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By Donald C. Moore

INTRODUCTION Published laboratory procedures used by the major crusher manufacturers for estimating crusher size are based upon techniques developed in the mid 1940's. Specifically, the two largest U.S. crusher manufacturers are using the Bond impact procedure. Although the procedure is still in use, there is little confidence in the results. Unless the laboratory results fall within a preconceived range, personal experience is used for selecting the number of crushers and connected horsepower (Coleman, 1978). There have been numerous theoretical studies of the communition of particles. However, no procedure has been widely acclaimed for predicting crusher power requirements. Experimental studies have included breakage by slow compression, slow speed impact and high speed impact. Theoretical results have increased our knowledge of the comminution process, but the procedures have not been capable of analyzing the complex mechanism of industrial crushing machines. The purpose of this chapter is to review the empirical crushing procedures that have been used, including advantages and disadvantages. A new procedure which has been in development at Allis-Chalmers Corp. from 1977 to 1982 is detailed. Actual results of the new procedure on a concentrator feasibility study are included. EXPERIMENTAL GOALS The goals of a laboratory crushability procedure are accurate predictions of: (1) Rock crushability, measured as energy per unit mass. (2) Crusher product size analysis. A procedure capable of predicting these parameters should be inexpensive and require a minimum amount of sample. CRUSHABILITY TESTS Bond Impact Procedure F. C. Bond (1946) detailed the development of the pendulum impact device that is still used by the leading crusher manufacturers (Bond; Rexnord, 1976). The device (Fig. 1) is comprised of two bicycle wheels with 13.6 kg steel hammers tangentially attached to the rims. The hammer faces are 50 mm apart at rest. On opposite ends of the hammers lifting

Jan 1, 1982

SEVERAL distinctions can rightfully be accorded the Bagdad enterprise. For one thing, it has the most romantic name among the Porphyry Coppers and this is said with all due deference to Copper Queen and Inspiration! Bagdad was one of the richest and most magnificent cities of the glamorous world of the Arabian Nights. The record does not say who was responsible for applying the name Bagdad to the company that in 191 1 took over the property of the Arizona-Nevada Copper Company; but whoever it was must have had visions (or at least hopes) of a fabulously profitable mine. So far as I know, Bagdad is the only Porphyry whose owners, or officials, ran afoul of the law because of alleged sins of omission or commission in vending shares of the company's stock. E. B. Bronson, of New York, had been interested in Bagdad since 1909; and, during the lean period of the 1930's he had, as president of the corporation, endeavored to raise needed funds by the sale of 140,000 shares of treasury stock. Some legal questions arose as to the need for registration under the Securities and Exchange Act; but, when Mr. Bronson finally filed a registration statement, the New York office of the Securities and Exchange Commission found 155 "deficiencies" in the document. According to the judge who later heard the criminal case against Bronson, no evidence was introduced to show that he had personally benefited "to the extent of one dollar." However, it was charged that the setup was such that he was in position to profit if he had wanted to! A somewhat quixotic position, it would seem. In any event, he was convicted, on highly technical

