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By A. W. Fahrenwald

THE absolute efficiency of crushing and grinding in a ball mill is not known. A number of investigators have made calculations to this end and have presented efficiency figures. Two factors have prompted further investigation of this subject: (1) the unbelievably low magnitude of the values offered, and (2) a desire to obtain, if possible, true relationships between the relative efficiencies of a ball mill operating under varying conditions. A useful forward step in the study of mill efficiency was made when Martin1 and Gross and Zimmerley2 proved the correctness of Rittinger's law, and incidentally the incorrectness of the so-called Kick law, and when Gross and Zimmerley3 determined and gave surface values for Tyler sieve-sized quartz. These data are probably accurate throughout the range of the sieve scale, but on -400 mesh (which is the finest sieve available), the surface data, as obtained by the hydrofluoric acid disso-lution method, are of doubtful reliability. Any inaccuracy existing in surface determinations of -400-mesh material, especially when comparing runs in which varying quantities of this product are formed, will cause the resulting relative mill efficiency values to be distorted. Moreover, knowing surface accurately, the efficiency calculations require a surface energy figure. Two such figures are to be found in literature, one by Edser4 and one by Martin.5 Edser's surface energy

Jan 1, 1931

By J. C. Holm

Although the main constituents of Portland cement are the oxides of calcium, silicon, aluminum, and iron, characteristics of the cement are seriously affected by such contaminants in the raw materials as magnesium, phosphorus, sodium, potassium, sulfur, and others of lesser importance. Sources of cement raw materials comprise a long list of minerals occurring in nature in various degrees of purity. The calcareous raw materials are generally limestone of purity varying from calcite to cement rock (a low-grade limestone of natural, almost correct chemical composition), chalk, marl, seashells, coral, and coral sand. The argillaceous raw materials supplying silicon, aluminum, and iron are mainly various forms of clay and shale, to which may be added silicious sand, iron ore, bauxite, or kaolin for minor adjustment of the chemical composition.

Jul 1, 1956

By Martin Weinstein

A technique is described for preparing finegrained lead telluride by ultrasonic agitation of a solidifying melt. Material prepared by this technique is dense and chemically homogeneous. N-type PbTe, containing 0.03 mole pct PbIz, has been made and its thermoelecCric Properties have been measured as a function of temperature. For comparison, the properties of similarly doped PbTe made by cold pressing and sintering, and by extrusion, have also been measured. The ultrasonically prepared material compares favorably with the others in its thermoelectric-efficiency factor. Comparison of compressive-flow curves for the three kinds of PbTe show that the ulhasonically prepared material has much superior ductility. The cleavage strength of the ultrasonic material is related to the grain size, D, by the Petch relation:Extrapolation to infinite grain diameter yields a fracture strength of 5000 psi for single-crystal PbTe. WHEN metals and semiconductors solidify in a mold they normally assume one of three cast structures illustrated in Fig. 1.' Solidification in a casting starts at the mold walls where a large number of fine crystals of random orientation can be nucleated to form the chill zone. Because of the anisot-ropy of the growth rate, those crystals whose direction of maximum linear growth is parallel to that of the heat flow grow faster and crowd out the crystals of less favorable orientation. A second zone, having a preferred orientation, called the columnar zone, thus forms adjacent to the chill zone. The speed of growth of the columnar grains will depend, in the case of limited undercooling of the melt, on the rate at which heat can be abstracted. The columnar zone can extend to the center of the casting, Fig. l(a), but it is frequently followed, in solid-solution alloys, by another zone of equiaxed randomly oriented grains in the central portion of the casting, Fig. l(b). The equiaxed structure in Fig. l(c) represents the completely grain-refined case where the equiaxed grain size is small. The third type of structure is the most desirable because it imparts a somewhat higher strength for all except high-temperature applications, it reduces segregation of the doping constituent, and it reduces the possibility of hot tearing (the separation of grains due to the melting of a low-melting point constituent in the grain boundaries). In order to obtain fine-grained castings, the nu-cleation frequency must be increased and grain growth must be restricted. Various techniques have been employed for obtaining this end, namely: rapid cooling, vibration, and inoculation of the melt. The success of these techniques depends upon the characteristics of the metal species and on factors controlled by heat transfer through the crucible walls. Recent studies2" have shown that the application of ultrasonic energy to the solidifying ingot is an extremely powerful tool in the improvement of the crystalline structure of metallic castings. Both the mechanical properties and homogeneity of the ingots are improved. Ultrasonic oscillations may affect the crystallization process by 1) permitting subcritical nuclei to agglomerate and thus form nuclei of sufficient size to cause crystallization, 2) changing the state of surface adsorption of various catalysts found in the liquid melt, 3) breaking pieces of solid from the solidified surface near the supercooled region thereby increasing the number of possible nuclei, 4) causing temperature fluctuations to occur in certain parts of the melt thereby increasing the supercooling at specific points in the liquid, and 5) decreasing the critical nucleus size by increasing the pressure at specific points in the melt.' Various investigators have concluded that the effectiveness of the ultrasonic oscillations results from cavitation which disrupts the growing solid-liquid interface The present paper describes the application of ultrasonic oscillations to the crystallization of the semiconductor N-type PbTe. The purpose of this study is to prepare crystalline

