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By Robert U. King, John W. Vanderwilt

THE Climax molybdenite deposit in Lake County 100 miles southwest of Denver is located in the central part of the mineral belt extending northeasterly across the state. Principal geographic features and geology are shown on Fig. 1. The first period of molybdenite mining, which began in 1918, ended in April 1919 because of limited demand and a price drop to about 72¢ per lb. During this time the ore came from the Leal level and surface outcrops at a higher elevation. Rate of mining was 250 tpd and several million tons of ore averaging 0.7 pct molybdenite were developed. Since April 1924, when the second period* began, Climax Molybdenum Co. has been the only operating company. Production in 1924 was 400 tpd and finding ore was a continual problem. When the White tunnel was extended, however, further ore was encountered. The orebody was thought to be tabular until 1926, when B. S. Butler recognized the relation of the developed ore on the Leal and White levels to a central area of fine-grained hydrother-mal quartz, and by 1929 diamond drilling had blocked out indicated ore reserves in excess of 100 million tons. In 1946, on the basis of information obtained from 25 miles of mine workings and a completed exploratory program involving over 200,000 ft of diamond drilling, the present authors reviewed and brought up to date the geology of the orebody. More recently Sears," employing microscopic techniques, made a study of hydrothermal alteration and mineralization, and Howell and Schassberger'" restudied available geologic data. Production (1953) of molybdenite ore has been expanded to over 25,000 tpd and total production from 1918 through 1953 has been: Tungsten, tin, and pyrite are byproducts and monazite also was produced from 1949 through 1951, after which it was not saved. A maximum of 15 to 20 tons of monazite was produced. Geology of the Area Pre-Cambrian crystalline rocks constitute most of the Mosquito Range for several miles to the north, east, and south of the Climax molybdenite deposit, see Fig. 1. To the west the crystalline rocks are in fault contact with shales and sandstones of Pennsyl-vanian age. Both crystalline rocks and sediments are intruded by dikes and sills of Tertiary age. Numerous faults with small displacements are to be found in the crystalline rocks east of the Mosquito fault and in the sedimentary beds to the west. Pre-Cambrian Rocks: The pre-Cambrian rocks consist of schist and gneiss, identified with the Idaho Springs formation, and granite with minor pegmatite correlated with the Silver Plume granite of the Silver Plume area. The Idaho Springs formation is a general term applied to pre-Cambrian schist and gneiss found over a large part of the Colorado Front Range. At Climax this formation consists largely of biotite-schist and quartz-biotite gneiss with minor quantities of plagioclase and orthoclase, although in places appreciable quantities of feldspar and quartz are present in the more gneissic varieties. Locally, especially along the contact with granite, recrystal-lization of the schist has produced coarser texture and a more pronounced than average gneissic appearance. The gneiss and schist have been mapped as a single unit by Butler and Vanderwilt (1933)" and by Singewald (1951).12 Schist predominates at the higher elevations of the Mosquito Range and in the area to the north and east of Climax. The regional trend of schistosity is northeast with varying dips to the east. Silver Plume granite and associated pegmatite intrudes the Idaho Springs formation. Silver Plume granite in many places and in the Climax district in particular has an irregular form, and many large and small inclusions of schist and gneiss occur within the granite. Granite predominates at the surface in the immediate vicinity of the area of hydrothermal alteration and extends for several miles to the northeast and southeast. As more schist is present at lower levels of the mine than in the upper levels, the suggestion is that the granite is sill-like in form,

