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By J. C. Bokros

At temperatures above 950°F, zirconium which has been strained a critical amount will experience critical recrystalli-zation. The large grain size thus formed can result in a reduction in the fatigue life by a factor of 2 to a factor of 9 at both high and low temperatures. The critical strains for zirconium vary from 15 pct at 900°F to about 2 pct at 1125°F, while those for zircaloy III vary from 15 pct at 1050°F to 5 pct at 1200°F. Zircaloy II ,experiences no critical recrystallization up to 1200°F. ZIRCONIUM has become increasingly important for nuclear applications and is being employed in reactors at temperatures where recrystallization can occur. Recent work' on the fatigue properties of zirconium has shown that coarse-grained structures developed in zirconium during recrystallization have much lower fatigue lives than fine-grained material. The development of these large grain sizes under such conditions is well known to be the result of critical recrystallization.2-4 Briefly, critical recrystallization occurs when a metal is strained a critical amount and annealed in the recrystallization range. The critical strain is defined as that minimum strain necessary to promote nucleation in the time unit and temperature considered. The maximum grain size occurs at the critical strain, since at this strain the fewest stable nuclei per unit volume grow into new grains. Recrystallization is not evident below this; strain since the nucleation rate is vanishingly lolw, and metal strained more than the critical amount has a higher nucleation rate per unit volume which results in a finer grained structure. This paper describes the critical recrystallization observed in reactor-grade zirconium, zircaloy 11, and zircaloy I11 as a function of annealing temperature and temperature of strain. EXPERIMENTAL The zirconium used was hafnium-free, double arc-melted sponge obtained from the Bureau of Mines. The ingots were forged and hot reduced to 0.08 to 0.10-in. sheet and subsequently cold reduced to 0.035-in. sheet with intermediate and final anneals at 1200 OF for 15 min. The zircaloy II and zircaloy III used were 0.035-in. sheets in the annealed condition. Compositions of these materials as tested are given in Table I. To determine the critical strain at a given temperature, tensile specimens having a0.065-in. taper in a 2-in. gage length were machined from the sheets parallel to the rolling direction. The specimens were polished, etched, and examined metallographically to ensure that all of them were strain-free, initially. Tukon indentations were made every half millimeter along the gage length of each specimen. These served as fiducial marks enabling the plastic strain to be measured with a microscope and micrometer stage. The specimens were pulled to failure at a rate of 0.002 in. per min in an Instron tensile-testing machine. Three temperatures were used for straining: room temperature, 500 ºF, and 900 ºF. The 500º and 900 ºF tests were run in an argon atmosphere. Since the rate of work hardening changes with temperature, a different critical strain was obtained for each temperature of strain. Specimens, prepared in the manner described, were annealed in vacuunl at various temperatures ranging from 900" to 1200 F for up to 1000 hr, after which they were examined metallographically. The critical strain and the recrystallized grain size as a function of strain were determined for each specimen. Results for the same temperature and time indicated that the critical strain measured was reproducible to within 5 pct of each other. RESULTS AND DISCUSSION Since increasing the time of anneal increases the probability of the nucleation of a new grain, the critical strain decreases with time at a decreasing

Jan 1, 1961

By A. W. Schlechten, C. M. Hsiao

The apparent vapor pressures of a number of metal sulphides were determined by measuring their rate of weight loss when they were heated under vacuum. The calculated pressures are due in some instances to the volatility of the sulphide and in others to the decomposition pressure. FIE direct reduction of metallic sulphides, as in the precipitation method for lead or antimony, is not a widely used process today. However, it might be employed for the production of a number of metals if the operation were carried out under reduced pressures. Two general procedures are possible; the reducing agent could form a stable nonvolatile sulphide from which the valuable metal could be removed by volatilization or liquation. The other approach would be to choose a reducing agent which would form a sulphide that could be volatilized away from the valuable metal. A vacuum operation would serve to protect the sulphides and metals from oxidation and would increase the evaporation rates. A related process is the separation of metallic sulphides by selective volatilization either at atmospheric pressure or under vacuum. This procedure is already used commercially for the elimination of lead and cadmium as PbS and CdS from zinc calcines; it might well have other applications. To predict such processes it is necessary to know the relative volatilities of the metallic sulphides and to know whether they volatilize as sulphides or whether the predominant weight loss is due to decomposition. Such data would also be of value in studying problems such as the use of sulphides for refractories, as described by Brewer,] or in the evaluation of the theory of ore deposition from the vapor state, as proposed by Brown.' Qualitative statements concerning the volatility of metallic sulphides can be found frequently in the literature and are well summarized by Mellor, but accurate determinations of rates of evaporation or vapor pressures are very scarce. Kelly" lists vapor pressure data only for PbS; his reference being to the work of Schenck and Albers,4 who measured the vapor pressure of PbS by a dynamic method between 850" and 995°C. More recently Veselovskii5 has determined the vapor pressures of the sulphides of antimony, lead, cadmium, and zinc at temperatures ranging from 360" to 1000°C using Knudsen's method. A second Russian worker, Pogorelyi,6 determined the vapor pressures of CdS and ZnS at temperatures from 900" to 1250°C. The results obtained by these workers are shown in subsequent graphs in comparison with the data of this paper. Brewer and coworkers1 have studied some of the metallic sulphides to determine their suitability as refractories in vacuum. Veselovskii's determinations on PbS checked well with those of Schenck and Albers, and his determinations of CdS check almost exactly with Pogo-relyi. For the vapor pressure of ZnS the data of Veselovskii and that of Pogorelyi are in fair agreement, as shown in Fig. 1, but it should be pointed out that Lumsden7 has discovered that the equation given by Veselovskii for the vapor pressure of ZnS: - 14,200 log P9.495 is in error by a factor of ten when compared to the experimental data. In contrast with the scarcity of data on vapor pressures, the decomposition pressures of many metal sulphides have been determined and are summarized by Smithells.8 Theoretical Considerations The experiments described in this paper consisted of determinations of the rate of weight loss of certain metallic sulphides under very low pressures at different temperatures. These data plus observation and analyses of the products reveal the mechanism of the weight loss and also provide a basis for the calculation of the vapor pressure or apparent vapor pressures of the sulphides.

