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By H. I. Aaronson, C. Laird

Although the past results of X-ray experiments indicate that the broad faces of 0' plates are coherent with their matrix, dislocations lying in arrays have frequently been observed at these boundaries by transmission electron microscopy. Critical experiments employing the latter technique have been carried out in order to determine the origin of these dislocations. It is concluded that 8' plates are essentially coherent with the matrix at their broad faces throughout the aging temperature/time envelope studied. Virtually all of the dislocation arrays observed are deduced to have been formed by plastic deformation accompanying transformation. The proportion of dislocations arising from convexity of the plates is shown to be negligible by comparison with that from plastic deformation. At the higher aging temperatures, a[001] dislocations appeared in moderate numbers. These dislocations were traced directly, however, to the ledgewise dissolution of 0' occasioned by the formation nearby of 0 crystals. On the other hand, since there is a parametric difference normal to the broad faces of the ?' plates, mismatch dislocations do form at their edges. A previous conclusion that these dislocations have Burgers vectors of type a[001] was confirmed directly. The edges of 0' plates were observed to develop octagonal shapes when growing, but circular shapes during dissolution. 1 HIS paper presents the results of an investigation of the interfacial structures of plates of the transitional phase, 8', formed in an A1-4 pct Cu alloy. In a companion paper, Part 11, the effects of these structures upon the migration kinetics of a:?f boundaries are reported. This work is pa.rt of a general program designed to establish the basis of precipitate morphology. The present authors in Al-Ag,1 and whitton2 previously in U-C alloys, have used transmission electron microscopy to examine directly the vander Merwe3-6 networks of dislocations anticipated7 to compensate the small amount of lattice misfit normally founda at the broad faces of Widmanstatten plates. Since the broad faces of 0' plates are considered to be perfectly coherent with the corresponding habit planes in the a matrix,' no dislocations should be present at these faces. Many reports have been published, however, giving evidence to the contrary.10-18 The primary objective of this investigation was therefore to ascertain the nature of these dislocation structures. An attempt to do this is described in the first three sections of this paper. Inspection of the matching of the a and 8 ' lattices at the orientations of the 0:0' boundary corresponding to the edges of 0' plates raises the possibility that these edges may be made up of rather closely spaced edge- type misfit dislocations oriented so as to be sessile with respect to the lengthening or shortening of the plates. Since this structure should severely inhibit migration of the plate edges (Ref. 7, Part II), a situation not originally anticipated,' an experimental determination of the interfacial structure of the edges of 8' plates was clearly in order, and is reported in Section III. Those aspects of the experimental procedure applicable to both Parts I and I1 are presented in the next section. Specific procedures applicable to individual aspects of each investigation, and also the relevant surveys of the literature, are then individually reported in the appropriate sections. I) GENERAL EXPERIMENTAL PROCEDURE The material used in both parts of these studies was the same as that of a previous investigation:" strips of A1-3.93 pct Cu, 0.009 in. thick, prepared as before, solution-annealed at 548°C for 6 hr, and quenched. Details of subsequent aging, and in some cases deformation treatments, are given in the Experimental Procedure sections of the individual parts of both papers. Specimens of the heat-treated strips were electro-thinned as beforeLg and examined in a Philips EM 200 microscope equipped with a goniometer stage. A commercial hot stage, of the grid-heater type and capable of * 30-deg tilt about one axis in the plane of the specimen, was also used for kinetic studies. The usual precaution of calibrating for the additional heat supplied by the electron beam was taken.19 A 16-mm cine cam-I era mounted outside the viewing window was frequently used to record the transformations. Conventional selected-area diffraction and dark-field viewing techniques were used to identify the precipitates in the foils. Normal bright-field images corresponding to two-beam diffracting conditions or dark-field images were employed to characterize the dislocations observed at the interfaces of the precipitates. The application of these techniques to the study of an interphase boundary, and the interpretation of the images,20'21 has been fully described in a previous paper.'

Jan 1, 1969

By H. Rush Spedden, A. M. Gaudin

IN the belief that a critical study of its operating problems might be a sound investment, the Cuban American Manganese Corporation initiated an ore-treatment research in cooperation with the Massachusetts Institute of Technology. One of the early objectives of this research naturally became the relationship of the microscopy of the Cuban ores of the Corporation to their flotation treatment. The operations in Cuba have already been described by F. S. Norcross, Jr.7 and the laboratory study of manganese oxide flotation goes back a number of years .4 Broadly speaking, the difficulties encountered in the flotation of manganese ores are that the consumption of reagents is extremely high, the concentrate contains more silica than is desirable and the tailing losses are relatively high. An appreciable betterment on any of these scores would achieve a definite betterment in costs, quantity of minable ores, and quality of product. The microscope study discussed in this paper was made on samples from the Quinto mine, from the Ponupo mine, and from mill products at various stages of passage of the ore through the mill. The writers have had access to Company records and in particular to the petro¬graphic studies made on thin sections of ore by the late Professors R. J. Colony and Philip Krieger, of Columbia University. They acknowledge their debt to both of these men for the help derived from the reports. Manganese oxides are black, friable, smudging. It is, therefore, very difficult to judge operations by inspection. The mineralogy of manganese compounds seems to be confused, and the authors believe that many more minerals have been described than actually exist. Much of this difficulty is due to the prevalence of the structural conditions that will be discussed further in this paper; namely, the porosity and the friability of the ores, and the extremely intimate association of minute manganiferous mineral crystals with impurities of various sorts. By all odds the most important manganese mineral in Cuba is the one that in this paper is called "psilomelane." The name "psilomelane" has been used in so many different ways that the choice of it for this ore may not be approved by all. However, it seems to be the best under the circumstances. This mineral accounts for about 97 per cent of the manganese in the ores of the Quinto and Ponupo mines and in the mill feed. The remaining odd 3 per cent consists mostly of pyrolusite together with minor amounts of other manganese oxide minerals. DESCRIPTION OF PSILOMELANE Aggregate Structure In grains or lumps, psilomelane has a characteristic fibrous appearance and seems

