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By J. L. Lytton

The flow-stress recovery of high-purity aluminurn following a 10 pct tensile prestrain was studied in terms of a fractional flow-stress recovery parameter fr. The flow-stress recovery behavior was related to the dislocation arrangements using transmissiort electron rnicvoscopy. During recovery at 120° and 160°C, nearly stable strength levels were attained, the strength level for 120°C recovery being greater than that for 160°C. This stabilization of flow stress was related to the formation of meta-stable dislocation networks bounding nearly perfect cells. Both network formation and the annealing of dislocation loops were found to be recovery mechanisms, and the stronger metastable strength level joy 120°C recovery was related to a smaller average cell size. Analysis of the networks was consistent with the reaction of sets of dislocations with a/2 (110) Burgers vector to give product Burgers DURING isothermal annealing of cold-worked metals, a degree of softening occurs without re-crystallization, and the processes responsible for this change are termed recovery processes. During recovery annealing, the dislocations generated during cold work become rearranged into low-energy configurations, and as much as 50 pct of the stored energy is released."' The relationship between this rearrangement of dislocations and mechanical behavior is of considerable importance, since the dislocation substructures formed during recovery provide a significant degree of low-temperature strength3j4 and can favorably alter the course of primary creep at high temperatures.4 The purpose of the present study was to relate the flow-stress recovery behavior of high-purity aluminum to the substructural modifications that occur. Electron transmission microscopy was therefore employed for direct observation of dislocation substructures at various stages of recovery following 10 pct prestrain. Several investigators5-' have proposed that dislocations can become rearranged or lost during the preparation of thin foils. It was found early in the present study that the dislocation structures in the thicker regions of the foils changed in a systematic way during the course of recovery. Therefore, it is unlikely that substantial losses or rearrangements occurred during thinning. This point will be discussed in more detail later. The results of various investigators indicate that recovery processes in fcc metals can result in release of 50 pct or more of the total energy stored in the as-prestrained metal, this percentage decreasing with increasing prestrain.' Alloying elements or impurities tend to increase this percentage. The release of stored energy of fcc metals during recovery appears to occur by 1) annealing of point defects if the deformation occurred at sufficiently low temperaturesg and 2) rearrangement of dislocations into low-energy Configurations.1,2In bcc metals, the annealing of dislocation loops has also been observed during recovery after prestrain,10-12 and it has been proposed that this is a recovery mechanism for unidirectionally strained fcc metals.' The density of dislocations in bcc metals has not been observed to decrease appreciably during recovery,10 although the formation of regular dislocation networks has been observed. has shown that the formation of such networks can result in elimination of long-range stresses and can lead to significant release of stored energy without dislocation annihilation. It might thus be expected that network formation is a significant recovery mechanism in fcc metals, although extensive network formation has apparently not been reported in controlled recovery experiments. The formation of sub-boundaries in aluminum has been observed by various investigators13'17 during recovery studies of aluminum, but the structure of these boundaries was not resolved. In this regard, it is significant to note that Bailey and Hirsch,' using transmission electron microscopy, detected no network or sub-boundary formation during recovery of 99.99 pct Ag. Furthermore, Clarebrough et al.2 found no such rearrangements during recovery of copper. EXPERIMENTAL PROCEDURE The high-purity aluminum used in this investigation was obtained in the form of 0.125-in.-thick sheet. Spectrographic analysis revealed that the sheet was 99.995 pct A1 with the following weight-percent impurities: 0.001 Cu, 0.002 Fe, 0.001 Si, and 0.0004 Mg. The as-received sheet was in the heavily cold-rolled condition. The as-received sheet was cold-rolled at room temperature to 0.040-in.-thick sheet in the longitudinal direction, which was the original rolling

Jan 1, 1965

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

Self-diffusion coefficients have been measured for iron in wustite (700° to 1000°C) and for cobalt in cobaltous oxide (800&apos; to 1350°C) by means of radio-isotopes. Both sectioning and decrease of surface-activity methods have been used and a particular shortcoming of the latter method has been disclosed for wustite. The effects of oxygen pressure on the composition of cobaltous oxide and on the diffusion coefficient of cobalt in the oxide have been established. The effect of the preparation conditions of the cobalt-oxide specimens on the diffusion measurements has been determined. It has been concluded that diffusion of cobalt occurs via vacant cation sites and that a cobaltous-oxide disk reaches equilibrium with its environment in a time which is very short compared with that needed for diffusion of the radio-isotope. THE availability of radioactive isotopes in recent years has permitted the measurement of many self-diffusion coefficients which were hitherto impossible to determine. With the advent of radioactivity, the method of measuring diffusion coefficients has also changed. The earlier sectioning method by which the concentration profile of the diffusing species was determined in the diffusion specimen has often been rejected in favor of the decrease of surface-activity method first developed by Von Hevesy,&apos; and extended by Steigman, Shockley, and Nix,&apos; and Raynor, Thomassen, and Rouse." With the experimental arrangement where an infinitely thin deposit of tracer is diffused into a semi-infinite cylinder, the decrease in activity of the active face due to diffusion of the tracer into the specimen is measured by counting the active face before and after diffusion. Under these conditions, the appropriate solution of the diffusion equation is R = e*(l-<K/Z) [1] where R is the ratio of the counting rates after-to-before diffusion, $& is the Gaussian error integral of \/Z, and Z is defined as Z = p2Dt, p being the linear-absorption coefficient of the detected radiation in the diffusion specimen, D the self-diffusion coefficient, and t the diffusion time. In the older sectioning method the concentration distribution of the tracer is found after diffusion by analysing thin parallel sections cut from the active face of the diffusion specimen. As seen from the solution of Fick&apos;s second law for the distribution of an infinitely thin source after diffusion into a semi-infinite cylinder the log of the concentration plotted against x&apos; will be a straight line of slope log e/4 Dt. The diffusion coefficient thus can be calculated directly. The units of the tracer concentration are completely arbitrary, since any change in units does not change the slope of the log c vs x2 lot. Although both of the above methods have been widely used, a thorough experimental comparison does not appear to have been made. Birchenall and Mehl,&apos; during an investigation of the self-diffusion rate of a and r iron by the surface method using Fe" tracer, diffused and sectioned one welded couple. The diffusion coefficient from this run agreed with those by the surface method. Buffington, Bakalar, and Cohen," during an investigation on a and y iron