Jan 1, 1953

By R. F. Steigerwald

The effects of heat transfer on the corrosion behavior of type 304 stainless steel in boiling water have been studied. Heat transfer conditions increase the tendencies of the stainless steel toward stress-corrosion mucking when the water is contaminated with Cl-. Surface preparation is the most important variable in determining the severity of the stress-corrosion problem in water with a given Cl- content. Heat treatment, chemical cleaning, and degree of wet film boiling also affect the corrosion of stainless steels used as heat transfer surfaces in boiling water. An up-paratus for corrosion testing under controlled heat transfer conditions is described. THE principal objective of this investigation was to study the corrosion behavior of AISI Type 304 stainless steel in boiling high-purity water under conditions of heat transfer. The principal variables in the study were: a) boiling conditions: limited boil, agitated boil; b) metallurgical structure: annealed or sensitized; c) surface condition: rolled, pickled, or ground. The results of the study should elucidate the role of heat transfer in the corrosion of stainless steel in boiling high-purity water and provide a base line from which to assess the severity of this type of corrosion. Although there has been an investigation of the effect of heat transfer on the corrosion behavior of stainless steels in alkaline waters,' work on the corrosion of stainless steels under heat transfer has been largely confined to various acid solutions.'-4 Furthermore, the study of the corrosion of stainless steels in high-purity water has been generally restricted to auto-clave and instream testing in superheated (e.g., 300°C) water and steam.5'6 Cooling water problems led to this study of the corrosion behavior of type 304 stainless steel in high-purity water at its atmospheric boiling point. In addition to the effects of heat transfer, this study also considered the influences of the type of boiling,7 metallurgical structure, and surface condition on the corrosion behavior of stainless steel in high-purity water. Two boiling conditions were investigated in this study: a) limiting boiling, i.e., when the heat-transfer surface had just reached the boiling point and boiling nucleated randomly over the specimen surface and b) agitated boiling, i.e., when a mild degree of superheat had been achieved on the specimen surface and boiling occurred generally over the specimen surface. Both boiling conditions are broadly classified as wet-film boiling. Originally, this program included the study of a third type of boiling, dry-film conditions. At dry-film boiling the temperature of the heat transfer surface is high enough so that it is covered with a continuous film of steam. Experimental difficulties made it impossible to study this kind of boiling with the available apparatus. Since surface condition affects heat transfer rates, three typical surfaces were chosen for study: a) as-rolled, the 2B finish received from the supplier, b) as-pickled, 30 min in 8 pct HNO3-1 pct HF, and c) as-ground on 120 grit paper. In order to evaluate the effect of improper heat treatment or welding on hot wall corrosion, both annealed and sensitized mi-crostructure were included in this study. EXPERIMENTAL Test Apparatus. The particular problems of interest in this investigation required a knowledge of the thermal gradient through the test specimen. From this gradient, the heat flux to the surface and the surface temperature could be determined. In order to satisfy this need, an apparatus similar to the boiling-disk apparatus of Fisher and whitney2 was designed. The solution is contained in a thermally-insulated, steel pipe lined with TEFLON resin. A stainless steel _______;________________________________________

Jan 1, 1970

By F. Weinberg

In developing a mechanism for the solidification of metals from the melt, it has been proposed that solidification proceeds by the growth of platelets parallel to close packed planes. The evidence for this is based primarily on observations of decanted interfaces of lead1,2 and tin on which platelets 1 to 10 µ thick4 were observed. In recent observations of decanted eutectic alloys, 5,6 it was found that the eutectic structure on the decanted surface was markedly different than that of the bulk material, with the surface structure extending approximately 10 µ behind the interface.' This suggested that, at least for these experiments, a residual liquid layer 10 µ thick had been left on the decanted interface, which solidified subsequent to decanting. If a similar thickness of residual liquid was left on the decanted surfaces in the lead and tin observations referred to above, then it is questionable to what extent the observed platelets can be related to the solid-liquid interface before decanting. The purpose of the present investigation was to measure the thickness of the residual liquid layer on a decanted surface of tin, using relatively standard decanting procedures. The technique used was to add approximately 200 ppm of Tl204 (PI) to the melted portion of a high purity (99.999 pet) bar of tin, which was being progressively melted from one end, and then decant during melting. Since only the melt contained the radioactive tracer, the activity emanating from the decanted surface could be used as a measure of the thickness of the residual liquid layer. Progressive melting was carried out in the same fashion as single crystal growth, namely, in a horizontal graphite boat, in an argon atmosphere, using a moving furnace. The decanting was done in two ways; 1) removing the furnace and suddenly dropping the melt end of the boat, and 2) suddenly jerking the solid away from the liquid by the action of a falling weight (estimated peak acceleration 3 x 105 cm per sq sec), using a split graphite container. In all cases the melt was vigorously agitated by bubbling argon through it. The activity of the decanted surface was measured through an aperture 1.5 cm by 0.5 cm in a lead shield with an Anton tube geiger counter. Assuming that the active layer on the surface had the same concentration of Tl204 as the decanted liquid, the thickness of the layer could be determined from the measured activity of the decanted material, and the relationship between activity and material thickness. The latter was determined by rolling some of the decanted material into foil and measuring the activity of multiple layers of the foil. The activity At of material of thickness t (in mm) was determined to be A, = Ao(1 - e-22.5t) where Ao is the activity of the bulk material. The results of the measurements of the thickness of the residual liquid layer for six decants are given in Table I. The variation in t is attributed to variations in the decanting procedure and the rate of melting, the latter being difficult to control because of the vigorous agitation of the liquid. The rate of melting was in the order of 2 cm per hr, estimated from the position of the solid-liquid interface during melting. The results indicate that a residual liquid layer of the order of 10 µ in thickness is left on the decanted interface in agreement with the observation on eutectic alloys referred to above. If the mixing of the liquid during melting is not complete, as was

