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By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By Herman F. Kaiser, Charles S. Barrett, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By Charles S. Barrett, Herman F. Kaiser, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

By Roswell H. Johnson

What becomes of the water which must have filled the oil and gas sands at the time of deposition, has long puzzled students of oil and gas and has found expression in Munn's well-known article on the hydraulic theory. Both Munn and Clapp have pointed out that in the Appalachian field the deeper sands carry increasingly less proportionate amounts of water. It seems to me probable that the principal source of oil and gas has been in the shales in proximity to the sands which now contain these products. The sand spits which mark off the lagoons from the sea comply particularly with the requirements of a limited sand imbedded in shales rich in organic matter. Cunningham Craig has objected to this view that the rich organic muds of lagoons are found only at the surface. That such muds do extend to considerable depth 1 am assured by Prof. Douglas W. Johnson, who has made an extensive study of the Atlantic Coast marshes. As any particular sand body becomes weighted by a heavier and heavier overburden, the result of increasing deposition, a part of the very large percentage of water in the uncompacted sand and mud is forced out. The water percentage of freshly settled mud is vastly higher than that of the resultant shales, or even of a very porous sand. If beds of less compressible material meet or underlie the shales in question, there will frequently be a lateral motion along such beds to some point where the upward movement will be resumed. We find in our laboratory work here that oil, gas, and water have extremely slight capacity for gravitational sorting while in a state of rest, but when moving the gravitational sorting is readily accomplished. As the oil, gas, and water pass a body of larger pores, the gas, owing to its lack of capillary attraction, is retained in the large pores. This has been predicted by Washburne, Blatehley and others on the ground that the water has a higher capillarity and grips the finer pores in such a way that there will be a greater proportion of oil and gas in the large

Jan 1, 1915

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors' laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris's review,' the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert's analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969

By F. Keller, A. H. Geisler

ALTHOUGH the subject of precipitation from solid solution appears to be one of the more profitable fields in metallurgy for study with the electron microscope, few comprehensive studies have yet been made. Occasionally electron micrographs have been published that illustrated alleged precipitation in various alloys, but frequently the apparent size, shape and distribution of the particles do not fully agree with those expected from theory or from observations of the precipitate when the particles have grown to a size resolvable with the light microscope. The presence of a Widmanstätten pattern for submicroscopic precipitate particles has been demonstrated for only a few aged alloys.1 The initial problem has been the development of suitable techniques for applying the transmission-type instrument to a field that has been inherently associated with reflection-type microscopes. The various techniques have been the subjects of numerous publications, and instead of describing them individually here it will suffice to say that the oxide film method has proved to be the most satisfactory method yet found for studying the microstructure of aluminum alloys with the electron microscope. This method has the definite characteristic advantage that the actual surface layer of the specimen is examined and not a plastic or silica replica. Doubtless suitable methods for forming and removing the oxide film could be developed for alloys of other metals. The purpose of this report is to point out the characteristics of the oxide film method that have been observed during the studies of numerous aged aluminum alloys and to present the results of these studies. PREPARATION OF SPECIMENS The oxide film method for preparing specimens of aluminum alloys for examination in the electron microscope has been described in detail previously.1,2 Briefly, the procedure consists of preparing the metallographic specimen, forming the film by anodic oxidation and removing the film from the prepared surface of the oxidized specimen. The specimen is polished according to the usual procedure for microscopic examination.3 The specimen may then be etched to remove flowed metal but etching to attack the alloy constituents or to leave them in relief as in the replica processes is not necessary. Electrolytic polishing is not generally recommended. Deep-etched specimens are used frequently, however, since they provide information that is not revealed by polished specimens and frequently present the same information more clearly than do the polished specimens. The surface preparation of specimens to be deep-etched is not important, since specimens that have been subjected to the first wet polishing operation are generally used, but frequently the as-rolled surface is suitable. These specimens are then etched using a suitable macroetching reagent.