Jan 1, 1956

By Y. A. Chang

Phase relationships in the system Cr-Si have been established based on the melting point, X-ray, metallo-graphic, and DTA studies. The three intermediate phases, Cr3Si, Cr5Si,, and CrSi,, melt congruently at 177V ± I@,Cr3Si, 1680"i 20°, and 1490" *20°C, respectively, while the fourth intermediate phase CrSi, melts peritectically at 1413" i 5°C to Cr5Si3 and a melt containing 51 at. pct Si. The temperatures and compositions of the four eutectic isotherms occurring in this system are given below: DTA and metallographic evidences indicate that Cr5Si, undergoes a phase transformation at 1505" i20°C. The high-temperature form of this phase could not be retained by the quenching techniques used in this study. TECHNOLOGICAL interest in the developing of composite systems, consisting of Sic on the one hand as a fiber-reinforced material and metallic substances such as chromium, nickel, or Cr-Ni alloys as a binding agent on the other hand, stimulated the present investigation of phase relationships in the binary system Cr-Si. Earlier works concerning this system have been evaluated and summarized by ansen and Anderko.' Their phase diagram was based mainly on the works of Kieffer, Benesovsky, and schroth2 and Kurnakov.~ According to these authors, the three intermediate phases Cr3Si, CrSi, and CrSi, all melt congruently at approximately 1730°, 1600°, and 1550°C. However, they did not agree on the compositional stability of the fourth intermediate phase between Cr3Si and CrSi. Later Parthe, Nowotny, and schmid4 determined the structure of this phase to be tetragonal T-1 type using the single-crystal method, and concluded that this phase had a formula of Cr5Si3. Since the compilation of Hansen and Anderko,' a new phase diagram for the system Cr-Si has been proposed by Elliott5 based on the works of Goldschmidt and rand,' Guseva and ~vechkin,~ and Trusova, Kuzev, and Ormont8 and the earlier works quoted by Hansen and Anderko.' According to this proposed phase diagram, all four intermediate phases have large ranges of homogeneity and all melt congruently. More recently, Svechnikov, Kocherzhinskii, and yupkog studied the system Cr-Si by the DTA-method. According to their findings, the three intermediate phases, Cr3Si, Cr5Si3, and CrSi,, melt congruently at 1700°, 1720°, and 1475"C, respectively, while the fourth intermediate phase, CrSi, melts peritectically at 1475°C to Cr5Si3 and a melt containing 50 at. pct Si. The temperatures and compositions of the four eutectic isotherms were found to be: In view of the discrepancies existing in the literature concerning the system Cr-Si, it was decided to rein-vestigate the phase relationships in this system. EXPERIMENTAL a) Starting Materials. Chromium disilicide and chromium or silicon powders were used in the present study to prepare the melting point and DTA samples. CrSi, was obtained by directly reacting cold-pressed elemental powders in an atmosphere of Hz at a temperature of about 1250°C. Chromium powder, purchased from Stark Chemical Co., had the following impurities in ppm: Fe, 200; Mg, 1000; and 0, 250; while silicon powder, purchased from the Welded Carbide Co., had the following impurities in ppm: Ca, 700; and Fe, 3500. b) Melting-Point Determination and Differential Thermal Analysis. Cylindrical melting-point samples of approximately 13 mm in diam and 30 mm in length with a rectangular groove in the center were prepared by hot-pressing of well-mixed powder mixtures in graphite dies. Before the melting-point determination, the hot-pressed samples were ground on a sand paper to remove any minute surface contamination of graphite. A small hole of 1 mm in diam, drilled on the center portion of the samples, served as a blackbody cavity for the temperature measurements. DTA samples approximately 13 mm in diam and 15 mm in length were prepared in a manner similar to the melting-point samples. Melting points were determined using the Pirani technique under a helium atmosphere of 40 psi. The design, performance, and operation of this apparatus have been described in detail by Rudy and ~ro~ulski.'~ The temperature measurements were carried out with a calibrated disappearing-filament-type micro-pyrometer. The measured temperature was corrected for losses from the quartz window of the melting-point furnace and for deviations from blackbody conditions of the observation hole. The procedure for temperature correction has also been previously described." The DTA method of Heetderks, Rudy and Eckertl' was also used to check any phase transformations of selected alloys in the system Cr-Si. It was not possible to make remated runs on the same sample once melt-

Jan 1, 1969

By N. Tiner

THE mechanical properties of magnesium-alloy castings are greatly improved by grain refinement, and at present considerable attention is being paid to methods of obtaining fine-grained castings. One method of achieving this end is the use of proper melting and superheating techniques. These have been employed commercially to a great extent, but no comprehensive study of the subject appears to have been published at present. Numerous investigations found in the literature include some reference to superheating techniques, 1-4 and Achenbach, Nipper and Piwowarsky,5 based principally on thermal analysis, ascribe the grain-refining action of superheating to the influence of solid foreign particles or dissolved gases present in the melt upon the course of crystallization. The primary purpose of this paper is to present the principal facts concerning the effect of superheating on grain size of magnesium alloys. Attempts are also made to explain the experimental results in terms of a general hypothesis. The investigations are limited chiefly to common commercial casting alloys. In order to carry on this work, it was necessary to determine the factors influencing grain size and to develop a proper technique for the preparation of samples. The preliminary tests made by the author indicated that the grain size of magnesium alloys resulting from the solidification of a melt is determined by alloy composition, presence of impurities, rate of cooling during solidification, thermal history of the melt and to some extent the structure of the charge used. The rate of cooling is in turn dependent upon the mass of the melt, pouring temperature, and dimensions, properties and temperature of the mold into which the melt is poured. The final grain size of the alloys is still further modified by heat-treatment subsequent to casting. It is not within the scope of the present paper to discuss all of these factors, and it would suffice to note here that when equal amounts of magnesium alloys are prepared from the same alloying materials, melted in graphite crucibles under the same thermal conditions, then cast into graphite molds at a constant temperature, the .resultant solids have the same grain size. By maintaining all other factors constant, it is thus possible to vary thermal conditions of a melt and to examine the grain size of resultant castings. PREPARATION OF SAMPLES AND GRAIN-SIZE TESTING The alloys investigated in this paper were taken from ingots made by Permanente Metals Corporation or prepared by the author with pure carbothermic magnesium and necessary alloying elements. Melting was carried out under a flux in a graphite crucible heated uniformly by an