Jan 1, 1962

By A. L. Lee, M. H. Gonzalez, R. F. Bukacek

Experimental viscosity data for methane are presented for temperatures from 100 to 340F and pressures from 200 to 8,000 psia. A summary is given of the available data for methane, and a comparison is presented for that data common to the experimental range reported in this paper. Correlation of the data is presented, and predicted values are given for temperatures up to 460F and pressures up to 10,000 psia. INTRODUCTION The increasing ranges of temperature and pressure at which fluids are produced, transferred and processed in the petroleum and chemical industries stress the need for accurate information on physical properties, both for engineering calculation and for improving the methods used to estimate physical properties. A survey of the literature reveals that disagreements between published data on the viscosity of methane are common and that most investigations have been conducted over restricted temperature and pressure ranges. This situation made it desirable to undertake an investigation with a scope common to most of the literature data available. APPARATUS AND MATERIALS The apparatus used in this investigation was the capillary tube viscometer'described by Dolan,10 with modifications introduced in the general design and operation of the instrument. It has an effective pressure range from 14.7 to 10,000 psia and a temperature range from room temperature to 400F. The design of the viscometer is based on the establishment of a manometric head between two vessels containing the test fluid and a volume of mercury. The reservoirs are connected by a capillary tube through which the test fluid flows and a tube through which mercury flows. A pressure gradient is established by elevating one of the vessels above the other, the resulting flow of mercury displacing the test fluid through the capillary. The schematic diagram of the system (Fig. 1) shows the arrangement of the equipment auxiliary to the viscometer. The density cells assembly (E, Fig. 1) was not used in this investigation since reliable data are available on methane. 23 The assembly consists of a bank of eight 316 stainless steel pycnometers. Experimental values of the density of a natural gas19 and i-butane14 samples have been obtained for pressures up to 8,000 psia and temperatures up to 340F. The methane used was obtained from the Southern California Gas Co. Mass spectrometric analysis showed a composition of 99.8 percent CH4, 0.1 percent C2H6 and 0.1 percent C3H8. EXPERIMENTAL VALUES AND ACCURACY OF DATA Determinations were carried out at several temperatures. With the temperature in the cabinet controlled at a given level, a series of runs were made at various pressures. To establish pressures lower than that obtained from the methane cylinder, it was necessary to vent the gas slowly to the atmosphere until the desired pressure was reached. The consistency of the test run time for a particular condition can be used as a criterion for the accuracy of the data. A further check is obtained by comparison of the viscosity values obtained using different driving heads. To establish the instrument's reproducibility, a large number of runs were made at three completely different conditions of temperature and pressure. Data obtained were analyzed statistically to determine the most reliable value for the variance of the experimental data. It was found that the variances of the data taken at different experimental conditions were not statistically equivalent, but they were small. The largest variance was found at 8,000 psia and 100F, where the standard deviation was 0.385 micropoise. Therefore, 99.9 percent of the data can be expected to fall within 1.15 micropoises of the population mean, except for the intervention of systematic errors in operation.

By P. M. Kelly, E. P. Butler

The stability of a 70/30 Mn-Cu alloy aged to peak damping has been investigated using electron microscopy, X-ray diffraction, and torsional pendulum measurements. Storage at room temperature or at 100" C causes a reduction in damping capacity. This is shown to be due to the formation of subdomains which "lock" the main domain structure and so hinder their movement. After storage the damping capacity can be restored by a retransformation treatment, which generates structures identical to those found in newly aged specimens. Plastic deformation by rolling also causes a decrease in damping capacity. In this case the damping capacity can only be restored by retransformation if the amount of deformation is less than about 5 pct. THE general metallography and structure of these high damping capacity alloys has been discussed in Part I of this work.1 Part II deals with some of the variables that affect the damping capacity. In particular, the stability of the damping capacity of a 70/30 alloy aged for 2 hr at 425° C and quenched has been investigated. The temperature sensitivity of the damping capacity of a 70/30 alloy aged for 2 hr at 450° C has been reported by Birchon.2 The damping capacity begins to decrease with increasing temperature, and is very low above the M, temperature of 125°C. The cubic — tetragonal transformation is completely reversible and there is no apparent thermal hysteresis associated with the change in damping capacity. Another important effect was first reported by Dean and his coworkers.3 They noticed a decrease in the damping capacity with time for specimens of a quenched tetragonal alloy. More recently workers at the Admiralty Materials Laboratory 4 have studied the stability of an aged 70/30 alloy. They found that the damping capacity decreased to half its original value after about 1000 hr at room temperature. EXPERIMENTAL The techniques used for electron microscopy and X-ray diffraction have been described in Part I. The damping capacity was measured by means of a torsional pendulum, using rectangular specimens, 3 by 0.3 mm with a 6 cm gage length. The specific damping capacity, S.D.C., was calculated as a percent amplitude decay in free vibrations over 10 cycles, starting at an amplitude which corresponded to a 700 psi surface shear stress. Because of the stress dependence of the damping,' the values obtained were about a third those reported for a 5000 psi surface shear stress.' RESULTS a) Effect of Aging Temperature. The effect of aging temperature on the damping capacity is shown in Fig. 1. The damping capacity reaches a peak of 12 pct after aging at 400° to 425°C) then begins to decrease as the volume fraction of a Mn increases. At higher aging temperatures the structure becomes cubic again with a low damping capacity. b) Stability of the Aged Structure. The damping capacity of the aged alloy decreases with time at room temperature. This process could be accelerated by storing at 100°C, when about 100 hr were required for the damping to fall to half its original value. The results of room temperature and 100°C storage, for times up to 1000 hr, are shown in Fig. 2. The damping capacity starts to decrease after about 24 hr at 18° C and 1 to 2 hr at 100°C. It was found, however, that the damping could be almost completely restored by retransformation. The specimens were held at a temperature above the M, for a short time, 250° C for 5 min, and then quenched. The values of damping capacity for specimens that were aged, stored, and then retransformed are shown by the full points in Fig. 2. X-ray measurements of the c/a ratio and hardness readings on the specimens did