Jan 1, 1946

By Earle E. Schumacher, W. C. Ellis, John F. Eckel

Copper-calcium alloys are of interest as materials for use in deoxidized conductors of high conductivity. That calcium is effective in deoxidizing and degasifying copper is well known. Brandenberg and Wiensl have described the use of calcium in the casting of sound copper and state that the deoxidation can be carried out without difficulty. The castings that they prepared were sound and sufficiently ductile to permit wire drawing. Pratt,2 in British Patent No. 1699 (1907), has claimed the use of calcium for the deoxidation and degasification of copper. Masing3

Jan 1, 1930

BASIC open-hearth slags have no obviously unique features when compared with slags from other metallurgical operations. Open-hearth slags form and exist at temperatures ranging from 2500 to 3100 F (1370 to 1700 C). In the course of an open-hearth heat, the liquid slag changes slowly and continuously in chemical analysis-the changes reflecting changes in temperature, changes in metal analysis, solution of charged materials, solution of feed additions, and solution of refractories. Throughout the process, the slag performs specific primary functions that are responsible for a large measure of the technical and economic importance of basic open-hearth steelmaking. It is intended in this chapter to present the chemical reactions by which the primary functions of basic open-hearth slags are carried out, to describe the physical and chemical principles governing the extent to which these reactions proceed and can be regulated, and finally to indicate the limitations imposed on other features of the process by the fulfillment of the primary functions. Basic open-hearth slags perform three primary functions. First and foremost, the slag provides a means of removing phosphorus from the liquid metal. The ability to remove phosphorus is largely responsible for the widespread use of the basic open-hearth process. Second, the slag serves as a controlling factor in transferring the oxygen required for the other oxidizing reactions. Third, the slag provides a means of eliminating some sulfur from the open-hearth bath. While the extent of sulfur removal is not comparable to that of phosphorus, the ability to remove some sulfur contributes much to the value of the process. The effectiveness with which the slag fulfills its functions varies with temperature and composition. Since operating temperatures are fixed largely by the specified nature of the product and the equipment, .the speed and extent to which the functions of the slag are carried out depend largely on its composition. The necessity for regulating slag composition to accomplish the re-

Jan 1, 1964

By Carl Henrich

Aspen, the flourishing mountain- and mining-town of Pitkin county, Colorado, is located in the valley of the Roaring Fork, 11 miles above Glenwood springs, where that stream empties its waters into Grand river, a tributary of the Colorado. The Roaring Fork heads on the western slope of the Sawatch range near Grizzly peak, and runs in a general northwesterly direction to its junction with the Grand river. Of its numerous tributaries, Castle creek joins it just below the town of Aspen, the town being built on an extensive flat hounded on the northeast by the Roaring Fork and on the west by Castle creek. The latter heads at the junction of the Sawatch and the Elk mountains and flows northward between the two chains, until it empties into Roaring Fork. Opposite the town of Aspen, Hunter creek, coming westward from the western slope of Mount Massive, joins the Roaring Fork. About a mile north of Aspen, the bed of Hunter creek is at least 300 feet higher than that of the Roaring Fork at Aspen. Hunter creek forms thus, at its mouth, one of the best water-powers in Colorado. A portion of it is now utilized for electric lighting in Aspen, while in the near future, the whole of this magnificent natural power will be applied, through electric transmission, for hoisting, pumping and ventilating at different mines of the district. The mountain opposite the town of Aspen, on the east side of Hunter creek (which near its mouth flows southerly), is called Smuggler mountain, from the famous mine at the foot of it. On the other, or western, side of Hunter's creek (see map, Fig. I), a higher mountain rises, on the slope of which the regular dip of the Triassie or Upper Carboniferous red sandstone strata, alternating with white layers of the same rock, can be clearly seen from town. This mountain is called Red mountain, from the prevailing color of its rocky

