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By K. H. Coats

This paper describes an approximate technique for handling the problem of percolation of evolved gas upwards through the oil column in computer simulation of natural depletion. This technique has been incorporated into a general model for simulating three-phase flow in one, two or three dimensions. The mathematical model for perfonning these calculations is described in detail in a separate article. 1 While vertical gas percolation occurs during natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle reel or bioherm. The reel may have an areal extent less than one section with a thickness of up to 800 It. The upward percolation of evolved gas often limits the time step in calculations as little as one day. Using this small time step, computer expense for a single 30- to 40-year simulation on even a one-dimensional basis has exceeded 92,000. The method described here for handling the percolation allows time steps of 60 days or more (depending on reservoir size and production rate), resulting in a considerable reduction in computing expense. The method also allows calculations in which secondary gas caps build up in tight zones of the oil column below the main gas cap. The validity of the method is indicated in connection with an example pinnacle reef field. Calculated results using a 2-day time step (where the method in question is not needed and not invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results from one- and two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was also performed and the required computing time is given. INTRODUCTION A general analysis for simulating three-dimensional, three-phase flow in reservoirs has been developed. 1 In applying this model to reservoirs undergoing natural depletion, a time-step restriction was encountered due to the flow of evolved gas upwards through the oil column and toward the gas cap. A remedy for this problem has been incorporated in the analysis and is described here. The time-step restriction is encountered only in calculations which include flow in the vertical or near vertical direction. The restriction occurs to some extent in reservoirs of any geometrical configuration, but it is especially pronounced in the pinnacle reef or bioherm where the ratio of thickness to areal extent is unusually large. This paper describes the problem, a method of handling it, incorporation of the method in the three-dimensional, three-phase model, and, finally, a test of the method's validity in an application to an example pinnacle reef reservoir. THE PROBLEM During the early stages of reservoir depletion, pressure falls below bubble point in progressively lower regions of the oil column. Continuing production results in evolution of dissoived gas throughout the oil column. This gas then percolates upwards toward the top of the reservoir. If the gas encounters a sufficiently low permeability zone in its travel upward, then it can accumulate and form a secondary gas cap. If no zones are encountered which are tight enough to hold gas against the gravity forces, then the gas travels on until it reaches the top of the sand or the main gas cap. Numerical simulation of multiphase flow in reservoirs is generally performed with time steps such that the flow of a fluid into or out of a block in one time step is a fraction (considerably less than one) of the total amount of that fluid present in the block. Use of a time step where the time step's

Jan 1, 1969

By E. T. Dumble

The history of the several petroleum deposits of Texas and Mexico, or of the sediments in which they now occur, if the deposits are not indigenous to such sediments, is known in a general way only, but it nevertheless casts strong light on the conditions surrounding them and is of great importance in the search for and exploitation of them. The petroleum deposits of Texas are separable into two main divisions: 1. The deposits of northwestern Texas, which are directly connected with the Oklahoma fields to the north, and have no representatives at all in the Mexican area. 2. The deposits of the coastal area, which extend into Louisiana on the east and connect with those of the Mexican coast to the south. Early in the Pennsylvanian period a series of bituminous shales and limestones were laid down over a broad area in Texas, Arkansas, and Oklahoma. These are known as the Bend series in Texas, the Caney shales in Oklahoma, and the Fayetteville beds in Arltansas. Following their deposition an uplift occurred, forming the Lampasas geanticlinal, which runs northeastward from the old Paleozoic land area of the Llano region toward Red River. The Bend series is petroliferous in places and has furnished a few producing wells on each side of the Lampasas uplift. This uplift forms the barrier and dividing line between the two divisions of the Texas petroleum deposits. To the west of it, in waters which were the southcrn extension of the interior continental seas, in connection with the sedimcnts and coal beds of the Pennsylvanian and Permian, great quantities of petroleum were deposited either as oil or as "potential petroleum." These sediments have been subject to very slight disturbance, and only very gentle folds are found, with no signs of volcanic action in any part of the area. The conditions, therefore, indicate that the greater part, if not all, of the oil in this area is indigenous to the beds in which it is found. East of the anticlinal the oldest beds which appear in contact with the Bend are the Trinity Sands of the Lower Cretaceous. No evidence has