Jan 1, 1955

By A. M. Turkalo

IT is a well-known fact that martensitic steels show a greater resistance to brittle fracture than do pearlitic and bainitic steels. It was, therefore, thought worthwhile to investigate the mode of brittle fracture with respect to structure by studying the effect of various austenite decomposition products on the propagation of brittle fracture in steel by means of electron microscopy. Newly developed replication techniques together with the advantages of the electron microscope such as great depth of field, available high magnification and easy adaptation to stereophotography make electron microscopy very suitable for fracture studies. EXPERIMENTAL PROCEDURE An essentially plain carbon steel containing 0.56 pct C, 1.30 pct Mn, 0.02 pct P, 0.03 pct S and 0.22 pct Si was used in this investigation. The following table gives the heat treatments used to obtain the various austenite decomposition products: The resulting austenite grain size from the 870°C austenitization treatment was about an ASTM No. 7 grain size. The specimens which were 2 in. long, 1/4-in. diam bars were austenitized in a tube furnace through which argon gas was blown. The tube was not, however, air-free and the specimens were not completely oxide-free. Isothermal treatments were done in a lead bath. With the exception of the fully hardened specimen and the one as-isothermally transformed at 300°C the heat treated specimens were notched in the following fashion with a jeweler&apos;s saw. A cut about 0.08 in. deep was made perpendicular to the length of the bar. The specimen then was rotated about 45 deg and another cut about 0.08 in. deep was made. In the case of the hard martensitic and bainitic specimens, only one cut was made and the depth was not controlled. The design of the two-cut notch caused fracture to initiate at the point of intersection of the two saw cuts. The specimens were broken at -196°C in a Charpy impact testing machine. In order to hold the specimens securely in the impact machine two square pieces of mild steel were made about 5/8 in. long having the same cross section as that of a standard Charpy specimen but containing a hole 1/4 in. diam through the center of the cross-section. These adapters were slipped over the ends of the test specimen which was then secured tightly by means of set screws in the adapters. The specimen with the adapters was cooled to -196°C in liquid N,, then placed in the impact machine and broken within 3 sec. One half of the broken specimen was used for the electron microscope study of the actual fracture surface. The other half was nickel-plated and a cross section through the notch and fracture was polished for electron microscope examination. Carbon replicas of the fracture specimens for the electron microscope study were made essentially according to Bradley&apos;s evaporation technique.&apos; Both direct carbon and two-stage carbon replication techniques were used. In the case of the direct carbon technique, a thin layer of carbon was evaporated first at an angle of about 45 deg to the mean fracture surface and then another film of carbon was evaporated normally to the fracture surface. The carbon replica was freed electrolytically.2 The specimen was made an anode in a 10 pct Nital polishing solution. It was etched intermittently by shutting off the power now and then. The freed replica was washed in 40 to 50 pct water solution of nitric acid for 10 min or so, then washed in water and picked up on a screen for examination. The two-stage carbon replication technique involved first making a primary replica of cellulose * acetate from which a carbon replica was then made. One side of a strip of cellulose acetate wet with acetone was pressed lightly against the surface of the specimen, allowed to dry and then stripped. Prior to the deposition of carbon, which was done at 90 deg to the cellulose acetate replica surface, chromium was evaporated at 45 deg. After the carbon evaporation the cellulose acetate was dissolved in acetone according to the Jaffe method3 leaving the carbon replica preshadowed with chromium for examination.

Jan 1, 1961

By P. A. Witherspoon, R. W. Donovan, T. D. Mueller

The use of petroleum-barren aquifers for underground storage has become extremely important to the natural-gas industry. A critical problem in assessing the feasibility of a specific aquifer for such use is the permeability determination of the caprock over the proposed storage project. The approach used here is to conduct both static and dynamic field tests on the aquifer being analyzed. Valuable information on the possibility of communication between the storage aquifer and any other aquifers above can be obtained by measuring hydrostatic water levels and water analyses. Significant differences in such data give evidence of the lack of communication between the intended storage reservoir and other horizons. The dynamic approach requires that one well be pumped in the storage aquifer, and changes in fluid levels recorded in both the aquifer and its caprock. The interpretation of the data from such pumping tests involves the solution of nonsteady radial flow in an infinite aquifer and the influence on such flow of a leaky caprock. A finite-difference model has been used to investigate this problem, and the transient behavior has been solved numerically with a digital computer. It has been found that the pressure transients in the storage aquifer are not affected significantly by moderate caprock leakage. The pressure behavior of the caprock is a much better indicator of the degree of leakage, and generalized solutions for this behavior are included. Field data are presented to demonstrate both the static and dynamic approach. If is concluded that appropriate investigation of the groundwater hydrology in an aquifer-type gas-storage project can provide much valuable information for determining the effectiveness of the caprock to hold gas. INTRODUCTION Underground storage of natural gas in the United States has been developing at a rapid rate over the past few years. In 1955, the total gas-storage capacity was about 1.6 trillion cu ft; by 1961, this figure was almost 3.2 trillion cu ft, an increase of 100 per cent in six years.&apos; This trend un- doubtedly will continue because the economics favor the development of gas storage, as opposed to the construction of new pipelines, to meet the inherent cyclic demand for fuel in the metropolitan areas of this country.&apos; About 15 per cent of the current underground gas storage has been developed in petroleum-barren aquifers, i.e., geological domes or anticlines in which no commercial quantities of oil or gas had been produced prior to the storage operations. The necessity for using barren aquifers outside many metropolitan areas of this country has been due to the lack of depleted oil or gas fields that were near enough and large enough to meet the demands of such consuming areas. Pipeline companies have developed aquifer storage along their transmission lines to meet the fluctuating needs of their complex systems. Considerable thought has also been given to the problem of storing gas in a structureless aquifer, both in this country&apos; and in the Soviet Union outside the city of Leningrad.&apos;," Conditions such as these have led to the development of aquifer gas-storage projects in many parts of the U. S. Most of these developments have centered in the Mid-Continent area, and the greatest amount of activity has been concentrated in Illinois.6 Thus, the use of petroleum-barren aquifers for gas-storage purposes has become extremely important to the natural-gas industry. There are three basic problems in developing aquifer-type storage: (1) finding an adequate geologic structure, (2) finding a suitable storage reservoir within the structure and (3) determining the tightness of the caprock over the intended storage zone. The first two problems can be solved by applying conventional methods of exploration geology, but once these problems are solved, the question arises as to why no oil or gas is present in an otherwise favorable setting. Two situations are possible: (1) an adequate source bed was never present, or (2) a source bed was present but the petroleum seeped away because of a leaky caprock. Determining the tightness of the caprock is one of the most critical problems in assessing the feasibility of a specific aquifer for storage purposes. In attacking this problem, one usually takes cores of the caprock and subjects them to a rigorous investigation. Such core data are desirable, but they only detail the matrix properties and cannot be expected to reveal the gross characteristics of the caprock. Several gas-storage projects in the U. S. have had considerable leakage where

