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By George R. St. Pierre, John Chipman

METALLURGISTS have been studying the chem-ical behavior of sulfur in steelmaking for many years in order to have a better control of the sulfur content of finished steel. During the refining period in the open hearth, molten steel is separated from a gas phase by molten slag. Chemical reactions occur principally at the slag-metal interface and at the slag-gas interface. A need for physical-chemical investigations of reactions between sulfur-bearing gases and steelmaking slags was recognized some time ago.'.' From the early work, it can be qualitatively concluded that increased sulfur content and low partial pressure of oxygen in the gas phase favor the passage of sulfur from gas to slag. Using radioactive sulfur S Koch and Fink' have demonstrated the rapid rate of exchange of sulfur between gas and slag in an open hearth furnace. Gurry and Darken and Darken and Shields (as reported by Derge and Marshall') have equilibrated lime-iron oxide slags with SO—O2 gas mixtures. The major conclusion from the reported results is that sulfur content increases with increasing lime content in lime-iron oxide slags equilibrated with a gas of high oxygen pressure (10-2). The data were interpreted as indicating the presence of SO, and S,O, ions. Richardson and Fincham' have conducted the most extensive experimental study of sulfur equilibria between gas and slag. Their results confirmed many of the conclusions drawn from calculations of Richardson" and Withers. Richardson and Fincham's data fitted very well into the sulfur scheme represented by the reactions 1/2 s2 (g) + (0) melt - 1/202(g)+ (S) melt [II 1/2 S, (g) + 3/2 O (g) + (0) melt - (SO,) melt. [2] At oxygen pressures greater than 10 to 10 they found that reaction Eq. 2 was predominant while reaction Eq. 1 was controlling at oxygen pressures less than 10." to 10.". The slag compositions and gas mixtures used in their investigations were different from those used in the present study. Wherever possible, comparison has been made between their results and these, and agreement is excellent. It is evident that the distribution of sulfur between slag and gas depends upon the oxygen pressure of the gas. In FeO slags, a change in oxygen pressure produces a change in ferric oxide content, and a knowledge of this equilibrium is a prerequisite to studies of sulfur distribution. The data are found in the work of Darken and Gurry" on the FeO system and the more recent experiments of Gurry and Darken" and of Larson and Chipman" on FeO slags containing lime and silica. The effect of oxygen pressure on the ratio Fe /(Fe" + Fe ), the so-called j-ratio, reported by these investigators will be used in interpreting the results which follow. Experimental Method The purpose of the experimental program was to determine the equilibrium sulfur content in slags exposed to gases of known oxygen and sulfur pres- sures. The slag compositions selected for study were from the lime-silica-iron oxide system. Additions of magnesia were made to some of the slags. Apparatus—The apparatus used by Larson and Chipman was modified slightly to accommodate the addition of SO2 to the gas mixtures. As in their work, slag samples of 0.5 to 2.0 g were held at temperature (lcc) in platinum crucibles under a steady stream of gas, 100 to 200 ml per min, for several hours and then rapidly lowered to the bottom of the furnace where they were quenched in mercury. Preparation and Analysis of Gas Mixtures—Mixtures of SO,-CO were prepared from Virginia Smelting Co. Extra Dry liquid SO, and Pure Co. CO,. After removing traces of water vapor with an-hydrone, the CO, was passed over graphite at 1200°C, at which temperature the conversion to

Jan 1, 1957

By J. C. Melrose

The contact angle is one of the boundary conditions for the differential equation specilying the configuration of fluid-fluid interfaces. Hence, applying knowledge concerning the wettability of a solid surface to problems of fluid distribution in porous solids, it is important to consider the complexity of the geometrical shapes of the individual, interconnected pores. As an approach to this problem, the ideal soil model introduced by soil physicists is discussed in detail. This model predicts that the pore structure of typical porous solids will lead to hysteresis effects in capillary pressure, even if a zero value of the contact angle is maintained. The model is generalized to situations in which the contact angle takes on values between zero and 40 degrees. For the imbibition branch of the capillary- pressure function, the model predicts a considerable departme ftom the usually assumed cos 0 relationship. In fact, according to the model, it is possible that a displaced wetting phase will not be able to reimbibe, even when the contact angle does not exhibit hysteresis. INTRODUCTION The subject of capillarity in porous media has long been of interest in many branches of engineering and applied science. The earlier investigators were those concerned with the physics of soils. 1-5 More recently, petroleum engineers and others dealing with the problems of petroleum production from reservoir rock have given much attention to the subject.6-10 Also, important additions to the literature of capillarity have been contributed from the field of chemical engineering.11-12 These attest to the wide range of industrial applications in which capillary phenomena play a role. The present paper is concerned with the role which wettability plays in capillary action in porous media. As is well known, capillary-rise (or capillary pressure) phenomena have frequently been interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This approach has enjoyed a certain degree of success in correlating experimental results.13 The generalization of this model, however, to situations which involve varying wettability, has not been established and, in fact, is likely to be unsuccessful. In this paper another approach to this problem will be discussed. A considerable literature relating to this approach exists in the field of soil science, where it is referred to as the ideal soil model. Certain features of this model have also been discussed by Purcel114 in relation to variable wettability. The application of this model, however, to studying the role of wettability in capillary phenomena has not previously been attempted in detail. In the present paper, additional features of the model are introduced. These features are critical in determining the quantitative behavior of the model. GENERAL FEATURES OF CAPILLARY HYDROSTATICS BASIC PRINCIPLES When the interstices of a typical porous solid are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. Hence, fluid-fluid interfaces are found within a certain fraction of the pore openings. The fundamental equation of capillarity specifies the configuration of these fluid-fluid interfaces. This is known as the Laplace equation, when derived from mechanics, and as the Gibbs-Kelvin equation when derived thermodynamically.15 Given two fluid phases, a and ß, in hydrostatic equilibrium, the Laplace equation states that the respective fluid pressures in regions close to the interface are related by Here oaß is the surface or interfacial tension and rl and r2 are the principal radii of curvature of the surface or interface. The pressure difference, Pa-Pß, is the capillary pressure, PC. As Buff15 has shown, Eq. 1 states the condition for hydrostatic equilibrium within the two-phase confluent region, which is referred to as the interface. It thus can