Jan 1, 1964

By F. J. Menzer, E. M. Schern

The Morenci/Metcalf porphyry copper mining operation, located in southeastern Arizona, currently processes approximately 91,000 tonnes of ore per day and has copper ore reserves estimated to be in excess of one bill ion tonnes. Functional groups within the Geology Department (currently staffed with six professional and two support personnel include mine geology, project geology, and hydrogeology. The primary task of mine geologists is daily preblast bench face mapping with grade and mill amenability estimates. Auxiliary duties include detailed in-pi t metal distribution evaluation, mineragraphic work and flux quarry geology. Project geologists conduct exploration and preliminary development projects both within and outside the Morenci district and provide support to ore reserve block modeling and geotechnical work performed by the Morenci mine engineering group. Hydrogeologists handle exploration for and development of groundwater resources and groundwater flow modeling, mine dump leach solution penetration and recovery evaluation, and tailing dam water reclamation.

Jan 1, 1984

By Edward Keller

(Canal Zone Meeting, November, 1910.) UNDER the title, Labor-Saving Appliances in the Works-Laboratory, I published a paper1 in which was described how multi-manipulations, in a works-laboratory, and in the furnace-room of an assay-laboratory, can be condensed into single manipulations by applying the proper mechanical devices. For example, I now deposit in, or withdraw from, a muffle a set of 48 cupels as one unit. The front row. (8) of these. are blanks or heaters; the other 40, when they have attained the proper temperature in the muffle, are charged simultaneously with the 40 lead-buttons. Three manipulations here accomplish an operation which by the generally customary method requires 136, and this number is only limited by the size of muffle and cupels. This operation is an enlargement of what I have already described in my former paper, and Fig. I shows the improved implements. In the paper referred to I described a gold-silver bead parting-bath, which is the last of the devices used in regular sequence in practice. This bath was designated as being convenient, but was not a labor-saver properly. Fig. 2 of the present paper shows a new device. Instead of the original tray, there are now sectional holders for the test-tubes, each having a wooden handle on either end, so that the holders may be removed from the boiling bath, and the acid or water poured off from each set of tubes (in this case, 7) without waiting to cool. The tubes, held in place by clutches, as shown in Fig. 3, rest in holes in the base-strip, having a smaller diameter than the tubes. Each holder is stamped at either end with a number, so that the bath becomes further useful by permitting several men to use it at the same time without interference. Apart from the handles, the holders are made of sheet-copper. ' Trans., xxxvi., 3 to 18 (1906).