Jan 1, 1889

By F. A. Forward, V. N. Mackiw

The paper relates to the laboratory and pilot plant studies that have been carried out by Sherritt Gordon Mines Ltd., Metallurgical Research Div., in developing the ammonia pressure leach process for extracting copper, nickel, cobalt, and sulphur from high grade nickel concentrate produced from Lynn Lake ores, and describes in some detail the chemistry of the process. IT is well known'.' 2 that copper, nickel, cobalt, zinc, ferrous iron, and a number of other metals combine with ammonia in aqueous solution to form complex ions of the form [Me(NH,)x]"+. The stability and solubility of these ions depend on the concentration of the metal ion in solution, on the amount of NH, present, and on the amount and type of anions present, e.g., OH-, C0;-, NO,, C1-, SO;-. If ammonia is partially or completely removed from such solutions, for example by boiling, the soluble ammines tend to decompose and the metals precipitate as basic salts. These properties of metal ammines have found practical application in the commercial recovery of copper, nickel, and cobalt from a variety of ores. In an operation formerly conducted at Kennecott"" the mill tailing containing 0.80 pct Cu as copper carbonate was leached by percolation with an ammonia-ammonium carbonate solution to dissolve the copper as the ammine. At Calumet and Hecla0-" With a mill tailing containing about 0.4 pct Cu as metallic copper, it has been found necessary to aerate the ammonia-ammonium carbonate leach solutions between stages to oxidize the solubilized copper. At Nicarol"-" where nickel and cobalt occur as oxides and silicates which are not soluble in ammonia, the ore is heated to decompose silicates and to selectively reduce the nickel and cobalt to metal, leaving the iron as Fe,O,, and is then leached with ammonia-ammonium carbonate solution accompanied by aeration to dissolve nickel and cobalt as ammines. In each of these leaching operations, the anion present is CO, and the metals can be precipitated from the leach solution as oxide (copper) or hydroxide and carbonate (nickel and cobalt) by boil- ing off NH, and C02 both of which are recycled to treat a subsequent ore charge. The products-—oxide, hydroxide, or carbonate—can be treated by conventional smelting, calcining, or electrolytic methods to convert them to refined metals. Thus the procedures mentioned utilize the properties of the ammines to extract copper, nickel, and cobalt from nonsulphide ores and separate them from the leach solutions. These processes have the advantage that they can be carried out in closed vessels at atmospheric pressure, that the leaching solutions are specific for the desired metals, that the metals can be recovered as relatively pure compounds by the boiling operation, and that the NH, and CO, can be recycled. Also, as the leach solutions after boiling and filtration are substantially free of metals, NH,, and CO,, they can be discarded, thus facilitating the control of the water balance in the leaching circuit. When, as is the case with Sherritt Gordon concentrates, sulphides are treated with ammonia solution in the presence of oxygen, the leach solution contains SO,--, and an entirely different set of conditions is encountered. The ammine sulphates (of nickel, for example) are more soluble than the carbonates and can be only partially decomposed by boiling. The SO, and NH, in the solutions can not be recovered by boiling. Thus, despite the more favorable leaching conditions resulting from high solubility of the ammine sulphates, the recovery of metals, NH,, and SO, from the solutions must be effected by other means. Sherritt Gordon Nickel Concentrate Treatment The Ni-Cu-Co flotation concentrate produced at Lynn Lake'" contains 12 to 16 pct Ni, 1 to 2 pct Cu, 0.2 to 0.5 pct Co, 33 to 40 pct Fe, 28 to 34 pct S, 8 to 20 pct insoluble, and less than 0.02 oz per ton precious metals. The nickel is present chiefly as pentlandite, the copper as chalcopyrite, and the iron as pyrrhotite and pyrite. Most of the cobalt is thought to be present in pentlandite, although it is known that a small amount occurs as Co-Ni-pyrite.

Jan 1, 1956

By J. B. Warriner

Stripping is the name given to the process of removing clay, rock, or other cover from deposits of coal or ore. In this paper it is intended to cover the methods used in carrying on this operation in the anthracite coal regions of Pennsylvania. In doing this, attention will be chiefly devoted to those methods wherein practice in different sections of the region differs, or is susceptible to change or improvement, though it is intended to give as complete data as possible concerning all stages of the operation. The data from which this paper has been prepared have been collected and submitted by a committee† representing the larger users of stripping methods, of which committee the writer has acted as chairman. Data and assistance have also been obtained from various mining men, engineers, contractors and manufacturers of stripping equipment, to all of whom our appreciation is due. Early History and Statistics The earliest mining operation on a commercial scale in the anthracite region was a stripping operation. This was the famous Quarry mine at Summit Hill, where this method was used only because no other method of mining a deposit of the nature found there seemed feasible to the early operators. A description of this stripping from a report published in 1821 is as follows: "The coal mine at present worked by the company lies on the top of a mountain, and appears to extend over some hundred acres of land covered by about 12 ft,. of loose black dirt resembling moist gunpowder, which can be removed by cattle with scrapers, and thrown into the valley below so as never to impede the work. The thickness of the coal is not known, but a shaft has been sunk in it 35 ft. without penetrating through. More than an acre of mine has been uncovered and presents a huge rock of coal, which is easily quarried without blasting."