Jan 1, 1966

By Paul B. Crawford, Melvin B. Burton

A procedure is given which describes how the gelatin model may be-used to study the effect of mobility ratio on areas swept before and after breakthrough in fluid injection programs. Differences in mobility ratio are achieved through the proper selection of electrolytes for the invading and displaced fluids. The progress of the front is followed visually and photographed or traced onto plates (it desirrd positions before and after breakthrough. Example applications to standard flooding pattrrrls, vertically and horizontally fractured reservoirs and the in-situ combustion recovery process ore presentrtl. INTRODUCTION In water flooding, gas cycling and other fluid injection programs, the sweep efficiencies and swept areas after breakthrough are known to depend on the mobility ratio. Previous investigators have described the application of the X-ray technique, stepwise use of the poten-tiometric model and numerical procedures for studying these problems.1,3,4,6 Others have described the application of the electrolytic and gelatin models for studying sweep efficiencies at a mobility ratio near one.2,5,7,8,9 It is a purpose of this paper to describe a procedure for using the gelatin model to study swept areas at mobility ratios other than one. PROCEDURE The technique developed for gelatin model studies is composed of four phases: the construction of the model, the selection and preparation of electrolytes, the running procedure, and the recording of the swept areas. Each phase is discussed independently in order that the over-all procedure will not be confused. Construction of the Model Since some of the advantages of the gelatin model are its economy, and speed, it is desirable to have as small a model as is possihle without creating error through the inability to follow visually the progress of the colored front. For this work, it was found that a distance of 4 to 6 cm between salt bridges is convenient to use. Since the size is relatively small, it follows that the gelatin layer must be thin. For this study, 1/8 in. was used as the gelatin thickness in each case. The model was constructed on a flat 1/2-in. plastic (Lucite) base with boundaries constructed from 1/8-in. plastic strips. The well pattern to be studied was outlined with the 1/8-in. plastic strips on the base with narrow apertures (- - 2 mm) in the boundary to represent the wells. Behind each well opening, a rectangular area of some 8 to 12 sq cm was outlined by additional plastic strips. The plastic strips were fastened to the base by any suitable non-conducting cement so that the boundary system was liquid tight. The electrodes were constructed from sheet copper in a fashion that would allow easy removal. In this work, it was found that by simply forming a large U-shaped clip from a strip of the copper that would slip over the boundary was satisfactory and easily removed. The electrodes should be as wide as one of the sides of the rectangular area behind the well opening. If a fractured pattern is studied, fractures inside the well pattern may be represented by strips of copper of the desired shape mounted in some easily removable fashion. The reason that apertures (or salt bridges) were used for wells instead of metallic electrodes is that the plating of the electroactive ion at the cathode and the introduction of an electroactive ion at the anode has a detrimental effect on the swept area outline if these operations \rere permitted to be carried on within the well pattern itself. The anode may be used within the well pattern

Jan 1, 1957

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By J. L. Moriarty, Irving Johnson, H. M. Feder

The crystallization of ternary alloys has been studied as a coprecipitation phenomenon by measuring the substitutional carrying of trace metals with CeCd11 precipitating from liquid cadmium. The Doerner-Hoskins logarithmic distribution law has been found to apply in all cases; the coprecipitation coefficients obtained were: 1.48 (La), 1.06 (Th), 0.63 (Pr), 0.24 (Gd), 0.17 (Sm), 0.13 (U), 0.10 (Er), 0.09 (Sr). Li, Na, K, Ba, Y, Sc, and Zr were not measurably carried. It has been observed that coprecipitation was most extensive for those tracers which form with cadmium an intermetallic compmdnd isostructural with CeCd11 or closely related thereto. For these tracers an inverse relation between Solubility in cadmium and coprecipitation coefficient was noted. THE partition of impurities between the liquid and solid phases of a metal or a congruently melting intermetallic compound has been extensively studied by the methods of zone melting.' However, when the composition of a liquid alloy and of the solid phase crystallizing from it differ grossly, partition of an impurity cannot be investigated in this manner. Partition of the impurity under equilibrium conditions may be studied by investigation of the appropriate phase diagram and partition under nonequi-librium conditions may be studied by observation of coring in the solidified alloys.2 The nonequilibrium case is of special interest in metallurgical practice because many complex alloys are cooled too rapidly to permit the uniform diffusion of impurities throughout the crystallizing phase(s). With this in mind, the present study was undertaken to obtain quantitative data on the phenomenon of coprecipitation via substitutional solid solution in certain metallic systems. It will be noticed that rather than adopting metallurgical ter- minology we have chosen to refer to the partition of impurities during alloy crystallization as coprecipitation.3 In the terminology of coprecipitation the impurity is referred to as the tracer and the precipitating phase as the carrier. From aqueous solution, coprecipitation may occur as a result of adsorption on the surface of the carrier, by occlusion of the liquid within the crystals, or by solid solution of the tracer in the carrier. By slow cooling of liquid metallic solutions it is relatively easy to form large, regular crystals of the carrier; the effects of adsorption and occlusion may be minimized and the influence of substitutional solid-solution formation may be made to predominate. Previous studies of the crystallization of some intermetallic compounds4 and of copper, silver, and gold5 have shown that the coprecipitation or partition behavior of trace metals is entirely analogous to that observed in aqueous systems when ionic substitution occurs, e.g., coprecipitation of Ra++ with BaSo4. The precipitation of CeCd11 from liquid cadmium was chosen for study. This choice was influenced by the following consideration. If the relative atomic sizes of the tracer atom and the atom for which it substitutes determine the tendency to coprecipi-tate, then a lattice having a substitutional site of well-defined size would be desirable. In CeCd116 (structure type cubic BaHg117) the cerium atom is completely surrounded by a cage of twelve nearly equidistant cadmium atoms. Thus, atoms much larger or much smaller than cerium should be poorly accommodated in this cage. The choice of a lanthanide central atom allowed the testing of the size hypothesis with a number of lanthanide tracers which differed in size but not in valence or electro-negativity. EXPERIMENTAL The general technique of this investigation was to prepare a slightly undersaturated solution of carrier in liquid cadmium to which a tracer was added. The concentration of tracer was always so low that saturation over the entire temperature range investigated was never exceeded. The solution was cooled in a stepwise fashion. After each step a por-

