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By L. J. Cabri

The calculation of metallurgical balances for precious metals is very dependent on a precise mineralogical understanding of the distribution of each element. Determination whether the precious metals occur as dilute solid solutions in major minerals is not always easy because of the relatively high levels of detection (9200-500 ppm) of the precious metals by the most common methods of in-situ analysis (e.g. electron microprobe). Particle Induced X-ray Emission (PIXE) analysis of sulfides from Izok Lake, N.W.T., Canada and from the Hilton mine, Mount Isa, Australia with a proton beam (proton microprobe) confirms solid solution of Ag in chalcopyrite from both deposits. In addition, chalcopyrite and sphalerite from Izok Lake both contain indium.

Jan 1, 1984

By Sherwin F. Kelly

MANY baffling problems of crustal geology-of warping and folding, elevation, subsidence, and great dislocations of the earth's surface-may now be on the verge of yielding to the science of geophysics. Electric, magnetic, gravitational, geothermal, and seismic methods are being turned to the gathering of geological evidence buried by deep layers of rock, or lying beneath the waters of the oceans. In this hope, B. L. Miller expresses the opinion that these geophysical studies will sup- ply useful data bearing-on some of the more theoretical problems of North American geology. Among these for example, is the explanation of how Appalachia disappeared. This ancient land mass is supposed to have foundered beneath the Atlantic Ocean after the close of the Paleozoic era and the question arises, was it warped or faulted downward? The geophysical data, though meagre, indicate that the surface of the dense, basal rocks, the probable remnant of ancient Appalachia now underlying the Continental Shelf, slopes downwards to a depth of some two miles below sea level at a distance of 140 mi. from shore: thus suggesting that the subsidence was the result of warping downward rather than abrupt faulting.

Jan 1, 1938

By Arnold Hoffman

A RESPONSIBLE steel executive recently declared that scrap shortages, despite fantastic prices reaching up to $50 per ton, are responsible for the loss of 140,000 tons of steel a month and that in March 1947 alone 25 more steel furnaces could have been operating were it not for scrap scarcities. His answer to this serious situation was to ask for a speedier flow of scrap and also abolition of Government control over pig iron distribution. It would be more logical, perhaps, if an answer to this growing problem of scrap deficiency were sought within the steel industry itself. As long ago as 1933, L. B. Lindemuth, a consulting steel metallurgist, warned the steel industry that a shortage of scrap was inevitable and that beyond 1938, adequate supplies for open-hearth furnaces could not be expected. The outbreak of war, with consequent phenomenal demands on the industry, accelerated production of steel and further worsened the scrap situation. Today we are suffering from a condition which could have been prevented had the industry been more far-seeing and provided for an inevitable contingency. However, better late than never, and measures can now be taken to alleviate permanently scrap shortages in the future. This can be done by greater utilization of heavy sinter which experience proved is an excellent substitute for scrao and lump ore.

Jan 1, 1947

By Thomas V. Falkie

These are exciting times for the coal mining community. Although the industry is in the middle of a healthy boom, there are strong forces tending to counteract or at least temper the rate of growth. There are many pushing and pulling factors of interest to mining people, and a few salient ones will be mentioned here. Primarily because of a tremendous demand for energy, a demand that can't be met by other fuels, the coal industry is in boomsville. Another contributing factor to this situation is the increased overseas demand for metallurgical coal. These demands are being counteracted by a lack of people, the lead-time required to develop new capacity and wildcat strikes, among other things.