Jan 1, 1942

By N. O. Gray, John Henderson

Hydrogen-reduction data for naturally occurring single crystals and Prepared polycrystals of dense hematite have been presented. Results cover the temperature range 400o to 1000oC, for particles from ten sources, ranging in size from 0.07 to 10 mm and in shape from spheres to cylinders, cubes, and thin slabs. A consistent pattern of behavior has been demonstrated for single crystals and the reduction mechanism shown to be temperature-dependent. Below 579oC reduction is a simple topochemical process but at higher temperatuves it is complex and occurs in two distinct stages. Prepared particles from these laboratories behave in a similar manner to the single crystals. Data from two investigators showing topochernical reduction of Prepared particles above 575°C are inconsistent with that for other dense hematites. It is concluded that topochenzical reaction should not be used as a model for generalized rate expressions for dense hematites. SINCE 1958, McKewan1-6 has brought to prominence a simple concept of dense hematite reduction. This model is that oxygen is lost from a hematite particle undergoing reduction only from an oxide-iron interface that recedes in such a way that the oxide remaining retains the original shape of the particle, i.e., reduction occurs topochemically. An adjunct to this concept is that any intermediate oxides in the transition from hematite to iron only form thin layers so that oxygen cannot be lost from the particle without movement of the oxide-iron interface. Further, the rate of oxygen loss from the particle is said to be proportional to the area of the receding interface so that the iron layer grows linearly with time and the over-all reduction process can be described by the equation where ro and do are the initial particle radius and density, respectively, R is the fraction of the original oxygen lost, i.e., the fractional reduction, at time t, and K is the rate constant. The idea of an underlying simplicity in hematite reduction is attractive because it gives a tractable basis from which general theories of hematite reduction can be developed and it has received wide support,7-14 based mainly on the large amount of data13 that can be fitted to Eq. [I]. However, despite the fact that this equation has been derived for dense materials, the bulk of the data that have been used to test it13 have been for materials of only about 90 pct of theoretical density (5.26 g cm-3) or less, so that its generality for dense hematites has not been demonstrated. In any case, as will be seen, adherence of reduction data to Eq. [1] does not necessarily imply that reaction occurs topochemically. In this work only data for hematites approaching theoretical density are considered and it will be shown that in only one study besides McKewan's is topochemical behavior observed over the whole range of temperature investigated. For the majority of materials a linear rate of interface advance is observed to complete reduction only when wustite is not a stable intermediate phase in the transition of hematite to iron, i.e., at temperatures below about 575°C. Above this temperature, reduction is an exceedingly complex series of reactions that takes place in two distinct stages and it is only in the first stage that reaction in any way resembles a topochemical process. This means then that, far from representing general behavior as has commonly been supposed, topochemical reaction for dense hematites is only a particular behavior that may be observed under some circumstances. EXPERIMENTAL Hydrogen-reduction data have been collected and cross-checked in these laboratories by three techniques, weight loss, collection of water evolved in the reduction reactions, and direct metallographic examination. Details of these techniques are discussed elsewhere," where it is shown that results obtained by the three methods are in close agreement. The weight-loss method, by which most of the results were obtained, consisted of hanging the sample in a platinum mesh basket from an Ainsworth Model AV-AU-1 vacuum recording balance inside a vertical l 1/4-in.-ID alumina tube furnace. Dry deoxidized hydrogen was flowed downwards through the tube at 2 to 4 liters min-1 (stp). Single crystals from two sources and artificial oxides from three sources have been examined. The single crystals were from hematite deposits at Yampi Sound, Western Australia, and Brazil, the latter being obtained from Gregory, Bottley and Co., London, U.K. The "Yampi Blue" crystals were hand-picked from washed, magnetically concentrated, sized fractions, -200 mesh BSS (mean diameter ca 0.07 mm) and —36 + 44 mesh BSS (mean diameter ca 0.4 mm) while 10-mm cubes were cut from the Brazilian crystals with a diamond saw. The starting materials for the prepared particles were hematites designated, respectively, "Specpure Iron Oxide", Laboratory No. S639 from Johnson Matthey & Co. Ltd., London, U.K., "Calcined Ferric Oxide" from B.D.H. Laboratory Chemicals Division, Poole, U.K., and "Pigment Grade Oxide", EPR-50, from C. K. Williams & Co., Easton, Pa., U.S.A. Approximately spherical particles were prepared from the artificial oxides by rolling the material, moistened if necessary, in a glass jar, and cylindrical compacts approximately 10 mm in diam and of approximately equal height were pressed in a steel die at 200 psi. These spheres and cylinders were subsequently fired in oxygen for 20 to 100 hr at 1370°C. The