Jan 1, 1945

By J. Leja, J. H. Schulman

FROTH flotation is usually effected by the addition of a collector agent and a frothing agent to an aqueous suspension of suitably comminuted mineral ores. The action of collectors is to adsorb onto the surfaces of minerals to be separated, sensitizing them to bubble adherence. The action of frothers has, in the past, been accepted as that of froth formation only, brought about by a lowering of the air/water interfacial tension. Substances capable of producing froth are classed1a,b according to their relative capacities for production of froth-volume and froth stability in the simple frother-water system. The purpose of this paper is to show that the surface active agents acting as frothers become effective only when there is a suitable degree of molecular interaction taking place between collector molecules and frother molecules at the air/water and solid/ water interfaces. Further, the discussion will demonstrate that the actual mechanism of adherence of an air bubble to a suitably collector-coated particle is due to the molecular interaction collector-frother. This leads to the formation of a continuous interfacial film of associated molecules, anchored to the mineral by polar groups of the collector, and enveloping the whole bubble. The tenacity of adhesion mineral-to-bubble results from the strength and the visco-elasticity of this mixed film. Some 20 years ago Christman2 postulated mutual dependence of collector and frother in effecting flotation. This view was, however, strongly opposed by Wark,3 who pointed out that an addition of frother had no effect on the value of contact angle once this was established in the solution of collector. More recent work by Taggart and Hassialis' indicated that the presence of frother, namely, cresol, leads to the immediate establishment of a contact angle on sphalerite, partially coated with xanthate, whereas an air bubble fails to make contact in potassium ethyl xanthate solution alone, even after 60 min induction time. Wrobel5 raws attention to the selectivity of frothers in flotation. Many instances of antagonistic effects of certain mixtures of frothers (or collectors and frothers) on flotation froth have been known to flotation operators and have been reported in literature. Taggart6 and Cooke7 give several examples of incompatibility of certain ratios of frothers and collectors, e.g., oleate and long-chain sulphates, pine oil and soaps. Monolayer Penetration. Properties of insoluble films produced by molecules of surface active agents orientated at the air/liquid interface are conveniently studied by the Langmuir trough technique, described fully by Adam.' Using the trough technique Schulman and Hughes" and Schulman et al.10a. b, c, d,e established the existence of molecular interactions occur- ring between certain types of surface active agents. Their experiments revealed the phenomenon of penetration of an insoluble monolayer (e.g., a film of a long-chain alcohol) by a soluble agent (e.g., sodium alkyl sulphate) injected into the substrate (water or salt solution). The degree of molecular interaction taking place on penetration is determined by changes in the surface pressure of the resulting film, changes of its surface potential and its mechanical properties (viscosity and rigidity). When the interaction takes place between both polar groups and both hydrophobic groups of the two participating amphipathic molecules a molecular complex is formed. Complexes formed on penetration of the monolayer at interfaces are not necessarily true chemical compounds: they are labile in solution, the activity and reactivity of individual components are greatly different from those of the molecularly associated complex, and on crystallization they usually separate out into components. However, when formed in the orientated state at interfaces they are found to be very stable, although some mixed films spread as monolayers of stoichiometric complexes can show further penetration by subsequent additions of the soluble component injected into the substrate.'" The degree of association between two or more types of surface active agents is very sensitive even to small changes in electric (dipole) moment of the polar groups of the amphipathic molecules as influenced by magnitude and position of neighboring ions or dipoles, their size, concentration, and stereochemistry. In addition, the molecular association is greatly influenced by concentration and type of inorganic salts in the substrate, by its pH, and by temperature. The nonpolar groups of interacting molecules greatly affect the stability of molecular complexes. Progressive shortening of the aliphatic chain of one of the reacting molecules weakens (at an increasing rate) its tendency to form stable complexes. Similarly, introduction of a double bond of cis-form into one of the reacting chains, which changes the straight hydrocarbon chain into a kinked one, or introduction of a branched chain, reduces the stability of the associated complex. Monolayer Adsorption. Using the trough technique and injecting metal ions into the substrate (water or salt solution) underlying insoluble films of fatty acids, alkyl amines, and sulphates, Wolsten-holme and Schulman11a,b,e. ' and Thomas and Schulman" have established conditions, namely, pH, concentration. and steric factors, under which molecular interactions take place between the polar groups of the surface active agents and the metal ions. These interactions are marked by great changes in the solubility and mechanical properties of the monolayer of the agent; no surface pressure increases are observed as in monolayer penetration experiments. The results of these adsorption studies, correlated with flotation experiments, indicated that in the case of fatty acids and alkyl sulphates their adsorption onto minerals of base-metals takes place by a similar

Jan 1, 1955

By Roy A. Lindgren

Since the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced1, at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces1. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a superior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1937