By L. O. Brockway, W. C. Bigelow, J. A. Amy

Specimens of Inconel-X alloy solution-treated at 2050°F and aged for periods of 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F have been examined by electron microscopy and by electron and X-ray diffraction. Four minor phases were identified: titanium nitride, niobium nitride, an M23C6 complex carbide, and the intermetallic ? phase. The two nitrides were found in all of the aged specimens and in the solution-treated alloy, the y&apos; phase formed at all aging temperatures, while the M23C6 carbide formed only on aging at 1200° and 1400°F. Variations in the hardness, rupture strength, creep strength, and yield strength of the alloy have been shown to be related to variation in the size and distribution of the particles of the y&apos; phase within the matrix grains of the alloy, with maximum values of these properties occurring when there is a maximum amount of the phase present and a fine state of dispersion of the particles prevails. THE nickel-chromium alloys containing titanium and aluminum are widely used in applications requiring high strength at elevated temperatures. Studies on relatively simple ternary and quaternary alloys&apos;-4 have indicated that the favorable high-temperature properties of these alloys are related to the precipitation of an intermetallic ?&apos;-phase having a structure based On that of the Ni3A1 phase of the nickel-aluminum system. The present investigation was undertaken to identify the minor phases and to study the microstructural changes occurring in one of the more complex commercial alloys as a result of aging in the service temperature range, with particular emphasis on investigating the role of the ?&apos; -phase. The microstructural changes were studied by electron microscopy and the minor phases were identified by X-ray and electron diffraction. MATERIALS AND METHODS Inconel-X alloy was selected for this investigation because the previous studies of Frey, Freeman, and white6 provided extensive information on the variations in metallurgical properties of this alloy resulting from high-temperature aging treatments. Specimens aged 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F were made available for the present use. These were taken from 1-in. round-bar stock of a commercial heat having the following weight composition: 0.04 C, 0.56 Mn, 6.59 Fe, 0.007 S, 0.38 Si, 0.03 Cu, 73.22 Ni, 14.97 Cr, 0.78 Al, 2.38 Ti, and 1-02 Nb. They were solutjon-treated at 2050 for 4 hr and then water-quenched prior to aging. Powder X-ray diffraction patterns were obtained from insoluble minor phases which were separated from the alloys by digestion in the reagent of Mahla and Nielsen.6 Back-reflection patterns were obtained from electrolytically polished surfaces of the bulk search to detect the ?&apos;-phase&apos; Cu-K a radiation was used in both cases. In the electron-diffraction studies, the general method developed by Heidenreich, Sturkey, and

Jan 1, 1959

By S. R. Balajee, I. Iwasaki

The adsorption mechanism of corn starch and its derivatives at mineral-solution interfaces was investigated by the adsorption of cationic starch, unmodified corn starch, British Gum 9084, and anionic starch on quartz and hematite. The adsorption of these starches, which decreases in the order mentioned, is dependent on the balance between the magnitude of the electrostatic interaction and the magnitude of the hydrogen bonding. There exists a critical starch concentration for both optimum flotation and flocculation conditions of iron ores, which corresponds to a point where the starch adsorption reaches a saturation coverage. Flocculation occurs due to the adsorption of starch via electrostatic and hydrogen-bonding forces and by interparticle bridging as a result of the conformation of starch molecules at the interface. The depressant property of starches and starch derivatives in flotation&apos; and their flocculation char: acteristics in clarification and filtration2.3 have long been recognized on a wide variety of ores. The effectiveness of a starch as a depressant for iron minerals has been the subject of much investigation in recent years both in the amine flotation of siliceous gangue and in the anionic flotation of activated silica from iron ores. It has been reported that the depressant activity of starches and dextrins in the cationic flotation of quartz from hematite increases with molecular weight, branching, and number of hydroxyl groups, 1 and that the selectivity is affected by changing the configuration of starch molecules and the composition of its polar groups.4 ,5 The manner in which starches are solubilized was shown to exert a significant influence as a depressant in the anionic silica flotation, and a series of articles covering the practical aspects of flotation and flocculation have already been reported.618 Chemical modification of the starch structure, the pulp pH, the calcium ion, and the residual starch concentration were identified as some of the more important variables affecting the flotation behavior. In the flocculation of iron ores, it was noted that most starches flocculated suspensions of hematite in water but did not flocculate similar suspensions of quartz,9 and that an excessive use of starch restabilized the suspensions due presumably to protective action. 6 An admirable application of such an observation to practice may be cited in the selective flocculation and desliming in the anionic silica flotation of iron ores, which resulted in superior metallurgy and lower reagent cost. 10 From detailed adsorption measurements, Schulz&apos;and Cooke4 established that the adsorption of starches and their derivatives depended on the types of minerals and of starches, pH, and electrolytes present. Their adsorption data and the foregoing flotation and flocculation observations suggested that an electrical interaction between starches and charged mineral surfaces might be playing a role in their adsorption process. Adsorption of organic polymers, particularly of synthetic origin, at solid-liquid interfaces has been extensively studied in recent years,&apos; and it is realized that their adsorption mechanism is considerably more complex than that of simple ions or molecules. A polymer molecule possesses a number of functional groups, and the adsorption at a point may restrict the adsorbability of adjacent groups. The mechanism may be further complicated by the conformation of the polymer molecules which may exist as coiled spheres, helices, or extended chains as a result of intramolecular interactions among functional groups as well as intermolecular interactions with solvent molecules. The object of the present investigation was to examine the effect of the chemical modification on the adsorption characteristics of starches and starch products on quartz and hematite at several pH values, so that by correlating this information with flocculation and flotation results, adsorption mechanism of starches on mineral-solution interface may be elucidated. EXPERIMENTAL MATERIALS Quartz: St. Peter sand was screened at 35 mesh and the undersize was scrubbed and deslimed at a Fagergren cell. The deslimed sand was cleaned with 0.1 N hot hydrochloric acid and washed repeatedly with distilled water, For anuscript, measurementsl the -200-mesh fraction of the sand was ground dry in a porcelain mill for 3 hr. The specific surface of the finely ground quartz was

Jan 1, 1970

By Rodney L. Stone, David S. Cahn

As part of an over-all laboratory and plant test program to determine mixing ad other techniques for a more economic use of bentonite as an iron ore pellet binder, a settling test for measuring the bentonite content within a pellet or a batch of pellets has been developed. Through this test, it has been shown that dry fracture load is directly proportional to bentonite content in batches of pellets, but inversely propor tional to bentonite content in individual pellets of the same batch. This apparent paradox is explained by a negative correlation between a pellet&apos;s size and its bentonite content and the fact that large pellets can withstand a higher fracture load than small pellets. In past attempts to characterize green and dry iron ore pellets, the authors found large variations in the results of strength tests on closely sized pellets from the same batch.&apos; Reasons advanced for such variations in the quality of pellets in which the binder is bentonite were the presence of internal flaws and the nonuniform distribution of the binder. Even when resulting pellet strength is good, there is still the question of whether the same strength could have been attained through a more effective use of a smaller amount of bentonite. The authors&apos; own and other studies 2-3 have pointed out the strong dependence of pellet strength on the degree of "mixedness" of the iron ore concentrate and the bentonite binder. However, before such a relationship could serve as a guide for the development of better mixing techniques and the associated economy of