Jan 1, 1967

By K. Mukai, M. Ishihara

This report is a brief discussion of the impurity levels both in primary aluminum and super-purily alnminim in connection with raw materials and proc-essing methods. Particularly, truce amounls of im-purities were analyzed by introducing nittss-speclro-gruphy and nenlron-aclivalian analysis techniques. Vanadium and gallium content in primary aluminum metal corresponded to theor amounls in anode coke. but the nickel content in primary aluminum was hide-pendent oj its amount in the anode cake. Sulfur in the anode colic might result in an increase of the iron content in the molten metal in the reduction cell. The content of sodium and calcium increased with increasing bath ratio. In the holding furnacc sodium content decreased rapidly, and nonmetallic inclusions merit separated front the mollen metal. Three-layer elctrolysis was effectire in eliminating many impuri-ties with the exception of copper, aluminum oxide. aluminum nitride, and some rare-earth elements. THE amount of impurities and nonmetallic inclusions in aluminum metal depends on impurities in the raw materials and various production processes. This paper presents an investigation of the behavior of impurities and nonmetallic inclusions in aluminum during the electrolysis process, the period in the holding furnace, and the process of three-layer electrolysis. Chemical analysis and emission spectrometric analysis have generally been used as methods to determine small amounts of impurities in both primary aluminum and super-purity aluminum; however. mass spectrography and neutron-activation analysis have been recently introduced into this field, and trace amounts of impurities can accurately be determined by these latter methods. EXPERIMENTAL WORK Common impurities were determined by means of absorptiometric. polarographic, flame-photometric. and emission-spectrometric methods. However, in the determination of trace amounts of impurities and non-metallic inclusions, the following methods were applied. In the analyses of trace impurities by mass-spec- trographic analysis, samples were exposed in the vacuum spark of double-focus ing Mattauch-Herzog type mass spectrograph (Japan Electron Optics Laboratory, Ltd.). Ilford Q2 photographic plates were used as ion detectors. Fe was used as the internal standard, and the atomic concentration of each element was calculated by the following expression and converted into the weight concentration: where E, and Ei are the exposures (coulomb) when isotopes of the internal standard and impurity elements (on which the estimate is based) show the same density, X is the percent (atomic) concentration of the standard, IF and Ii are the percent abundances of the isotopes of the standard the impurity elements (on which the estimate is based), and Ms and hfi are the mass of the isotopes of the standard and impurity elements (on which the estimate is based). The coefficient of variation in this method is about 40 pct in the range of 0.1 to 1 ppm. In neutron-activation analysis, irradiations were done in the nuclear reactors TRIGA-I1 (neutron flux: 4.7 x 10 11 n per sq cm per sec; Rikkyo University) or JRR-2 (neutron flux: 2 x 1013 n per sq cm per sec: Japan Atomic Energy Research Institute). After the chemical separation, a NaI (3 by 3 in.) scintillator connected to a 256-channel y-ray spectrometer (R.C.L.) was used for counting and recording various activated impurities. The coefficient of variation in this method is about 20 pct. In the analyses of nonmetallic inclusions, aluminum-oxide determination was carried out according to Fischer's method, 3 as follows. A slice of sample was cut off and the surface was cleaned. It was dissolved in bromine-methanol. The solution was filtered and the residue was washed. The residue was fused with potassium bisulfate flux. Then it was dissolved in weak acid, and oxine solution was added. The aluminum oxinate was extracted with benzene. Finally, aluminum was determined absorptio-metrically. Aluminum nitride determination was carried out as follows. A slice of sample was cut off and the surface was cleaned. It was put in the distillation apparatus and decomposed with sodium hydroxide solution. The solution was distilled. Then ammonia was absorbed and

Jan 1, 1967

By AIME AIME

FOR the following notes and pictures we are indebted to Sumner S. Smith of Oakland, California: Gold was discovered on Squaw Creek in the fall of 1927 by an Indian named "Paddy Duncan," and most of the stream was staked by natives. This stream is about 12 miles in length and flows into the east fork of the Alsek River, 10 to 15 miles below the old Dalton Post in British Columbia, near the international bound-

Jan 1, 1929

"For many years it has been known that large bodies of iron ore existed in Iron and Washington counties in Utah. The ore is chiefly hematite—both hard and soft—though some magnetite is found. No definite and complete estimate of the iron ore reserves of the state have been made. The U. S. Geological Survey estimated that 40,000,000 tons of ore were disclosed by development work averaging only 35 feet below the surface of the ore. The ore is found along an area about one and a half miles wide by twenty miles long, and for the most part on the eastern and southern slopes or foothills of Three Peaks, Granite Mountain and Iron Mountain. Later estimates by others have gone as high as ore in sight 164,000,000 tons, probable ore 300,000,000 tons and possible ore 1,000,000,000 tons. Whether this last estimate is too great or not there is sufficient iron ore in Utah to justify the starting of an iron industry.Two companies are now mining iron ore in Utah, the Columbia Steel Corporation and the Utah Iron Corporation. The mine of the Columbia Steel Corporation is at Iron Springs a few miles west of Cedar City. About 650 tons, of ore a day is being shipped to the blast furnace at Ironton. The ore is mined by the glory hole method. After being drilled it is blasted to the bottom of the several glory holes and is dropped through chutes into cars on the ore haulage level below. It is then hauled by electric locomotives to the crushing plant, where it is crushed to blast furnace size before going to storage bins. Some of the softer ore is brought to the chutes by Fresno scrapers."