Jan 1, 1957

By M. O. Abo-el Fotoh, J. B. Mitchell, J. E. Dorn

The effect of strain rate and temperature on the tensile flow stress of a polycrystalline bcc alloy of magnesium containing 14 wt pct Li and 1.5 wt pct Al was investigated for strain rates of 3.13 x lom5 to 3.13 x 10-3 per sec over the range from 20° to 300°K. From about 180° to 300°K the alloy exhibited an ather-ma1 deformation behavior where the flow stress was independent of strain rate and increased only slightly with decreasing temperature. At lower temperatures the flow stress was strongly strain-rate- and temperature-dependent, characteristic of deformations controlled by thermally activated mechmzisms. The activation volume for thermally activated plastic defornzation was between 5 and 30 cu Burgers vectors, independent of plastic strain. This low-temperature thermally activated deformation behavior was found lo be in satisfactory agreement with the theoretical dictates of the Dorn-Rajnak1 formulation of the Peierls mechanism where deformation is controlled by the rate of nucleation of pairs of dislocation kinks over the Peierls energy barriers. SEVERAL studies of the low-temperature thermally activated deformation of bcc metals and alloys (molybdenum,1 tantalum,1 Fe-2 pct Mn,2 Fe-11 pct MO,3 and AgMg4) have revealed that the strain rate is controlled by the activation of dislocations over the Peierls-Nabarro energy hills. Although there is some uncertainty as to the nature and effect of solute atom-dislocation interactions during low-temperature deformation of bcc metals, it has been concluded by Dorn and Rajnak,1 Conrad,1 and Christian and Masters6 among others that overcoming the Peierls-Nabarro stress which arises from the variations in bond energies of atoms in the dislocation core as it is displaced is the probable mechanism controlling low-temperature deformation. The purpose of this research was to investigate the low-temperature plastic deformation of the bcc alloy Mg-14 wt pct Li-1.5 wt pct A1 to determine if the behavior of this alkali metal alloy might be analogous to that for other bcc metals. This alloy was selected because of its availability and its current industrial importance as a lightweight material for aircraft and aerospace applications. I) EXPERIMENTAL PROCEDURE Polycrystalline tensile specimens having cylindrical gage sections 2 in. long by 0.2 in. in diam were machined from as-received alloy sheet stock of Mg-14 wt pct Li-1.5 wt pct Al. Specimens were annealed in an argon atmosphere at 423°K for 4 hr and maintained in a kerosene bath together with the sheet stock to prevent corrosion. The resulting specimen microstructure consisted of a coarse uniform dispersion of incoherent precipitate MgLi2Al particles7 in a bcc 0 phase matrix having an average grain size of 150 p. Prior to testing the specimens were chemically polished in dilute hydrochloric acid. Comparison of tensile properties and microstructures of specimens cut from center and edge sections of the sheet stock revealed no effects of inhomogeneities in the sheet material. Tensile tests were performed on an Instron machine at crosshead speeds corresponding to tensile strain rates of 1.56 x 10-5 and 1.56 x 10"3 per sec. Stresses were determined to ±2 x 106 dynes per sq cm and strains to within ±0.0001. Average values of shear stress t and shear strain y reported were taken as one half the tensile stress and three halves the tensile strain, respectively. Flow stresses were taken at 0.05 pct strain offset. Test temperatures down to 77°K were obtained by immersing the specimens in constant-temperature baths. Lower-temperature tests were performed in a liquid helium cryostat to within ±2°K of the reported values. Prior to testing at the various temperatures and strain rates all specimens were prestrained at 2 35°K at a shear strain rate of 3.13 x 10-5 per sec to a stress level of 0.606 x 10' dynes per sq cm to obtain a uniform initial state. Additional tests were made to determine the effect of changes in strain rate and strain on the flow stress by rapidly changing the crosshead motion during testing. Shear moduli of elasticity, needed for analyses of the data, were obtained at several temperatures by a common technique of determining the resonant frequencies of vibrations of rectangular test specimens. 11) EXPERIMENTAL RESULTS Fig. 1 shows the experimentally determined flow stress vs temperature for two strain rates. Two distinct regions of behavior are evident. Below about 180°K the strong increase in flow stress with increased strain rate and decreasing temperature indicates that deformation is controlled by a thermally activated dislocation mechanism. At higher temperatures an athermal region is evident where the flow stress is independent of strain rate and only slightly dependent on temperature. The applied stress t to cause plastic flow was separated into two components:

Jan 1, 1969

By C. R. Kuzell, G. H. Wigton

Knowledge of the thermal capacity of gases is of great importance in making metallurgical calculations. The metallurgist is frequeqtly called upon to investigate and determine furnace efficiencies in which the heat carried into or out of the furnace by gases is a large item in the heat balance. Not only do such problems present themselves in the determination of furnace efficiency, but also in the study of the application of heat in accessory apparatus, such as stoves, regenerators, waste-heat boilers, driers, etc. The thermal effect of the use of excess air in the combustion of fuel, the theoretical temperatures of combustion, the quantity of heat in hot blast at various temperatures, the effect of hot blast on furnace temperatures, are a few more examples of frequently occurring calorific problems involving gases. So many are the applications of the data on the heat capacity of gases that the subject merits careful study. The heat in a gas maybe due to its heat of combustion, if it is a combustible gas, and to its temperature. The latter is called its sensible heat and is the heat absorbed or evolved by a gas as its temperature is raised or lowered. The heat of combustion of gases is well established and is commonly known. The values can be found in almost any modern treatise on metallurgy. The sensible heat of gases has not been so well established because it is in most cases a function of the temperature, and the values of specific heats of gases over a wide range of temperatures have only recently been determined. It is the purpose of this paper to deal with the sensible heat of gases. - The calculation of sensible-heat capacities1 from specific-heat equations is a comparatively long and tedious operation. This is especially

Jan 1, 1915

By A. Whillier

Methods are given for estimating heat flows into mining excavations of various types, with an example to illustrate how the refrigeration requirements are then determined after allowing for the cooling effects of the ventilation air.

Jan 1, 1981

By John A. Riddle

Some of the pitfalls and problems in selecting and applying corrosion-resistant materials in uranium plants are discussed, together with some suggested solutions. Includes some cost data.

Jan 1, 1982

By Bertrand S. Summers

The technologist who has devoted much attention to the foundry-business will perhaps have noticed that the present scientific development of foundry-practice is in a condition similar to that of the steel-business some twenty years ago. In many cases chemistry is looked upon with suspicion, and the old cutand-try-methods are still in vogue, especially in the smaller foundries. The larger works have laboratories and more extensive means for applying science, and have devoted considerable time and attention to the improvement of foundry-practice. This is more especially true in the East, although in the West there are numerous firms devoting considerable attention to improving their metllods through the application of chemistry to work in the iron-foundry. It is hardly necessary to dwell extensively upon the effects of the different metalloids associated with iron, in pig- or castiron, in the way they are given in most text-books. The writer has thought proper to consider more particularly new developments in eupola-practice, particularly those pertinent to the discussion of the physics of cast-iron. In this connection some new ideas which recent practice has developed will be mentioned, and some results of practical tests along the same line will be described. Yet it has been deemed advisable also, by way of introduction, to outline the effects of the metalloids as they are described in most text-books, without going into detail. The question is sometimes asked, What is the most important element governing the quality of cast-iron 'for any particular purpose ? It would seem that right here lies the basis for the greatest difference of opinion. Some twenty years or more ago, silicon was regarded by foundrymen as one of their worst

Jan 1, 1899

By Willard H. Tracy

The method of seismic reflection prospecting has many times been compared to sound ranging, a process that became familiar to many during the World War. According to this very simple theory, the dynamite goes off and sends out a compression wave, which meets a reflecting horizon and returns to the surface, where it is recorded and the elapsed time of its travel in the earth accurately determined. Computations are then made on the general theory that the longer the elapsed time, the greater the depth of the reflecting bed. While this serves to give an idea of the fundamental basis of the process, it suggests a simplicity that does not exist in the life history of the various waves set up by a dynamite explosion in the earth. To begin with, a seismic wave in the earth does not obey the same simple laws of propagation that apply to a sound wave in the air. The property of strength in shear possessed by solids introduces a factor that sets such waves apart from the ordinary air waves. Also, the transmission charactcristics of the earth vary widely from place to place, and a fairly accurate knowledge of the space relationships of these variations is necessary if the final results are to be understood. Besides the waves recorded and used in the reflection computations, there are many

Jan 1, 1940

By Willard H. Tracy

The method of seismic reflection prospecting has many times been compared to sound ranging, a process that became familiar to many during the World War. According to this very simple theory, the dynamite goes off and sends out a compression wave, which meets a reflecting horizon and returns to the surface, where it is recorded and the elapsed time of its travel in the earth accurately determined. Computations are then made on the general theory that the longer the elapsed time, the greater the depth of the reflecting bed. While this serves to give an idea of the fundamental basis of the process, it suggests a simplicity that does not exist in the life history of the various waves set up by a dynamite explosion in the earth. To begin with, a seismic wave in the earth does not obey the same simple laws of propagation that apply to a sound wave in the air. The property of strength in shear possessed by solids introduces a factor that sets such waves apart from the ordinary air waves. Also, the transmission charactcristics of the earth vary widely from place to place, and a fairly accurate knowledge of the space relationships of these variations is necessary if the final results are to be understood. Besides the waves recorded and used in the reflection computations, there are many