Jan 1, 1964

By Pablo Hadzeriga

Great Salt Lake brine was subjected, in laboratory scale, to conditions simulating solar evaporation. Solid phases and the variation in composition of the liquid phase throughout the potassium salts crystallization zone are presented. These experimental results are discussed and compare with stable equilibrium data of the quinary system Cl-, SO4, Na+, K+, Mg + + and H2O. The Great Salt Lake brine in Utah is a vast reserve of several potential chemicals which has attracted much attention in the recent past. From the standpoint of an ore reserve, it may be said that the lake contains a low grade ore which has to be concentrated by evaporation of water. Because of the fairly favorable weather conditions in the Great Salt Lake area, it seems reasonable to consider solar evaporation as an economical means of concentration. From the view of phase chemistry, the main constituents of Great Salt Lake brine make it belong to the five component system: C1-, SO4=, Na+, K+, Mg++ and H2O. Because of their low concentration, the presence of other elements may be regarded as having little effect on the equilibrium of the five main components. Equilibrium data for the quinary system of our interest has been available for many years. Using these data, it is possible to calculate how the brine of the lake will concentrate when subjected to solar evaporation. In practicing solar evaporation, the weather factor and supersaturation conditions cannot be ignored, but their introduction into calculations using equilibrium diagrams is almost an impossible task. With the experimental work presented in this paper, an attempt is made to compare the stable equilibrium data of the quinary system as applied to the case of the Great Salt Lake brine and the dynamic equilibrium when that brine is subjected to continuous solar evaporation. Sea water brine belongs to this quinary system when only the major constituents are considered. The study of this system has been carried on since the last decades of the nineteenth century. The reason for these intensive studies was to give a geological explanation to the underground potash deposits. AS a result, many theories were presented trying to relate the equilibrium data with the geological formation, paragenesis and metamorphism of these deposits. Two main approaches were followed for the equilibrium studies of this quinary system. One of them, and the best known to us, was the school started in Germany in the last century by J. H. Van't Hoff. The other one, which started about the same time, was the school of N. S. Kurnakov in Russia. Both approaches were different and as a consequence generated opposite theories about the geological formation of potash deposits. The Van't Hoff school studied the quinary system of sea water under careful laboratory control, resulting in stable phase diagrams. During these studies, Van't Hoff recognized the difficulties in crystallizing some double salts.' ". . . . we unexpectedly found that some compounds whose formation in the solutions under investigation was possible at 25°C, nevertheless totally failed to put in an appearance. These, not to mention the calcium salts, were leonite, MgSO4 . K2SO4 4 H2O; kainite, KC1-MgSO4 . 3 H2O; and kieserite, MgSO4 .H2O. Even exceedingly slow crystallization with the addition of the compounds themselves did not remove the condition of supersaturation in the case of these bodies." However, those salts (leonite, kainite, and kieserite) were included in the stable phase diagram at 25°C as shown in Fig. 1 using D'Ans data.3 The figure also shows the sequence of crystallization of the Great Salt Lake brine according to the stable diagram. In later studies by the Van't Hoff school, especially by D'Ans,3 Karsten,4 Autenrieth,5,6 attention

Jan 1, 1968

By M. R. J. Wyllie, H. W. Patnode

In the quantitative interpretation of electric log data it is essential to know the formation factor, defined as the ratio of the resistivity of the formation 100 per cent saturated with brine to the resistivity of the brine.' This concept implies that the formation factor for any given rock is constant irrespective of the resistivity of the brine or solution with which it is saturated. It is apparent that this can be true only when the rock matrix is wholly non-conductive. As reservoir rocks may contain clay or shale having an appreciable conductance one may expect these constituents to influence the determination of true formation factor. The formation factor may be theoretically derived from log data by dividing the resistivity of the mud filtrate invaded formation by the resistivity of the mud filtrate. Such a method of calculntion has implicit in it the assumption that the fluids in the invaded formation are wholly replaced by mud filtrate. that the solid matrix is non-conducting, and that the formation factor of the invaded zone is identical with the formation factor of the uninvaded zone. Since the validity of the first two basic assumptions regarding the insulating character of porous matrices and the displacement of the interstitial fluids in porous media do not appear to be fully established, the formation factors of a number of cores and clay slurries have been measured under conditions suitable for verifying the assumptions and the extent of any errors inherent in them. CORE STUDIES Apparatus and Procedure Resistivity measurements were made on short cylindrical permeable cores which had been previously mounted in lucite.2 The cores were clamped by means of insulated bolts between brass plates about 5 cm square and 1 cm in thickness. The plates were provided with a ring seal to prevent leakage between them and the core mount, and had a centrally located orifice so that fluids could be flowed through the mounted core. The brass mounting plates were used as electrodes and any current flow between them necessarily passed only through the constituents of the intervening core. Fluid saturation of the core, and fluid flow through the core, were effected by a centrifugal pump connected to the outflow end of the core, thus providing a differential pressure across the core of approximately one atmosphere. The procedure used was first to evacuate each core by means of the pump and then to saturate the core with an aqueous sodium chloride solution of known resistivity. The resistance of the core was measured and flow of the solution through the core continued for sufficient time to establish a constant resistance reading. After equilibrium had been reached with one solution, another sodium chloride solution of a different resistivity was flowed through the core and the flow continued until a constant resistance reading was again obtained. This procedure was continued until resistance measurements of the core had been made with a series of solutions within a salinity range from 1.0N NaCl to distilled water. The data obtained enabled the apparent formation factor of given porous rocks when saturated with fluids of different resistivity to be computed and also provided information regarding the ability of an invading fluid to displace interstitial water from a core. Results Berea Sandstone — The first core examined was a specimen of Berea sandstone." This core had been cut essentially parallel to the bedding for permeability studies. The core was clamped in the core holder and saturated with 1.0N NaCl solution and the resistance determined. It was subsequently flushed and the resistance measured when saturated in turn with 0.1N, 0.025N, 0.01N, .005N sodium chloride solutions and finally with distilled water. In flushing the core with each