Jan 1, 1971

By W. S. Sanner

Experiments were conducted to determine the quantity and purity of ultraclean anthracite that could be prepared in the laboratory, using conventional separating techniques. A low, a medium, and a high-volatile anthracite were studied. Specific gravity separation followed by grinding, screening, and refloating at lighter specific gravities yielded small quantities of material purified to 1.0% ash, as follows: from low-volatile anthracite, 0.7%; from medium-volatile coal, 1.0%; and from high-volatile coal, 2.3%. The reduction in ash had no appreciable effect on the volatile matter or sulfur content of the coal. The limited quantities of material containing 1.0% or less ash obtainable indicate that if ultraclean coal is desired, a practical approach should include the processing units as an integral part of a convc.ntiona1 dense-media washing plant. Anthracite preparation practices during much of the industry's history were geared to maximum recovery of the larger sizes, pea through egg, which were used in hand-fired, domestic furnaces. Those sizes were cleaned to meet trade requirements, and the smaller sizes were usually higher in ash content. The impression, thus, was that ash content of anthracite always increased as the sizes got smaller. It was presumed that it was impossible to wash the finer sizes to extremely low ash contents. Following World War 11, the classical domestic market began to decline and the finer sizes assumed an increasingly large share of the market. For example, in 1949l 61% of the production was still pea and larger. Fig. l2 shows that -by 1955 these sizes accounted for only 50%, and in 1965, they were only 39% of the total anthracite produced. With the reduction in the market, increased quality was demanded, especially in export markets, and an increasing number of dense-media magnetite washers were installed in new and existing cleaning plants. In 1965, the coarse coal prepared at 59 breakers in the anthracite fields was sampled by the U.S. Bureau of Mines (USBM); approximately 50% of these plants were equipped with dense-media magnetite washers.3 Since 1950, more attention has been focused on the use of finer sizes for numerous industrial uses, including iron-ore sintering, pelletizing, foundry coke-making, cement manufacture, production of calcium carbide, and of carbon electrodes, etc. Most industrial uses require relatively clean anthracite, such as 10 to 11% ash for sintering and foundry coke, 7% for aluminum melting-pot cathode carbon, and 5% for carbide production. Hence, cleaning methods have been improved to the extent that dense-media washers, hydraulic cyclones, and flotation cells have been introduced as fine-coal-cleaning devices. It is now possible to wash the buckwheat, rice, and barley sizes (9116 X 3132-in.) to ash contents as low as 8 to 10% in dense-media devices, but washing the -3132-in. sizes to those limits presents more difficult problems, due mainly to the fineness of the material. This USBM investigation was conducted to determine the amount and purity of ultraclean anthracite that could be prepared in the laboratory, using conventional separating techniques. The goal was to reduce the ash content to a level acceptable for industrial carbon uses, including electrode manufacture, which generally requires an ash content of 1% or less. While low-ash content is of primary importance in selecting industrial carbons, the amounts of other constituents are also important, including iron, silicon, titanium, nickel, vanadium, and sulfur. They were not considered in this work, since their occurrence in deashed anthracite has been studied elsewhere.4 The results of the present investigation were used to design a flowsheet, suggesting a method for producing ultraclean anthracite as part of conventional preparation practice, using dense-media vessels, crushers, pulverizers,

Jan 1, 1970

By P. E. Baker

An experimental study of heat flow in steam flooding was carried out with steam displacing water in a plane-radial fluid-flow model. Temperature distributions in the model reservoir, overburden, and substratum were measured at frequent intervals during flooding by means of a fixed array of thermocouples. Heat losses to overburden and substratum and the division of heat between the steam and hot-water zones in the reservoir were calculated from the temperature data by performing numerical integrations over the appropriate volumes. Temperature profiles and heat distribution results are presented. Some results were (1) the fraction of injected heat that is lost to overburden and substratum, when expressed as a function of time, did not depend on injection rate; (2) a significant portion of the injected heat was contained in the hot-water zone ahead of and underlying the steam front in the reservoir. The division of heat between the steam and hot-water zones did depend on injection rate; and (3) considerable gravity override was observed. The experimental results are compared with those of several published theoretical studies of heat transfer in hot-fluid injection; approximate agreement on heat losses is found with some of the most idealized theories. A valid comparison cannot be made in regard to steam us hot-water zone; basic interpretation of the hot-water zone, in terms of a vertical steam front, is clouded by gravity override in the experiments. INTRODUCTION The experimental study reported here primarily concerns two problems of heat transfer in steam flooding that have economic and engineering importance. These are (1) the fraction of injected heat lost to the overburden and substratum, and (2) the division of the remaining heat between a zone containing steam and a zone of hot water at lower-than-boiling temperature. The volume of the steamed region, which has a direct effect on oil recovery, can be calculated readily from these results. Several valuable theoretical studies have been published on this problem, but no experimental tests of the theories have previously appeared. Tests were needed because the effects of the necessary simplifications in the theories could not be determined otherwise. The basic, untested theoretical problem is the effect of "decoupling" heat and mass transfer, and the resulting inability to include the effects of heat transfer and condensation on fluid flow. The theoretical problem solved so far has been a heat transfer problem in which fluid is present as a heat carrier and flows in a stipulated manner, either linear or plane-radial. The simplifications that have sometimes been made in regard to thermal conductivity by, for example, Marx and Langenheim,l Lauwerier2 and Thomas3 apparently do not have an important effect on heat loss calculations, although the results of the different methods disagree to a certain extent, as shown by Spillette4 and by Ramey.5 A recent paper by the author6 compared the results of experiments in hot-water flooding with several theoretical results and showed a rather poor agreement. It will be seen that the experimental heat loss results for steam flooding, however, show acceptable agreement. These comparisons are discussed in a later section. EXPERIMENTAL APPARATUS AND PROCEDURE The system studied was one in which a sand pack, initially water saturated and at a uniform temperature, was flooded with steam at a constant rate and temperature. The temperature distribution in the "reservoir" and adjacent "strata" was measured with an array of thermocouples, and heat losses were determined from these measurements. The sand pack contained no oil because the only concern of the experiments was heat flow, and it was important to have the flow pattern as simple