Jan 1, 1925

By Lyon F. Terry

SPEED-UP of production of crude oil and its products, accompanied by rising prices and the organization of the industry on a war basis, featured the economic aspects of petroleum in 1941. Early in the year American tankers were urgently requested by the British to replace losses and offset slower transit under convoy. Some forty American owned tankers were first assigned to Britain and an additional forty-odd ships were transferred during the summer. This threatened to reduce our transportation facilities from Gulf ports to the Eastern seaboard below requirements, especially should sinkings have increased and the British needed more ships. Co-ordinator Ickes began preparations for restricting gasoline consumption in the Eastern district and plans were formulated for the construction of an emergency trunk pipe line from Texas to New York and Philadelphia refining centers, and for a gigantic tanker-building program. Sales of new oil-heating units in the East practically ceased. The companies were urged to transport as much oil as possible by tank car and by October 140,000 barrels of oil per day were reaching the East Coast district by rail, sufficient to meet 8 per cent of total requirements. But British sinkings from July through October decreased 63 per cent compared with the four months ended June 30, Britain began the return of tankers, the construction plans were dropped, and the threatened shortage was thus averted.

Jan 1, 1942

By COURTNEY DE KALB

IRON ore is the cause of the present trouble in Morocco. At least three nations are interested in the outcome and private syndicates have been active. The iron deposits are found in that mountainous northern coast line known as the Rif. This is an uplift that has been cut through, by the northward drainage, representing an ancient land surface. Erosion has produced .a fiordlike coast, which circum- stance has aided contraband' traffic to the tribes dominated by Abd-el-Krim, the chief of the clan of the Beni Urriaguel, near the center of 'the north coast, opposite Alhucemas. The iron deposits are extensive in the territory of the Beni Urriaguel. They were "located," if such a term is permissible, many years ago. The first arrangements, through direct contracts with the tribal chieftains, have been reinforced by compliance with the subsequent code under the Spanish protectorate in 1914. Under those terms, the location had to be made through the Arbitral Commission sitting in Paris. These locations, or "denouncements," were made by the I-louse of Mannesmann, of Hamburg.

Jan 1, 1925

By Arthur Mitchell

POSSIBLY in no other of the non-ferrous mining districts of this country has the use and develop-ment of mechanical loaders been carried to such an extent as in the "lead belt" of Southeast Missouri. It has become apparent to the four mining companies in the district that it is imperative to apply satisfactory mechanical methods to the chief remaining stage of the entire operations-mining, milling, smelting and refining-in which manual labor is still largely used to handle material in process. With increasing wages and with the reduction of the metal divisor by the extension of mining into lower-grade orebodies, the shoveling cost per ton of lead produced has become relatively so large that in an effort to reduce it there is ample justification for considerable capital expenditure. Hand shovelers load about 18 tons of ore per shift and the average grade is less than five per cent. lead. Further, the ore is relatively heavy, about 21 cu. ft. to the ton when broken, and is often so coarse and so closely compacted after shooting that it requires much more block-holing, sledging, and muscular effort to shovel than, for example, does the cherty and more granular ore of the Joplin district or the finer ore in the headings of a drift mine. No mining company desires to pay for mere back muscles if it be economically feasible to avoid it, and labor saving machinery should be susceptible of operation by older employees, who are no longer capable of the more strenuous manual occupations.

Jan 4, 1923

In an earlier day, a moderate-sized 600 tpd mine could easily require 60 working faces and might use five supervisors. The miner had a tonnage rate as an incentive and was largely his own boss. With the advent of conventional mining machine crews, the typical pattern of resource used changed radically. The number of work places could be cut by a factor of ten, but supervision only by a factor of somewhere around three, or at most, five. Obviously, supervision was increased. Capital use rose at the same time by a factor of approximately eight. Materials used, such as powder and bits, probably in- creased in both quality and unit cost, too. It certainly required a better-trained man to run the machines, but fewer miners were needed. It is clear that each input factor such as land, labor, capital and management, has changed significantly and it would be foolish to attribute all the gain to improved machines. However, concentration of work was a vital consideration in the change, sketched above, and such focusing of work in fewer areas could not have occurred without high capacity mining machines.

Jan 11, 1968

By R. F. Mehl, R. F. Bunshah

A fast amplifier technique has been developed for the measurement of the rate of propagation of martensite in an Fe-29.5 pct Ni alloy. The time of formation of one plate of martensite is 3x10 sec and the rate of propagation is 3300 ft per sec approximately. IT has been known for some time that the plate-like structural unit of martensite forms from austenite with great rapidity. Wiester1 and Hane-mann, Hofmann, and Wiester took motion-pictures of the transformation as it occurs in a 1.65 pct C steel; they demonstrated that a single plate formed fully in the time interval between successive frames, viz., 1/20 sec, thus setting an upper limit. Forster and Scheil,3 using an Fe-Ni alloy with 29 pct Ni, recorded the sonic characteristics of the process electrically, upon an oscillograph, setting the upper time limit at 0.002 sec. Forster and Scheil,~ measuring the change in electrical resistance in the same alloy upon a cardiograph, set a limit of 0.02 sec. Forster and Scheil5 later, employing the same alloy, improved their technique, reporting an upper limit of 7.10 sec. In studying signals of such short duration, it is an important question whether the frequency response of the electrical system used is high enough compared to frequency of the pulse measured, or, put differently, whether the system is able to reproduce without distortion the signal arising, in this case, from the formation of a single martensite plate. Forster and Scheil (referring only to their last paper) obtained signals of a frequency of 30 kilocycles (hereinafter kc); this was about the frequency response of the equipment used; thus, if the signal had a frequency higher than 30 kc, it would still appear as a signal of frequency 30 kc. All of these results thus provided upper limits only. Recent developments in electronics have made available equipment with very high frequency response, very high sweep-speeds, high gain, etc. The electrical characteristics of such equipment, used in the present study, are given in Table I. Such equipment offers obvious attraction in the study of the rate of propagation of a martensite structural unit—and perhaps of other structural alterations proceeding at a very high rate. This paper reports an attempt to develop a technique employing such equipment to measure the time of propagation of a martensite structural unit and the variation of this with temperature, with the mode of formation—athermal and isothermal—in both polycrystalline and single-crystal samples; and from such measurements to obtain the rate of propagation. As will be seen, the results obtained are useful theoretically. Materials All data presented here are for an Fe-Ni alloy of the following analysis: 29.5 pct Ni, 0.027 pct C, 0.135 pct Mn, 0.094 pct Si, balance Fe. There were several reasons for choosing this alloy: 1—it is substantially the one used by previous investigators; 2—it exhibits both the athermala and the isothermal' mode of formation of martensite, both studied in detail by Machlin and Cohen; 3—the subzero temperatures of transformation in this alloy are experimentally very convenient; 4—it exhibits the "burst phenomenon";" 5—the change in electrical resistance upon the formation of martensite, a decrease, is great, approximately 50 pct.' The polycrystalline specimens were in the form of wires of 0.025 in. diameter; the single crystals were 1x1/4x1/4 in. Experimental Methods Electrical Apparatus: Fig. 1 is a schematic drawing of the electrical circuit used. The principle used in these measurements is the same as that used by Forster and Scheil." A small direct current, about 1 to 2 amp, is passed through the sample. When a martensite plate forms, the resistance of the sample changes and a high frequency signal is generated. This signal is picked up by the probes attached to the sample, fed into the bank of amplifiers and thence to the vertical deflection plates of a cathode-ray oscilloscope. The signal itself triggers the oscilloscope trace which flashes across the tube face and is photographed by means of a 35 mm movie camera at the end of a light-tight hood. The camera has no shutter. As soon as the signal flashes