Jan 1, 1950

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-

By G. Sachs, E. J. Riping

All ferrous alloys can be made brittle by straining at sufficiently low temperatures. However, the changes in mechanical properties for different ferrous materials with decreasing testing temperature do not appear to follow any universal law. In particular, complex effects of testing temperature have been observed if cold worked steels were subjected to tensile tests at low temperatures. EFFECTS OF PRESTRAINING AT A TEMPERATURE ABOVE THE TESTING TEMPERATURE ON THE FRACTURE CHARACTERISTICS‡ A considerable amount of data has been presented by a number of investigators on the fracture characteristics of various cold worked steels.' These data usually relate to a two-step procedure first used by Davidenkov,² consisting of stretching by tension to a certain strain or " prestraining" at room temperature and then completing the tensile test, or "testing" at the temperature of liquid air. On the basis of data of this type made available to date, ferrous alloys can be classified into two groups with respect to their fracture characteristics observed on testing at a low temperature after prestraining at room temperature. Very complex phenomena have been observed for all annealed steels. On the other hand, some observations indicate that steels in certain other conditions represent a fundamentally simpler relation. In considering the effect of prestraining at one temperature on the properties obtained at some lower temperature, it should be expected that any cold work reduces the ductility retained in proportion to the magnitude of the cold work. However, the test data presented to date indicate that only heat treated (quenched and tempered) steels appear to conform to this expectation, according to the very limited test data in Fig 1, presented by McAdam, Geil and Mebs. This series of tests, Fig 1, shows that the retained ductility became smaller the larger the prestrain. However, this decrease is less than the amount of prestrain or, in other words, less than the decrease in ductility at the prestraining temperature. These effects of prestraining are fundamentally identical with those observed by Bridgman3 when a steel was prestrained (in tension) under hydrostatic pressure and then subjected to a regular tension test. It appears, therefore, that the basic effect of prestraining under conditions which yield a higher ductility than the (subsequent) testing procedure, consists of gradually increasing the total ductility of the metal from the initial low value of testing to the higher value of prestraining. On the other hand, all annealed steels, if cold worked by tension at room temperature and then tested at a lower temperature, provided that some ductility is retained, showed a far more complex behavior than that discussed above. This relationship is exemplified by Fig 2, for three pearlitic steels.4,5 These particular steels were selected because of the various shapes of their ductility-prestrain curves. All three steels, and any other investigated so far, suffered a rapid decrease in retained (and consequently also in total) ductility when subjected to small pre-strains. Then, after exceeding a certain prestrain it was generally observed that the ductility recovered.* This rather complex behavior of annealed steels may be tentatively correlated with the presence of stretcher strains at small restrains. Heat treated steels do not exhibit stretcher strains. This fact might possibly explain their simpler prestrain-retained ductility relationship. The destructive effect of these stretcher strains may possibly be associated with the presence of triaxiality, which may occur in any highly non-uniform stress and strain state (and which is retained as residual stress after unloading). Even a small degree of triaxiality may then cause a reduction in ductility, or even embrittlement at a sufficiently low testing temperature. The discussion presented above deals with the effects of cold working at a high temperature on the fracturing

Jan 1, 1950

By Nigel B. Pearson

INTRODUCTION Chingola Division of Nchanga Consolidated Copper Mines Limited is situated in the Copper- belt of Zambia, approximately 30 kilometres south of the border with Zaire. It is the country's leading producer of copper and its principal foreign exchange earner, and has been, in its time, the largest single copper producer in the British Commonwealth and the second largest in the world. There are two 'primary' copper sources at the Division, namely Underground producing approximately 100 000 tonnes of contained copper annually, and the Open Pits, producing approximately 200 000 tonnes annually. Following the commissioning of the Tailings Leach Plant in 1974, treating final tailings, metallurgical recovery increased from approximately 70% to in excess of 80%. Extensive deposits of cobalt are present and following the rise in the market price in 1979 and 1980, plans were made to extract this separately. Cobalt production commenced in 1980 from Underground and will increase substantially when the Open Pit cobalt reserves become available in approximately 2 years time. This paper covers the development of the production method of the principal Underground Orebody, known as the Lower Orebody, and the control systems applied to it. HISTORY The Lower Orebody, formerly known as the Nchanga West Orebody, was discovered by extensive Diamond Drilling operations in the late 1920's. Development of the Shaft complex and the orebody commenced and continued until 1931 when flooding from development on the 480 foot horizon necessitated closure. The mine remained closed until 1937 and production commenced from the Lower Orebody in 1939. Various expansion schemes of the Metallurgical Plants and the Underground workings were completed over the years with the result that Underground production increased steadily to in excess of 150 000 tonnes copper annually in the 1960's. In recent years production has levelled out at slightly less than 100 000 tonnes annually. This decrease is as a result of producing from a lower grade reserve, available within a more limited production front, and the application of production constraints in the light of experience gained. GEOLOGY Within the Nchanga Mining Licence Area of Chingola Division, there are a total of 14 known copper orebodies in the basal part of a thick succession of sediments of Pre-Cambrian age. The sediments rest on a Basement Complex of granites, gneisses and schists. Three superimposed stratiform orebodies, known locally as the Lower, Intermediate and Upper Orebodies, occur over a vertical interval of approximately 150m. Current annual copper production is approximately 300 000 tonnes. The ore originates from four different mining operations, one Underground mine and three Open Pits. Approximately 9 million tonnes of ore grading between 3 and 3.5% copper are milled annually. The two largest sources of ore, the Under- ground mine and the Nchanga Open Pit are on the gently dipping south limb of the Nchanga Syncline (Figure 1). In the Nchanga Open Pit the major source of ore is the Upper Orebody with lesser tonnages from the Intermediate and Lower Orebodies. In the Underground mine the Lower Orebody is the only orebody being mined, underground mining of the Upper Orebody being suspended for economic reasons in 1978. The typical stratigraphic column is illust- rated in the legend on Figure 1. The footwall rocks comprise either Nchanga Red Granite or the Arkose formation, both of which are hard competent rocks, offering generally good mining conditions for footwall development. Copper mineralisation of the Lower Orebody extends from the upper part of the Arkose to the top of the Lower Banded Shales. Overlying the Arkose is the Transition zone (0-18111 in thickness). The Transition zone comprise a lower member, Transitional Arkose, consisting of incoherent kaolinised sandstone, and an upper member, Transitional Lower Banded Shales consisting of normally soft bleached and silicified shale. The soft nature of the Transitional rocks is