Jan 1, 1916

By B. Prof. Silliman

THE occurrence of diamonds of some size in the gold-fields of California is by no means uncommon, and was noticed by me in a communication, to the California Academy of Science in 1867, when specimens of this gem, from at least five different localities, were exhibited. I then suggested that a more attentive examination of the heavy sands left in the sluices of hydraulic washings would in all probability detect diamonds, mingled with other rare species not commonly believed to have occurred in these sands. Mr. George A. Treadwell, of San Francisco, has lately sent me a small package of these sands, collected by him from the sluices of the "Spring Valley Gravel Mining Claim," Cherokee, Butte County, California. A microscopic examination shows these sands to abound in beautiful colorless zircons (hyacinths), of the form well known in the hyacinths of Expailly (France), associated with crystals of topaz, quartz in fragments, rounded grains 'of chromic and titanic iron, and

Jan 1, 1873

By B. Silliman

THE occurrence of diamonds of some size in the gold-fields of California is by no means uncommon, and was noticed by me in a communication, to the California Academy of Science in 1867, when specimens of this gem, from at least five different localities, were exhibited. I then suggested that a more attentive examination of the heavy sands left in the sluices of hydraulic washings would in all probability detect diamonds, mingled with other rare species not commonly believed to have occurred in these sands. Mr. George A. Treadwell, of San Francisco, has 1at.ely sent me a small package of these sands, collected by him from the sluices of the " Spring Valley Gravel Mining Claim," Cherokee, Butte County, California. A microscopic examination shows these sands to abound in beautiful colorless zircons (hyacinths), of the form well known in the hyacinths of Expailly (France), associated with crystals of topaz, quartz in fragments, rounded grains 'of chromic and titanic iron, and

By Werner Engelmaier

Constant-strain rotating-bending fatigue tests were conducted on 2024-T3 aluminum alloy constant-strain McAdams-type specimens in ultrahigh vacuum, 10-lo Torr, and in atmospheric air. In the elastic strain range the ratio of vacuum-to-air fatigue life varied from about 10 at a maximum bending stress of 37 ksi to near unity at the endurance limit. After 10 pct of the fatigue life, intergvanular microcracks appeared on the surface which did not appreciably propagate further until the last 5 pct of the fatigue life, where trans-granular cracks propagating first in slip-plane cracking and then in the stress-dominated mode led to failure. No reduction in residual tensile strength resulted from the fatigue of the specimens short of fracture. The mechanism governing the fatigue life operates between the occurrence of the intergranular microcracks and the initiation of the trans granular cracks. MORE than forty years ago, Mc Adam' and Haigh2 published the first systematic studies showing that the fatigue properties of metals were greatly affected by environments. Gough and sopwith3 found in a later study that the fatigue life of metals subject to corrosion can be substantially increased by reducing the atmospheric pressure. This and their later work4'5 was, however, done in a vacuum of only 10~3 Torr. Subsequent studies6-' at a vacuum of 10- Torr showed that water vapor is the primary agent affecting the fatigue properties of aluminum alloys. Only recently was ultrahigh vacuum used for fatigue studied.l Various theories have been put forward to explain this phenomenon. Wadsworth and Hutchings12 postulated that cracks form very early in the test and that the chemical attack by the corrosive components of the atmosphere at the root of the cracks enhances the speed of the crack propagation. They also noted that chemisorbed layers of gas on the fresh crack surfaces prevent cold welding of the crack and make the separation irreversible. Ham and Reichenbach, on the other hand, reported that their specimens showed no cracks after a run in vacuum, even though the runs were long enough to have caused the specimen to fracture in atmospheric air. They also reported that in argon at 0.14 Torr the fatigue life was about 5 times longer than at 7 X lo-' Torr. Jacisinll reported that fatigue tests in dry nitrogen showed results close to those obtained in ultrahigh vacuum. The present experiment was designed to determine the extent to which cumulative fatigue damage, i.e., the accumulation of length of fatigue cracks, reduces the residual static tensile strength of an aluminum alloy in both ultrahigh vacuum and atmospheric air and to obtain fatigue-life data for this aluminum alloy at various strains. It was also hoped that information ex- tracted from these data might support one of the previously mentioned theories. 1) EXPERIMENT Test Specimens. The material tested was commer-cial 2024-T3 aluminum alloy. In addition to aluminum, this alloy contains approximately 4.4 pct Cu, 0.5 pct Fe, 0.5 pct Si, 0.6 pct Mn, 1.5 pct Mg, plus smaller amounts of other elements.13 Some typical mechanical properties of this aluminum alloy are listed in Table I.'~ The material was used in the as-received condition, i.e., solution-treated and cold-worked. Mc Adam-type1' constant-stress specimens and notched fatigue specimens were machined from 4 -in. -diam rods, Fig. 1. The critical section of the McAdam-type samples was polished with a 45-deg spiral motion to a No. 8 microfinish. The notch in the notched specimens was machined on a lathe with a forming