Aug 1, 1910

Jan 1, 1941

By D. Turnbull, J. H. Hollomon, J. C. Fisher

The concepts of nucleation and of growth have adequately described the isothermal phase transformations to which they have been applied.ls2 However, these concepts have not yet been used successfully to describe the kinetics of a number of transformations that are not observed to take place isothermally. A typical reaction of this type is the austenite to martensite transformation in steels, for which the new phase appears only during cooling of the parent phase. If the cooling is interrupted, transformation ceases; yet had the cooling continued, transformation would also have continued. Nuclei of a new phase do not leap into existence all at once by the simultaneous cooperation of a large number of atoms or molecules of the parent phase; rather they are formed at finite rates by gaining or losing atoms one at a time from the surrounding materiaL3,4 Further thermo-dynamic considerations require a finite concentration of small transitory nuclei of all unstable phases to exist at equilibrium in a stable phase.= For steel in particular, nuclei of ferrite (a iron) exist at equilibrium in austenite (y iron) at temperatures where austenite is the stable phase. If a high-temperature phase a be cooled sufficiently rapidly from temperature TI above the a-ß equilibrium temperature To, to temperature T-1 below To where ß is the stable phase, the equilibrium distribution of ß nuclei corresponding to the high temperature will be retained. There are two limiting possibilities of particular interest: I. The steady state rate of nucleation of ß may be appreciable at T_1, and may require a concentration of sub-critical nuclei exceeding that retained from the high temperature. Time will be required then for the concentration of nuclei to build up to the steady state value, and an induction period will be observed during which the rate of nucleation will increase to the steady state value. 2. The steady state rate of nucleation of ß may be negligible at T-l, while the critical size for continuous growth of ß nuclei, which decreases with increased subcooling of the a phase, may reach a value so small that some. of the retained high-temperature nu-

Jan 1, 1949

By R. E. J. Putman

Introduction Self-tuning regulators are a class of controllers built around the concepts of sampled data theory, and are especially suitable for implementation in a digital microprocessor or minicomputer control system. The algorithms used are distinctly different from those based upon analog control techniques and include automatic adjustment features which permit them to adapt to unmeasured changes (in, for example, ore grindability) or process nonlinearities (as exhibited by cyclone classifiers). They are also designed to handle transport lags in a simple manner, for example, anticipating the effects of a variable recycle rate on particle size distribution. The advent of distributed control systems will encourage the exploration of these techniques in the minerals processing industries, and particularly for improving the control of comminution circuits, which are especially energy intensive. This paper outlines some current work in progress on this topic. Background Those engaged in the practice of process control have long had two philosophical problems for which solutions have been actively sought - what is optimal control and how can we attain it in some heuristic fashion automatically. The basic analog controller can be represented by the differential equation: [V = Ko + K1 f y • dt + K2 dt(1)] where: v and y are the instantaneous values of output and error respectively and K0, K1, and K2 are tuning constants. The empirical rules for establishing the values of K0, K1, and K2, which provide stability, have evolved from the initial suggestions of Ziegler and Nichols(9) in 1942 and have served their purpose well. However, later analyses demonstrated that there are in fact many combinations of the values of K0, K1, and K2 which, besides being stable, behave better or worse in relation to other process control criteria; some examples are duration of error, amplitude of a damped response, magnitude or rate of movement of control valve or adjustment of speed regulator, etc. The definition of optimality had broadened. In 1964, Kalman(4) published his classic paper which tried to resolve these problems. He defined a

Jan 1, 1982

By A. L. Moore

KAISER Bauxite Co., a subsidiary of Kaiser Aluminum & Chemical Corp., has been mining and shipping Jamaican bauxite for over a year. On Feb. 10, 1953 the first boat load of bauxite left Port Kaiser, Jamaica, for the company's alumina plant at Baton Rouge, La. To provide its own source of the aluminum ore, a Kaiser Aluminum & Chemical Corp. exploration party started initial reconnaissance in 1947. This work, and subsequent exploration, led to the acquisition of reserves sufficient to warrant a full-scale mining operation for several decades.