Jan 1, 1981

By S. S. Marsden, S. H. Raza

An experimental study of the flow of line-textured. aqueous foams through Pyrex tubes is described. The foams range in quality F (ratio of gas volume to total volume) from 0.70 to 0.96 and behave like pseudoplastic fluids. At lower flow rates they exhibit laminar flow ad have apparent viscosities which increase with quality, and which cover a range of 15 cp to 255 poise for tubes of 0.25- to 1.50-mm radius rj. At higher flow rates a plug-like type of flow is developed, the extent of which increases with both T and ri. When the same foams flow through either open or packed Pyrex tubes, remarkably high streaming potentials ?E are often generated. These can easily reach 50v if nonionic foaming agents are used, but are at least an order of magnitude less for ionic foaming agents. A linear relationship between ?E and the pressure differential ?p is observed; this usually extrapolates to positive values of ?p at ?E of zero. The slope of the line increases with both F and ri. An equation was derived to describe the streaming potential of non- Newtonian fluids in circular tubes and was used to correlate experimental results. The calculated < potentials are of the right order of magnitude. INTRODUCTION Foams are both unusual and inniguing in their physical properties, and have been the subject of many scientific studies. However, present knowledge of foams is still fragmentary, specific and often contradictory. Apparent viscosity of foam is the physical property of greatest interest to both rheo1ogists and engineers. sibreel reported that the apparent viscosity decreased with increasing shear rate in a manner similar to some non-Newtonian fluids. Penny and Blackman2 reported that fire-fighting foams had both a limiting shear stress and a tensile yield stress. There is little doubt that some foams at least behave like non-Newtonian fluids, and have apparent viscosities considerably higher than those of either constituent phase. The high apparent viscosity of foam with its concomittant effect on mobility ratio and sweep efficiency no doubt prompted several attempts by research groups to use foam as a displacing agent in porous media. Based on recent experience, most of these groups probably succeeded in completely blocking fluid flow in the porous media and then abandoned their efforts. Two groups apparently found the successful combination of experimental parameters at about the same time.3,7 Others have recently added to our knowledge of foam flow in porous media and its use as a displacing agent.8-13 An experimental problem encountered by Fried3 was a transient blockage of foam flow in porous media when distilled water was used to prepare the foam-producing solution. Fried surmised that this was due to an electrokinetic effect and he eliminated it by using electrolytes in preparing foaming solutions. He also measured the streaming potential of a number of foams in capillary tubes which he found to be appreciably higher than those obtained when the constituent liquid flowed under comparable conditions. This paper presents results of a more comprehensive study of the streaming potential generated by aqueous foam flowing in both open and packed Pyrex tubes. It also adds to knowledge of the rheology of these foams as deduced from their flow behavior in open tubes. APPARATUS AND PROCEDURE A diagram of the apparatus used is shown in Fig. 1. Details of its construction, testing and use are described elsewhere.14 Careful selection of materials, extreme cleanliness and rather elaborate electrical insulation and shielding were necessary to obtain reproducible results (±5 percent). Both streaming potential and streaming current were measured with an electrometer. The design of the foam generator developed for this work is novel (Fig. 2). It will produce uniform fine-textured foams at pressures sufficiently

By W. C. Knopf, G. Samsel

For several years International Minerals & Chem-ical Corp. has used a radiation method to assay potassium content of products from potash and feldspar beneficiation. The procedure is rapid, accurate, and inexpensive and is easily handled, if necessary, by nontechnical personnel. Data are presented to show the accuracies that may be expected if the technique is used for control of pilot plants or large-scale plants. Natural potassium is composed of three isotopes —K, K and K. Five other isotopes, artificially produced, have been detected. In natural potassium only the K isotope, with a half life of 1.4x10 years, is radioactive. Its modes of decay are beta and gamma rays, positrons, and x-rays. Only the more abundant beta rays, however, are important in radiation measurements using geiger tubes. Barnes and Salley&apos; measured radiation of potassium salts in solution in 1943. Gaudin and Parnell2 first reported the use of solid salts arranged in a vessel surrounding the ß counter in 1948. Later, Scheel used the method to assay potassium content of various crude and finished potash salts. Experimental: Dip-type Geiger-Muller tubes (TGC-5) supplied by Tracerlab Co. were used in all radiation counting measurements. The tube was encompassed by a glass container about M in. larger in diameter than the tube. This container, which served as a sample holder, was closed at the bottom with a rubber stopper to facilitate removing the samples. Samples were not weighed, but about 40 g of sample were needed for each test. Electrical impulses from the tube were counted on either a Tracerlab scaler or a rate meter. To obviate the need for constant attendance, preset features were incorporated into the scalers, so that at a predetermined time or count the units were automatically deactivated. When rate meters were used, counting rates were read directly from instrument or from a recorder used in conjunction with the rate meter. Each tube was calibrated, according to the manufacturer&apos;s instructions, to determine the correct operating voltage to insure reproducible results. A linear calibration plot of percent K2O vs counting rate was also obtained for each tube by recording the counting rate plus background count of several standards of different K2O content chemically analyzed by the chloroplatinate method.&apos; These standards were of approximately the same particle size distribution as samples to be assayed. Specific background count caused by cosmic rays and other surrounding radiation was checked periodically by counting a sample of pure NaCl. Fig. 1 is a representative calibration plot. Assays were determined directly from the standard plot or calculated by subtracting the background count from the counting rate, then multiplying by the slope of the line. Chemical assays of the test samples were made by the Sherril method," a flame photometric technique, or the chloroplatinate method. Data: The radiation assay method has been used for three years by International Minerals & Chemical Corp. in the laboratory and in pilot plants processing ores containing potassium. These dry concentration plants process sylvinite and langbeinite ores at Carlsbad, N. M., and feldspar ores at Top-sham, Maine. Sylvinite ore is predominantly a mixture of syl-vite (impure KCl) and halite (impure NaCl). Contaminants include sulfates, such as langbeinite (2MgSO - K2SO4), kieserite (MgSO H2O), poly-halite (MgSO4.K2SO, 2CaSO, . 2H2O), and slimes. Langbeinite ore is predominantly langbeinite and halite with small amounts of sylvite, sulfates other than langbeinite, and slimes. Several variables, in addition to correct calibration and standardization of tubes, were found to be important in obtaining reproducible results. Particle size distribution of standard samples should be

Jan 1, 1959

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi&apos;s solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith&apos; have applied Raimondi&apos;s solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,&apos; Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By Klaus Schwerdtfeger