Jan 1, 1970

By A. Lubinski, J. E. Hansford

Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through Such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs. INTRODUCTION Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to unde-sired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated.' However, in wells where the maximum permissible dogleg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll.' The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in doglegs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures. FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffce to read only through the section Abrupt Dog-Legs. 1. Concept of the two extreme kinds of idealized doglegs: gradual and long dog-legs and abrupt dog-legs,' 2. Concept of why the bending moment in drill pipe un- der tension is the largest in the vicinity of the tool joint,' 3. Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension,' and 4. Definition of the rate of change of over-all hole angle (dog-leg severity)." Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.

Jan 1, 1967

By J. Groyecki, M. Markuszewicz, J. Lassota, A. Zawada

The ratio of stable to unstable inclusions was found to ploy an essential role in the process of sccorldar-y recrystatlizalion in Si-Fe. The analysis of the free energy of inclusions in the range of heat-treatment of individual inclusions to be predicted. The effects MnS. ns inslable inclusions. were investigated. TO secure a high induction, the secondary recryslulliztt-lion associated wilh the texture is necessary. To obtain a low core loss an additional refiuing in the solid state is required. It has been found that sulfur can be more easily removed in racunm than in hydrogen and thai this process was hindered by the prescrzce of INCLUSIONS play an essential role in the development of cube-on-edge texture in Si-Fe. Their function consists in restraining the growth of primary grains up to about 900°C and in passing subsequently into solution at higher temperatures. This process is accompanied by the selective growth of secondary grains with (110)[001] orientation. The general effect of inclusions depends on such factors as the type of impurities, their amount. dispersion and stability, the conditions of diffusion in the space of lattice of metal, and the reactions at the metal/gas interface. In recent years, some of these factors were the subject of a special investigation. A positive influence of Mns, siN,' and vN3 has been established. The quantity of impurities4 and their dispersion5 have been found to be of major importance. Attention was called to the vital importance of diffusion and the conditions under which the impurities are removed from metal., It has also been demonstrated that in Fe-Si alloys by the techniques of powder metallurgy a special opportunity exists to obtain the (110)[001] type texture. 6 The aim of this work was to conduct qualitative investigations on the influence of inclusion stability on the development of cube-on-edge texture in a metal containing approximately 3 pct Si. Experiments were carried out on cast alloys and on those manufactured by powder-metallurgy techniques. The results obtained from these experiments were utilized to explain the phenomena involved and to analyze the relationships between stable and unstable inclusions and the magnetic properties of alloys. EXPERIMENTS AND RESULTS The raw materials used in these experiments were the powder of carbonyl iron with the analysis (in pct) 0.044 C, 0.01 Mn, 0.005 Si, 0.009 P, 0.002 S, traces of Cu, 0.06 Ni, 0.0015 Al, 0.03 Cr, 0.02 Mo, 0.01 Ti, 0.002 Co, traces of Pb, and the powder of silicon containing 94.14 Si, 0.003 S, 0.048 C. The powders were ground and mechanically mixed in 100-g batches. and then pressed at 9 tons per sq cm into 74 by 24 by 8 mm blocks. Sintering was carried out at 1100°C for 12 hr in vacuum (2 x lo-' Tr) or in hydrogen. In this instance the material was heated slowly and subjected to prolonged soaking at 350°, 650°, and 750 2C, respectively, to secure reduction of ferro-oxides. This was checked by making measurements of the dew point, which was found to change from -15" to -35°C after reduction. The compacts after sintering were hot-rolled to 2.4 mm, annealed at 800 C, and finally cold-reduced to 0.35 mm with intermediate annealing at 800°C at a gage of about 0.8 mm. Impurities were added in the powdered form and mixed with iron and silicon powders. Sulfur in the elemental state, electrolytic manganese, and pure aluminum oxide were employed. Besides, to obtain a material with low contents of impurities, especially