Jan 1, 1940

By H. B. Northrup

Mineral Industries Extension instruction was pioneered by The Pennsylvania State Colleges Extension work was organized in 1893 and constituted what is believed to be the first vocational adult educational effort in that field in America. From 1894 to 1899, twenty-seven extension bulletins were printed and distributed free for the benefit of classes in the coal-mining industry and the records show that free lectures wore delivered by a corps of teachers of the mining department of the College "to the mining employees at their customary lace of assembly upon matters of interest to them in their occupation." In 1899, the State Legislature reduced the appropriation to the College and therefore the extension pamphlets and lectures were discontinued. Several sporadic attempts were made to resume the extension services in mining through industrial grants for travel and publications, and through voluntary contributions by members of the resident staff. The work. consisted mainly of lectures and demonstrations and served the purpose of creating the desire for more training and information of a more formal character. In 1928, the nave of the school was changed, by trustee action, from School of Mines and Metallurgy to the School of Mineral Industries and the working structure of the school was organized under the three functional collaborating headings: Resident Instruction, Correspondence and Extension Instruction, and Mineral Industries Research. The three functional bodies are separate, yet interdependent. The Federal Smith-Hughes law, passed in 1917, made Federal and State funds available for vocational educational work. Mining extension was revived in 1919 and the College employed one full-time extension professor to reorganize the work and instruct the classes. In 1923, the State Department of Mines and the State Department of Public Instruction entered into, a formal agreement with the School of Mineral Industries to assist the College in its extension program.. Classes were organized to study the State mining laws and State Department of Mines' previous examination questions and answers, in preparation for coming state examinations for certification of competency as underground officials. Mimeographed lesson material was used at first, and in 1947 and 1929 mining instruction and mining teacher-training lessons were printed. In 1931, the extension activities of the school were placed on an organized basis compatible with the newly formed school organization and a director was appointed to tale full charge of the work. During that year, at a conference in Harrisburg, an agreement was consummated between the State Departments of Public. Instruction, Mines, Labor and. Industry, and the College whereby extension classes in the field of the, mineral industries could be organized by the College, throughout the State, under "public supervision and. control," in close cooperation with the State Department.

Jan 1, 1941

By P. G. Shewmon, J. Y. Choi

The surface-diffusion coefficient for , has been measured on (111) and (100) surfaces of copper from 1000" to 620°C. D,(Ge) on the (111) is two to three times that on the (100) as was found earlier for copper and gold on copper. D, (Ge) on both (111) and (100) is about thirty times that found for gold or copper tracers on the same surfaces, while in the temperature range where both D,(Ge) and Ds(Au) have been measured the activation energy for germanium is the same as that for gold. The apparent activation energy for Ds(Ge) is not a constant, but decreases with temperature. In a recent paper we reported on the application of a new tracer technique to the determination of the surface-diffusion coefficient (D,) for gold and copper on (111) and (100) surfaces of copper.' In this paper, we shall give the results obtained when the same technique was used to measure Ds for germanium on the (111) and (100) surfaces of copper. In addition to providing data on D., for an additional element on copper, the longer half-life of germanium (275 days) meant that Ds could be measured down to a much lower temperature and thus over a much wider temperature range (1000" to 620°C) than was used in our gold-tracer work (1060" to 780°C) or copper mass-transport studies (1060" to 800). The apparent activation energy for D, (Ge) is essentially the same as that found for gold or copper in the same temperature range, though the values of D, (Ge) are thirty times greater than those found for gold or copper tracers. The most interesting new result found is that the apparent activation energy for Ds(Ge), and thus Do, definitely increases with temperature. Such a trend was much more apparent in Gjostein's mass-transport work on copper than in our own, though in an earlier paper we mentioned the difficulty of fitting all of our points with one straight line:= No real explanation of this is given though experiments done on grain boundary groove growth at various ambient pressures demonstrate unequivocally that vapor transport plays no part in the increase in activation energy with temperature.