Jan 3, 1954

By T. M. Olson, B. G. Lewis

The adsorption of selenite on bentonite, kaolinite, and an iron--coated illite was studied to determine the importance of several soil variables on selenite removal from uranium mill tailings pond seepage. Adsorption capacities of the clays of selenite varied by orders of magnitude and decreased in the following order: illite > kaolinite > bentonite. Maximum adsorption of selenite on the clays was observed between pH 2.5 and the clay's zero-point-of-charge. Substantially less selenite was adsorbed on these clays in actual mill tailings solutions than in model systems. Virtually all selenite was removed from the tailings at pH 7. The principal removal mechanism at this pH is suggested to be the adsorption of selenite on freshly precipitated metal hydroxides. It is concluded that selenite can be removed from tailings seepage in soil or in clay liners in the presence of kaolinitic clays and iron oxides. Selenite would also tend to be removed from tailings seepage in calcareous strata.

Jan 1, 1984

By AIME AIME

The 102d meeting of the Institute was held at the Institute headquarters in the Engineering Societies Building, New York, N. Y., on Feb. 19, 20 and 21, 1912. A Bureau of Information, in charge. of Mr. George Buckman, was maintained during the meeting. The proceedings opened with an informal social meeting on Monday evening, Feb. 19, in Assembly-Room No. 1, on the

Mar 1, 1912

By P. R. Sperry

In an investigation of the decomposition of the solid solution in a cold worked high-purity aluminum alloy containing 7 pct Mg, aged at temperatures from 30o to 82°C, the nucleating sites at the earliest stages of precipitation were observed to be of two types. Nucleation occurred at the high angle grain boundaries both when the alloy was initially cold worked and when solution annealed. Nucleation also occurred at certain unique deformation markings which began to appear in abundance at approximately 30 pct reduction in thickness by cold rolling. These deformation markings were identified as deformation (kink) bands rather than as the usually assumed "slip planes." Zn material that was cold rolled 15 pct, only the grain boundary Fig. 2—A1-7 pct Mg alloy, cold worked 60 pct and heated at 230° C for 5 min. Etched with Perryman's reagent. X500. Reduced approximately 25 pct for reproduction. (a) Bright field illumination, precipitate deeply pitted. (b) Phase contrast, showing slip markings.

Jan 1, 1962

By AUGUSTUS J. MONKS, Norman L. Weiss

THE Santa Barbara Unit of the Compania Minera Asarco, of which the San Diego mill is a part, is in the Parral District of southern Chihuahua. Although the concentration of sulfide ores has been practised in Santa Barbara since 1900, the San Diego mill, completed in 1921, was the first plant in northern Mexico to attempt the treatment of oxidized lead ores. From the milling point of view the many ores that have been treated at San Diego are very similar, the differences among them being rather of degree than type. Since 1921 the number of ores from different sources treated simultaneously has varied from four to eleven; in no case have any distinctive characteristics warranted the separate treatment of any of these. The zone of oxidation, source of the ores milled at San Diego, extends to a depth of 300 to 400 ft. below the surface. These ores carry more gold and less silver, lead, copper, and zinc than the underlying sulfide ores; the gangue minerals appear comparatively unchanged by oxidation and leaching. Lead occurs in diverse minerals, chiefly in cerussite, galena, and angle-site, the proportion of the lead in galena varying considerably in the different mines. An average of the feed to the mill would show the following approximate distribution of the lead content:

Jan 1, 1930

By Richard G. Warren, Michael M. Minor, Gayle J. Thomas

INTRODUCTION Los Alamos Scientific Laboratory (LASL) initiated its effort in the Hydrogeochemical and Stream Sediment Reconnaissance (HSSR), a part of the Department of Energy (DOE) National Uranium Resource Evaluation (NURE) program, in late 1975. Since that time, LASL has completed sampling of the Rocky Mountain states of New Mexico, Colorado, Wyoming, and Montana at a density of about one water or waterborne sediment sample per 10 km2 and has sampled about 85% of Alaska at a density of at least one per 25 km2. Analytical results for these samples are reported by National Topographic Map Series (NTMS) quadrangle. All collection and analytical procedures have been standardized from the outset (Sharp, 1977; Sharp and Aamodt, 1978). Until early 1979, only uranium results were reported for these samples; thereafter, results include analyses for at least 42 additional elements in the sediment samples. Each LASL HSSR report also includes a discussion of the relationship of these analytical data to known or possible uranium resources; more recently, these data have been re- examined for their relationship to resources for other metals (Beyth et al., 1980; 1980a). Analytical results for LASL HSSR sediment samples are both comprehensive, including 43 elements, and precise, allowing close inter-comparison of data between quadrangles. A recent HSSR study shows that elemental concentrations in sediment samples from the Dixon Entrance quadrangle in Alaska are insensitive to the choice of sieve size fraction and do not vary significantly between stream locations a few meters apart, except for extremely high elemental concentrations (Warren, et al., 1980). Elements that are particularly reproducible include thorium, hafnium, and the .ram earth elements. Fortunately, sensitivities for these elements, which are often associated with uranium, are excellent by the nondestructive analytical technique of neutron activation analysis that LASL employs. Wet chemical techniques may not always give reliable results for these elements in sediment samples due to the difficulty of dissolving the resistate mineral phases that normally contain these elements. LASL has recently open-filed results for a large number of NTK3 quadrangles; to date analyses have been reported for about 605 of the quadrangles within the states of the Rocky Mountain region. As a result, uranium analyses am now complete for all sediment samples collected from the state of Wyoming. We have chosen to sumnarize the analytical results for Wyoming and portions of adjoining states hereafter termed "the ~ Wyoming regionn (Fig. 1 ) ; nearly 24 000 uranium analyses and nearly 17 000 analyses for 42 additional elements are available for sediment samples collected from this area. The DOE open-file report numbers are shown in Fig. 1 for reports open filed before September 1, 1980. The Wyoming region provides an ideal area for an examination of regional geochemical patterns ex- hibited by sediment samples. It is endowed with a variety of exposed geologic units and with widely distributed uranium districts associated with host units of several ages. However, discussion will focus on rock units of Eocene and Precambrian ages because they are widely exposed and host the majority of the uranium resources within the region (Fig. 2). Miocene units are also widespread and host mineralization in the Brown's Park Formation (Fig. 2). Epigenetic uranium mineralization occurs in sand- stones of lower Eocene age such as the Wasatch, Battle Springs, and Wind River Formations whereas vein type mineralization occurs in Precambrian crystalline rocks. Precambrian rocks within the region consist of a variety of granitic and meta- morphic rocks with l .4-2.8 billion year ages, except within the Uinta Arch, where they consist of a sequence of very low grade metamorphosed or unmetamorphosed 1.0 billion year old sedimentary rocks. Precambrian rocks have served as sources for much of the clastic material comprising the lower Eocene units, and may also have provided the source for the uranium in mineralized Eocene or Miocene sandstones (Stuckless, 1979). The remainder of this paper describes the relationship of elemental concentrations in HSSR sediment samples to exposures of Eocene and Precambrian rocks. The results are used primarily to determine where these Precambrian rocks might provide the most suitable uranium source areas and to infer the direction of transport toward adjacent depositional basins during the Eocene.

Jan 1, 1980

By W. H. Burke

Deeper drilling, resulting in greater circulating distance and pressure, has directed attention to the advantages of the study of properties and control of rotary muds, which until recently have not had much consideration. One fundamental property of muds is viscosity, and viscosity is influenced by the quantity and character of colloidal material and can be controlled by chemical treatment. Colloidal Matter of Rotary Muds Two types of colloids are found in muds; the hydrophobic and the hydrophilic. Hydrophobic colloids do not associate intimately with water and are sensitive to small quantities of electrolytes. Hydrophilic colloids associate intimately with water, but are not so sensitive to electrolytes. The colloidal particles of rotary muds are derived from clay; In clay the particles may range in size from submicroscopic to macroscopic; a substance is a clay if the greater proportion of the particles are within the size limits prescribed for clay. The larger particles are inert and have no effect on the viscosity of normal hydrophobic colloidal muds. There are two theories accounting for the colloidal properties of clay-water suspensions: (1) the physical theory, that clay in water is a coarse colloidal suspension, and (2) Ashley's1 theory, that clay is a granular material with a colloidal gel surrounding the crystalline grains. The most important colloidal substances known to exist in clays besides the clay particles are: (1) colloidal silica, (2) colloidal alumina, (3) colloidal ferric hydroxide, (4) colloidal silicates, and (5) colloidal organic matter. Plasticity, a peculiar property of clay-water suspensions, is due to the colloidal particles. It is commonly (although not with strict accuracy) measured in terms of viscosity, and depends upon the amount and the state of flocculation of the colloidal matter present in the suspension. Fluidity in a rotary mud may be caused by a lack of colloidal clay particles or by deflocculated or flocculated clay particles, while viscosity in a