Jan 1, 1967

By C. D. Stahl, R. Sandrea

This investigation was made to evaluate the comparative effects of the viscosity and the phase behavior of the buffer fluid in the composite solvent displacement of Bradford crude from waterflooded sandstone cores. Buffer slugs of propane, naphtha and other refined hydrocarbons exbihiting increasingly favorable viscosity ratios and decreasing solubility relationships, respectively, with Bradford crude, were used in long Berea sandstone cores. The secondary slug was isopropyl alcohol. The results indicate that higher oil recoveries are obtained for increasingly favorable phase relationships even when these are accompanied by unfavorable viscosity ratios within the range studied. Moreover, when propane is used as a buffer slug with an adverse viscosity ratio of 36, it gives higher oil recoveries than at a similar size slug of an any1 alcohol having a viscosity ratio of 1.09. The investigation was extended to the study of the effect of flooding rate on oil recovery. Residual Bradford crude was displaced from a 6-ft Berea sandstone core at rates varying from 0.3 to 30 ft/ day. The results show that as flooding rates were increased above or decreased below a minimum range of 1 to 2 ft /day, displacement efficiency increased considerably. INTRODUCTION In recent years, the alcohol slug process as a means of tertiary recovery has been the subject of many investigations. Gatlin and Slobod showed the advantages of the combination solvent slugs over the previous single-slug process.1 The combination slugs require less total slug material to obtain similar oil recoveries. The basic combination process involves injecting a primary or buffer solvent which is preferentially oleophilic, followed in turn by a water-driven slug of isopropyl alcohol. This procedure ensures that the buffer slug, which is miscible only with the reservoir oil, displaces and replaces the oil and is in turn displaced, together with the water, by the isopropyl alcohol slug miscible with both fluids. Likewise, for those reservoir oils that show some degree of phase incompatibility with isopropyl alcohol, as does Bradford crude, a proper buffer solvent can artificially make the alcohol process technically feasible. From an economic standpoint, propane or LPG would be the most appropriate primary solvent to be used in the field; however, Taber, et a12 have indicated that the alcohol process becomes highly inefficient in the displacement of light hydrocarbons because of the entrapment of these hydrocarbons during the stabilized bank formation. Moreover, since materials such as propane have such low viscosities, adverse viscosity ratios with most reservoir oils would be penerated, thereby possibly further reducing the efficiency of the buffer solvent. This paper presents the results of an experimental study of the comparative effects of viscosity ratio and phase relationships on the displacement efficiency of Bradford crude by means of dual solvents. The work was extended to include the effect of flooding rate on oil recovery. Rates within the range of field and laboratory values were used. EXPERIMENTAL PROCEDURE APPARATUS The porous media used in this study consisted of two 10-ft and one 6-ft Berea sandstone cores, 3-in. in diameter. These were cast in galvanized steel pipe of 31/2-in. ID and the annulus was filled with Armstrong cement. The 10-ft cores were assembled by connecting two 5-ft units, which were joined together by 8-in. steel flanges fitted to the pipe. Intimate contact between the two sections was obtained by inserting a thin disk of the same sandstone between the core faces. The outlet and inlet ends of the cores were covered with threaded pipe caps. The injected fluid was gravity fed to two variable-rate positive-displacement pumps. The fluids were filtered before entering the core and the effluent was collected in an automatic fraction collector and