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-B alloys has been measured up to the solubility limit for the formation of boron nitride. The activity coefficient of nitrogen increases with increasing boron content in the range 0 to 7 wt pct B. From experimen -tal data, values have been calculated for the B-N interaction parameter e3 at temperatures in the range 1550" to 1750°C. A value of 0.038 has been estimated for the boron self-interaction parameter eg at 1550°C. The standard free energy of decomposition of boron nitride into the elements dissolved in liquid iron has been determined to be: ?F° = 45,900 -21.25T in the range from 1550° to 1750°C. The nitride is assumed to be of composition BN. BORON nitride has an unusual combination of properties which make it appear attractive in a wide range of engineering applications. Some of its more important and most recent applications are in the nuclear area, particularly in connection with the liquid-metal cooled reactor concept now receiving considerable emphasis. Boron nitride has a high degree of stability at elevated temperatures. It also has excellent ma-chinability and the ease with which its crystals deform suggests applications as a lubricant. These properties stem from a hexagonal layer-type structure similar to the structure of graphite. One of its primary uses to date has been for seals in liquid-metal pumping systems. It is also used in nuclear reactors as an insulating layer to separate two solid metals which are not themselves compatible under the conditions of temperature and atmosphere in which they are used. Its inertness to liquid metals has also suggested use as a mold-release agent in casting processes. In addition to its excellent machinability and reported inertness to liquid metals such as iron, silicon, aluminum, copper, and zinc, boron nitride has high thermal conductivity and excellent thermal shock resistance. This combination of properties would make it appear ideal as a refractory crucible material for refining of high-purity liquid metals, for example high-quality steels. However, since it is known that concentrations of boron as low as 50 ppm can have a marked effect on the physical properties of certain steels,' in particular on the creep and stress-rupture properties, an investigation was undertaken to define accurately the chemical equilibrium among boron, nitrogen, and liquid iron in the range of steelmaking temperatures. EXPERIMENTAL PROCEDURE Two experimental approaches to this problem were employed: a Sieverts' method and a quenching method. In the first method, the Sieverts' technique was used to measure the equilibrium nitrogen solubility in liquid Fe-B alloys of 0 to 7 pct B as a function of nitrogen gas pressure over the melt. The solubility limit of the boron nitride phase formed was determined by the point of departure of the nitrogen absorption from Sieverts' Law. This technique has been applied to liquid Fe-Ti alloys by Rao and parlee,' to liquid Fe-A1 alloys by Evans and Pehlke,3 and to solid Fe-V alloys by Fountain and Chipman.4 In the second method a melt of liquid iron was held in a crucible of boron nitride under a known partial pressure of nitrogen gas. After thermodynamic equilibrium was attained, the melt was quenched in a stream of helium and then analyzed by wet-chemical methods for boron and nitrogen. The Sieverts' apparatus used in the first method was essentially of the same design as the one described by Pehlke and Elliott.5 The charge materials were vacuum-melted high-purity iron (Ferro-vac E) supplied by the Crucible Steel Co. and -325 mesh boron powder supplied by Cooper Metallurgical Associates of Cleveland, Ohio. The boron contained less than 0.02 wt pct O, according to supplier's analysis. Recrystallized alumina crucibles were used to contain the melt. Examination of solidified melts showed these crucibles to be satisfactory with no evidence of any reaction or physical penetration of the crucible wall by the melt. The melt temperature was measured by a disappearing filament-type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diam sight hole in the crucible lid. The pyrometer was calibrated against the melting point of pure iron in the same apparatus, taking the emissivity of

Jan 1, 1964

By E. H. Jr. Dix

OF all the alloying elements used in commercial aluminum alloys, copper stands out as by far the most important, and it is perhaps for this reason that the constitution of the aluminum-copper system has received the attention of a number of experimenters covering a period of approximately 20 years. It would be expected that during this time the equilibrium relations had been thoroughly and exactly worked out. In a general way this is true, but there is a surprising lack of agreement in the details of the high aluminum end of the diagram, particularly in regard to the solid solubility of copper in aluminum, which has been given variously as 2 per cent. to 5 per cent. at the eutectic temperature. The importance of this is much greater than might at first appear to one unfamiliar with modern commercial aluminum alloys. This is true because, with one exception, the susceptibility of the strong alloys to heat treatment depends, in part at least, upon the solid solubility relations of copper in aluminum. In 1919, Merica, Waltenberg, and Freeman1 published the first detailed information on these solubility relations. They found that the solubility of copper decreases with falling temperature from about 4 per cent. at 5.25° C. to about 1 per cent. at 300° C. and is apparently still diminishing at lower temperatures. In 1921 there was published a brief account of the results obtained in the National Physical Laboratory, Teddington, England.2 This laboratory, however, reported that 5 per cent. of copper is soluble in aluminum at 540° C., and that this amount decreases to about 3 per cent. at 20° C.

Jan 2, 1926

By Reno Sales

THE present-day application of geological knowledge to mine opera-tions owes much to Survey activities. Early publications covering developed deposits at Comstock and Eureka in Nevada, and Leadville in Colorado, aroused great interest in mine geology among mine owners and operators. In later years personal contacts between Survey geologists, notably Lindgren, Spurr, Emmons, Weed, and Ransome, to name only a few, and mine managers, mine superintendents and mine foremen, brought directly home the importance of geological mapping and study in connection with mine operations. However, the Survey had recognized from the beginning that it was not practicable, either from the viewpoint of cost or policy, to supply direct help to the miner. The situation was met by many large mining companies through the organization of geological departments to deal with problems of geology which concerned not alone the every-day mine operation but also the life expectancy of the ore deposit. The mine owner therefore looked to the mine geologist to apply the "laws of ore deposition" in estimating the future of his mine. The examination of outside properties also became a duty of the company geologist where replacements were needed or where expansion of operations was contem-plated. And finally, out of this situation there developed the inde-pendent consulting geologist, specializing in geological examinations of prospects, mines, and mining districts, whose duties included the highly important but often difficult task of appraising ore reserves and ore possibilities. Thus, while it may be considered by many that the work of the mine geologist overlaps that of the Survey geologist, their respective fields of endeavor are not in conflict. The appearance of the mine geologist has lessened in no manner the need of intensive field and research work by the Geological Survey and related organizations.