Jan 1, 1935

By Joseph P. Hodgson

In 1880, mining operations were commenced at the Copper Queen mine. The famous Queen ore body, which extended to the surface, was first quarried from a large open cut in the outcrop. The ore body was followed down to the 300 level with the Queen incline, and stoped. This, we believe, marks the introduction of square setting in the Bisbee district, which is still the method most generally used. Orebodies The orebodies in the Copper Queen mine occur in the limestones, and the main portion of the ore has been mined from the Abrigo, Martin, and Escabrosa limestones. mile the orebodies outcrop in the extreme western end of the mine, the general dip is to the east and south, at an angle of about 20°, although this dip is not by any means regular, being, in fact, very irregular locally. The ore is remarkable for its variableness in character, some of it being very soft, requiring a large amount of timber, and other portions consisting of extremely hard sulphides. The orebodies, in general, while remarkable for their continuity, are very irregular, both as to shape and size. The mine having been in operation so many years, and mining having been prosecuted over such a large area, the operations have caused the shrinkage of the overburden, and there is a constant movement, which is shown by large cracks and interstices in the surface rocks, which largely contribute to the very high deadwork or maintenance cost of the mine. It is surprising that for year 1913 it cost almost $400,000 just for the one item of repairs and dead work in this property. Haulage and Hoisting The underground openings have been extended in the neighborhood of 200 miles. The ore hoisting is performed at a centrally located shaft, the Sacramento, to which all the ores from different parts of the mine are conveyed by electric haulage, of which there was slightly over 9 miles in operation in 1913. The hoisting levels at the Sacramento shaft are placed 200 ft. apart, commencing at the 400 level and continuing down to the 1,600 level, the average hoisting distance being 1,000 ft. The

Jan 1, 1915

By E. W. Shilling Harwick Johnson

The separation of hematite by hysteretic repulsion was first brought to the attention of the public in 1922, by W. M. Mordeyl. Three years later another paper2 was published and after another four years a third paper3 appeared in the South African publications. Certain data were lacking in these papers. In order to continue the work intelligently a knowledge of the shapes of the hysteresis curves for certain minerals was very necessary. This information was not available until the present year4. It was known that reduction of certain ores rendered them amenable to this process of separation but definite data in the form of curves showing exactly the effect of such treatment were lacking. Probably our best source of information on the separation of minerals by the use of alternating-current magnetic fields today is the reports from the U. S. Bureau of Mines5"7. It is not the purpose of this paper to tell the reader in detail how to make a commercial separator. Experimental models have recently been made? and the results obtained have been so good that it is the opinion of the authors that the public will soon take an active interest in the subject and its development. The writers have constructed a separator that is considerably different in construction and operation from the two types described by Mr. Davis. This will be described, but the real purpose of this paper is to outline certain experiments and give curves showing data that have a fundamental bearing upon the practical construction of a separator of this type. Specular hematite is usually considered nonmagnetic; that is, it is very feebly magnetic as compared to some other minerals. If specular hematite is placed in a steady magnetic field there is no apparent attraction. At the moment of closing the switch, however, some particles may be seen to move. If the field is alternating, the particles are con-