Jan 1, 1969

By Robert Thomas

DURING the past 20 years the advantages of reinforced concrete as a substitute for timbering in so-called permanent mine openings have been fully recognized, and its use has become almost general practice in the larger mines. The term "permanent mine openings" is used advisedly and is assumed to embrace such openings as ventilation shafts, material shafts and main hoisting shafts, with their adjacent stations, ore pockets, etc. In the concreting of such openings, the actual cost as compared with that of timbering has been of secondary consideration, the support of large openings, elimination of fire hazards, and prevention of inter-ruptions to production being the primary objectives. The ultimate economy, however, of lining such openings with concrete when they are to remain in use during the entire life of the mine, and especially when they are in bad ground, will seldom be questioned. During this 20-year period there have appeared in engineering publi-cations a number of interesting articles on the use of concrete in mines, nearly always describing some specific project of major proportions, such as the concreting of ore pockets, large stations or main hoisting shafts. Such articles are unquestionably of interest, since the projects require considerable engineering thought, not only in the method of excavating large openings, but in their engineering design as well. Concreting of main hoisting shafts, particularly when this is done with the least possible interruption to production, provides some interesting problems. The concreting of haulage drifts of the dimensions commonly found in mines, on the other hand, soon develops into a routine operation, there-fore it is with some hesitancy that the author attempts to prepare an article on this subject. The writer can recall only one article on the concreting of mine haulageways, although several articles have been written concerning the concreting of tunnels considerably larger in dimensions than those required in general mine practice.

Jan 1, 1936

By D. M. Milne, R. F. Stoner, W. Bakiewicz

The Lower Indus Basin deposits form a substantial unconfined alluvial aquifer of excellent quality. This aquifer contains basically highly saline groundwater, overlain in places by considerable amounts of fresh water whose origin can be traced to the present and historical courses of the River Indus. In the past, the main source of groundwater recharge has been direct river seepage and water tables were generally deep. Since the establishment of a perennial irrigation regime however, deep percolation from the increased irrigation supplies has predominated and the water table has risen to within a few feet of the surface. The river system itself is being progressively devel-oped for irrigation and very shortly a situation will arise where the entire low winter flow will be utilized. Fresh groundwater will then be exploited to supplement the surface supplies, and at the same time a drainage system, mainly based on wells will be used to stabilize the water table at safe depths. This paper discusses some of the methods used to ensure optimum economic development of the fresh groundwater and describes the general design philosophy evolved by the authors&apos; firms for both irrigation and drainage wells, with respect to both well configuration and operation. Water quality standards are discussed insofar as they affect subsequent use of the groundwater. A few particular aspects are considered, including the values of the relevant aquifer constants, the construction of wells, and the determination of screen losses. A major problem solved during the Lower Indus Project investigations has been the design of wells to produce fresh water from layers overlying saline water. This solution is also discussed. The recent interest in the groundwater of the Lower Indus Plains of West Pakistan has two main aspects. Firstly, soil waterlogging and the associated salinity hazards caused by rising water tables are a serious problem in agriculture, and the ease with which drainage requirements can be met by aquifer pumping makes this an obvious solution. The second interest stems from the rapid intensification of irrigation agriculture and the growing shortage of water supplies. In the areas where the groundwater is of suitable quality it can be used immediately for irrigation at relatively small cost and with large financial returns. In addition, the aquifer forms a potential storage reservoir which could be recharged from high river flows and depleted by pumping at times of scarcity. SOURCE OF GROUNDWATER The Lower Indus plain is a relatively long and narrow alluvial basin on a north-south axis, some 23,000 sq miles in area, bounded by higher land to the east and west. One hypothesis to explain the distribution and quality of groundwater in the region1 presupposes a river system considerably larger than, but very similar to the present river. This is characterized by a single mainstream, with subsidiary overspill channels in times of flood, running along the crest of a self-deposited ridge and with an extensive advancing delta. Sea water is contained in the alluvial pores of the advancing delta, forming the native groundwater. This has been partially displaced from two sources, namely direct seepage of fresh water from the river channel in meander flood plain areas and percolation from flood spillage in cover flood plain areas. Percolation has been subject to much re-evaporation and is thus slightly saline even as it reaches the groundwater. The whole complex has been further affected by two main influences: evapotranspiration from the land surface that tends to salinize the groundwater and down-valley flow that tends to bring fresher water

Jan 1, 1970

By E. F. Koppe

The Upper Freeport coal in the Freeport and New Kensington quadrangles, Pennsylvania, varies from a bony streak to a thick coal deposit often exceeding ninety inches, the "Double" or "Thick Freeport". Distinctive basal partings, a central bone layer, and a canneloid top bench may be present. The appearance of a sandstone roof, sandstone rolls, and bony coal at the top of the main coal bench can be anticipated in thin Freeport areas when basal partings are absent. When the two basal partings are present, a shale roof is normal. These effects are correlated with the original topography upon which the coal was deposited. The original depositional high areas tend to coincide with present structural highs. Preliminary data indicate that coal quality, in part, is affected by the deposi-tional setting. In "high" areas, a tendency exists for the main coal bench to contain higher percentages of fusain and mineral matter. Within limits, some-what higher ash fusion temperatures appear to correlate with paleotopographic highs. As a result of these findings, critical examination of the paleotopography and related sediments is indicated in other areas and other coals. The Upper Freeport coal is quite variable both in thickness and composition in the Freeport and New Kensington quadrangles of Pennsylvania (Figure 1). The coal horizon in these quadrangles is marked either by a thin carbonaceous shale bed or by a single bed containing a variable number of partings (binders). The complex coal zone known locally as the "Double" or "Thick Freeport" contains the Upper Freeport Coal Bed at the base; but in addition, it has an overlying bone layer and an upper coal bed occasionally capped with a canneloid layer. The "Thick Freeport" often exceeds 90 inches in thickness, whereas the normal Upper Freeport coal usually varies between 34 and 50 inches.