Jan 1, 1969

By O. L. Culberson, J. J. McKetta

Experimental and smoothed data are presented for the solubility of methane in water for temperatures of 77, 100, 160. 220. 280, and 340°F at prejsures to 10.000 psia. The minimum solubility phenomenon exists within this temperature range to pressures of 10.000 psia. INTRODUCTION The study of hydrocarhon-water systems has been extended to the determination of the solubility of methane in water at pressures to 10.000 psia. The experimental apparatus, and the technique. are the same as that previously reported.' - In the determination of the solubility of methane in water, only two phases were present at temperatures between 100 and 340°F. these being the vapor phase and the water-rich. liquid phase. The determinations involved the agitation of methane and water in an equilibrium cell. withdrawal of a sample from the liquid phase, and the analysis of the sample. The experimental value; determined in this manner are pre9ented in Table I and in Fig. 1. Since experimental and analytical techniques have improved since the initial experiments with this equipment, it was decided to repeat the 77°F isotherm determinations.' Fig. I shows that the individual results for this isotherm are much

Jan 1, 1951

By J. J. McKetta, O. L. Culberson

Experimental and smoothed data are presented for the solubility of methane in water for temperatures of 77, 100, 160. 220. 280, and 340°F at prejsures to 10.000 psia. The minimum solubility phenomenon exists within this temperature range to pressures of 10.000 psia. INTRODUCTION The study of hydrocarhon-water systems has been extended to the determination of the solubility of methane in water at pressures to 10.000 psia. The experimental apparatus, and the technique. are the same as that previously reported.' - In the determination of the solubility of methane in water, only two phases were present at temperatures between 100 and 340°F. these being the vapor phase and the water-rich. liquid phase. The determinations involved the agitation of methane and water in an equilibrium cell. withdrawal of a sample from the liquid phase, and the analysis of the sample. The experimental value; determined in this manner are pre9ented in Table I and in Fig. 1. Since experimental and analytical techniques have improved since the initial experiments with this equipment, it was decided to repeat the 77°F isotherm determinations.' Fig. I shows that the individual results for this isotherm are much