Jan 1, 1966

By S. E. Bronisz, R. E. Tate

s-plutonium samples possessing a strong growth texture have been produced by allowing them to transform under pressure from p to a. A fiber texture with [010] parallel to the pressure axis results. The textured samples are expected to be useful in determining the effects of crystallographic orientation on the physical properties of a plutonium, and initial results of measurements of resistivity and mechanical properties are described. THE crystal structure of a plutonium1 is mono-clinic, P21/m, and many of the metal's properties should reflect the crystallographic anisotropy. Unfortunately, it has not yet been possible to grow useful sizes of single crystals of a plutonium. Therefore, few of plutonium's orientation-sensitive properties have been determined as a function of crystallographic orientation. One way to gain information about at least some of the orientation-dependent properties is to study a highly textured sample. Such samples have been produced by cold rolling a plutonium,2 but they are necessarily very small in one dimension. We have now successfully used two other techniques to produce highly textured samples, not limited to small thicknesses. METHODS OF PRODUCING PREFERRED ORIENTATION The texture is produced by causing the plutonium to transform from ß to a while under pressure. It was observed by Gardner3 that applying a compres-sive load during the transformation resulted in the formation of columnar grains of a plutonium, and Cramer4 observed a similar structure in some diffusion couples rolled in the P phase. Neither of these workers, however, investigated the subject beyond these observations. The more flexible of the two methods developed is that of compressive loading. The technique is to enclose a sample of plutonium in a die assembly before applying the load. It is possible, of course, to dispense with the die and simply press the sample between two platens. In this case, however, the unrestrained sample deforms during the pressing, making it difficult to maintain the load and to control the final sample thickness. This compressive loading technique has been used on specimens ranging from 1/4 to 3 in. diameter, with height-to-diameter ratios ranging from 5 : l to 1:6. The procedure begins with loading the sample, a right cylinder of a plutonium, into the pressing die. Plastic deformation of the sample while it is being pressed is minimized by machining the sample so that its diameter is nearly the same as that of the die barrel. Then the loaded die assembly is placed in a vacuum pressing can that fits on a hydraulic press. After a vacuum is achieved the die assembly is heated to 180°C and equilibrated. The load is then applied and the specimen and die are allowed to cool to about 40° to 50°C before the pressure is removed. The resulting sample is composed of rod-shaped a -plutonium grains, the rod axes being parallel to the cylinder axis and the pressing direction. Photomicrographs of the oriented structure are shown in Fig. 1. Although most of the specimen is composed of grains whose rod axes are parallel to the cylinder axis, a thin, peripheral layer consists of rod-shaped grains whose rod axes are perpendicular to the cylinder axis. Presumably, the highly plastic nature of p plutonium leads to approximately hydrostatic conditions during the initial stages of the P — a transformation under pressure. At this time, the grains in the peripheral layer would have grown parallel to the local force direction. During the latter stages of the transformation, the accompanying volume contraction would have eliminated the radial forces, leaving only the axial force and resulting in the growth of the observed structure. The growth texture did not form without the application of pressure. Attempts were made to produce the texture by repeating the standard temperature cycle without

Jan 1, 1965

By B. M. Larsen, T. E. Brower, J. W. Bain

A mass of circumstantial evidence is presented to indicate that the main source of alloy losses in open-hearth tapping is oxidation by air, with the steel apparently reacting with an amount of oxygen equivalent to about 30 times its own volume of air. The effect is erratic from heat to heat, depending largely on turbulence and distance of free fall of the stream of liquid metal. THIS paper reports another phase in a general study of oxidation in the open-hearth, various aspects of which have already been discussed in previous papers.1,2,3 It is based on experiments conducted on commercial, basic open-hearth furnaces at various times when opportunity offered, beginning about 1938, in an attempt to determine the mechanism and measure the amount of air oxidation during the flow of the tapping stream through the air into a ladle. This effect is closely connected, not only with alloy losses and control of chemical analysis, but possibly with various questions regarding inclusion content and steel quality and with a true picture of the deoxidation of steel in general. Thus it is believed that discussion of a large part of the results to date may be of assistance to others who are studying problems related to deoxidation or to steel cleanliness and quality. The literature reveals that strangely little attention has been devoted specifically to the effect of pouring steel through open air. Bardenheuer and Henke4 in 1939, in a paper devoted largely to overall losses of manganese in the basic open-hearth, reported that for a number of heats tapped into a tilted ladle held just beneath the runner so that the maximum distance of drop of the stream through the air was held to less than about 30 in., there was in most cases almost no loss of manganese from furnace to ladle. Hultgren,5 in 1945, showed that in high-carbon basic electric steel deoxidized in the furnace and containing no large inclusions as it left the furnace, large silicate inclusions, often rich in manganese oxide, were present in samples dipped from the pool in the ladle; also that the rise in content of large inclusions (above 0.01 mm dim) was greater when the metal stream was made to spray or flow in a turbulent manner. Our interest in this phase of oxidation in the open-hearth was first aroused by a study of alloy efficiencies on ladle additions. The frequency curves of manganese efficiency (net recovery of metal added in ladle) given in fig. 1 are of interest in this connection. Lowest, and also most variable (47 to 95 pct), recovery was in low-carbon heats having no coal additions to the ladle, progressing upward to a maximum average and least variable (82 to 97 pct) recovery in high-carbon heats killed with aluminum and silicon. Both coal additions and higher carbon contents in the tap stream, as well as additions of silicon and aluminum, help to lower the amount of manganese loss. But the most interesting point is the amount of manganese oxidized in many heats tapped at 0.50 to 1.06 pct carbon. It has been shown in a previous paper3 that the amount of oxygen in the tap stream in such heats is very small, usually below 0.01 pct, too small to oxidize any appreciable amount of manganese. Also, the fact that manganese should be oxidized at all in a metal solution containing such more stable oxide-forming elements as aluminum and silicon is an indication of some rather intense oxidizing effect such as could be caused by reaction with the air during ladle filling. Oxygen Balances from Tap Stream to Teeming Stream: Data in the form of alloy efficiencies, such as those shown in fig. 1, are not a proper measure of such a general oxidation effect. Having available