Jan 1, 1969

By J. C. Deppe

A method is presented for calculating approximate injection rates in secondary recovery operations. The method can be applied to cases of unequal fluid mobilities, irregular well patterns and boundary patterns. The steady-state pressure distributions for the four flood patterns reported by Muskat and for five additional patterns reveal that most of the difference in pressure between the injection and producing wells occurs in regions around the wells which can adequately be described as regions of radial flow. This leads to a method of calculating injectivity by approximating the flood pattern with radial flow elements (or a combination of radial- and linear-flow elements for some patterns such as the direct line drive). Irregular and boundary patterns can also be approximated by radial and linear elements. Each of these elements can be described by radial-and linear-flow equations and the results combined as series flow resistances to give an approximate equation for the initial injection rate. The mobility ratio does not affect the initial rate; therefore, if the well pattern is one of those regular patterns for which theoretical rate equations have been derived for unity mobility ratio, the approximate initial rate equation can be improved by adjusting it to match the theoretical equation. The available theoretical rate equations are listed, including five new cases. As the flood progresses, the injectivity changes because in general the flood front will divide the pattern into areas of different fluid mobilities. Simple shapes can be assumed for the flood front so that both areas can be divided into radial- and linear-flow elements. Radial- and linear-flow equations are applied to these elements to account for the change in flow resistance behind the front. To calculate injection rates after breakthrough, it is necessary to know the sweep efficiency at breakthrough. Areal sweep data are available in the literature for a number of patterns, and sufficiently accurate breakthrough sweep efficiency can be estimated from these data if it is not otherwise available. Again, simple shapes for the flood front can be assumed after breakthrough, and injection rates can be calculated for the remainder of the flood. When areal sweep data are available, these data can be used to cbeck. the calculated injection rates after breakthrough. Injection rates calculated by this approximate method compare favorably with available model data. INTRODUCTION When the fluid mobilities in the swept and un swept regions are equal, the injectivity will not change as the flood front advances; and for regular patterns it can be calculated by mathematical formu1as.l When the fluid mobilities in the swept and unswept regions are not equal, the injectivity will increase or decrease as the flood front advances. In this case, the injectivity has not been calculated by analytical means for any practical well pattern; and, furthermore, scale model and analog4,6 results have been published only for the five-spot pattern. The main object of this paper is to present an approximace method for calculating injectivity for the case of unequal mobilities. The method can be applied to regular, irregular and boundary patterns. Before the approximate method is discussed, the analytical formulas for equal mobilities will be summarized, and the analytical solution for radial flow with unequal mobilities will be used to show how the injectivity changes as the flood progresses. EQUAL MOBILITIES, REGULAR PATTERNS In a flooding operation the injectivity, the rate at which fluid can be injected per unit difference in pressure between injection and producing wells, depends on basic physical properties and, in addition, on three variables to be treated here—the area of the swept region, the fluid mobilities in the swept and unswept regions, and the well geometry (pattern,

INTRODUCTION Mineral explorationists range throughout the world looking for mineral deposits which can subsequently be made into mines. Mines are not found! Mines are made, usually at great cost and not often without significant risk. The process of making a mineral deposit into a mine involves a great deal more than a complete appraisal of the deposit. The making of a mine demands detailed feasibility studies of many factors, any one of which, if shown to be negative, could prevent the deposit from becoming a successful mine. Total feasibility analysis involves at least three major fields of study: (1) economic analysis, (2) financial analysis, and (3) political and environmental analysis. Economic analysis is essential for proper decision making at many stages in the evaluation of a mineral deposit. It is the yardstick by which the proposed mining project and alter- native investment opportunities are measured. Economic analysis is concerned with costs and potential profits and can be applied at various stages in the evaluation of a mineral deposit to determine if the project merits the additional funds necessary to bring about each succeeding stage. The nearer any deposit approaches to becoming a mine, the more carefully the economic analysis should be made. Financial analysis has reference to how, where, and at what cost the investment funds can be obtained to finance the proposed mine project. Political and environmental analysis has reference to the many intangible factors that can affect the making of a successful mine. These factors loom larger today than ever before, due to the profusion of government regulations and various environmental constraints now imposed upon the mineral industry both by law and by the weight of public opinion. Ultimately, many of these intangible factors can be resolved back into the economic analysis as an added cost to mine development, but more and more often they have become insurmountable obstacles to any development of certain deposits. The role of financial analysis and the analysis of intangible factors must never be underestimated when making a feasibility study upon which to base investment decisions; however, the emphasis of this text will be upon economic factors. THE PARAMETERS OF MINERAL ECONOMIC ANALYSIS The two major elements of economic analysis are: 1) The potential earnings or annual generated cash flow of the project. 2) The investment costs necessary to realize such earnings. If the difference between the two elements is large enough, i.e., if the return on investment from the cash flow is high enough to attract investors, the project can be said to be financially feasible. The mineral economic analysis must take into consideration many parameters, some of which are known or knowable within certain limits, and others of which are unknown or unpredictable within certain limits and for which estimates must be made. Because both known and estimated parameters enter into the same analytical computations, it is important for the analyst to realize the nature of each when considering the results of an analysis. Some parameters such as the grade of mining block, although estimated, are said to be known within mathematically defined limits. Other parameters, such as the future price for minerals produced, etc., can only be estimated or "guestimated" within reasonable limits for which no precision can be assigned. Known or Knowable Mineral Economic Parameters Known or knowable parameters are: 1) Tonnage and grade of valuable minerals for the total mineral body and for individual mining blocks. 2) Metallurgical recovery of valuable mineral. 3) Minimum operating life of mineral de- posit at any specified production rate. 4) Royalty schedule, property payments, etc. 5) Sales-purchasing agreements, smelter schedules, marketing contracts, etc.