Jan 1, 1961

By W. M. Robertson

The kinetics of grain boundary groove formation on copper surfaces immersed in liquid lead have been studied over the temperature range of 400° to 900°C. The groove widths were Proportional to the cube root of the annealing time, indicating that the diffusion of copper through the saturated liquid-lead solution is the mechanism by which grooves form. The rate constant for the process can be calculated by a theory due to Mullins. Using published data for the solubility of copper in liquid lead, for the interfacial energy of the solid copper-liquid lead interface, and for the diffusion coefficient of copper in liquid lead, the calculated rate constants almost exactly reproduce the measured values over the entire temperature range. The decay of scratches placed on copper surfaces has also been studied. The rate constant for scratch decay agrees with that for grain boundary groove growth, though scratch decay is sensitive to convection currents in the liquid. The interaction of solid and liquid metals has been studied extensively and has been found to be rather complex. Many of the studies have been complicated by a host of competing effects, including temperature gradients, concentration gradients, the formation of one or more intermetallic phases, natural or forced convection, and the presence in both the solid and liquid of considerable amounts of impurities and alloying elements. Recently theories have been developed of changes in surface profiles driven by capillary forces,&apos; which allow the interaction of the solid and liquid to be analyzed quite directly. The present paper reports a study of the formation of grain boundary grooves on pure copper immersed in liquid lead, which allows the theory to be checked quantitatively. The Cu-Pb equilibrium diagram is quite simple: there are no intermetallic compounds, copper is just slightly soluble in liquid lead, and lead is almost completely insoluble in solid copper.2 The Cu-Pb system has been studied extensively,3-9 and all of the quantities—interfacial energy, diffusion coefficients, and equilibrium solubilities-necessary to calculate the rate of groove growth by a volume-diffusion mechanism are known. The kinetics of grain boundary grooving and scratch smoothing have been studied on the noble metals and the iron group metals in a reducing atmosphere or in vacuum.10 The main interest of these studies has been the determination of surface-diffusion coefficients at metal-gas interfaces using the theories developed by Mullins.1 The present paper uses similar methods for the study of diffusion processes at the interface between two condensed phases. There has been one previous study" of the kinetics of groove growth in a solid-liquid system, which, however, was troubled by the fact that neither interface energies nor diffusion coefficients were known in the Ni-S system studied. THEORY The theory of grain boundary groove growth has been developed by Mullins for the cases of volume diffusion," surface diffusion," and a combination of the two processes.14 He has also analyzed the kinetics of the flattening of a scratched surface by these processes.l5,l6 Several assumptions and approximations were used in the derivations of the surface profile shapes. The applicability of these assumptions and approximations to the present system will be considered in the discussion. At the intersection of a grain boundary with an initially flat interface the equilibrium between the interfacial energy and the grain boundary energy establishes an equilibrium groove angle. This induces curvatures in the interface. The chemical potential of material at a curved interface is higher than at a flat interface, so that material moves away from the region of the grain boundary. Mullins&apos; calculations indicated that the groove profile would be similar to that shown schematically in Fig. 1. Small humps form above the level of the original flat surface. For a volume-diffusion mechanism the separation, w, of these humps at a time, t, is given by and where co is the equilibrium concentration of the solid in the liquid, y, the solid-liquid interfacial free energy, O the volume occupied by a solute atom in the liquid, D the diffusion coefficient of the solid in the liquid, and kT has its usual meaning. For a surface-diffusion mechanism the groove width is proportional to the fourth root of the time. For grooves forming by a combined surface and volume-diffusion mechanism the exponent of the

Jan 1, 1965

By N. Mungan

Formation damage, i.e.. reduclion in permeability, has been generally attribuled to clay minerals which expand or disperse upon contact with water that is less saline than the connate water. Luboratory, studies show that penneahility reduction can also occur in formalions containing only nonexpandable clays such as illite or kaolinite, and can be caused also by changes in pH. Furthermore, pH changes can damage even formations that are essentially free of clays. It is suggested that permeability reduction is due to the small passages being blocked by particles, which may be dispersed clays, cemenlion material or other fine parricles. These particles are dislodged by dispersion of clays due to changes in salinity or by dissolution of calcareous cement by acids, or of silicaceous cement by alkaline solutions. In working with reservoir cores, it was found that extracted cores damaged more easily and extensively than nonextracted cores. The extent of damage depended also on tenlperatltre. INTRODUCTION Permeability is an important property of porous media and has been the subject of many studies by engineers and geologists. Many of these studies are conccrned with formation damage, i.e., reduction in permeability, resulting from exposure of oil-producing formations to water substantially less saline than the connate water. This effect causes understandable concern since during drilling, completion and production phases formations are often exposed to fresh water. The damage resulting from contact with relatively fresh water has been attributed to expansion and dispersion oF clay minerals. During laboratory investigation of the use of NaOH as a wettability reversal agent to increase oil recovery from oil-wet reservoirs, several cores used in the displacement studies suffered loss in permeability. Despite the traditional usage of NaOH for conditioning aqueous mud systems, the role of the caustic filtrate in wellbore damage seems to have been overlooked. Browning2 as recently reported on the effects of NaOH in dispersing clay minerals but he was concerned only with complications that may arise in drilling massive shale beds. The following study was made to examine the role of pH and salinity changes in core damage. Where cores from reservoirs were used, tests were performed with extracted and nonextracted cores both at room and reser- voir temperatures, since it was felt that the test environment and core condition may affect the results. Because of its limited coverage and exploratory nature, this study is not intended to provide answers to field formation damage problems. It is hoped that it will encourage research into new aspects of the permeability reduction problems, particularly those allied to new recovery and production processes. PROCEDURE In all permeability tests, fluids were pumped through the cores at a constant volumetric rate. Only deaerated fluids and reagent grade chemicals were used. The fluids were passed through two ultrafine filters before injection to remove any entrained particles. The cores, with the exception of the unconsolidated cores, were mounted in Hassler holders. Water was used to transmit pressure to the sleeve. The inlet endpiece had two entry ports which permitted scavenging one fluid with another to avoid any mixing in the small holdup volume. The cores were flushed with CO2 gas, evacuated for 5 to 6 hours and saturated with the first liquid at a pressure of 1,000 psi for 24 hours to eliminate any free gas from the cores. Pressure differences up to 20 psi were measured by transducers, calibrated in inches of water and continuously recorded. For greater pressure drops, gauges were used. All reservoir cores were cleaned with a light refined mineral oil, then with heptane, and finally dried with CO2. Compatibility tests showed that no precipitates formed when mineral oil and the crudes were mixed. Some cores were extracted in Dean-Stark-type solvent extractors using xylene and trichloroethane and dried in a vacuum oven at 450F. Each test consisted of a sequence of water, test solution, and again water flow. RESULTS AND DISCUSSION STUDIES IN BEREA CORES Salinity Contrast Berea cores 2-in. in diameter and 12-in. long were cut from sandstone quarried in Cleveland, Ohio. The clay minerals were identified by X-ray diffraction to be chlorite, kaolinite, illite and incerlayered illite. Flow of fresh water or 30,000 ppm brinc does not cause any permeability reduction (Fig. 1). However, after injection of brine the core is readily damaged by fresh water. Damage starts almost instantly as the fresh water injection is begun, and at a cumulative injection of 1.2 PV fresh water, the permeability has dropped from 190 to 0.9 md. Upon continued injection, the effluent contains clay minerals dislodged from the core. The final core per-