Jan 1, 1964

By M. F. Werneke, J. A. Jones

The use of a unique class of sulfhydryl collectors, the monoalkyldithiocarbamate salts (RNHCS2M) as direct collectors for malchite and azurite is presented. Microflotation and laboratory scale flotation tests were performed to define the collector properties of these reagents under a variety of flotation conditions. On the basis of the results, it is proposed that some property of the amine-hydrogen atom in the reagent has a signification influence on the unusual activity of these collectors for oxide copper minerals.

Jan 1, 1979

By E. C. Wade, R. D. Valentine

This paper describes a computer applications engineering system and it's use to apply a thermal dryer fan motor in a coal preparation plant. The computer hardware and software systems are described to indicate the general approach taken and a specific case study is reviewed to show how computer power is brought to projects in the coal industry.

Jan 1, 1983

By R. P. Carreker, R. L. Fullman, J. C. Fisher

CREEP tests are usually constant load tests. As deformation occurs, the cross section of the specimen changes so as to maintain approximately constant volume. Until necking starts, A _ l0 A0 - 1 where A is the cross-sectional area, 1 is the specimen length, and the subscript o indicates initial values. Thus, during a tensile creep test under constant load, the stress increases in proportion to the elongation. A A, 1, where S is the stress and F the load applied to the specimen.

Jan 1, 1954

By Nicholas J. Grant, Olaf Troili, John Chipman

IN recent studies of the factors which affect the rate of desulphurization and its equilibrium, it became apparent that certain concurrent reactions were operative which had a significant effect on desulphurization. This is emphasized in the experiments of Hatch and Chipman1 and of Grant, Kalling, and Chipman' by the slow approach to a final state of equilibrium which is in marked contrast to the initial rapid transfer of sulphur from metal to slag. Since the removal of sulphur is of such profound importance in iron and steelmaking, it appeared necessary to investigate the reactions responsible for this behavior. It is now known that the presence of iron oxide in the slag interferes seriously with the principal reaction of blast-furnace desulphurization: CaO (slag) +-S + C - CaS (slag) + CO [l] The interfering reaction is most simply expressed as: CaS (slag) + 0 = CaO (slag) +-S 121 and a small concentration of oxygen (or FeO) is sufficient to hold a considerable amount of sulphur in the metal. It has been shown by Grant, Kalling, and Chipman2 that the addition of MnO to blast-furnace slag slows the removal of sulphur from the metal. This effect overshadows the contribution of MnO to basicity and is ascribed to its oxidizing power. It will be shown in this paper that SiO, also has sufficient oxidizing power to interfere with blastfurnace desulphurization. This is, of course, only one of its several effects. Primarily it is an acid and therefore reduces the concentration of excess lime. But when silicon is reduced to the metal the oxygen to which it was previously bonded becomes in part available for reaction 2. The proof of this statement is found in the following experiments. Experimental Procedure and Results Utilizing the same procedure and apparatus described by Grant, Kalling, and Chipman' five additional heats were made using slags IV and 11, the starting compositions of which were: slag IV—40 CaO, 10 MgO, 35 SiO,, 15 A1,0,; and slag 11—50 CaO, 10 MgO, 25 SiO,, 15 Al3O3. An important difference between these heats and those previously reported was that silicon to the extent of 1 to 4 pct was added to the present heats whereas the starting silicon content was formerly about 0.2 pct. Table I shows the slag and metal analyses for heats 82 to 87, and Table I1 shows the silicon addi- tions made to the charge. These additions are based on 400 g of metal and 400 g of slag. All heats had 1.65 400pct S charged before the cold slagadditions. The temperature was maintained at 1525°C. Rate of SiO, Reduction: Fig. 1 shows the silicon content of the metal in contact with slag IV at 1525°C as a function of time. Heat 70 from the work of Grant, afunctionKalling,of and Chipman is included as the lowest starting silicon. It will be noted that eeven with 4 pct Si in the starting metal, there is an increase in silicon content with time. Heat 84 is apparently approaching silicon equilibrium very slowly. Heats 70 and 82 with very much lower slowly.starting silicon show a more rapid initial rise in startingsilicon content but do not reach equilibrium during a long holding period. Fig. 2 shows 3 different initial silicon contents for Fig.2shows3differentheats 73 (from Grant, Kalling, and Chipman) 86 and 87, in contact with slag II, the most basic slag. Heat 73 is increasing in silicon with time, whereas heat 87 with an initial silicon content of 3.7 pct shows a decrease with time. Heat 86 shows a very close approach to equilibrium. The rate of transfer of silicon from slag to equilibrium.metal is very slow in all of those heats, even those which are initially far from equilibrium. ____