Jan 1, 1980

By V. M. Dobrynin

Experimental data demonstrate that physical properties of porous rocks change under pressure. In this paper an assumption is made and proved that under pressure the changes of physical properties such as porosity, density, permeability, resistivity and velocity of elastic waves are controlled to a large extent by the pore compressibility of rocks. It is also shown that the pore compressibility of rocks can be determined, within the range of pressures from 0 to 20,000 psi, by knowing the maximum pore compressibility and the magnitude of the pressure. Mathematical equations were developed which permit one to define changes in physical properties of porous rocks under pressure. These equations were verified by experimental data obtained from the study of sandstones. INTRODUCTION In studying the behavior of porous rocks under pressure in the field of petroleum technology, the most interesting aspect is the observation of those properties which characterize the rocks as possible reservoirs — for example, porosity, permeability, resistivity, density and the velocity of elastic waves. The literature dealing with this problem mainly contains data concerning the study of only one or at most two of these parameters, but not of the group as a whole. An attempt is made in this paper to find general equations involving each of these parameters, which will permit the study of the behavior of rocks under pressure. All experimental data used here were obtained from the investigation of consolidated sandstones. EXPERIMENTAL In addition to the use of published experimental data, an experiment was carried out which studied the main physical properties of sandstones under pressure. Two homogeneous quartz sandstones were chosen for this purpose: (1) the Torpedo sandstone from Kansas, and (2) the Medina sandstone from Ohio. The porosity of the Torpedo sandstone was 20.2 per cent, and that of the Medina 8.7 per cent. Permeabilities were 45 md and less than 1 md, respectively. Each sandstone contained about 5 per cent clay minerals, consisting mostly of kaolinite and chlorite, which were distributed quite evenly throughout the samples. One cylindrical sample 2 in. in diameter and 5 in. in length was cut from each sandstone and then saturated in a vacuum with a 3N solution of NaC1. This high concentration was used in order to obtain true formation factors and to decrease the swelling of the clay minerals. The methods of mounting the samples and measuring the changes in porosity and resistivity were practically the same as those described by Fatt and Mann.1,2 Changes of resistivity under pressure were studied for sandstones with 100 per cent water saturation, and for sandstones with the irreducible water saturation. The irreducible saturation was obtained by enclosing the saturated rock samples in relatively fine silicate powder so as to remove the water by capillary action. This procedure is described by Orkin and Kuchinski.3 Changes of permeability with pressure were determined at room temperature using nitrogen as the flowing medium. In studying the effects of pressure, one series of measurements was made using an internal pore pressure Pi equal to the atmospheric pressure, while the overburden pressure Pe ranged from 0 to 20,000 psi. A second series of measurements was used over the same range of overburden pressure, but with an internal pore pressure of 1,800 psi. When the results were compared on the basis of net overburden pressure (Pe — 0.85 Pi ), there was practically no difference for these two sandstones. The origin of the factor 0.85 in the expression for net overburden pressure is given by Brandt,4 Fatt5 and Geertsma.6 The relatively large bulk volumes of the sample (about 15 cu in.) made it possible to observe a

By R. J. Reynik

A semiempirial small flunctation theory of diff- sion in liquids is presented, which employs a fluctuation energy assumed quadratic for a small atomic or molecular displacement and Einstein's random-iralh model. The resulting diffusion equation is given by In these equations. D is the diffusivity, is the average liquid shite coordination number (at interatomic distance d. cm. T is the absolute temperature, xu. em, is (the diffusive displacement. K, is the quadratic fluctuation energy force constant, and rg, cm, are the radii oj diffusing atoms A and B, respectively. The quantities Xn and K are calculated from the computer-filled values of the slope and intercept. respectively. The radius of self-diffusing atom or radii and of diffusing atoms A and B are eta United and compared with values reported in the literature.. The predicted linear variation of diffusivity with. It tempera lure htm been observed in approximately thirty-iire metallic liquid systems, and in over seventy-fiee other liquid systems, including the organic .alcohols, liquified inert gases, and the molten salts, ALTHOUGH the average density within a macroscopic volume element of liquid is constant for fixed total number of atoms. pressure. and temperature, there exist microscopic: density fluctuations within the respective volume element. As such the microscopic volume available to an atom and its Z first nearest neighbors at any instant of time fluctuates above and below the average volume available to these atoms. If one assumes that liquid state atoms vibrate as in a solid. and further postulates that the mean position of any atom in the liquid state is not stationary. but shifts during every .vibration a distance 0 5 j 5 xo. then every atom in the liquid state continuously undergoes diffusive displacements which vary in the range 0 5 j 5 ro. Mathematically. for a binary liquid system consisting of atcrms A and B. the maximum diffusive displacement. .YO, is defined by the equation: where d is the average liquid state interatomic distance at specified liquid state coordination number Z. and v~ \ and vg are the effective radii of diffusing atoms A and B: respectively. For self-diffusion. r^ equals rg , and Eq. [I.] reduces to: It is interesting to note that Eq. [l] or [2] can be used to compute the radii of the diffusing atoms, provided one had an experimental evaluation of xo. As such. the computed radii could be compared with metallic or crystallographic ionic radii to ascerlain the electronic character of the diffusing atoms. Thus it is proposed that in the liquid state the n~otion of an atom relative to its original equilibrium position of oscillation represents the thermal vibration of any atom and its Z first nearest neighbors. while the small and variable displacements. 0 5 1 5 xc,. of the centers of oscillation represent the complex diffusive motions of the atoms at constant temperature and pressure. This is consistent with data obtained from slow neutron scattering by liquids1 ' and resembles an itinerant oscillator model of the liquid state.'" It is further postulated that the atomic displacements characterizing the liquid state diffusion process are essentially a random-walk process. As such. it nlay be described by Einstein's equation:' where D is the diffusivity. sq cm sec-'. j2 is the mean square value of the diffusive displacement. and i> is the frequency of density fluctuations giving rise to diffusion. FORMULATION OF DIFFUSION EQUATION The effective spherical volume occupied by an atom, as a consequence of a microscopic density fluctuation which enlarges the volume available to any atom, exceeds its average liquid state atomic volume by an amount: where AV is the enlarged spherical volume, v is the radius of the diffusing atom. and j is the elementary displacement distance from the original center of oscillation of the vibrating atom to a new center of oscillation position. For small atomic displacements. where c is a constant whose value depends upon the assumed geometry of the enlarged volume. For a spherical increase in volume, c equals 4nr2. Following the treatment of Furthl' and ~walin." assuming the enlarged volu~nes AL7 for the diffusing atoms are distributed in a continuunl. the probability of finding a fluctuation in the size range 0 5 j 5 xo defined by Where c includes the geometric constant cl and Eij) is the fluctuation energy causing the volume change. But the proposed model assumes all the Z first nearest-neighbor atoms are centers of oscillation. and hence the probability that any of these atoms is adjacent to a fluctuation of magnitude 05j5xo is unity. Thus:

Jan 1, 1970

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By L. R. Raymond, J. L. Hudson

This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well-bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time. Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed pertneability value. From the slope of the injection-rate curve. a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result. Graphs of pressure and injection rate us functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can he used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested. The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility. INTRODUCTION To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimu- lation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists. Several techniques for determining reservoir transmissi-bility from well tests have been presented in the literature. 1,2,3,4 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry Out. and this paper contains the first available method for the analysis of constant-pressure well tests. Determination of wellbore damage from transient well tests has been the subject of several papers."" From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage. All previous studies of well testing to determine wellbore damage have been based on the two-zone perrneability model. In this model the damaged zone has a permeability k,, extending to a radius r,,, and the formation permeability k obtains from r, to the drainage radius r,.. Consequently, there is a discontinuity in permeability at r = r,,. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests. ANALYSIS OF CONSTANT-PRESSURE WELL TESTS The mathematical analysis associated with the injection of fluid at constant wellbore pressure into a single-zone, horizontal reservoir completely filled with a fluid of small and constant compressibility and constant viscosity is given in Appendix A. In this analysis it is assumed that the well is located at the center of an undamaged, circular drainage area. From this analysis, the formation permeability can be obtained as follows. 1, Estimate a value for the formation permeability k. 2. Prepare a plot of injection rate q vs

Jan 1, 1967

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?') is described. Essentially it involves the 'floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?' and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?' is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,' or foil,' specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.' Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?') is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?'/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?'/? or the absolute value of ?' for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?' for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?'/? is large; that is, for cases where no other technique is available for measuring ?'. Aside from trying to learn more about surfaces through measuring ? and ?', the primary reason for wanting values of ? or ?' is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.' where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?' vs ki, it is thus possible

Jan 1, 1963

By Evans B. Mayo

This study examines the structural framework of the Southwest for evidence of the four principal trends of lineament tectonics. It attempts to classify their intersections and compares the positions of those trends that appear most favorable with the positions of the presently known mining districts. This is a controversial topic. The author, in presenting his analysis, is aware that the study of lineament tectonics and relation of ore districts to regional structure is complicated by insufficient data and, unavoidably, by personal bias. The development of lineament tectonics has been summarized by Umbgrove.' Early attempts to fit ore districts into the Cordilleran framework were made by Billingsley and Locke, who do not refer to lineament tectonics, although their appoach is similar; they observe that heat and fluids, including the ore-depositing fluids, are most likely to rise at or near intersections of major structures where the crust is fractured, or weakened, to great depth. As a result of studies distributed over the earth-including ocean basins as well as continents— some tectonists recognize four dominant structural trends: 1) northwest; 2) northeast; 3) nearly east-west, or equatorial; and 4) nearly north-south, or meridional. Baker' proposed a theory to account for these trends and Sonder" called their world-wide arrangement the regmatic shear pattern. Moody and Hill proposed a much more complicated shear network which, although fascinating and perhaps ultimately useful, will not be followed here. In a recent review of deformation within the Cordillera, Wisser mentioned the four fundamental directions. The fact that many geologists deny the existence of the regmatic shear pattern implies that the fundamental structures are far from obvious. It may mean, also, that some geologists are not accustomed to examine regional and world maps analytically. The maps require much study, and certain features should be isolated on overlays. Even so, with the present limited knowledge, uncertainties remain. The following analysis is a qualitative experiment, subject to change as information accumulates, and should be supplemented by the western sheet of the Tectonic Map of the United States.' Many have probably gained the impression that the Cordillera of the West is oriented northwest-southeast and from this, unless experience rules otherwise, it is natural to assume that the structure likewise trends northwest-southeast. To an important extent this is true, yet anyone tracing off the western sheet of the Tectonic Map all the recorded north west-southeast structures may be surprised to see what a small part of the entire area they occupy. In southwestern U. S. (Fig. 1) the northwest-southeast structures are mostly restricted to the eastern, southern, and western parts. The eastern margin of the Cordillera from northern Colorado to the International Boundary near El Paso, Tex., is obviously determined by some structure other than northwesterly ones. In eastern Nevada and far southward toward the Gulf of California many mountain ranges, valleys, and faults are meridional. In the Rocky Mts. of Colorado, and at many places in southern Arizona, the crystalline Pre-Cambrian is foliated northeast-southwest. The Uinta Mts. of Utah trend approximately east-west, in much the same way as a broad belt of transverse, west-northwest structures—the Texas lineament of Hill",' and Ransome10 in southern Arizona, southwestern New Mexico, and southern California. It seems, then that there are four regmatic shear directions in the Southwest, but at many places they are discontinuous, and their projections must be inferred. To clarify these trends the four sets have been isolated into two systems: 1) northwest-northeast and 2) east-west-north-south (Figs. 2 and 3). Northwest-Northeast System: A number of prominent northwest-trending zones of structure are easily recognized. They are designated by circled Roman numerals, the northeast-trending structures by circled capital letters. Perhaps no two geologists would agree completely on the positions of all these belts. Names given below are for convenience only, and may be discarded where other names have priority. (I) The Sierra Nevada-Lower California belt contains the Jurassic-Cretaceous granitic massifs of the Sierra Nevada and Lower California. These