Jan 1, 1966

By P. A. Witherspoon, S. P. Neuman

Evaluating the permeability of a caprock overlying a potential gas storage reservoir is a very critical problem. Pumping water from the reservoir can be used as an evaluation tool in analyzing this problem. Fluid level changes that occur in the aquifer us well as in the caprock can be measured with appropriately placed wells. If the leakage of water from the caprock into the aquifer is considerable, the effects will be apparent in the aquifer. If the leakage is slight, however, it will not be possible to detect it with certainty from observations in the aquifer alone. Fluid level measurements in the caprock must be relied upon. and improved methods of analyzing such effects have been developed which are based on a theoretical analysis of fluid flow through a caprock of infinite thickness. An example applying these methods to field data is discussed. INTRODUCTION One of the most critical problems in evaluating an aquifer gas storage project is determining the tightness of the caprock overlying the formation to be used as the storage reservoir. A formation that has previously held oil or gas obviously has a suitable caprock, but an aquifer that contains only water gives no such assurance. A number of aquifer projects in the United States have been troubled by gas leaking out of the intended storage zone, and the ensuing difficulties have led to the development of new evaluation methods. One of these new methods is pump testing wherein water is removed from the aquifer at some controlled rate prior to injection of gas. This fluid withdrawal causes a pressure drop to move out through the aquifer for considerable distances in a matter of days or weeks. Depending on the properties of the caprock, a pressure transient can also pass upward (as well as downward) through the caprock layers adjacent to the aquifer. Thus, if the operator has placed observation wells at appropriate distances from the pumping well, the rapidity with which the pressure transients reach different points in the system can be used to investigate the fluid transport properties of both the aquifer and its caprock. The usefulness of pump testing has been recognized by groundwater hydrologists for many years as a means of determining the potential yield and properties of aquifers used in water supply They have introduced the term "leaky aquifer" for a system in which an aquifer is overlain (or underlain) by semipermeable caprock layers. The ease with which water leaks into the aquifer during pumping can, of course, be very beneficial in bringing additional water to the pumped well. Hydrologists have therefore devoted considerable attention to this prob-lem. From the gas storage standpoint, however, the tighter the caprock layers that overlie the intended storage reservoir, the better are the conditions for minimizing or eliminating any vertical migration of gas. Thus, after a suitable geologic structure has been found, the emphasis in aquifer storage projects is in determining that the caprock is tight. Attention has recently been focused on the use of pump testing as one approach to solving this problem.23,24 This paper presents a further development on evaluating the permeability of a slightly leaky caprock when the caprock is of infinite thickness. From the practical standpoint, this means that the caprock layers are thick enough that pressure transients do not reach the outer boundaries of the system during the pumping test. In a subsequent paper, an analysis of the case where the caprock is of finite thickness will be presented. PREVIOUS WORK ON LEAKY AQUIFERS Jacob" developed a partial differential equation describing the flow of water in an aquifer of permeability k that is overlain by a leaky caprock of permeability k&apos;. Fig. 1 shows a schematic cross-section of the system under consideration. One of his principle assumptions was that if k > > k&apos;, the direction of flow is essentially vertical in the caprock and horizontal in the aquifer. Neuman19 confirmed the validity of Jacob&apos;s assumption using a mathematical model. Another assumption was that a permeable source layer overlies the caprock (Fig. 1) and is able to maintain a constant hydraulic head at the upper boundary of the caprock. By neglecting the effects of compressibility within the caprock, Jacob1* developed a solution for a bounded circular aquifer. Later, Hantush and Jacobx5 used the same assumptions to solve the case of an infinite radial aquifer that is pumped at a constant rate. Their solution may be expressed in di-mensionless parameters by

By J. B. Wagner, p. Hembree

The iron tracer diffusion coefficient of umstite has been measured at 110(fC across the phase field and at a single composition at 800°C. Assuming a simple cation vacancy model the tracer diffusion coefficient was found to be a linear function of the cation vacancy concentration at 1100°C. The equation is D = 3 x 20 29 where denotes the concentration of vacancies in numbers per cc. The tracer work at 800°C was carried out to investigate the reported "pinning" of tracer to the wustite surface at low temperatures. No evidence for the "pinning" of the tracer was found at 800°C in COz-CO gas mixtures. HIMMEL, Mehl, and Birchenall,&apos; Carter and Richardson,2 and Desmarescaux and La combe3 have measured the diffusion of iron tracer in wustite at several temperatures and compositions. The present work was undertaken to extend the measurements over a large composition range at 1100°C and to resolve certain apparent discrepancies in the data, expecially at lower temperatures. EXPERIMENTAL Wustite was prepared by oxidizing rectangular iron plates* in C02-CO mixtures. The samples were •The iron was supplied by the Battelle Memorial Institute courtesy of the American Iron and Steel Institute. The analysis is presented in Table I. quenched. Due to the inward flow of cation vacancies during oxidation, the center of the sample contained a thin void. The edges of the wustite slab were sanded until the sample could be split into two parts. Each part was then sanded on the front and back flat area until a smooth surface was obtained. The specimens were then replaced in the furnace and equilibrated at llOO°C in a predetermined COa-CO mixture by methods described elsewhere.4"6 The specimens were again quenched and the surfaces were lightly sanded to remove any roughness following the first equilibration. The specimens were then reequi lib rated in the same C02-CO mixture for thirty minutes in order to relieve any mechanical damage on the surface due to the polishing. The specimens were then quenched and the tracer was applied by an electroplating technique. The work of Carter and ~ichardson&apos; demonstrated that there was no systematic difference in the iron tracer diffusion coefficient in wustite if the tracer was plated, dried, or evaporated on the specimen. In the present study a piece of filter paper was saturated with an iron chloride solution of pH <* 3 that contained the tracer FeS5. The wustite was placed on the filter paper and made the cathode. A current density of 0.4 to 0.6 ma per sq cm was passed for about five to ten minutes. The thickness of the tracer layer was estimated to be about 7 x lom6 cm. This estimate was made by considering the area plated, the current flow, and time for plating and the activity of the iron in the plating solution. Different areas of the specimen were counted using a collimator to determine the uniformity of the tracer. Any specimen which exhibited a variation from the initial count rate (about 1500 cpm) by more than 15 pct was rejected. An estimate of the time necessary to convert the thin layer of iron tracer to wustite was made using the data of Pettit and wagner." he estimated time was 1 sec at 1100°C assuming linear oxidation kinetics. The shortest diffusion anneals were 1800 sec. The samples were suspended in the hot zone of a furnace by two platinum wires. Two separate specimens were run at the same time. Only the edges of each sample were in contact with the wires. The C02-CO gas of the same composition as that used in the pre-diffusion anneals flowed freely around the samples at a linear velocity of 0.9 cm per sec. To initiate a run, the specimens were lowered from the cold zone of a furnace to the hot zone by a magnetic lowering device." bout 60 sec were required for lowering. To terminate a run, the sample was withdrawn from the hot zone to the cold zone. Time zero for the beginning of the experiment was taken when the sample blended into the red glow of the furnace and conversely for the end of the experiment. The surface decrease method of measuring the tracer diffusion coefficient was used to collect the data. This method requires that counting geometry be reproducible because the specimen is counted before the diffusion anneal and after the anneal. A special jig was constructed for each specimen so the specimen could be removed from the jig and returned to the jig such that the well geometry was reproducible.