Jan 1, 1951

By C. Wachmann

The theory presented ill this paper makes possible examination of the phenomenological aspect of secondary oil recovery by alcohol flooding. Limitutions of the theory are contingent on three primary assumptions: (1) chemical equilibrium, (2) no fingering, and (5) no dispersion. The second assumption implies one-dimensional flow. In a geometric sense the theory extends the Buckley-Leverett construction to systems of two slightly miscible fluids and to systems of three components. This is made possible by considering single-phase fluids to be made up two phases, namely of an excess of one phase and a negative amount of the other phase. The procedure is discussed in the paper. The theory also permits direct determination of the relationship between the aqueous phase saturation and the concentration of water in the aqueous phase in a zone of variable composition. The velocity of planes of constant water concentration and of constant saturation can be computted likewise and the existence of saturation discontinuities inferred. Consequently the behavior of such a Zone, which may exist at some time between a displaced and a displacing fluid, May be determined. mathematical details are given in Appendices. Problems of experimental verification are pointed out on the basis of a supporting experiment. Implications of the theory and effects of violations of primary assumptions are discussed briefly. The major conclusion is that, if the primary assumptions are met, with pure alcohol and alcohol-rich .slugs piston-like displacement of oil and water is possible. INTRODUCTION The recovery of oil from porous media by alcohol displacement has been studied for several years. Extensive experimental investigations into alcohol flooding have been carried out in the laboratory although little has been done in the field. A large amount of practical information is available, the extent being indicated by the first three papers cited 1-3 and their respecrive bibliographies. This has permitted the Formulation of inferential theories. A more analytical approach in which theories are developed primarily by reasoning from known physical principles and relationships has, however, lagged behind. In fact, an analytically derived theory of alcohol displacement has not been available. The theory presented in this paper on oil and water displacement by alcohol from a porous medium is a result of the analytical approach. The theory is idealized, as certain assumptions had to be made to make the mathematics tractable and reduce complexity of argument. In particular, major assuptions concerning conditions of equilibrium, interfacial stability, longitudinal mixing, etc., led to the exclusion of fingering, for example, from all considerations. In many laboratory experiments reported in the literature fingering could not be avoided. There is, therefore, disagreement between theories based on experimental evidence available and the analytically derived theory presented here. This theory presented is based on known physical data and makes use of the Buckley-Leverett construction and its suggested extension. The mathematical derivation of the theory is given in Appendices. Three examples relevant to alcohol displacement are discussed to explain the use of this theory: (1) system of two immiscible fluids (the Buckley-Leverett case); (2) system of two slightly miscible fluids involving an extension of the Buckley-Leverett construction; and (3) system of three components, including injection of pure alcohol or alcohol-rich fluid as a special case, which involves a more general extension of the Buckley-Leverett construction. In these discussions strict assumptions were made to impose equilibrium conditions and exclude mixing and fingering. Effects of relaxing these assumptions and consequent extensions of the theory are indicated. The complexity of the alcohol displacement process makes experimental verification of the theory essential. Some relevant evidence is offered in this paper.