Jan 1, 1918

By A. Hellawell

Binary alloys of compositions intermediate between solid-solubility limits and eutectic compositions have been completely separated into primary phases and eutectic by freezing unidirec-tionally at very slow rates (10-6 to 10-5 cm per sec). The alloys examined were Pb-1 wt pct Ag, Al-20 wt pct Cu, and Al-42 wt pct Cu. The compositions and proportions were close to those expected from the phase diagrams and provided information about the solid/liquid interface at certain free zing rates. DURING the directional freezing of an alloy the solute distribution is controlled by the efficiency of mixing in the liquid,'" whereas diffusion in the solid state is of negligible importance. It is known3 that mixing by convection is very efficient, but complete segregation is only achieved at very slow freezing rates4-6 or with forced stirring in the liquid. ' Yue9 and Yue and clark10 have previously illus- trated partial separation of primary phases in alloys close to eutectic compositions. In the present work, taking binary alloys of compositions intermediate between the limits of solid solubility and eutectic compositions, it has been possible to achieve complete separation of the primary phases by directional freezing at very slow rates. METHODS AND RESULTS The alloys concerned were Pb-1 wt pct Ag, A1-20 wt pct Cu, and A1-42 wt pct Cu. As may be seen from the relevant diagrams,11 these alloys should segregate into approximately equal proportions of primary solid solutions and alloy of eutectic compositions. Specimens, -12 cm long and 1 cm wide, were frozen in horizontal tubes by withdrawal from a furnace. The lead alloy, prepared from materials of 99.999 pct purity, was sealed into evacuated Pyrex tubes and the aluminum alloy of similar purity contained in graphite boats under vacuum. The molten alloys were seeded with some 3 cm of solid to prevent irregular initial freezing rates and the last portions to freeze were ignored. At the slow freezing

Jan 1, 1965

By G. M. Schwarz

There has been considerable controversy regarding the structure and mineral constituents produced when iron ore is sintered. This investigation was undertaken in order to establish the fundamental reactions that take place in the sintering process by determining the nature of the resulting minerals. The writer's immediate interest in the subject arose mainly from the request of E. W. Davis for information based on a microscopic study of sinter submitted by him in May, 1926. In the author's preliminary work, samples of iron-ore sinter were secured from the Minnesota School of Mines Experiment Station and from commercial plants. These were polished by the usual methods for polishing opaque ores. In order to study these surfaces satisfactorily, it is necessary to magnify them rather highly, a range from 100 to 1000 dia. being used. For the higher magnifications oil-immersion lenses and an intense source of light are necessary. After the preliminary study had shown the problems involved, a series of small samples were sintered under carefully controlled conditions and with analyzed materials. Variations in the relative amounts of ore, coal and water were made in order to study the effect of each constituent. The attempt has been to arrive at a clearer understanding of the sintering process and the reactions involved without reference to any preconceived notion as to sinter. It is clear that the study of polished surfaces has yielded results not possible with thin sections alone. The thin sections made in this work were found unsatisfactory at magnification greater than 75, whereas magnifications of 1000 were easily studied with reflected light on carefully polished surfaces. A rather complete statement of observed facts is made so that the reader may form his own conclusions. The writer's interpretations are suggested. It is to be hoped that a more complete understanding of the structure arid composition of iron sinter, as well as the changes which go on during