Jan 1, 1952

By Herbert Haas

The following notes describe a laboratory for metallurgical chemistry and technical analysis which I built late in 1903, while engaged, as constructing engineer, in erecting a pyrite smelter at the Afterthought mine, Ingot, Shasta county, California. This design partly supplements the paper of Mr. C. H. White, which was presented at the Atlantic City Meeting of the Institute in February, 1904.' The work of a chemist at a busy smelting-plant differs radically from the work of a student, who takes all possible care to have his analysis exact within hundredths of a per cent., and has plenty of time to devote to the operation. The works-chemist, having the shortest time in which to make his determinations, should have a laboratory arranged as conveniently as possible to save time in carrying out his work. By a conveniently-arranged laboratory, I do not mean an elaborately furnished one; but rooms suitably fitted up and supplied with the necessary apparatus to do the work expected from the chemist within the requirements of technical analyses. It is not uncommon at large smelters to have the night ae-sayer prepare 30 or more samples for titration, in time for the

Jan 1, 1905

By Carl S. Westerberg

Coal preparation practice and trends follow, among other factors, production trends in any given area. Considering an area the size of a state, some broad predictions may be made after a review of the annual production records. As this paper is concerned with coal cleaning in Utah, data on its production record are pertinent. Table 1 shows the percentage relation of coal production in Utah to the national total as a single figure up to 1935 which includes all recorded production. From 1935 through 1947 these data are presented by years. It is evident from these data that the production of Utah coal is ascending. The reason for this trend is industrial growth in the West resulting in a population shift which accounts for more people than the normal increase would supply together with Utah's relatively fortunate geographical location and its abundance of good-quality coal. Utah is also hopeful of supplying more coal in the future for West Coast power generation.I Utah is not unique among coal-producing states in anticipating greater production in the future. Coal Age states, " . . . it is now evident that a billion-ton yearly production of anthracite and bituminous by 1960 is not impossible." At present it is about 610,000,000 tons, the all-time high in 1947 was approximately 687,803,000 tons. In view of the trend outlined above, obviously more new mines will be required to produce the necessary tonnage. These in turn will require more mechanical cleaning capacity. Whether the required new plants will be built by present operators of mines and mechanical cleaning plants or by others now in the business of producing coal or expecting to enter it is of no consequence in this discussion. The fact is— they will be built.

Jan 1, 1950

Discussion of the paper of L. W. BAHNEY, presented at, the New York meeting, February, 1915, and printed in Bulletin No. 9S, February, 1915, pp. 339. to 344. E. J. HALL,* New York, N. Y. (communication to the Secretary+).- The Chiddy method for determining gold and silver in cyanide solutions has been subjected to so many proposed modifications, of which L. W. Bahney's is one, it is natural to suppose the method is defective. There is no denying that this method is capable of giving inaccurate results, but so is any other method of quantitative determination. However, proof has not come to my notice that the troubles are inherent and not in the detail application, and I am inclined to think from our experience that in many cases it is the latter. Errors in this method may be occasioned by: (1) The retention of zinc in the sponge, which tends to desilverize the molten lead in cupellation, similar to the action in the Parkes process, removing gold and silver in a crust of zinc oxide. Failure to remove zinc may result from lack of concentration of hydrochloric acid, clue to neutralization by salts present, volume of liquid too great for the specified amount of acid, or the use of weak acid. (HCl rapidly loses its strength unless kept in perfectly tight containers. The HCl gas escapes even from the ordinary glass-stoppered acid bottles after the plaster seal has been broken.) Undissolved zinc, is likely to be held in the upper part of the lead sponge, which floats above the liquid, and unless the solution is boiled it will escape action. Mr. Bahney's modification makes this