Jan 1, 1934

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By E. T. Turkdogan, P. Grieveson, J. F. Beisler

Experimental results are given for the rate of reduction of silica from silicate melts by paphite-saturated iron in the presence of carbon monoxide. It is shown that, when gas bubbles are present at the slag-metal interface, the interfacial chemical reaction is the rate-controlling process in the transfer of silicon from slag to metal. From the silicon-concentration profiles in the metal sample, the diffusivity of silicon in paphite-saturated iron is found to be (5.4 * 0.4) x 10 sq cm per sec at 1600°C. Some consideration is given to the transport of oxygen from the slug-metal interface to the walls of the gvaphite metal container as becoming the rate-controlling process in the absence of gas bubbles at the slag-metal interface. ATTEMPTS were made by Fulton and chipman1 to investigate the kinetics of reduction of silica from calcium alumino-silicate melts by graphite-saturated iron in an atmosphere of carbon monoxide. In these experiments with 400 to 500 g of metal and slag, both phases were stirred in such a manner that the interface was essentially undisturbed. Initially, the graphite-saturated iron contained about 15 pct Si and, after about 8 or 10 hr of reaction time at 1600°C, the silicon content of the metal in- creased by about 0.2 pct. In a written discussion on this paper of Fulton and Chipman, schuhmann2 pointed out the possibility that this observed slowness of the reduction of silica could be due to the transport of oxygen across the liquid metal boundary layer at the slag-metal interface. Although this explanation of Schuhmann is quite feasible for the experimental data of Fulton and Chipman on silica reduction, such a reasoning should not be extended to other rate data on slag-metal reactions unless sufficient evidence is available satisfying the boundary conditions for such a transport process. The hydrodynamics of stirred liquids are very complex and even for a simple method of stirring there is no exact mathematical solution which will predict the mass transfer coefficient accurately. The best available solution of this problem is that given by Lewis' and later modified by mayers~ for a two-liquid system where liquids are stirred by counter-rotating stirrer blades without disturbing the interface. In such a system the mass transfer coefficient is estimated from an empirical relationship using the data on viscosity and density of the two liquids, rate of revolution, the length of stirrer blades, and the diffusivity of the element which is transferred from one phase to the other. It was found in these investigations' that the estimated and observed mass transfer coefficients, in systems containing two immiscible aqueous solutions, agreed within *40 pct. Although this is not considered to be an unreasonable error for the study of industrial processes, uncertainties of this magnitude cannot be tolerated in any theoretical study of reaction kinetics. In view of the complexity of the

Jan 1, 1963

By Robert V. Pierce

In the last few years, much study has been devoted to increasing stoping efficiency. The reasons for this are shortage of manpower, shorter working hours, operating regulations, and shortages of essential materials. More efficiency in mining methods is needed to offset these adverse factors. In the past, attention has been centered upon haulage, hoisting equipment, mill flowsheets, etc., but recently the spotlight has been focused on the cost of stoping and the cost of handling materia,ls. Scrapers and scraper hoists have thus assumed greater importance. In order to make it possible for certain ore bodies to be mined at a profit, it has been necessary to apply assembly-line practices to the streamlining of mining methods. All cycles of the mining operation must balance, and the sooner broken ore is removed from the working face, the sooner another round can be started. Since the introduction of scraper hoists in metal mines more than thirty years ago, much progress has been made in their design and application. Alert operators are now constantly watching for methods in which to apply scrapers. The saving of: manpower in development work and the changing of mining methods that once employed manual handling of materials are increasing vital wartime tonnages. Essential ores from newly discovered ore bodies are moving rapidly from stopes to reduction plants—because it is now possible to develop an ore body and place it in production with a minimum of manpower and development work. Today, speed is one of the prime essentials of mining. Everywhere, there is a concentrated effort to use experienced miners in breaking rock, in timbering, and in carrying out the various phases of mining that require many months of training. Much effort is being made to mechanize the working places because experienced men naturally prefer to work where the majority of materials are handled mechanically. In line with this policy, many new men are being taught the details of scraper work, because even green men can quickly become acquainted with scrapers and thereby release older heads to perform the more skilled phases of mining. In some places it has been found economical to change from .one system of stoping to another that more readily allows the application of mechanical muck-handling equipment. Where blocks are worked faster, the cost of materials, time, and labor is cut drastically. This favorable situation allows more manpower to remain on straight breaking and timbering—or straight production mining. Moreover, when blocks are mined faster, more floors can often be mined vertically before the mucking or wheel floor is moved. This results in several direct savings. There are cases where it has been proved that by working a given block faster more area, longitudinally or vertically, could be mined at one time, thus permitting the reduction of development cost. (Fig. I.)