The rate of formation of silicon monoxide from silica spheres has been measured at 1500°C in H2, H2-H2O, H2-He, H2-Ar, and CO-CO2 gas mixtures. Indications are that in the hydrogen-containing gases the reaction rate is mainly determined by convective diffz~sion. In the CO-CO2 mixtures the rate approches a constant value which is independent of sphere diometer (and gas velocity). This suggests that a surface reaction becomes rate controlling in CO-CO2 gas. WHENEVER silica is exposed at elevated temperature to a strongly reducing atmosphere there occurs, inevitably, a volatilization of silica by the formation of gaseous silicon monoxide. Because of the importance of this reaction in metallurgical processes and laboratory experiments, its kinetics were studied in the present work. EXPERIMENTAL The spheres made of vitreous silica were suspended by a molybdenum wire in the hot zone of a gas-tight high-purity recrystallized alumina furnace tube of 3.1 cm internal diam and 100 cm length. Molybdenum wire resistance heating was used. A purified H2, H2-H2O, H2-He, H2-Ar, or CO-CO2 gas mixture was passed through the tube, from top to bottom. The amount of silicon monoxide formed was determined by weighing the silica balls before and after the experiments. The silica balls were made from commercially available translucent fused quartz glass. In experiments with hydrogen-containing gases the silica stayed vitreous during the experiment, whereas in experiments with CO-CO2 mixtures, which were performed over longer times, the balls were always crystallized to cristobalite (as determined by X-ray examination) at the surface. Constant-pressure head capillary flowmeters were used to control the composition of H2-He, H2-Ar, and CO-CO2 gas mixtures. The oxygen and water vapor were removed from the gases containing hydrogen by passage through columns containing platinized asbestos (450°C) and an-hydrone. The CO was purified from O2 and CO2 by passing it through activated copper (200°C) and through ascarite. The H2-H2O gas mixtures were prepared by passing purified Hz through a mixture of oxalic acid dihydrate and anhydrous oxalic acid held at a constant temperature in a water bath. The equilibrium water vapor pressures of oxalic acid dihydrate-anhydrous oxalic acid mixtures were taken from the available data.1 The furnace system was checked for sufficient gas tightness at regular intervals. As an additional check, the H2O and CO2 contents were measured in the exit gas and were found to agree closely with the metered contents when H2-H2O or CO-CO2 mixtures were used. When purified H2 was used, H2O pressures found in the exit gas were always below 0.1 mm Hg. These contents originate either from an incomplete reoxidation of silicon monoxide in the cold part of the furnace or from small leaks which cannot be avoided. If the latter is the case, such small uncontrolled H2O contents decrease the partial pressure of SiO in equilibrium with SiO2 by less than about 7 pct, which is considered small in comparison to other experimental uncertainties. The temperature of the furnace was controlled automatically in the usual manner. The reported temperature was measured with a Pl-Pt/l0pct Rh thermocouple and was accurate to ± 5°C. TRANSPORT-CONTROL LED RATE OF REDUCTION The gaseous convective diffusion from the surface of a sphere can be predicted from the semiempirical relationship obtained by Ranz and Marshall2 in a study of the evaporation of water and benzene drops in air. The following equation applies:

Jan 1, 1967

By K. Mukherjee

Instantaneous resistance change during martensitic transformation in Fe-30 at. pct Ni alloy has been studied using a low-noise electronic system. The smallest signals recorded in this investigation were of the order of 10 pv. These small signals did not show the initial increase reported by earlier investigators to support a double shear mechanism.&apos; A variety of pulse shapes and sizes was observed during "burst" transformations, and these signals were neither a linear function of the size of martensite plates nor of the volume fraction transformed. Even the smallest signals, presumably from single plates, showed complications resulting from elastic and/or plastic deformation, shock wave propagation, and so forth, which are inherent in the growth process of a martensite plate. The time of formation and interface velocity determined froni this experiment agree very well with the pioneering work of Bunshalz and Mehl.&apos; AN Fe-30 at. pct Ni (c0.005 pct C) alloy was used to study the time of formation of martensite plates. Martensitic transformations, unlike the nucleation and growth processes, are usually characterized by an extremely fast reaction rate. During the transformation, the crystal structure changes and this change is propagated through a finite volume of the parent crystal lattice within a very short time interval. The interface between the two phases probably consists of moving dislocations, and the time of formation of the plate depends on how fast this dislocation interface can move. Knapp and Dehlin~er or Cottrell and Bilby mechanisms, or similar dislocation models, can be used to calculate the time of formation of a martensite plate of a given size. In the past, conventional photographic technique475 as well as electrical resistivity techniques"~-" have been used to measure the time of formation of a martensite plate. The specific resistance of the martensitic phase in Fe-30 at. pct Ni alloy is lower than that of the austenite phase. Therefore if a current is passed through a small austenite sample in series with a large external resistance, then one would observe a voltage change across the sample as martensite is formed. Such dc measurements are shown in Fig. 1. The initial large voltage drop in Fig. 1, at the M, temperature, is due to a "burst" transformation where a large number of plates are formed in a cataclysmic manner within a very short interval of time. Even during the later stages of transformation as shown in Fig. 1, one can observe discontinuous voltage changes due to small bursts. In order to resolve the time scale of such discontinuous stages, the voltage signals are amplified and fed into a highspeed oscilloscope. In this investigation a low-noise amplifier was used for the first stage of amplification. The signal to noise ratio was further improved by the design of a pulse transformer. This transformer was capable of amplifying the signal by a factor of six. Voltage signals were studied over a wide time scale ranging from 2 sec to 0.1 psec. I) EXPERIMENTAL PROCEDURE A) Specimen Preparation. Specimens were cut from induction-melted Fe-30 at. pct Ni (<0.005C) alloy and cold-rolled to 0.2 by 1 mm cross section and an average length of 5 cm. During mechanical shaping, the specimens were strain-annealed at 950°C for 24 hr in vacuum. Finally the finished samples were vacuum-annealed at 1000°C for 6 hr and water-quenched to room temperature. The average grain diameter was 0.02 cm. B) Cooling System. The M, temperature of the alloy was -55°C. Fig. 2 shows the arrangement which was used to cool the specimen at a slow rate. The specimens were mounted inside a i -in.-diam hole in the 2-in.-long section of the copper specimen holder. This cavity was filled with silica gel. A dummy specimen was used under identical conditions for

Jan 1, 1969

By W. van der Knapp

A theoretical and experimental ana1ysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The result enable one to deduce directly the effect of large increlents in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical rules surface, the generating lines of Which have a slope according to the solid rock compressibility. Analytical expression for such a ,surface is very simple. It follows that the bulk and pore compressihilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be conduded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could he related by means of a simple empirical formula. Results from the described study find a direct applicxtion in material balance calculations and in prob1ems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equatiorls for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 1.5 to -10 prr cent porosity that laboratory measured porosities may differ from those lender reservoir conditions by about I per cent of their value. The difference for low porosity limestotnes can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to he very small. General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot1, Gassmann2 and Geertsma.2 Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension. It has been known for a long timei that the stress-strain relations of a packing of spheres are essentially noninear. Our experiments show that for almost all reservoir rocks which arc elastically deformable the relation between volume and loading is also a nonlinear one, resembling that of a packing of spheres very closely. The behavior of these media is often described by using the linear stress-strain relations for small incremental stresses and strains in the vicinity of a pre-stressed condition." The present study differs from these considerations in that it enables one to deduce the effect of large increments in the stresses directly. In analogy to the stress tensor for a homogeneous body the stress tensor for a porous body can be written in the conventional way: where the tensor components, o, and t, represent the total forces acting on the faces of a unit cube of porous material. This tensor can be split into two parts. a hydrostatic and a deviatoric part, as follows2,3,1 where the component of the hydrostatic stress system, a. equals The hydrostatic stress causes a change in volume whereas the deviatoric stress system gives rise to a change in shape only. One of the difficulties in describing changes of volume occurring in reservoir rocks is that the relations connecting these volume changes with external and internal stresses are essentially non-linear. A complete description requires the bulk volume, V,,, as well as the pore volume,V,,. to be known as a function of both the changes in pore fluid tension (v) and the hydrostatic tension on the outer boundary.

