisting gas and liquid phases from a vessel containing a heterogeneous mixture of methane, propane and n-pentane. Provision was made so that

Jan 1, 1943

By E. W. Hough, B. B. Wood, M. J. Rzasa

An apparatus for the determination of fluid-fluid interfacial tension by the pendant drop method has been constructed. The apparatus is refined beyond those previously described in that the samples are introduced into an evacuated windowed cell without contacting air or mercury. Interfacial tension data are reported for the water-methane system between 74 and 280°F and 15 and 15,000 psi. The variation of wettability of the stainless-steel dropper tip with pressure and temperature was observed incidentally to the measurements. INTRODUCTION The most refined previous apparatus --for the determination of fluid-fluid interfacial tension at reservoir conditions was built by Hauser and Michaels.' These authors used the pendant drop method, previously investigated by Andreas, Hauser, and Tucker.' Recently, Fordham3 has made the pendant drop method an absolute one by numerical integration of the differential equation of drop shape. It is necessary to know the difference in density of the two fluids and the acceleration due to gravity in order to evaluate the interfacial tension from measurements of drop dimensions. Contact angle is not involved in the measurements by this method. Some precise tests of the method have been made at atmospheric pressure and 77°F by Douglas," who found agreement with established values to within about 0.1 per cent for water and air, cyclohexane and air, benzene and air, and benzene and water. No values of interfacial tension from the recent pendant drop apparatusJ have been published by Hauser and Michaels. However, values for the water-benzene and water-decane systems are given in Michaels' thesis5 or Dressures from 15 .to 10,000 psi and temperatures from 73 to 268ºF. Some determinations on gas-oil and gas-water systems in the range of 15 to 4,000 psi and 78 to 178°F have been made by Hozott,' by the drop-volume method. The capillary rise method has been used to investigate the interfacial tension in gas-oil systems at 88°F to several thousand psi by Swartz.7 Other determinations in gas-oil systems at pressures under 1,000 psia have been made by Jones: and Beecher and Parkhurst.9 The scarcity of data for pressures above 5.000 psi is apparent. APPARATUS An assembly drawing of the working section of the interfacial tenqion apparatus is given in Fig. 2. 'The endanant drop (A) is housed in a pressure chamber having glass windows (B). An agitator (6) is provided. The metal parts of the apparatus coming into contact with the sample are made of AISI: Type 316 steel. Drain grooves are provided around the whdows so that the sample in contact with the O-rings is not returned to the working section when the pressure is reduced. A schematic arrangement of the apparatus is given in Fig. 3. The working section containing the pendant drop (A) is filled by samples from bombs (B) with the aid of the vacuum system (C). The O-ring sealed pistons (D) used to separate the sample from the hydraulic fluid are shown together with the pressure production and measurement system (E). A front view of the apparatus is shown in Fig. 1. Most of the hydraulic system is at the top of the panel. The pump and displacement piston are at the lower right. The Variacs for the air bath heaters. the camera. and the vacuum gauge are a1so visible on the panel. The working section together with a window closure and a drop-forming tip closure are shown in Fig. 9. The carbon arc light source with filter is visible in the upper part of the picture. Two sides of the air bath with the impeller and a part of the convection shield can also be seen. The assembled air bath is shown in Fig. 10.

Jan 1, 1951

By R. G. Hudson, H. W. Paxton

The activities of iron and chromium in their binary system have been measured by the Knudsen orifice technique. The system is close to ideal at 1200- 1250 C with slight positive deviations. The effect of this on the liquidus and solidus is discussed and these are calculated for two limiting assumptions. The vapor pressure of pure iron, pure chromium, and one alloy is compared with that obtained by the Langmuir free-evaporation technique. The results agree, indicating a vaporization coefficient close to 1. HERE are no reported data on the thermody-A namic activity of iron and chromium in the solid portions of the phase diagram. It is generally assumed'.' that the liquid solutions of iron and chromium obey Raoult's law. Chen and Chipman" have inferred that the liquid solution obeys Raoult's law. The minimum' in the solidus-liquidus curves for the iron-chromium system shows that there are deviations from ideality in either the solid or liquid or both. Because of the importance of developing reliable techniques for obtaining activity data in alloy systems at high temperatures and of the data so obtained, an investigation of the activity of iron and chromium in the binary at 1200-1250 C was undertaken using the Knudsen cell. Experimental The apparatus and experimental procedures used in this investigation were described in a previous paper." The various materials used for the construction of the Knudsen cell are listed in Table I. The metal used for the determination of the vapor pressure of chromium was 99.9 pet pure, obtained from A. D. Mackay, Inc. The iron was obtained as electrolytic grade from Fisher Scientific Company. The Fe-Cr alloys used are shown in Table 11. The largest error and controlling factor in the accuracy in the experiments reported here are introduced because of temperature uncertainty, which is estimated to be ±3 deg C. This introduces an uncertainty of 26 pet in the measured pressure. Experimental Results and Calculations The vapor pressures of pure iron and pure chromium were calculated from the measurements by the Knudsen equation3 on the assumption that only Cr or Fe atoms were present in the gas phase. For metal vapors, at the high temperatures and low pressures involved in these measurements this should be a reasonable assumption. Whitman" corrections for the cells were made. The data and results of pressure calculations are presented in Table I, and are plotted in Fig. 1. In addition the heat of vaporization at the absolute zero, ?E°°, has been calculated for chromium. These calculations are summarized in Table 111. The data used in these calculations are as follows kelley13 (F° - E°°/T ) Speiser, et al H (F° - E°°/T ) 010 where F" — standard free energy at temperature T It was necessary to calculate the total pressure above the alloys from the total weight loss W of the cell during a run, because of the fact that all attempts to collect and analyze the chromium and iron vapor effusing from the cell in the apparatus available failed. The failure resulted from the re-