Jan 1, 1943

By C. C. Mattax, J. E. Bobek, M. O. Denekas

ABSTRACT investigations in recent years have shown that rock wettability can exert a profound influence on the displacement of oil by water from oil producing reservoirs. Core analyses frequently show oil recoveries from preferentially water-wet rock to be significantly greater than those from preferentially oil-wet rock. Thus, an accurate prediction of water-drive or waterflood oil recovery is dependent on the evaluation of reservoir rock wettability. Laboratory and field studies have been undertaken to examine and develop methods which may be used to measure rock wettahililiy, to investigate factors which may alter the wettability of reservoir rock, and to determine the wettability of specific reservoirs. It has been found that measurement of the rate and volume of spontaneous imbibition of the wet-ting phase by a rock is a reliable and reproducible test for semi-quantitarive determination of preferential rock wettability. Laboratory tests have shown that the wettability of reservoir rock may depend on both the crude oil composition and the rock type. Field and laboratory tests have indicated that coring flulids and core handling techniques can cause significant changes in the wettability of rock surfaces. However, a few fluids, brine in particular, appear not to affect core wettability and may be used when coring to determine reservoir wettability. Core handling and packing procedures have been developed which preserve core wettability during storage and laboratory testing. The wetfability characteristics of six reservoirs have been evaluated by wettabilify tests performed in the field on fresh cores cut with brine or special water-base muds. The tests indicated that all six reservoirs are water wet; however, the de-gree differed from one reservoir to another. INTRODUCTION Although surface properties of reservoir rock and interfacial characteristics of rock, crude oil, and water systems have been discussed for many years, the full significance of these properties to the production of oil is still in the process of evaluation. It is known, however, that one surface characteristic—preferential wettability of the reservoir rock—-is of paramount importance when the reservoir is being produced by water-flood or water-drive mechanisms. The importance of rock wettability has been pointed out by several authors'.',%* who have found that pref- erentially water-wet cores flood more efficiently than oil-wet cores; that is, more oil is recovered from water-wet cores in the early flooding stages than from oil-wet cores. Other authors'," indicate that waterflood oil recovery from cores of intermediate wettability may be greater than that from either strongly water-wet or strongly oil-wet cores. These recent investigations emphasize that the true wettability of a reservoir must be known before the performance of waterflood or water-drive reservoirs can be accurately evaluated. When reservoir wettability is to be determined by core analysis, precautions must be taken to maintain the original wettability which can be altered readily during coring5 nd testing.' In the coring operation the core may be partially or completely penetrated by the drilling fluid which, if it contains surface active materials, may drastically change the wettability of the core. Also, improper core handling during stcrage and testing may change its wettability because of evaporation of fluids or exposure to oxygen or surface active contaminants. One purpose of this paper is to discuss methods for obtaining, preserving, and testing cores without altering their original wettability. In addition, the results of wettability tests on fresh and preserved cores from six reservoirs are presented where special precautions were taken to obtain samples without altering their wettability during the coring operation.

By Sherwin Kelly

The prime objective of geophysical exploration is to promote the economical and rapid dis-covery of mineral or oil deposits of commercial value. To a few this concept as applied in min-ing may signify the direct discovery of ore-bodies, but to the geophysical engineer this latter Idea is one of the most insidious and detrimental misapprehensions which he has to combat. The destruction of this annoying obstacle to the progress of geophysical exploration reveals the kernel of truth behind it, that the exploration geophysicist has for the better part of two decades been concerned primarily with the discovery of mineral formations favorable to the occur-rence of commercial ore. There is a very real distinction here, since geophysical methods are capable of discovering certain mineral formations such as sulphide bodies or quartz veins, but are totally incompetent to predict whether or not they constitute ore; that is. whether or not they contain minerals of economic value in the amounts requisite to repay extraction. The art of geophysical exploration is now, however, rapidly outgrowing these early limita-tions. The rate of this growth will in large measure depend on the recognition by the mining industry of the fact that geophysics can play a role far wider and more important than it usual-ly does now, in guiding the future exploration and development of mineral deposits. It is my own firm conviction that as time marches on we will see the methods of applied geophysics turned more and more to the delineation of both minor and major structural features. The outlining of such features having a bearing on the probable loci of mineral deposition will be of inestimable value in guiding the development of a mining district. It is in this field that there will In-evitably occur a meeting and overlapping of the activities of the exploration geophysicists and

Jan 1, 1940

By H. S. Price, J. C. Cavendish, R. S. Varga

This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure values near wells, as well as accurate pressure pdients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subspaces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. INTRODUCTION The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield9 or Peaceman and Rachfordl0). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and weber17 and Roper, Merchant and Duvall,13 have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite often cannot even be applied. In this paper, we present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: where G is a rectangle (with sides parallel to the coordinate axis) with boundary ?G, ?/?n denotes the outward normal, and y and B are non-negative constants such that y + B > 0.

Jan 1, 1970

By A. C. Freeze

The first use of electric punched card accounting machines as an aid in calculating reserves at the Sullivan mine in Kimberly, B.C., was made in January, 1948. At that time their use was limited to totalling individual reserve blocks for the various reserve classes and for calculating total metal content. The immediate objective was to increase speed, improve accuracy, and to effect some savings in labor that could be employed more usefully elsewhere. It was recognized also that the potential for achieving even greater advantages was excellent. The initial experiment proved so successful that it was inevitable that the use of the method would expand. Thus, for the past nine years assay data from core hole and development headings have been processed by these machines and the results integrated with the program of calculating reserves. It was also learned that the machines could store and classify a large amount of other information concerning the mining characteristics of each reserve block in addition to tonnage and metal content. This has proven very useful for the preparation of monthly production reports as well as in long term planning, in forecasting production schedules, and in analysing the results achieved.