Jan 1, 1936

By E. W. Shilling Harwick Johnson

The separation of hematite by hysteretic repulsion was first brought to the attention of the public in 1922, by W. M. Mordeyl. Three years later another paper2 was published and after another four years a third paper3 appeared in the South African publications. Certain data were lacking in these papers. In order to continue the work intelligently a knowledge of the shapes of the hysteresis curves for certain minerals was very necessary. This information was not available until the present year4. It was known that reduction of certain ores rendered them amenable to this process of separation but definite data in the form of curves showing exactly the effect of such treatment were lacking. Probably our best source of information on the separation of minerals by the use of alternating-current magnetic fields today is the reports from the U. S. Bureau of Mines5"7. It is not the purpose of this paper to tell the reader in detail how to make a commercial separator. Experimental models have recently been made? and the results obtained have been so good that it is the opinion of the authors that the public will soon take an active interest in the subject and its development. The writers have constructed a separator that is considerably different in construction and operation from the two types described by Mr. Davis. This will be described, but the real purpose of this paper is to outline certain experiments and give curves showing data that have a fundamental bearing upon the practical construction of a separator of this type. Specular hematite is usually considered nonmagnetic; that is, it is very feebly magnetic as compared to some other minerals. If specular hematite is placed in a steady magnetic field there is no apparent attraction. At the moment of closing the switch, however, some particles may be seen to move. If the field is alternating, the particles are con-

Jan 1, 1936

By D. Walton

The effect of small solute additions of Cu on the activation energies for creep A1 single crystals were determined over the range from 78° to 850° K. Below 240°K and above 800°K activation energies were unchanged. Between 240°K and 400°K strain aging causes the creep rate to become vanishingly small and the flow stress was independent of the temperature. Between 500° and 50°K the activation energy was increased to 41,000 cal per mole. NUMEROUS investigationsL have shown that solid solution alloying invariably increases the flow stress. A typical example is documented in Fig. 1. Such increases in flow stress can arise from two general effects: Alloying can increase the long-range stress fields through which dislocations must move by causing appropriate clustering; modification of dislocation densities, and so forth. Alloying can also modify the short-range stress fields that determine the activation energies for thermally stimulated migration of dislocations, such as occurs in some solute atom pinning processes, and so forth. Actually both long- and short-range stress-field effects can occur simultaneously. It was the purpose of this investigation to evaluate the effect of alloying on the short-range stress fields by determining the effect of alloying on the activation energies for creep. The resulting observations also shed some light on the effect of long-range stress fields on dislocation processes. EXPERIMENTAL TECHNIQUE Single-crystal bars (6 in. long 3/8 in. wide and l/4 in. thick) of dilute solutions of Cu in A1 were seeded, so as to provide extensive single slip, with the pole of the tensile axis located in the standard stereographic projection as shown in Fig. 2. Each crystal was grown under an argon atmosphere in a graphite mold containing a large reservoir of molten alloy for the purpose of obtaining rather uniform composition of Cu along the length of the bar. The nominal compositions of the alloys which were produced from 99.99 pct Cu and high-purity A1 containing 0.001 pct Fe and 0.001 pct Si, are given in Table I. Strains, measured by linear variable transformers attached by quartz rods to a 3 in. gage section were sensitive to and the stresses were ap- plied by direct loading of the specimen. Temperatures were determined by thermocouples attached to the gage section of the specimens. Below 400°K the apparent activation energies for creep, Q, were determined by the effect of small, rapid changes in temperature of about + 10°K from T1 to T2 on the corresponding creep rates ?1 and ?2 during primary creep according to where R is the gas constant.' Above 400°K, Q was evaluated from Eq. [1] for the secondary creep rate using temperature changes of about ±20K. A typical set of results is shown in Fig. 3. RESULTS AND DISCUSSION The previously obtained effect of temperature on the apparent activation energy for creep of single crystals of high-purity A12 is shown by the broken curve of Fig. 4. The datum points on the same graph illustrate the effect of dilute a solid solution alloying with Cu on the activation energy between 600" and 750°K. Each plotted point is the average of not less than five independent test values between 600° and 750°K and not less than three at other tempera-

Jan 1, 1962

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966