Jan 1, 1929

By O. W. Ellis

THE question of the influence of gases upon the properties of copper has received the attention of a number of investigators, among whom Sieverts,1 Iwasé,2 Lobley and Jepson3 stand preeminent. SOLUBILITY OF . GASES IN. COPPER Sieverts and Iwasé concerned themselves with the solubility of a variety of gases in the metal in the solid and liquid states. They determined the absorption coefficients of these gases and in all cases found a sharp change in solubility at the melting point of the metal. In this respect they disagree with Lobley and Jepson, who have based their opinions upon the appearance of small ingots of the metal which had been fused in an atmosphere of one or other of three gases and had then been rapidly cooled, while surrounded by gas, to the freezing point (rate-possibly 30° to 60° C. per sec.). The ingots that had been fused and cooled under nitrogen and carbon monoxide were free from blowholes and it was assumed that these gases were not absorbed in amounts much in excess of those which would dissolve in the solid metal; the ingots similarly treated under hydrogen were full of blowholes and it was assumed in this case that gas was ejected on solidification of the copper. The effect of varying the rate of freezing upon the character of the test ingots was not examined by these investigators; otherwise, it is felt, their views might have been subject to modification. Sieverts' most important contribution is that the solubility of a gas in any metal is proportional to the square root of its pressure or concentration. Knowing then the absorption coefficients of the various gases in copper, it should be possible to determine the analysis of the

Jan 1, 1928

By Ben L. Seegmiller

Introduction The profitability of an open pit operation depends to a large extent on the use of the steepest pit slopes possible, provided they do not fail during the life of the mine Optimum pit slopes can be designed by using rock mechanics technology. Such technology includes gathering and analyzing pertinent data prior to pit design, rigorous application of rock mechanics principles during the design process, remedial actions to improve slope stability, and monitoring slopes during the life of the mine. Ignoring rock mechanics technology in pit design may place the entire mining enter- prise in jeopardy Disruption of mining operations and safety hazards caused by slope instability can be severe. A classic case in point is the major slope failure (Seegmiller, 1972) that occurred at a southwestern US copper mining operation in 1970-1971 Minor slope stability problems initially amounted to no more than a nuisance, but in time, the unstable zones became larger, causing greater disruption of production and threatening safety Mining at or near the slide toe had continued throughout the period of slope failure, aggravating the already unstable condition The original plan for this pit called for mining the overall pit slope to 37.5" Mine operators were forced to lessen the back- slope angle in the hope that the failing rock mass would stabilize. However, stabilization did not take place, and when mining in the area of failure was completed, the overall slope had been reduced to approximately 27" Mining had been successful in removing only a small portion of the ore body at a high stripping ratio.

Jan 1, 1979

By S. K. Tarby, W. O. Philbrook

The rate of FeO and MnO reduction from silicate and aluminate slags by carbon-saturated iron is dependent on both slag composition and temperature. Owing to variable stirring rules during- the course of reaction, the reduction processes occur in two stages in stationary graphite crucibles. In the first stage the slirring caused by CO evolution results in forced convection conditions in the slag. As the boiling action subsides during reduction, the flow conditions within the system become those defined by natural convection. Analysis of the data by an unsteady-state penetration model indicates that the rate of reduction is controlled by the rate of cocur-rent flow of' cations and anions from the bulk slag to the interface during both stages of reduction. The hearth reactions of the blast furnace have been extensively investigated from the viewpoint of equilibrium by deductions from controlled laboratory experiments. However, the literature contains relatively few studies that have been directed toward the area of slag-metal reaction kinetics, and the majority of these have been concerned with the rate and mechanism of sulfur transfer between iron and slag. More recently, attention has turned to the kinetic factors in the reduction of oxides from liquid slags. One of the first investigations in this field was conducted by Dancy1 on the reduction of pure liquid FeO and pure liquid Fe3O4 by carbon-saturated iron. The integrated form of the rate equation indicated that the reduction of FeO was of the first order up to 80 pct reduction. Over the initial 30 pct of reduction, the magnetite reaction was also interpreted as a first-order process. The rates of reaction were extremely rapid as indicated by a 30 pct reduction of the liquid magnetite in a time interval of about 1 to 2 sec. Phil-brook and irkbbride' studied the reduction of FeO from a lime-alumina-silica slag by carbon-saturated iron and solid graphite in stationary crucible assemblies. With the use of the differential form of the rate equation, the rate of the reduction reaction was found to be proportional to the second power of the concentration of the reactant FeO for both the slag-metal and slag-graphite reactions. These authors presented a number of comments in an effort to explain the difference between the molecularity of the above reaction and the observed second-order relation. One such argument, recently extended by Wagner,3 was that the rate-limiting step may well be one of transport control. A complete discussion of the proposed mass-transport control mechanism of this reduction reaction will be presented in a later section of this paper. Kinetic studies of the reduction of other oxide species, namely chromous oxide, titania, and silica, have also been reported. McCoy and philbrook4 used rotating crucible assemblies to investigate chromium reduction from Ca0-SiO2-A12O3 slags. First-order kinetic law was obeyed for the slag-metal reduction reaction as determined by the integration method of data analysis. Due to scatter of the data, any dependence of the rate constant on temperature or slag composition was obscured. Concentration-time data for the reduction of titania from blast-furnace type slags under reducing conditions were obtained by Delve, Meyer, and Lander.' The data were too few, however, for a formal kinetic interpretation. Kinetic data for the very slow reaction of silica reduction have been observed by McCoy and Philbrook6 and Fulton and chipman.7 The former experimenters found the reaction-rate constant for silica reduction by carbon-saturated iron to be 20 to 60 times less than the rate constant for chromium reduction. In their work on the reduction of SiO2 in mechanically stirred systems, Fulton and Chipman also found small values for the specific reaction rate and derived a high value for the energy of activation for the reaction. In both of these investigations, the reduction process was assumed to follow first-order behavior. schuhmann8 proposed that the rate-limiting step in this reaction is the diffusion of oxygen from the interface through a boundary-layer film to the bulk metal phase, and Rawling and Elliott9 have reported experimental confirmation of this hypothesis for temperatures below 1600°C. Turkdogan et a1.10 have also concluded that the rate of reduction of silica is a slow process and controlled by the diffusion of oxygen in the metal, but only in the absence of carbon monoxide bubbles at the slag-metal interface. In the presence of bubbles, achieved either by injecting carbon monoxide at the slag-metal interface or by blowing it through the metal and slag, these investigators found a rather rapid reduction of silica which appeared to be controlled by an interfacial reaction involving the de-sorption of silicate ions from the slag-metal interface to the metal phase as silicon and oxygen atoms. In view of the unresolved nature of the kinetics of FeO reduction and the lack of kinetic data for the manganese reaction,