Jan 1, 1954

By J. Hall Carpenter, James E. Lawver

Shortly after the passage of the Taconite Amendment in Minnesota, several mining companies announced their intention to build new magnetite taconite plants and another announced its intention to augment present facilities. It is clear that Minnesota will enjoy an expanding magnetite taconite industry, but despite the fact that the reserves are large, eventually they will have to be supplemented by oxidized deposits. Furthermore, not all producers have magnetite taconite reserves. Due to the extensive oxidation of most of the western part of the Mesabi Range, there are no large blocks of unaltered magnetite taconite that lend themselves to open pit operations. Unless a commercial process can be developed to concentrate the oxidized, or so- called "nonmagnetic", taconite and semi-taconite, the existing mines operating in the western part of the range will be forced to shut down when the direct shipping, wash and gravity ores are depleted, or are no longer salable, because of their poor quality compared to high-grade pellets. KNOWN PROCESSES COSTLY The enormous reserves of the oxidized iron- bearing formation have offered a tantalizing challenge to metallurgists for many years. In fact, several processes for concentrating certain types of oxidized ore have been successful at both laboratory and pilot plant level, but to date no process for concentrating semitaconite or oxidized taconite has reached commercial fruition. Magnetic roasting, followed by low-intensity magnetic separation1, has shown considerable promise because the high iron recovery makes the ratio of concentration of many of the oxidized ores more favorable than that of magnetite taconite. However, the capital and operating costs are high and, in many cases, a high- grade concentrate cannot be made without resorting to flotation of the magnetic concentrate. Hence, most research groups are investigating alternate methods of concentration with the hopes of reducing the cost.

Jan 9, 1965

By K. F. Veith, R. L. Marovelli, T. S. Chen

An analytical study is made of thermal stress distribution in a thin circular disc subjected to a peripheral thermal shock at various rates of heat transfer. The problem is of importance in predicting the thermal shock response of a rock body of finite size. The theoretical analysis is based on radial heat flow by conduction in the disc and heat exchange by convection between the disc and the surroundings. The case of constant properties and plane stress is treated. Solutions of the stress distribution are presented for both cooling and heating shocks and an average stress theory is formulated. Preliminary experimental verification was obtained from the results of shock tests on thin rock discs insulated on both flat end faces so that heat exchange took place through the exposed peripheral surface. Physical properties vital to the analysis are Young's modulus, tensile strength, coefficient of linear thermal expansion, thermal diffusivity and thermal conductivity. Plots of these properties are presented. Historically, thermal energy has been used for primary rock removal throughout the ages. Although it is not widely known, the fire-setting method of thermal rock fragmentation was still in use 100 years ago in systematic underground mining operations in Scandinavia.' There, the availability of cheap labor and abundant wood fuel made the method competitive with the early blasting powders. By 1880, as high explosives replaced powder, use of the method declined and it was finally abandoned about 1885. Only 40 years ago, some experimental fire-setting methods were used for rock removal underground at Pribram and Zinnwald in Central Europe.2 Compressed air-oil burners replaced the earlier wood fuels. About 15 years ago, gaseous oxygen-oil burners were introduced in the United States and gained acceptance for difficult blasthole drilling and some quarry opera- tions. At present, there is renewed interest in the compressed air-oil burner designs. The literature included information on thermal secondary processes for rock weakening or particle liberation3,4,5,6,7,8 on thermal spallation of rock 9,10,11,12,13 and on the thermal fracture of materials other than rock. The 1955 Symposium on Thermal Fracture14 and the later work of Hassel-man, cover recent developments in thermal shock investigations on brittle ceramics. Although the number of published analytical and experimental investigations conducted on ceramic and refractory materials is large, the literature reveals that there is a lack of information on both the theoretical and actual response of rock to thermal shock. Many of the thermal shock studies on ceramic and refractory bodies are based on the case of heat transfer at the solid's surface by convection in either liquid or air. A similar heat transfer situation was adopted for a theoretical analysis of the thermal stresses in a thin circular disc subjected to a peripheral thermal shock. Experimental thermal shock tests were then conducted on rock specimens to check the analytical results. Specially insulated quartzite, basalt and taconite discs were shocked in either liquid or still air bath at various rates of heat transfer. The work was done in order to resolve the question as to whether theoretically determined tensile stresses are actually realized in a finite rock body undergoing thermal shock. Specifically, if theory predicts that the tensile strength of a rock should be exceeded in a particular type of controlled thermal shock, will fracture occur? This information is needed by Bureau researchers working on thermal and electrical rock fragmentation methods. The object of this paper is to present the main features of the theory and procedure being used in the authors' approach to quantitative prediction of rock response to a thermal shock. THEORETICAL ANALYSIS In the analysis to follow, simple geometry of a thin circular disc is considered. The disc is assumed to be isotropic, homogeneous and perfectly elastic, and to have constant thermal and mechanical properties. The effect of radiation is neglected so that heat is transferred by conduction inside the disc and by convection with its surrounding. In addition, the end