Jan 5, 1915

By R. L. Perrine

This paper presents results obtained by consider ation of unstable miscible displacement within a porous medium as a quasi-turbulent displacement process, that is, a process characterized by fluctuations around a simpler, mean flow behavior. The instability usually results from the miscible displacing fluid having a viscosity lower than that of the displaced fluid. Such instability is evidenced in suitable experiments by the presence of viscous fingering. A unified theoretical relationship applicable to both stable and unstable displacement is derived. Parameters in the theory are obtained by empirical means. Although the theory describes an idealized conceptual model, agreement with experiment is quite reasonable up to moderately adverse viscosity ratios, such as 17:1. INTRODUCTION Many experimental studies of miscible displacement in porous media have been conducted with prediction of reservoir displacement efficiency as the ultimate objective. Most such studies have utilized lower displacing than displaced fluid viscosity, scaled to potential reservoir fluid pairs. Theoretical approaches have been largely limited to unit viscosity ratios, however, in spite of the necessity for an understanding of the mechanism of the unstable, adverse viscosity ratio displacement process. An obvious reason is the difficulty of describing in mathematical form the viscous fingering characteristic of these conditions. Observation of experiments conducted with dyed fluids in transparent systems suggests an analogy between unstable miscible displacement and turbulent flow in a pipe. In both cases there are fluctuations around a simpler, mean flow behavior. An important difference is that flow behavior of interest in the porous medium is entirely transient, contained within a transition zone between displacing and displaced fluids. Transient behavior complicates description in that coefficients in the equations become variables rather than constants. In the study reported here, the analogy with turbulent flow has been used in treating unstable miscible displacement as a quasi-turbulent displacement process. The purpose has been to derive, even if restricted to an idealized conceptual model, a unified theoretical relationship applicable to both stable and unstable displacement. A relationship meeting these specifications up to moderately adverse viscosity ratios, such as 17:1, is presented. One fluctuation parameter in the theory and dispersion coefficients are obtained by empirical means. The idealized theory is compared with experimental results. UNSTABLE MISCIBLE DISPLACEMENT AS QUASI-TURBULENT DARCY FLOW The miscible displacement of one fluid by another within a porous medium is considered in this study. Flow conditions are such that Darcy's law is applicable. It is further assumed that, by the stability criterion proposed by perrine,1 initial flow conditions lie well within the regime of instability. Thus substantial viscous fingering is assured. We wish to show how this flow regime can be represented as quasi-turbulent. That is, the Reynolds number for the established flow conditions is below that for inertial or turbulent flow within a porous medium, and lies within the regime for which Darcy's law is valid. Yet flow behavior can be described as the combination of some relatively simple average result, and characteristic fluctuations that are superimposed on the simpler behavior. Stated another way, flow behavior includes the movement of layers of fluids with different velocities past or over one another. Such descriptions are characteristic of turbulent pipe flow. The fluctuations in the present case are a direct consequence of the local viscous fingering which accompanies the unstable displacement process. Should displacement become stable, fluctuations would die out. It is of particular importance to note that fluctuations such as these can interact in a way that contributes to material transport by the basic flow. The basic transport equations required for engineering calculations must be modified to reflect this fact.

By J. M. Floyd

The theory, construction and applications of oxygen sensors employing high-temperature electro- chemical cells with solid electrolytes are briefly reviewed. The application of disposable probes to measurement of the oxygen potential in matte and slag baths in tin, copper, and nickel smelting operations is described. Examples discussed include end-point determination in smelting and slag-cleaning operations, pilot-scale investigations of process chemistry to assist in the development of smelting strategies, and measurements in operating smelters to improve the efficiency of operation.

Jan 1, 1984