By D. S. Rowley, F. C. Appl

Assuming that rock behavior, during cutting with a single diamond, may be approximated by that of a rigid, Coulomb, plastic material, a theory of single diamond cutting action has been developed. Using this theory, the stresses on the diamond cutting surface and the components of the cutting force have been determined. Theoretical results agree reasonably well with available experimental data. The theory of cutting of single diamonds may be used as the basis for subsequent study of the perfonnance of surface set diamond drill bits and other surface set diamond cutting tools. INTRODUCTION For more than twenty years, surface set diamond bits have been used successfully in the mining and petroleum industries to drill and core rock formations that range from medium hard to the hardest known formations. Most extremely hard rock formations cannot be economically drilled or cored by any other means. In view of the growing use and importance of surface set diamond drill bits, it is reasonable to study the way in which these tools cut, and the factors that influence wear of the diamonds. Such knowledge will contribute to better bit design and will improve operating procedures. To analyze the cutting performance of these tools it is appropriate to consider the way in which an individual diamond cuts. Once this is established, the over-all performance of the bits can be determined by considering the total effect of the individual diamonds. In recent years there has been a growing interest in rock mechanics and there now exist several publications dealing with the deformation and failure of rocks. Notable experimental work has been reported by Bredthauer,1 Handin and Hager,2, 3 and Gnirk and Cheatham.4 An extensive collection of data pertaining to rock properties at low confining pressures has been given by Wuerker.5 Cheatham and Gnirk have recently presented an excellent review of the state of knowledge regarding analytical and experimental rock deformation and failure.6 Generally rocks are extremely weak in uniaxial tension, and weak or only moderately strong in uniaxial compression. Both tensile failure and compressive failure are generally brittle in nature. This means that there is little or no deformation or "flow" of the material before shear or tensile fracture occurs. Thus, until fracture occurs, rock behaves very nearly like an elastic material in uniaxial stress. Significant changes in behavior of rock occur under conditions of triaxial compressive stress. There is generally a marked increase in compressive strength and in ductility. It has been demonstrated that the failure becomes plastic (in a macroscopic sense) at sufficiently high values of confining pressure. Sharp wedge chisel indentation studies conducted by Gnirk and Cheatham indicate that many rocks behave in a plastic manner at relatively low triaxial compressive stress states.4 If "failure" under triaxial compressive conditions is considered to be either complete rupture or macroscopic plastic flow, then the general failure characteristics of a rock can be reasonably well represented by the commonly known Mohr envelope. This certainly is not a perfect failure criterion (since the effect of the intermediate principal stress is neglected) but it has been found to be adequate for most engineering purposes. Mohr envelopes usually are constructed graphically using experimental triaxial test data. For purposes of analysis it is convenient to represent the envelope in equation form. Among the several approximate forms appearing in the literature, a parabolic form is suggested by Cheatham,7 and an exponential form is suggested by Paone and Tandanand.8 The exponential form has been adopted for this study, and based on published data, appropriate parameters have been established for 19 rock types. A typical plot of the data compared with the approximate envelope, and a summary of the rock properties and

Jan 1, 1969

By F. P. Bullen

Empirical relationships between fracture stress, orientation angle, and diameter of crystal have been determined at 77°K. Orientation ranges of markedly different behavior were found—a law of constant normal stress&apos; of value a (diameter)-1/2 for the fracture of ductile crystals, and a condition of shear stress (or strain) for more brittle crystals. The observations are not consistent with current theories. An interpretation is advanced which is also applicable to observations on the effect of prestrain at room temperature on the subsequent fracture stress at 77°K and to the effect of cyclic stressing on the cleavage strength.&apos;&apos; The law of constunt normal stress&apos; and the brittle ductile transition are also explained. The interpretation is more consistent with the initiation of cracks by intersecting dislocations than with theories based on stress -concentration by dislocation arrays. ZINC single crystals are particularly suited to the study of cleavage because fracture occurs on the basal plane over a wide range of crystal orientations. Analysis of the conditions of stress and strain at fracture in crystals of different orientations should indicate which parameters control the cleavage process. Unfortunately, controversy has arisen over the correct empirical relationship between tensile fracture stress and orientation. Schmid&apos;s observations1,2 favored a &apos;law of constant normal stress&apos;, as observed in other materials.2 For zinc, however, the observed values are far below the theoretical strength and cannot represent the true limit of cohesion between neighboring atomic planes. Hence, the interpretation of such a &apos;law&apos; is not straightforward. Deruyttere and Greenough3,4 found a complex variation between tensile fracture stress and orientation; this variation did not agree with a &apos;law of constant normal stress&apos;. Two theories have been advanced to account for their observations: a) the propagation of cracks from low-angle boundaries,5 and b) the release of energy from piled-up dislocations during crack-propagation.4 The present work resolves the apparent discrepancy between the observations and shows that neither of the above theories are applicable to the tensile fracture of zinc single crystals. A phenomenological explanation, along the lines suggested by Gilman,&apos; is advanced and successfully applied to previously unexplained effects. EXPERIMENTAL DETAILS &apos;Crown Special&apos; redistilled zinc was used, except for one comparison series op tests using &apos;Tadanac&apos; electrolytic zinc. Crystals of 1 mm diam, subsequently called &apos;1 mm crystals&apos;, were grown from the melt in vacuo in precision-bore Pyrex tubes internally coated with graphite. Several specimens 1 in. long were cut from each crystal and chemically polished. Jigs were used to minimize handling strains, and crystals were mounted in the Polanyi machine the day prior to testing to allow recovery from any such strains. One-mm crystals were chemically polished for long periods to obtain 0.1 mm (approx) crystals. One-mm crystals were cemented into miniature gimbals by &apos;Araldite&apos; casting resin. The Appendix gives the reasons for using gimbals and the results obtained by other methods. More complete details of all techniques are given elsewhere.7 The symbols and terminology used are as follows: X = orientation angle (angle between tensile axis and line of greatest slope in the basal plane). T = tensile stress (on true cross-section) S,N = shear and normal stress (components of T with respect to the basal plane) ? = shear strain D = crystal diameter. The subscript &apos;f&apos; will be used to denote values at fracture. PART I-ANNEALED CRYSTALS EXPERIMENTAL OBSERVATIONS One-mm crystals were used to establish the variation of fracture stress at 77°K with orientation at fracture (Xf), Fig. 1. For 18 deg = Xf = 55 deg, a &apos;law of constant normal stress&apos; was observed. For Xf > 55 deg, the fracture condition approximated to a constant shear stress. At Xf< 18 deg, twinning occurred before fracture so that the results were not typical of homogeneous single crystals,4,8— such specimens will not be considered herein. The dependences of fracture stress upon Xf were of similar type for 6 mm,* 1 mm, and 0.1 mm crystals,