Jan 1, 1965

By L. H. Robinson

A proposed method of drilling utilizes sequential detonation of two types of explosive charges delivered to the hole by a conventional drilling fluid through pipe. A shaped charge first produces a long thin hole. A second charge, called a gauging charge, is pumped into the thin hole, explodes, and enlarges it to full gauge. In one suggested configuration, the explosives are contained in cylindrical capsules 4- to 5-ft long. A drilling head is positioned 2- to 3-ft off bottom. When a capsule is pumped to the bottom of the hole and stops, pressure inside the drill pipe increases and differential pressure detonates the explosive. Primacord along the length of the capsule disintegrates the capsule. The debris circulates out of the hole with the drilling fluid. The gauging-charge action was examined using 2-ft cubes of Berea sandstone. The sandstone (18 per cent porosity) was vacuum-saturated with water and surrounded by concrete. To prevent reflected tensile pulses, the acoustical impedance of the concrete matched that of the sandstone. A 750-psig pressure was applied to a drilling fluid within a shaped-charge-formed hole before detonating the gauging charge. In these tests, 190 gm of rock were removed for each gram of explosive detonated. A similar series of experiments on low-porosity (0.40 per cent) metamorphic limestone provided a more rigorous test. Extensive fracturing from the gauging-charge action prevented an estimate of the volume of the expanded hole. The diameter of the hole was irregular, ranging from about 2 to 4 in, or about fivefold larger than the hole created by the shaped charge. INTRODUCTION In the past, explosives have found a varied but somewhat limited use in the oil field. An early well stimulation technique, still in use today, in vo lves shooting ni troglycerin to en large the borehole and to increase matrix permeability near the wellbore. Bullets and jets are now the conventional method of perforating casing and tubing. Detonations are frequently used to "back off" or "shoot off" stuck pipe and, of course, seismo-graphic work has long depended on explosive-generated pulses to find attractive earth structures. Efforts to use explosives in drilling operations have received limited examinations1-3 which, in one respect, is surprising because explosives offer one way to transmit large amounts of energy directly to the bottom of the hole. Recently, Ostrovskii l described a Russian method of drilling with explosives that utilizes small capsules containing explosives which are pumped into the mud stream to the bottom of a borehole. As the capsules leave the end of the drill pipe, a detonation mechanism is armed. Impact detonates the explosive. In another configuration, two liquids (an oxidizing agent and fuel) in the capsule are separated by a frangible membrane. Separately, the liquids are nonexplosive. Near the bottom of the drill pipe, the capsule passes through a narrow constriction which ruptures the membrane. The mixing of the liquids produces an explosive. Impact is again used to detonate the explosive. About the time Ostrovskii was developing his method, Humble Oil & Refining Co. was independently doing research on another explosive drilling concept based on the sequential detonation of two types -of explosive charges. The proposed technique consisted of alternately pumping a shaped charge and then a "gauging charge" down a well. The shaped charge should drill a long, tapered hole, and the gauging charge should expand it to full gauge. This paper presents the visualized drilling concept and gives results of laboratory work which showed that sequential firing of charges can form hole at an attractive charge-to-rock removal ratio. An important finding was that increased environmental pressure, which is to be expected in wells, increases rock removal efficiency of the gauging charge.

Jan 1, 1966

By B. H. Caudle, R. L. Slobod, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.' These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.'! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By R. L. Slobod, B. H. Caudle, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.' These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.'! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By Nigel B. Pearson

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

Jan 1, 1981

By P. Chiotti, J. T. Mason

Thermal, X-ray, metallographic, and resistivity data were obtained to establish the phase diagram for the Yb-Zn system. Six intermetallic compounds and five eutectics have been identified. The compounds position at 695°C. No evidence for the compound YbZn,, was observed. Whether this compound is stabilized or inhibited by small amounts of impurities is uncertain. SEVERAL aspects of the Yb-Zn system have been reported in the literature. Much of this work deals with the crystallographic identification of some of the compounds. The YbZn compound has been reported by Iandelli and palenzonal and the YbZn, structure and thermal data for the composition range between YbZn and Yb3Znll have been reported by Michel et al. A compound of uncertain stoichiometry in the range 60 to 68 wt pct Zn with a cubic structure has been reported by Kuz'ma et aL4 The YbzZn17, YbZn,,, and YbZn13 compounds have been reported by both Kuz'ma et a1 and Iandelli and Palenzona.' YbnZn17 has also been identified by Laube. This investigation was undertaken to establish the phase diagram of this system. Ytterbium in many respects behaves as an alkaline earth rather than a rare earth metal6 and it is of interest to note the resemblance between the Yb-Zn system, the Ca-Zn,' and typical rare earth-zinc systems.g'10 MATERIALS AND EXPERIMENTAL PROCEDURES The materials used in this investigation were Ames Laboratory ytterbium and Bunker-Hill slab zinc, 99.99 pct pure. Analyses of the ytterbium showed 38 ppm Ta, 82 ppm 0, and 15 ppm N with Ca, Cu, C, Mg, Al, Si, Cr, Fe, Ni, Sc, Y, Er, Tm, and Lu all less than 50 ppm. The ytterbium was dehydrogenated by heating in tantalum under vacuum for 8 hr at 900°C. The metal was kept under argon except when being cut with shears and when being weighed. Tantalum was found to be a suitable container for alloys in the composition range between ytterbium and Yb2Zn17. With higher zinc concentrations the tantalum was penetrated by the alloy and failed after several days at temperatures of 600" to 700°C. Approximately 20 g of zinc and ytterbium metal were sealed under argon in *-in.-diam tantalum cruci- bles equipped with thermocouple wells. The crucibles were in turn sealed in stainless-steel jackets. The alloys were equilibrated in an oscillating furnace and given various heat treatments in a soaking furnace. The steel jackets were removed and differential thermal analysis data were obtained under an atmosphere of argon. The thermal analysis apparatus was calibrated against the melting points of pure zinc, aluminum, silver, and copper and found to give thermal arrests within 1°C of the accepted melting temperatures for these elements. The thermal analysis apparatus has been described in an earlier paper.g Alloys were further heat-treated as necessary and subjected to metallographic examination and X-ray diffraction analysis. Most alloys were etched with Nital (0.5 to 10 pct nitric acid in alcohol). EXPERIMENTAL RESULTS The results of the thermal analysis are summarized by the points on the phase diagram, Fig. 1. Six compounds and five eutectics were observed. The eutectic temperature and compositions in weight percent zinc are 491°C and 12 pct, 645°C and 32 pct, 687°C and 54 pct, 742°C and 67 pct, and 750°C and 77 pct. The compounds YbZn, YbZn2, Yb2Zng, Yb2Zn17, and YbZnll melt congruently at 650°, 751°, 75Z°, 754", and 755"C, respectively. The compound Yb3Znll undergoes a peritectic decomposition at 695°C. The transformation and melting temperatures for the ytterbium were observed to be 797" and 817°C. re-