Jan 1, 1967

By T. C. Poulter, B. M. Caldwell, D. E. Brink

The flash X-ray has been used more than a decade to study the configuration of the jet from a shaped charge. The high-speed, rotating-mirror smear camera has provided time-distance graphs of detonations and shock fronts in transparent materials, and the high-speed framing camera has given pictorial representations of the progress of explosive phenomena. Adequate means for measuring the paths and velocities of all parts of the shaped-charge cavity Iiner during the collapse phase have not existed heretofore. A technique enabling the single-lens framing camera to make stereoscopic photographs of the cavity liner while it is collapsing has been developed. Analysis of this photographic record gives the directions and velocities of various parts of the Iiner surface, permitting direct quantitative measurement where this has previously been impossible. Significant improvements in shnped-clrarge design are expected to result. INTRODUCTION The familiar oilwell jet perforating charge, generally referred to as a "shaped charge", is related to the Mun-roe charge first described by C. E. Munroe in 1888 and later by Neumann in 1910. It differs in construction from the Munroe charge in that its cavity is lined with some inert material (usually metal)', and it differs in performance by projecting a fast jet of dense liner material against the target instead of a stream of expanding detonation products. Fig. 1 represents a typical shaped charge in axial cross section. The charge is circularly symmetrical about its longitudinal axis. The cavity at the right is lined with metal, usually copper; and, with the exception of air, the liner is otherwise completely empty. High-explosive material is intimately in contact with the convex surface of the liner and extends in the other direction to the booster. This is a pellet of high explosive having somewhat different characteristics and serves to couple the detonator to the main charge. When the detonator is fired, a small hemispherical reaction zone of very high temperature and pressure occurs at its output end. The booster responds, adding its own latent energy to the reaction, thereby initiating the main charge. The reaction progresses throughout the main charge at a velocity of 7 to 8 mm/microsecond until all the explosive material has reacted. With a reaction pressure of about 160,000 atm, the surrounding material is moved rapidly away from the high-pressure zone. As the detonation proceeds along the cavity liner, moving from apex to edge, the liner is collapsed toward the axis of the cavity, where liner material from all parts of the concave surface converges. A zone of extraordinarily high pressure results. with only one escape path—outward along the axis. The particles from the liner, thus, become a jet of very high velocity, with a density characteristic of the material from which the liner was made. The kinetic energy of the jet, concentrated in a small area of the target, has great penetrating power. It overcomes the strength of any target, and the target material crumbles or deforms plastically to escape from the path of the jet. An unlined cavity charge, on the other hand, projects a turbulent body of hot gaseous material against a target and erodes the exposed surface. With equal quantities of explosive, the penetration effectiveness of an unlined charge is a small fraction of that of a lined charge. Given an explosive charge with a detonator at one end and an axially symmetrical metal-lined cavity at the other, one has a perforator of considerable potency. To maximize the penetrating and other desirable effects,