Jan 4, 1961

By L. W. McKeehan, W. C. Elmore

The magnetic powder method, long used for roughly mapping magnetic fields, has recently been refined1, "or investigating the microscopic variations in the surface magnetization of ferromagnetic crystals. Bitter2 first discovered regular powder patterns connected with the crystal structure of such specimens. Several other investigators:' have used Bitter's original technique, with slight modifications, to study the variation of the patterns with variations in the magnetizing field applied parallel to the surface, and their dependence upon the state of strain, of polish and of crystal cut. All of the explanations of these patterns on metallic ferromagnetics have been couched in general terms. In a preliminary report we have described an improvement ill the powder technique which led us to the discovery of a new effect throwing considerable light on the magnetic secondary structure of alpha iron4 and of nickel5 single crystals. We now report additional evidence confirming the existence and stability of a magnetic block secondary structure. Specimens The following list describes the specimens used in the present investigation. Designation Description A1 Silicon ferrite furnished to us by Dr. W. E. Ruder, of the General Electric Co., for which lie gave the following typical analysis: C, 0.05; P, 0.038; S, 0.026; Mn, 0.15; Si, 3.24. Disk, 0.60 cm. diameter, about 0.05 cm. thick. By X-ray analysis angles between disk normal and [100] 75o, [0101 76" [00l] 21o. A2 Same as A1 except: diameter 0.75 cm. A, Same as A1 except: diameter 0.68 cm.

Jan 1, 1936

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole'') and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-') is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-' using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- ' torr, Maiya and lakel measured y as 39 kcal mole-' using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-': there is evidence also for a low temperature value of about 20 kcal mole-'. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.'-'' Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A', C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2'3 M = mass of an evaporating molecule

Jan 1, 1970

By K. H. Kilgren

At high formation pressures the distillate produced from a gas-condensate reservoir may be black in color. In this event the dense gas phase existing above the dew point is correspondingly dark. Volumetric phase data and an analysis of a reservoir fluid exhibiting these characteristics, together with a description of the visual equilibrium cell in which these observations were made, are presented in this paper. INTRODUCTION Previously the author, like many others in the oil and gas industry perhaps, tacitly assumed that the expressions black or dark oil system, crude oil system and bubble-point system were synonymous. Crude oil reservoir fluids are bubble-point systems and yield a black or dark stock-tank oil of relatively low API gravity. Conversely, a clear or amber colored trap distillate of high API gravity is assumed indicative of a dew point system or a gas-condensate reservoir fluid. This broad classification appears satisfactory for shallow reservoirs, but as the following study demonstrates, may be misleading when applied to deep reservoirs. Theoretically, there is no reason to exclude the possibility of producing a dark, low-gravity distillate from a gas-condensate reservoir. At sufficiently high values of pressure and temperature, heavy, dark-colored hydrocarbons may exist in the vapor state of a multi-component system. If enough dark-colored components are present in the reservoir vapor phase, the resulting condensate will be dark. The reservoir fluid investigated in the present study supports this contention. Stock-tank production was black in color and measured 29" APT gravity. From outward appearances, the liquid closely resembled a medium gravity crude oil. Experimental measurements proved the reservoir fluid was in reality a gas-condensate system. Volumetric phase data for this high-pressure system and a description of the visual cell in which the study was conducted successfully are presented in this paper. THEORY Phase behavior of a reservoir fluid can be predicted accurately with reference to a pressure-temperature phase diagram. If the reservoir temperature is lower than the critical temperature of the hydrocarbon fluid in place, bubble-point behavior will be observed. If the reservoir temperature lies between the critical and cricondentherm temperature, dew point behavior and retrograde condensation will occur. For reservoir temperatures above the cri- condentherm, only a single gas phase can exist in the reservoir regardless of pressure. Providing the composition of the reservoir fluid were known, it would be possible to predict the critical temperature and estimate the phase behavior from equilibrium relationships. However, the usual practice is to obtain a sample of reservoir fluid, subject it to varying pressures at the reservoir temperature and observe the phase behavior experimentally. The latter method was used to obtain the data reported here. WELL AND TRAPPING INFORMATION A summary of pertinent data for the well from which the reservoir fluid was sampled is presented in Table 1. This well is located offshore Louisiana. Except for the pressure which substantially exceeds hydrostatic pressure, the information does not appear unusual. Prior to the sampling program, the well was produced for 22 hours at a stock tank oil rate of 139 B/D. Average trapping conditions and gauging data for the six-hour test period that followed are summarized in Table 2. Samples of the first-stage trap gas and liquid were obtained during the latter portion of the test period. Ambient temperature remained 5 to 10F below trap temperature and presented no problem for sampling. Surface wind and moderate foaming of stock-tank oil presented some difficulty in obtaining accurate stock-tank gauges. SAMPLE ANALYSIS Compositions of the gas and liquid samples are shown in Table 3. The trap gas was analyzed by isothermal chromatography which revealed only a trace of heptane in the stream. The trap liquid was initially analyzed by low-temperature fractional distillation, yielding a bottom product of heptane and heavier components. Specific gravity of this fraction was measured and the mol weight was determined by freezing point depression. The hexane and lighter overhead gas collected during distillation was