Jan 1, 1959

By Karl L. Fetters

In the process of making steel in the open-hearth furnace the refining of the metal during the working period of the heat is largely accomplished through the agency of the slag. From the birth of the process until the present day steelmakers have recognized the importance of the slag in determining the composition of the metal and the quality of the product. The general relationships between slag composition and metal analysis have long been known, at least in a qualitative or approximate fashion. For examples, the iron oxide content of the slag is higher on lower carbon heats; the more basic slags are higher in iron oxide for a given carbon content; certain amounts of iron oxide and lime arc required for phosphorus removal and a high lime-silica ratio is needed if the sulphur content of the metal is to be diminished. In recent years a number of quantitative relationships involving these and other variables have been developed through plant and laboratory studies by numerous investigators in this country and abroad. The direct comparison of laboratory and open-hearth data involves the question of the degree to which each approaches the conditions of chemical equilibrium, a question which, from the open-hearth standpoint, we are scarcely yet in position to answer. And, although a considerable body of dependable equilibrium data has been obtained in the laboratory, this work has not yet been extended to cover the ranges of slag composition encountered in basic open-hearth practice. In the present study we shall not attempt to draw comparisons between data from the two sources; nor do we attempt to draw conclusions as to the approach to chemical equilibrium in the open-hearth furnace. Many of the operating variables that are likely to be erratic or unrecorded during the earlier stages of the heat become more consistent and arc more readily subject to observation and control during later stages. For example, undigested lime or ore gradually goes into solution, the rate of carbon drop levels off, and the temperature of the metal is brought under control. For these and other reasons a greater degree of self-consistency is likely to be found among data obtained during the

Jan 1, 1940

By Karl L. Fetters

In the process of making steel in the open-hearth furnace the refining of the metal during the working period of the heat is largely accomplished through the agency of the slag. From the birth of the process until the present day steelmakers have recognized the importance of the slag in determining the composition of the metal and the quality of the product. The general relationships between slag composition and metal analysis have long been known, at least in a qualitative or approximate fashion. For examples, the iron oxide content of the slag is higher on lower carbon heats; the more basic slags are higher in iron oxide for a given carbon content; certain amounts of iron oxide and lime arc required for phosphorus removal and a high lime-silica ratio is needed if the sulphur content of the metal is to be diminished. In recent years a number of quantitative relationships involving these and other variables have been developed through plant and laboratory studies by numerous investigators in this country and abroad. The direct comparison of laboratory and open-hearth data involves the question of the degree to which each approaches the conditions of chemical equilibrium, a question which, from the open-hearth standpoint, we are scarcely yet in position to answer. And, although a considerable body of dependable equilibrium data has been obtained in the laboratory, this work has not yet been extended to cover the ranges of slag composition encountered in basic open-hearth practice. In the present study we shall not attempt to draw comparisons between data from the two sources; nor do we attempt to draw conclusions as to the approach to chemical equilibrium in the open-hearth furnace. Many of the operating variables that are likely to be erratic or unrecorded during the earlier stages of the heat become more consistent and arc more readily subject to observation and control during later stages. For example, undigested lime or ore gradually goes into solution, the rate of carbon drop levels off, and the temperature of the metal is brought under control. For these and other reasons a greater degree of self-consistency is likely to be found among data obtained during the

Jan 1, 1940

By G. R. Lehman

The Inspiration Consolidated Copper Co. had an orebody at Miami, Ariz., of close to 100,000,000 tons of low-grade copper ore, and the method of mining this ore most profitably was of great importance. The selection of a method was practically limited to a "top-slicing," a "shrinkage-stope" or a "caving" method. The "top-slicing" method would give a high extraction of the developed ore, at a high mining cost, and the "shrinkage-stope" or "caving" methods a lower extraction of the developed ore, at a lower mining cost. Ore-Drawing Tests To decide on the method to be used it was necessary to know about what extraction of the ore could be obtained by the "shrinkage-stope" or " caving " methods. As no definite information regarding the,question was available at the time, C. E. Mills, the general manager, thought that some information could be obtained by experimenting in drawing ore, covered with capping, from an experimental box. Some work had already been done along these lines by W. C. Browning for the Inspiration Copper Co. and by myself for the Live Oak Development Co. The idea was to represent as nearly as possible, in the experimental box, the conditions within an area of caved stopes of caved ore all ready for drawing. That is, the area was supposed to represent a semibroken mass with the capping above it in the same condition and ready to follow the ore downward as it was drawn out of the chutes under the ore. To represent the above condition, in the experimental box, crushed ore from the mine was placed in it to a given height, and red barren capping from the mine was placed on top of the ore. The Experimental Box The experimental box shown in Fig. 1 was made of wood and glass. The glass was used for the sides so that the drawing action of the outside row of chutes could be seen and noted, the latter being cut in the center by the glass sides. The length of the box was 30 in., width 20 in. and the

Jan 1, 1917