Jan 1, 1959

By J. D. Verhoeven

The effectiue distriblltion coefficient has been Measured in a series of vertical, normal freezing experirtzents with large current densities passing through the solid-liquid interface. The results indicate that the effect of the current on solute redistribution is due to electvotransport in the liquid. The high currents produced extensive mixing in the liquid which was considerably reduced by solidifying in small lubing. Analysis of the convection indicates that it probably vesulls from a horizontal temperature gradient produced by the Joule heating- of the electvic crirver~t. Due to the strong dependence of this convection upon the specimen radius, it is conclnded that only for specit~ens with radii of less than somewhere between 1 and 2 mm wilt electric field freezing be getlerally effec-tire at enhancing the purification of zone-melting experittierats in loe-melting alloys. Experiments on 0.8-mm lubes illustrate some interesting potential applications of this techniqne as a means of solute control on smcrll specimens. In a number of papers published within the last few years'-4 it has been found that passage of large dc currents through the solid-liquid interface of a freezing alloy produces a change in the solute redistribution accompanying the solidification. It had been predicted theoretically by Hucke et al.s and by Pfann and Wagner that such an effect would occur as the result of electrotransport within the liquid boundary layer at the solid-liquid interface. These authors independently derived the following relation between the effective distribution coefficient and the variables of the process: Where k0 is the equilibrium distribution coefficient, V is the mobility of the solute relative to the solvent, E is the electric field intensity, D is the solute diffusion coefficient, R is the rate of interface motion, and 6 is the boundary layer thickness. Both groups of authors show that this equation predicts the possibility of extending the purification ability of zone-melting experiments by the addition of an electric current. However, there are other effects in addition to electro-transport which could be produced by the high dc current and might, perhaps, invalidate the applicability of Eq. [I]. For example, high electric current might affect the interface reaction or perhaps the equilibrium distribution which was assumed to exist at the interface. It was the purpose of this work to determine the applicability of Eq. [I] by systematically investigating a simple system for which all of the necessary parameters were known. It was of particular interest for speculating on the potential usefulness of this technique to determine the maximum practical field intensities obtainable, and the effect of these high fields upon convective mixing in the liquid. The initial work in this study was published in a previous paper3 which will be referred to as I. In that work, a current density of 2000 amps per sq cm was used with specimen diameters of 5 mm. The results gave a qualitative confirmation of Eq. [I.], and also showed that a large amount of convective mixing was produced in the liquid by the current. The present study is an extension of that work to smaller specimen diameters and higher current densities. Two points were overlooked in I and will be emphasized here: a) the value of ko has not been well-established in the Sn-Bi system and b) the observed convection could be due to thermal convection produced from the Joule heating. EVALUATION OF k0 To evaluate Eq. [ I.] it is necessary to know the value of the equilibrium distribution coefficient, k,. Tn I the value of k, was taken as 0.3 from a published phase diagram.7 According to ansen' the best data on the phase boundaries of the Sn-Bi system are those of Davidson.5 The data of Davidson give a k, value ranging from 0.21 to 0.25 for the compositions studied in this work, or an average value of around 0.23. In a recent publication, Rigaud and Tougas'10 determined ko by means of a solidification technique. For an alloy of approximately the same composition as that used in this work they obtained a ko value of 0.39. Hence, there is considerable uncertainty in the value of ko and, consequently, a series of experiments were made to determine k, more accurately.