Jan 1, 1969

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

Jan 1, 1880

By G. R. Countryman, G. H. Thomas, I. Fatt

Procedures are described for scaling up turbulent friction pressure drops of inelastic fluids and laminar friction pressure drops of inelastic/elastic fluids in circular ducts. The laminar scale-up calculation method does not require the use of arbitrarily defined flow models, and can be performed directly from laminar capillary viscometry data, or by means of a numerical solution of the integral equation for Poiseuille flow, inputing true shear rate-shearing stress data from other simple shearing experiments. e.g. Couette and plane Poiseuille flows. The turbulent scale up procedure, based on the Dodge-Metzner correlation for inelastic fluids, requires evaluating the characteristic rheological parameters at the existing wall stress under laminar flow conditions. Since the wall stress is the quantity sought in a pipe flow scale-up problem, a trial-and-err or solution is indicated, and therefore a calculation method has been developed and programmed for a medium-size magnetic-drum-memory digital computer. Laminar flow data from other somces may also be adapted to this turbulent scale-upmetbod for inelastic fluids. Comparisons between predicted and experimentally observed friction losses for generalized Reynolds numbers ranging from 3 — 32.000 indicate an error band width of less than 10 per cent in circular tubes ranging in size from 0.5 to 1.89 in. in diameter. INTRODUCTION Considerable effort has been devoted to the problem of establishing an accurate procedure for predicting the laminar and turbulent flow behavior of non-Newtonian materials in pipes from data obtained with small scale laboratory or pilot plant equipment, as evidenced by the variety of reviews on the subject.1-3 Although there does not appear to be a universally accepted scale-up method for laminar flow, the various methods currently employed can be divided into two principal categories depending upon whether a functional relationship between shear rate and shearing stress is assumed, or whether a generalized correlation is adopted. The methods of Hedstrom4 and of Weltmann are typical of the first category, while the generalized correlation of Metzner and Reed6 illustrates the second category. Under appropriate conditions either approach yields a reasonably satisfactory description of laminar flow behavior. In contrast, the prediction of non-Newtonian transitional and turbulent friction losses is much more complex. For example, certain types of materials have been observed to sustain laminar flow at much higher flow rates than Newtonian liquids. When turbulence does develop, the level of agitation is damped to such an extent that the friction factor is lower than that of the original low viscosity Newtonian medium. Extremely broad transition regions and "diameter effects" have also been noted in the turbulent flow of certain chemically complex materials.' Aside from the latter complications, which are attributed in part to viscoelasticity, the existence of a variety of scale-up procedures for predicting transitional and turbulent friction losses is due principally to the chioce of viscosity parameter used in the definition of the Reynolds number. In contrast, Dodge and Metzner have demonstrated that the friction factorReynolds number relationship for inelastic fluids can be satisfactorily generalized provided the fluid property parameters are evaluated at the existing wall shearing stress.* However, the quantity usually sought in a pipe flow scale-up problem is the wall stress, and hence a trial-and-error procedure is required when dealing with non-power law materials. In this report we discuss two calculation methods: (1) for determining the wall stress, and hence the friction pressure drop, for inelastic fluids under conditions of turbulent flow by means of an iterative procedure, and (2) for predicting laminar friction pressure drops without recourse to arbitrarily defined flow models.