Jan 1, 1970

By M. A. Dayananda, R. E. Grace, P. F. Kirsch

Ternary diffusion experiments were carried out at 750°C with vapor-solid diffusion couples in single-phase copper-rich Cu-Zn-Sn alloys. The Philibert-Guy method was used to calculate intrinsic diffusion coefficients at compositions corresponding to the plane of inert markers imbedded in the diffusion couples. Inter diffusion coefficients were determined at common composition points of intersecting diffusion paths. Intevdiffusion coefficients were also obtained at compositions corresponding to maxima in the tin concentration pvofiles Relations between the interdiffusion coefficients and the expansion of vapor-solid diffusion couples are described in detail. Such relations permit the calculation of constant interdiffusion coefficients in binary couples from expansion data directly. In ternary couples expansion data provide an additional constraint on the interdiffusion coefficzents. ThE phenomenological analysis of diffusion in ternary solid solutions has been developed extensively, and various approaches taken in the determination of diffusion coefficients have been reviewed recently by Guy et al.&apos; Finite,&apos; semi-infinite,3 and infinite4 diffusion couples have been used in studies of ternary diffusion, but most of the work has been done with infinite diffusion couples. Semi-infinite diffusion couples3 (vapor-solid couples) have been used to determine both intrinsic and interdiffusion coefficients in the Cu-Zn-Mn system, in which two diffusing species, zinc and manganese, were supplied from the vapor phase. If only one component has a sufficiently high vapor pressure to be supplied from a vapor source, vapor-solid diffusion couples may still be used. In this case the boundary conditions at the gas/solid interface may be governed by partial equilibria rather than by virtually complete equilibrium between the phases. In the present work diffusion measurements were carried out at 750°C with vapor-solid couples of Cu-Zn-Sn alloys. Only zinc was transported between the vapor source and the diffusion disks, because the vapor pressures of both copper and tin are at least 108 lower than that of zinc. Both intrinsic and interdiffusion measurements were made at several compositions. A secondary objective was to relate expansion of the diffusion couples with the interdiffusion process. Such measurements for binary couples yield average values of the interdiffusion coefficients over composition increments. In ternary diffusion couples ex- pansion data provide an additional constraint on the interdiffusion coefficients. COMPOSITION-DEPENDENT INTRINSIC AND INTERDIFFUSION COEFFICIENTS As shown by Philibert and GUy5 the determination of intrinsic diffusion coefficients in a ternary system requires two independent diffusion couples containing marker planes with identical composition. In the case of vapor-solid couples such a requirement torresponds to two couples set up with the same vapor source exposed to two diffusion disks of different composition. Inert markers placed initially on the disk surfaces become imbedded during diffusion. If the pair of couples exhibits appreciable marker burial with marker planes of virtually the same composition, the intrinsic diffusion coefficient may be evaluated at the composition of the marker planes. Fig. 1 is a schematic diagram of the concentration of of a Cu-Zn-Sn ternary vapor-solid couple after diffusion of zinc from a vapor source into a binary Cu-Sn alloy. The areas, Ai correspond to the cumulative intrinsic fluxes of the three diffusing species across the marker plane:5 where Ji is the intrinsic flux of component i, t is the diffusion time, and D3i are the intrinsic diffusion coefficients. For the determination of interdiffusion coefficients a pair of diffusion couples with intersecting diffusion paths is needed. At the composition point of intersection (C1, C2) the coefficients are evaluated from the equation:3

Jan 1, 1969

By A. H. Geisler, R. F. Mehl, C. S. Barrett

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By J. Szekely, J. W. Evans

A formulation is given for radiant heat loss from the surface of molten steel held in a ladle and numerical solutions are presented for the resultant integrodif-ferential equations. The results are shown on plots of the net rate of heat loss against time, with the geometlry, emissivities, thermal properties of the walls, and Preheat as parameters. It was found that the rate of the vadiant heat loss from the exposed metal surface was comparable to the conductive losses from the Portion of the metal in direct contact with the walls. The radiant heat loss was markedly affected by the geometry and by the thermal properties of the walls the net radiant heat loss from the steel could be drastically reduced by providing a top cover and also by the provision of preheat. The results of this work are thought to be relevant to heat loss calculatious concerned with vacuum degassing and with operatzons in which molten metals are held in ladles. WhEN molten steel is held or transferred in ladles heat losses inevitably occur. The accurate assessment of these heat losses is of importance in process design considerations, as the temperature of the metal may have to meet rigid specifications in certain stages of the processing sequence. As shown in Fig. 1, the principal mechanisms responsible for heat loss are: i) Conduction into the walls and ii) Thermal radation from the top metal surface (possibly augmented by natural convection) The conductive heat loss may be readily calculated as much information is available in the literature on both the general theory1&apos;&apos; and on its particular applications to ladle heat loss calculations. Evaluation of the radiant component of the heat loss is less straight-forward. In two recent papers it has been shown that the presence of a slag layer 2 to 3 in. thick would prevent any significant heat loss for periods up to an hour,5&apos;" however, should bare metal be exposed, constituting the radiant surface, substantial heat losses could occur. This latter case is of considerable practical interest in various degassing operations and in the vacuum processing of certain specialty steels, where the top surface of the metal is not covered by a protective slag layer. Under these conditions a substantial radiant flux is emitted by the top metal surface; part of this flux leaves the system, part of it falls in the ladle walls. The radiant flux incident on the ladle walls is in part absorbed and conducted away, and in part reflected and re radiated. The purpose of the paper is to present a general formulation of the problem, the resultant solution of which should enable computation of the net radiant heat loss from the metal surface. The principal variables, the effect of which will be investigated, include initial metal temperature, geometry, thermal and radiative properties of the wall, and various modes of preheat. FORMULATION Consider a cylindrical enclosure, shown in Fig. 2, with a diameter D, height H, and wall thickness W, the cover at the top of the cylinder having a wall thickness L. If the temperature of the base (representing the top surface of the metal) is kept constant, say, Tb, the problem is to calculate the net rate of heat loss from the base as a function of time, geometry, the initial temperature distribution, and the thermal properties of the system. As customary, the formulation will consist of the mathematical statement of the conservation of thermal energy within the system.