Jan 1, 1968

By Craig R. Barreft, Oleg D. Sherby

The steady-state creep characteristics of pure polycrystalline copper were studied in the temperature range 400" to 950°C and in the stress range 400 to 7000 psi. Tests were conducted in dry deoxidized hydrogen and all specimens exhibited high ductility before fracture. Two activation energies for creep were established as a function of temperature. Above about T/T, = 0.65, the activation energy for creep was 48,000 cal per mole whereas between 0.5 and 0.65 T, it was 28,000 cal per mole. The observed temperature dependence of the activation energy for creep follows the same trend as exhibited by the self-diffusion coefficient of copper in copper single crystals and silver in silver single crystals. It is therefore believed that the rate-cmtrolling mechanism in creep of copper in the stress and temperature range studied is diffusion-dependent and is probably associated with a dislocation-climb process. The low activation-energy region is attributed to enhanced volume difFusion from the presence of dislocations which act as short-circuit paths for diffusion. THERE is extensive experimental evidence1,2 that the activation energy for creep, Q,, for pure poly-crystalline metals tested at temperatures above one half the absolute melting temperature (0.5 Tm) is a constant and equal to the activation energy for volume self-diffusion, Qsd This equality is generally interpreted as meaning that creep in this temperature range is controlled by a dislocation-climb process. The existence of high-temperature creep activation energies not equal to the respective self-diffusion values has been suggested both theoretically3"5 and experimentally.6-8 Two examples of apparent nonequality between Q, and Qsd have been reported for the cases of silver7 and copper,' where activation energies for creep much lower than those for self-diffusion persist to rela- tively high temperatures (up to 0.6 T,). These observations suggest that dislocation climb may not be the only important process in the high-temperature deformation of these metals. That dislocation climb does indeed occur relatively slowly in these two metals due to their low stacking-fault energy has been suggested by many investigators.9-10 Although the creep behavior of copper has been studied extensively at low temperatures, the high-temperature activation energy for creep is not well-defined. The data of Feltham and Meakin8 indicated that Q, is temperature-dependent above one half the melting temperature, equaling a value of -30,000 cal per mole at temperatures up to 550°C and increasing to a value of -49,000 cal per mole at 700°C. No data has been reported above 700°C. The value of 49,000 cal per mole is very near the value of Qsd for copper reported by Kuper et al." as 47,100 cal per mole. In view of the lack of high-temperature creep data and the apparent temperature dependence of Q, for copper the present investigation was undertaken to determine the value of Q, over the temperature range of 400" to 950°C. It was hoped that such a study would clearly document the temperature dependence of Q, and yield significant information as to the nature of the rate-controlling creep mechanisms. MATERIALS AND PROCEDURES The material used in this investigation was high-purity OFHC copper. After rolling and recrystal-lization treatments spectrographic and chemical analyses showed only 0.0008 pct Ag, 0.0002 pctCa, 0.0002 pct H2, and 0.002 pct O2 as trace impurities indicating a purity of greater then 99.995 pct. Specimens were machined from cold-rolled sheet and the gage sections polished with 2/0 emery paper prior to annealing treatments. Annealing was done in both vacuum and dry deoxidized hydrogen atmospheres. No variation in creep strength was found as a result of the different annealing atmospheres. The final annealing temperature was either 700°, 800°, or 1000°C depending on the temperature range to be studied. These treatments resulted in average grain diameters of 0.03, 0.4, and 1.0 mm, respectively. The precise mechanical-thermal history of these

Jan 1, 1964

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

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 N. K. Chen, R. B. Pond

IN the study of slip band* formation, there have been many examples to show that they do not always appear as lines traversing the entire crystal, but as segments whose ends seem to vanish in their path through the crystal. This characteristic appearance of slip bands has been witnessed under the optical microscope at various magnifications'-' and also under the electron microscope.' A typical example of this behavior seen with the optical microscope is shown in Fig. 1. However, the slip band studies were generally conducted on polished surfaces of single or poly-crystalline metals which had been previously deformed; i.e., the load was generally released so that the observation could be made. Any picture of slip bands so obtained can represent the surface phenomenon only in a static state of the strained material. The conditions prior to their formation cannot be definitely and clearly assigned. Thus, while a segmented slip band may suggest that slip is a growth process as supposed by the theory of the nucleation of slip,V he usual appearance of suddenly and fully developed slip bands around the crystal has generally been considered as a consequence of uniform shear of the entire slip plane akin to a cataclysmic process. Little clear-cut information is available with regard to the speed at which a slip band forms, its direction of motion, the geometry of its position with regard to its neighbors, and its dependence on orientation. A description is given in this paper of experimental apparatus by which the progressive formation of slip bands can be recorded while the specimen is undergoing deformation. Qualitative and quantitative data on the dynamic formation of slip bands will be presented with special interest concerning the propagation of slip bands, the spacing of slip bands, and their relations to strain hardening. Views on the formation of slip bands are discussed and a mechanism of the unit process involved in the formation of a slip band is proposed. Preparation of Specimens Single-crystal specimens of high purity aluminum (99.997 pct), 1/8 in. square in cross-section and 1% in. long in gage length, were made by the method of gradual solidification from the liquid state. Since no machining work could be introduced in preparation of crystals of such small size, a special mold was designed for casting them to final shape. The mold consisted of two, separate, high purity graphite blocks. Generally, 20 molds were packed together in one container so that 20 specimens could be obtained by one casting operation. This was desirable since it was possible by this method to obtain groups of crystals with similar orientations. The as-cast crystals were carefully clipped from the gate, etched, and homogenized for 24 hr at 600°C. They were then very gently polished using a 4/0 paper, re-etched, and finally electrolytically polished after the method previously described by Chen and Mathewson.6 The crystallographic orientations were determined using a back-reflection, Laue method. Tensile Testing and Photographic Method The tensile testing equipment for these tests was composed of a specially designed microtensile machine, microload cell and microclip gage with necessary appurtenances. The members of the microtensile machine consisted of three parts, as shown in Fig. 2. The chassis is equipped with an oil cylinder, A, and piston, the piston being part of the movable cross-head, B. Pressure in the oil cylinder is controlled and regulated by an external pneumatic-hydraulic cell, C, which is connected to the cylinder by a Vs in. high pressure copper tube. This cell is half filled with hydraulic oil and has a needle valve, D, on the oil exit side as well as a needle valve, E, on the gas inlet side. A quick-acting valve, F, as well as a pressure gage is provided for the gas side. The oil exits into the load piston on the microtensile machine. By connecting a tank of inert gas to the gas inlet, regulated pressures were provided over the oil so that the oil would leave the cell at a rate determined by the setting of the exit needle valve, the gas pressure, and the pressure of the oil in the load piston of the microtensile machine. With this pneumatic-hydraulic appurtenance it was possible to

Jan 1, 1953

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

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

Jan 1, 1956