By M. J. Marcinkowski, A. Szirmae, R. M. Fisher

Room -temperature hardness measurements obtained from single and polycrystalline samples of a 47.8 at, pet Cr-Fe alloy which were aged for various times al 500°C show a two-fold increase over that of the unaged alloy after annealing for 1000 hr. A detailed examination of the deformation markings in the neighborhood of the hardness imbressions reveals that twinning becomes an increasingly more important mode of deformation as aging proceeds. this observation is shown to be inconsistent with the Proposals that the transformation is eve of order-disorder On the other hand, the results are in agreement with previous observations of Fisher et al. of a coherent chromium-rich precipitate which forms in an iron-rich matrix as a result of a miscibility gap in this alloy system as proposed by Williams . Using the coherent precipitate hypotlzesis as a model, a detailed analysis of the various possible strengthening contributions to both the slip mid twinning stresses is made. In the case of' slip, lattice friction within the chromium-rich phase and the chemical energy associated with the interface between the two phases contribute about 60pet to the total strength. The contributions from coherency strains and modulus differences are thought to contribute the remaining 40 pet of the strength but are difficult to evaluate because of uncertainties regarding the flexibility of the dislocation line. All of the factors have nearly the same or else a smaller effect on the twinning stress in the aged alloy. Twinning is never observed in the unaged alloy because the twinning stress is much higher- than that for slip. With increased aging times, the various contributions to the total stress for both twinning and slip increase, but most of those for slip increase much more rapidly, so that, in the fully aged alloy, it surpasses the stress for twin propagation. When a twin is nucleated by the chance occurrence of an internal stress concentration during a test, the subsequent twin burst results in a low hardness reading. FeRNTIC Fe-Cr alloys from about 15 to 80 at. pet Cr content show considerable change in properties such as hardness, electrical resistivity, saturation magnetization, and so forth, after aging in the vicinity of 500°C.* The most marked change is a large increase in hardness accompanied by a sharp decrease in ductility, so the phenomenon has often been referred to as the 475°C (885°F) em-brittlement problem. Changes in microstructure are rather subtle and most investigators have not been able to observe any X-ray diffraction or metal-lographic changes during aging. There is little doubt that the phenomenon is inherent to the Fe-Cr binary system and is not directly related to the formation of a phase. Two distinct schools of thought have developed during the past decade concerning this problem. Masumoto, Saito, and sugiharal have concluded, from their own specific-heat measurements, that atomic ordering occurs in this temperature range. Pomey and Bastien2 have also attributed the changes in physical properties with aging in the neighborhood of 500°C to atomic ordering. In addition, Takeda and Nagai3 claimed to have found X-ray verification for superlattices corresponding to the compositions FesCr, FeCr, and FeCr3. However, all known attempts to observe superlattices in Fe-Cr alloys using neutron diffraction, which should be much more sensitive, have been unsuccessful. These have been reported by Shull et al.4 for 25 at. pet Cr, williams5 for 75 at. pet Cr, and Tisinai and samans6 for a 28.5 at. pet Cr. steel. The second and more prevalent opinion ascribes the 475°C embrittlement phenomenon to the formation of a coherent precipitate due to the occurrence of a miscibility gap in the Fe-Cr system below about 550°C. This latter concept was first indicated by the results of Fisher, Dulis, and Carroll,7 who were able to extract fine particles about 200Å in diameter from samples of 28.5 at. pet Cr steels aged from 1 to 3 years at 475°C. The extracted material was found to be nonmagnetic, to have a bee structure with a lattice parameter between that of iron and chromium, and to contain about 80 at. pet Cr. Williams and paxton8 and williams5 confirmed these results and first explicitly proposed the existence of a miscibility gap below the a region in the equilibrium diagram. Alloys aged within this gap

Jan 1, 1964

By M. E. Straumanis, J. -P. Krumme

In basic ([KOH + KCl] with a total polarity of 2) or acidic (2N H2SO4) electrolytes and at anodic current densities of more thun 2 to 4 ma per sq cnz, n-type GaAs single crystals of lozo resistivity preferentially dissol~je forming etch tunnels with triangular or civc~ilay cross sections and of a width between 0.5 arid 5 p. These etch tunnels are oriented along any one of the four possible (111) directions of GaAs. However, their growth occurs only in one direction of a given (111) whick apparently is determined by the atomic sequence Ga —As (and not the rezlerse) in respect to an individual valence bridge in the crystal. It is concluded from comparison with the cubic lattice structure of GaAs that the etch tunnels represent macroscopic evidence for the tetrahedral bonds and their polar properties. If the anodic current density is increased the tunnel fomation results in the development of a fibrous surface layer consisting of GaAs. The latter separates frorn the substrate (in an anodic s~irface disintegration process) by the growth pressure of an As,0, filnz forming in the interior of the fibrous layer, 100 to 200 µ under the surface, at more than about 50 ma per sq cni. The fibrous GaAs film has the same crystallographic orientation as the substvate and represents a skeleton of the original crystal. Since the etch-tunnel density in a separated GaAs layer is about 108 c?n-', and the etch tunnels develop only along (111) in a given polar direction, it is assurraed tlmt the dislocations have no influence on the growth of these tunnels. ElECTROLYTIC treatment of smooth surfaces of poly- and single-crystalline GaAs at high anodic current densities causes the formation of porous surface layers.' This phenomenon suggests comparison with effects being observed with magnesium,' indium,, gallium,4 and aluminum5 and known as "anodic disintegration". The purpose of the present paper is to explore and to explain the reasons for the formation of such surface layers on GaAs and, in particular, to investigate the influence of the lattice polarity of this III-V compound semiconductor in the (111) direction on the anodic dissolution behavior. GaAs SINGLE CRYSTALS For the experiments described below GaAs single crystals from the Monsanto Co., St. Louis, Mo., were used. Their impurity levels were below 1 ppm and their dopant levels between 1 and 100 ppm. They were grown in (111) using the Czochralski or the gradient-freeze technique. The crystals had n-type conductivity and electric resistivities between 1 and 5 ohm-cm. EXPERIMENTAL The GaAs single-crystal rods were cut perpendicularly to (111) into wafers of about 1 mm thickness using a wire-blade crystal slicer and an aqueous slurry of Sic or a diamond saw. The orientation of the faces of these wafers were checked by Laue back-reflection patterns. If there was a deviation from (111) the faces were abraded under a certain angle using grinding paper and distilled water. The damaged surface layer was removed from each crystal by chemical etching with a mixture of 1HF:1HNO3: 1H20 or 2HF:1HNO3:2HAc (glacial). {110) faces were obtained by mechanical cleavage, producing surfaces which did not require a further treatment. The GaAs wafers were mounted using "alligator" clamps instead of soldered electrical contacts.' Only the bare crystal surfaces were dipped into the electrolyte. The clamps were coated with insulating wax to prevent any contact with the electrolyte. The experiments were carried out in aqueous 2 N H2so4,' or in an aqueous solution of KOH and KCl1 (1 mole KOH + 1 mole KCl in 1000 cu cm solution). Anodic current densities up to several hundred ma per sq cm were applied for periods between 30 sec and 2 hr. For the purpose of investigating the initial steps of disintegration the anodic current density applied never exceeded 20 ma per sq cm. The films which partially separated from the anodic surfaces under high-field conditions were treated with KOH to further their detachment by dissolving the As2O3 formed. The washed and dried films were pasted to strips of filter paper, and Laue pictures were made. The back-reflection patterns obtained were compared with those of the original anode surface before and after anodic dissolution. Furthermore, space reciprocal lattices7 were constructed from asymmetric rotation crystal patternsa which permitted the determination of the crystallographic orientation of the detached films of the corrugated anodic surfaces. The disintegration products were identified from assymmetric powder patterns.8 The polarity of the {111) faces was determined by chemical etching with mixtures of 1HF:1H2O2(30 pct): 2H2O or 1HNO3:2H2O. Different patterns on each of two inverse (111) sides appeared.'-l8 The correlation of these patterns to the Ga{111) or the As(111) side has already been established by the use of light figures,18-20 by X-ray diffraction near the absorption edges of gallium and arsenic,'lmZ4 and by LEED measurements.25 The geometric structure of these surfaces and the interior of the anodically attacked crystals were observed and photographed with a high-power microscope using oil immersion objectives up to magnification of X1720.