Jan 1, 1968

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By J. R. Low, M. Gensamer

During the course of an investigation into the drawability of automobile-body sheet steel, it became apparent that certain advantages would be possessed by a deep-drawing steel with a very low yield strength, but almost normal tensile strength, provided a reduction in yield strength could be accomplished without sacrifice of ductility and fine grain size. It would also be desirable to have this steel free from strain-aging; that is, free from the tendency for the yield point to return after it had been eliminated by straining. It was known that, wet hydrogen treatment acted to eliminate aging, but as carried out by other investigators, at relatively high temperatures, this treatment resulted in grain coarsening. It has been established by some of the experiments reported in this paper that all of these objectives can be accomplished by treatment in wet hydrogen at a low temperature, in the neighborhood of 72o°C. The time of treatment is relatively short (about 3 hr, to completion with 20-gauge sheet) if the water content of the hydrogen atmosphere is made fairly high, say aimost 30 per cent by volume. At this temperature. the grain size remains fine in the time required. After this treatment sheet reduced the usual amount by cold-rolling has a grain size of about A.S.T.M. No. 7. The yield point is completely eliminated, and the yield strength is reduced to a very low value, in the neighborhood of 15,000 lb. per sq. in. The stress-strain curve departs gradually from the straight-line elastic part after the fashion of nonferrous deep-drawing alloys. This elimination of the yield point is accompanied by a verv low indentation hardness; for example, 32 Rockwell B or even lower. There is no aging as measured by increase in the yield strength upon aging at room temperature or for 3 hr. at 200°C., after stretching about 10 per cent in tension. Tensile strength is only slightly less than the box-annealed sheet, seldom dropping much below 40,-ooo lb. per sq. in. Elongation is practically unchanged, or increased slightly. The term yield point, as here used, refers to the phenomenon of heterogeneous deformation occurring at a substantiallv constant load, observed principally in annealed low-carbon steels. If such a steel is loaded in tension, the load increases steadily with elastic strain, suddenly falls, fluctuates slightly about some constant value for a time and then begins to rise again as deformation proceeds. The maximum initial load before the sudden drop is generally called the "upper yield point"; the value of the load where deformation proceeds at a

Jan 1, 1944