Jan 1, 1967

By R. R. Jones, R. W. Kraft

Zn-Mg2Znn eutectic alloys nzay freeze willr either rodlike or lanzellar rnorphology. Alloys with slighlly more than /he eutectic arrzount of rnagnesillrn usually contain three-cnned dendrjles of MgzZnll in a eutec-lic ttlulris. All three morphologies haue the same cryslallographic orientution relationship: (0UOl) zn - 11 (111) Mg2Znll and (2310)Zn 11(101) Mg2Znll, but u3ith different prej-erred groulth direclions. The lurnellae lo rods transifion in con/rolled ingols qf euleclic cotnposition occurs because lhe large kinelic undercooling due to MgzZnll minirrzizes /he ejj-ecl of the solid-solid inlerface energy. The eutectic morphology is influenced by the presence of lhree-nned dendrites 0-f MgzZn11 which may conlrol /he rricroslrccture by acting as nuclealion sites. In recent years there has been much interest in eutectic solidification and several theories have been proposed. One of the confusing factors is the existence of various morphologies in which the solidified phases may form. The lamellar microstructure seems to be most common in metal eutectics, and it has been claimed' that all regular eutectics should be lamellar if sufficiently pure. However, there still remain eutectic alloys which are not lamellar or which change their morphology as a function of growth conditions. The eutectic between zinc and the intermetallic phase Mg2Znll was chosen for this investigation because it has been found to solidify in more than one morphology. The diagram in anssen' locates the eutectic point at 3.0 wt pct Mg and 367°C. lliott gives 364°C as the eutectic temperature, leaving the phase compositions unaltered. Since the growth conditions determine the micro-structure of the solidified alloy, the factors controlling the transition from one morphology to another could be studied. The lamellae to rods transition is of particular interest. PROCEDURE Alloys were prepared from carefully weighed portions of 99.999 pct Zn and 99.97 pct Mg by melting in Pyrex containers under argon and casting into graphite boats. The resulting ingots were remelted under argon and solidified unidirectionally in a horizontal tube furnace at growth rates ranging from 2.0 to more than 50 cm per hr under a temperature gradient, measured over a 5-cm length, of 9" to 14°C per cm. The solid-liquid interface appeared to be planar at all growth rates although no attempt was made to confirm this by decantation or quenching. A few ingots were allowed to freeze uncontrolled. Most alloys were of the nominal eutectic composition, 3.0 wt pct Mg according to Hansen2 and lliott, but some contained as much as 3.35 wt pct Mg. Chemical analyses were not run since metallographic examination confirmed that the desired composition was achieved. Specimens were cut from the middle portion of the ingot normal to the growth axis, polished mechanically, and etched with 2 pct Nital. Suitable areas were selected for the determination of crystallographic orientation relationships by a tiontechniqueof described previously by one of the authors.4 The (2310) planes of zinc and the (8701, {944}? (1032) planes of Mg2Znll were found suitable for orientation determination; experimental error was on the order of 2 or 3 deg. RESULTS Three different morphologies were found in the unidirectionally solidified alloys: lamellar eutectic, rod-like eutectic, and a structure whose most predominant characteristic was the presence of three-vaned (cellular) dendrites of Mg2Znll. These dendrites were only found in alloys with more than the eutectic amount of magnesium. In some ingots fine hexagonal needles of Mg2Znll surrounding a core of MgZn2 were observed. They were probably due to incomplete alloying and seemed to have no effect on the eutectic morphology. In addition hexagonal spirals like those discussed by Fullman and wood5 and Hunt and acksonh ere observed in some ingots frozen without directional control. Both MgZZn,, and MgZnz were detected by X-ray diffraction in these alloys. Since the morphology could not be grown unidirectionally and no characteristic orientation relationship between the phases was found, further study was limited to the lamellar: rodlike, and three-vaned dendrite morphologies. Alloys of Eutectic Composition, No Dendrites. The mcrostructures of allovs with no three-vaned dendrites were either lamellar or rodlike depending on the growth rate. At rates below 10 cm per hr the morphology was lamellar, consisting of two sets of parallel plates intersecting at about 54 deg like the Mg-MgzSn eutectic described by raft.7 At growth rates faster than 14 cm per hr the microstructure showed rods of zinc in a matrix of MgnZnll, while intermediate rates yielded mixtures of rods and lamellae in small groups. The lamellar "grains" were often several millimeters in cross section, but contained small irregular areas which divided each grain into perfect islands 100 or 200 p in diam. Lamellae were parallel to each other throughout the grain in spite of these defects in the structure, Fig. 1. Rods, on the other hand, could only be produced in small groups arranged like fish scales and separated by irregular areas of appreciable thickness, Fig. 2. Alloys Not of Eutectic Composition, With Dendrites. In alloys with 3.1 to 3.35 wt pct ME,-. three-vaned dendrites bf MgzZnll were usually found surrounded by eutectic. At growth rates slower than about 10 cm per hr the dendrites were separated from each other by small areas of both lamellar and rod eutectic, Fig. 3.

Jan 1, 1969

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study' that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,' flow in packed columns,' fracture flow capacity' and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.