Jan 1, 1968

By S.S. Clarke

The sheet-ground deposits of the Tri-State district, because they are fairly uniform in thickness (7 to II ft.)—rather flat, with an easy dip to the west—and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. Developing Tractors and Trailers A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Tig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½-in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the spring: could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dud. After four months of use, the .tires are beginning to show signs of failure.* In

Jan 1, 1943

By S. S. Clarke

The sheet-ground deposits of the Tri-State district, because they are fairly uniform in thickness (7 to II ft.)—rather flat, with an easy dip to the west—and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. Developing Tractors and Trailers A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Tig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½-in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the spring: could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dud. After four months of use, the .tires are beginning to show signs of failure.* In

Jan 1, 1943

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By A. K. Csazar, L. W. Holm

This paper describes our investigation of a post-water-flood, oil recovery process which consists of injecting a slug of propane followed by water. Also described are the results obtained by applying a modification of the process in which gas was injected ahead of the water. Under the conditions of the latter experiments, misci-bility was not achieved between the propane and gas. Preliminary experiments or) uniform, watered-out sandstone cores showed that an oil bank could be formed and produced by applying this recovery process. However, since reservoirs are not uniform in structure, the process also was applied to porous media containing irregular porosity and to stratified sand systems. As a supplenzerrt to the experinlental work, a mathernatical procedure was developed for calculating the performance of the recovery process in a bounded, layered, porous system with crossflow between layers. As a specific example, the method was applied to predict the perforrnance of the recovery process in a 6-ft long, two-layer, stratified, unconsolidated sand model for comparison with experinlental data. The calculations were programed for the ZBM 704 computer. The equations and calcula-tional procedure presented can be extended to systems containing any number of randomly distributed permeability variations or any number of parallel layers. INTRODUCTION The problem of recovering the oil that remains in a reservoir which has been waterflooded is receiving considerable attention now as an increasing number of water floods reach an economic limit. A large number of the waterflood projects are in shallow reservoirs which are at pressures below 1,000 psi. It has been demonstrated in the laboratory that post-waterflood oil can be recover-ered by miscible displacement, but the LPG-gas, miscible flood and the enriched gas drive cannot be applied effectively at pressures below 1,000 psi. Only a few reports have appeared in the literature2-4 on low pressure, partially miscible recovery methods. However, it is possible to use LPG in a partially miscible displacement process in a reservoir where pressures of 200 to 1,000 psi can be achieved. Under these Pressures and at normal reservoir temperatures, propane is miscible with the oil; but, of course, gas or water used to drive the propane slug would not be miscible with the propane. Because of the lack of complete miscibility, it has generally been concluded that excessive amounts of propane would be required to recover oil and that such a recovery method would not be economical; however, we have found that under conditions present in certain reservoirs, an imrniscible recovery process can be applied effectively. The oil saturation in reservoirs at the economic limit of waterflood projects is usually in the range of 20 to 35 per cent of the pore space." A certain portion of this oil is left trapped by water in various size pores of the rock, but a good part of this so-called "residual" oil can be present in the less permeable lenses or layers of the reservoir rock which were by-passed to some degree by the water. The oil in these permeability traps can be produced only if favorable pressure gradients are formed in the reservoirs between adjacent zones of high and low permeabilities. A low viscosity liquid, miscible with the oil in place, which is driven by water through a stratified or heterogeneous porous system can aid in the development of these favorable pressure gradients. The oil that is released thereby from the permeability traps can be recovered by the subsequent water flood. Studies were made to determine how much oil could be recovered from homogeneous and stratified cores and models, which had been water flooded, by injecting a slug of propane and driving it with water. The effect of injecting a slug of gas ahead of the water was also determined. Most of the work described herein was done with the propane-water combination; unless otherwise specified, no gas was injected. The principal objectives of the investigation were to determine (1) if an oil bank could be formed and (2) what ratio of oil recovered to propane injected would be obtained. A further objective was to develop a method for calculating fluid-flow performance in stratified systems which would account for fluid transfer between zones in hydrodynamic communication but of different permeabilities. THEORETICAL ANALYSIS In a theoretical study of the recovery process, analytical expressions were derived to calculate the pressure distribution, the fluid flux in longitudinal (parallel to layers) and transversal (across the layers) directions, and the fluid distribution at any point in the system. The equations were developed for a two-layer porous system in which it was assumed that the fluids in the system were incompressible and that capillary and gravity effects were