Jan 1, 1963

By E. E. Underwood, L. L. Marsh

Aluminum single crystals, alloyed with 0.042 atomic pet Cu and 0.11 and 1.1 atomic pct Mg, were subjected to constant stress creep tests, tensile tests, and hot hardness measurements within a temperature range of 300° to 866OK. Calculations based on Dorn&apos;s temperature-compensated time parameter, 6, gave a value of DH, = 27,000 cal per mol for the activation energy of early creep in aluminum single crystals. Correlations have been obtained for aluminum alloy single crystals with the parameter E for solid solution strengthening, as well as with the parameter F for solid solution hardening, by using a valence of three for aluminum. Limited measurements on tensile specimens show that the slip band density tends to decrease with increasing temperature and with decreasing solute concentration. INCREASING interest is being shown in the mechanisms of plastic deformation in single crystals during tensile and creep testing. The complexity of deformational processes in polycrystalline materials has led to a search for simpler experimental conditions. Numerous creep and tensile investigations have been conducted with pure, metallic single crystals. To a lesser degree, the effects of alloying elements on the tensile properties of single crystals have been determined. However: the literature dealing with the effects of alloying additions in single crystals under creep conditions is vanishingly small. This paper represents an attempt to narrow this gap in the knowledge of the subject. Previous investigations of creep behavior at the Battelle Memorial Institute1-1 have been of great value in the analysis of the present single crystal data. It is equally desirable, however, to ascertain the extent of correspondence between the behavior of single crystal and polycrystalline materials. For this purpose, correlations, similar to those developed for polycrystalline aluminum alloys by Dorn and co-workers, have been made with the single crystal data. The results from this study have tended to confirm and extend those correlations to the case of alloyed single crystals. Materials and Procedures Three dilute binary aluminum alloys were prepared for this investigation from 99.99 + wt pct Al, 99.8 wt pct Mg, and 99.92 wt pct (electrolytic) Cu. The nominal compositions of the alloys were 0.042 atomic pct Cu, and 0.11 and 1.1 atomic pet Mg. Precautions were taken to avoid contamination of the stock during melting and casting of the alloys. After a heat treatment of 8 hr at 925°F the alloys were extruded, then machined into) threaded tensile specimens with a 3 in. reduced section and a 0.505 in. diam. Spectrographic examination showed less than 47 ppm metallic impurities in each alloy. The single crystals were grown by the strain-anneal method, with a critical strain of about 11/4 pet giving the optimum results. In general, 3 in. crystals were obtained with the Al-Cu alloy, but smaller crystals in the magnesium alloys necessitated the use of 2 in. and 1 in. gage lengths with the low and high magnesium alloy specimens, respectively. After an electrolytic polish, the orientation of that portion of the specimen containing the largest single crystal was determined from Laue back-reflection photographs. Tensile tests were conducted at a constant load rate of about 2 lb per min. Creep runs were made in a constant temperature room, under constant stress at the higher creep temperatures, and constant load at the lower temperatures. The eloneation was measured to within ±5 microin. by a specially designed capacitance extensometer. The ex-tensometer arms were attached to the 3 in. specimens at the shoulders of the test piece or, where the crystals were smaller than 3 in., by knife-edge grips.

Jan 1, 1957

By L. W. Holm

This study shows that in the presence of foam, gas and liquid flow separately through porous media representative of reservoir rock. These results were obtained by using tracer techniques to measure the flow of the gas and liquid comprising the foam. Foam does not flow through the porous medium as a body even when the liquid and gas are combined outside the system and injected as foam. Instead, the liquid and gas forming the foam separate as the foam films break and then re-form in the porous system. Liquid moves through the porous medium via the film network of the bubbles and gas moves progressively through the system by breaking and re-forming bubbles throughout the length of the flow path. The flow rates of the gas and liquid are a function of the number and strength of the films in the porous medium. There is no free flow of gas; i.e., no continuous gas phase. On the basis of these results, foam can be expected to improve a water flood or gas drive by decreasing the permeability of the reseruoir rock to a displacing liquid or gas. This improves the mobility ratio and thus the conformance of the flood. INTRODUCTION Foam is formed when gas and a solution of a surface active agent are injected into a porous medium either simultaneously or intermittently. During the past few years, several papers have been published on the subject of foam flow in Dorous media. Foam has been used successfully in the removal of capillary water blocks from producing formations.&apos;&apos;2 The use of foam in gas storage reservoirs to reduce gas leaks and to increase storage capacity has been considered in recent years. Foam has also been investigated as an oil displacing agent,3-5 and as an agent to improve the mobility ratio in a waterflood.6-10 However, the mechanism by which the gas and liquid phases comprising the foam flow through a porous medium has nor been described adequately. Normally, when two immiscible phases (gas and liquid) flow concurrently through a porous medium, each phase follows separate paths or channels. At given saturations of the two phases, a certain number of channels are available to each phase, and as saturations change, the number and configuration of the channels available for each phase also change. The effective permeability of each phase is a function of the saturation of that phase only, and the flow of each phase can be described by Darcy&apos;s law. When foam is present, the effective permeability of the porous medium to each phase is greatly reduced compaced with permeabilities measured in the absence of foam.6,11-13 Based upon the observed flow of surfactant solutions and gas in capillaries, it has been concluded that the gas and liquid may flow separately or they may flow combined as foam. At least four mechanisms have been postulated to explain how fluids flow with foam present: 1. A large portion of the gas is trapped in the porous medium and a small fraction flows as free gas, following Darcy&apos;s law.9 2. The foam structure moves as a body; the rate of gas flow is the same as the rate of liquid flow. 6,13 3. Gas flows as a discontinuous phase by breaking and re-forming films. Liquid flows as a free phase.12 4. A portion of the liquid and gas move as a foam body while excess surfactant solution moves as a free phase.14 It also has been suggested that different flow mechanisms exist for high quality (dry) foams made from dilute surfactant solutions and for foams made from more concentrated solutions. Studies conducted on the flow of foam through capillaries have shown that a plug-type flow occurs and that foam flows as a body.6,15 Fried also has described the flow of foam through porous media as

Jan 1, 1969