Jan 1, 1970

By L. C. Brown, J. S. Kirkaldy

AS part of a program to investigate the diffusive properties of dilute ternary austenites, we have made a determination of the effects of cobalt on the activity of carbon in y iron. Samples of pure iron and Fe-Co alloys were equilibrated at 1000°C in controlled CO-C02 atmospheres, following the procedure of R. P. smith.&apos; The 0.010-in.-thick samples were analyzed for carbon by microcombustion analysis2 to give a set of isoactivity curves. The latter were converted to activity-coefficient (standard state at infinite dilution) plots by combination with Smith&apos;s data&apos; for the activity of carbon in pure iron measured in a CO-C02 mixture. Table I shows the composition of the base alloys used, while Fig. 1 shows the experimental results superimposed on a set of curves generated by the relation In the notation of Wagner,&apos; the interaction parameter is the second coefficient on the right, Eq. [I] adequately correlates the experimental points for those alloys which were prepared from electrolytic iron by arc-melting (2,4, and 7 pct Co). The results for the 10 pct Co alloy (supplied by Crucible Steel Co.) do not correlate with the others. In fact, the experimental points for this alloy correspond to an interaction parameter of It is possible that the interaction parameter is a function of concentration for large cobalt additions, but we are inclined to attribute the discrepancy to the presence of a significant amount of aluminum added to this alloy for deoxidation purposes (Table I). Preliminary measurements for the system Fe-C-A1 have indicated an interaction parameter of Which implies that the effect of aluminum in solution on the carbon activity is sixty times greater than the effect of an equal weight percentage of cobalt. These observations cast some doubt on the precision of the results of Chandhok, Hirth, and Dulis who used this same 10 pct alloy for their experiments, obtaining an interaction parameter of E = 2.2. There is considerable doubt as to the activity of a plane Fe-C system. Using a CH4-Ha mixture, Smith obtains cg = 6.1 for the effect of carbon on the activity of carbon in austenite, rather than the value of 8.9 given in Eq. [I]. The use of CHa-Ha mixtures has recently been questioned by Kaufman, Radcliff, and cohens who state that there is some possibility that other hydrocarbons are formed. Fortunately, the determination of the interaction parameter is not sensitive to the coefficient of Nc. For example, using the CHI-H2 results we obtain a value which is almost the same as that obtained using the CO-CO, results. The authors wish to thank Mr. E. J. Dulis of the Crucible Steel Co. of America for supplying us with samples of the 10 pct Co alloy used in their original work. Financial assistance from the American Iron and Steel Institute is gratefully acknowledged.

Jan 1, 1963

By R. J. Burgess, A. R. Ramey, A. R. Adams

During interpretation of pressure buildup tests on gas wells in a tight dolomite gas reservoir, peculiar behavior was noticed. Two straight lines were apparent. Effective permeability to gas taken from either straight line was about the same, and the Miller-Dyes-Hutchinson dimensionless time check for the straight line was proper for both straight lines. Geological data indicated the likelihood of scattered trending fractures in the reservoirs. Since the first straight Iine yielded permeability values close to the geometric mean permeability from core analyses, it was postulated that the reservoir model was that of an acidized well completed in the tight dolomite, but that widely scattered hairline fractures caused the mean permeability of the reservoir distant from the well to be higher than the matrix permeability. Because all other studies of fractured reservoirs to the authors&apos; knowledge assumed that the fracture matrix was dense enough to communicate directly with the well, no interpretative methods were available. The Hurst line-source solution for a radial change in permeability for interference between oil reservoirs was adapted to pressure buildup testing. The result indicated that the first straight line should yield the proper matrix permeability and wellbore skin effect. The second straight line may be extrapolated to obtain static pressure. The time of bend between the straight lines was used to estimate distance to a fracture. Application to field test data is shown. It is believed that the methods developed and the case history presented will add to present tools available for pressure buildup interpretation. Introduction Since the pioneer studies by Miller, Dyes, and Hutchin-son1 and Horner&apos; in 1950 and 1951, well test analysis has become recognized as one of the most powerful tools available to both production and reservoir engineers. Well test analysis serves as a logical basis for well stimulation and completion analysis, and for long-term reservoir engineering. Since the early 19501s, much effort has been placed on the development of well-test analytical methods. Reservoir and well conditions of increasing complexity have been considered systematically to provide the analyst with a catalog of causes and effects. Matthews and Russella state that some 200 papers dealing with this subject have been published in the last 35 years. Developments in well test analysis appear to have originated in one of two ways. Either a physically realistic field condition was anticipated and analytical solutions for the condition achieved, or anomalous field test behavior was recognized and interpretative methods sought for the anomaly. In recent years, it has appeared that the latter has inspired an increasing number of studies. The analyst today finds an increasing number of known cause and effect studies available for well test analysis, the classic of which is that of finding the specific flow problem that generated the answer — the well behavior. Although it may be impossible to achieve this goal uniquely, the analyst often is able to select a useful interpretation that combines all known performance and geologic data — or to show that various logical alternatives would not significantly affect the interpretation. During a recent reservoir study, we observed gas well test behavior that did not appear to fit behavior described previously. Although it cannot be said that we have found a unique interpretation, we shall present in this paper the peculiar behavior observed, and describe the reservoir and interpretative methods developed. Reservoir Description The subject gas reservoir is a 9-mile-long, narrow dolomite reservoir lying within a limestone of Ordovician age. (See Fig. 1.) The dolomitized rock in the field consists of dark brown to buff, dense to coarsely crystalline, vugular dolomite containing numerous hairline fractures, many of which may have been closed in the reservoir and parted when cores were brought to the surface. Larger fractures are also apparent in core, but usually are filled and sealed with euhedral dolomite crystals. Portions of the north flank of the reservoir are known to be cut by a sealing fault downthrown to the north. Gas wells located near the fault have higher open flow potentials than those more distant from the fault. This is believed to be a result of higher permeability near the fault due to more extensive and open fractures. Detailed coring and core analysis have been performed on several of the wells in this reservoir. Fig. 2 presents permeability variation&apos; plots for both horizontal and vertical

Jan 1, 1969