Jan 1, 1951

By E. Miller, K. L. Komarek

Equatiorzs have been derived which related maximum solid solubilities in semicondcting compounds having retvograde solidus curves with 1iqllidus data. Liquidus curves in Lke Pb-Te, Pb-Se, ard PB-S systetris have been defermined by thertrzal aralyses. Fvotrz expevimental maximum solibilities ia CdTe, PbTe, uxd PbS vetvograde tetrperatures hale beep1 calculated. TIze resllts support the concept that under certaiz conditiots pronounced itjlections in the liquidis curves arc indzcatiz:e of retropade solidus curves and that the tenlperatltre of the lmaximum solid solubility will be close to the temperature of the point of inflection in the liquidus curve. The maximum solid solihility within a gvoup of homologous cottrpoods SeetlLs to increase with increasing flatness ol the liquidus curvres. The phenomenon of retrograde solubility in metals, i.e., maximum solubility in a solid terminal phase in equilibrium with a liquid phase, has been theoretically predicted by Van aar' in his calculations of hypothetical binary phase diagrams. It was not until 1926, however, that retrograde solubility was experimentally verified in the Zn-Cd system.' Since then many sys- tems with retrograde solubility have been found, so that at present approximately fifty binary diagrams with a retrograde solidus curve are known.3 Meijering4 has critically appraised the accumulated data and has presented calculations which alloy predictions as to whether or not a solidus line will be retrograde. Interest in retrograde solubility increased when it was found that the solidus curves of germanium and silicon alloyed with a great many doping elements are retrrade. The problem was treated thermody-namically by odkinson,% d all available data on solid solutions in germanium and silicon were summarized by Trumbore.7 Although it is to be expected that intermetallic compounds will also exhibit retrograde solubility, experimental evidence is much more limited. Until now retrograde solidus curves have been reported for the compounds de,' be, Ps:" ne," SnSe," and SnS.13 All these compounds are semiconductors, and the solidus curves were usually obtained by determining the carrier concentration at room temperature of samples equilibrated at elevated temperatures and then quenched. It has been hown,'' however, that it is not always possible to quench in the equilibrium compositions from above a certain temperature. Theoretical discussions have either explicitly excluded intermetallic compounds4 or not treated them with respect to retrograde slubilit.j In the following a thermodynamic treatment of retrograde solu-

Jan 1, 1967

By J. C. Bartlett

The following discussion was suggested by an experiment of Mr. Krom, the Manufacturer of air-jigs, to illustrate the superiority of air over water as a medium of concentration. The paper is written in the interest of no system of concentration, but simply to test the experiment, and, perchance, to add something to the general fund of information on the subject. To speak of testing an experiment by a theoretical discussion, may seem a misuse of terms, but the theories concerning falling bodies and the resistance of fluids are pretty well crystallized into laws, which may properly be used to show where experiments which seem to refute them were improperly performed, and that instead of refuting they only corroborate. It is well known that a sphere of galena & inch in diameter, and a sphere of quartz 1/2 inch in diameter, are equal falling in water ; that is, these two spheres, being placed together in a column of water at rest or in motion, will practically remain together, filling or rising together, or remaining in suspension. Mr. Krom, to show that these

Jan 1, 1879

By E. S. Machlin, W. R. Yankee

IN a previous study1 of the effect of heating com-mercial titanium in air on its subsequent friction coefficient against other metals, as well as itself, it was found that the friction coefficient markedly decreased from a value of about 0.7 to about 0.3. A tentative explanation was given that surfaces normally produced at room temperature are not contaminated sufficiently to prevent seizing or welding of the titanium to the softer mating metals. The latter tend to cleanse themselves during rubbing over the harder titanium. It was thought that the lack of a contaminant protective film on the titanium was due to the high solubility of titanium for oxygen and nitrogen and hence an inability to form a contaminant oxide or nitride. This explanation requires the ratio of the surface absorption rate to the diffusion rate to become much lower at room temperature than it is at high temperatures. In order to check the phenomenon further, commercial titanium specimens were nitrided or oxidized at 800°C for 20 hr in flows of prepurified N2 and 01, respectively, at about 1/2 in. H2O above atmospheric pressure. Friction runs were made in argon using a freshly cut copper hemisphere (cut in argon) on surfaces cut successively into the diffusion layers in the titanium (cut in argon) using the techniques described in a previous publication.' DPH values (100 gram load) were made as a function of depth into the diffusion layer using a Tukon tester. Also, micrographs were taken at separate cross sections to indicate the diffusion layers. The results obtained are presented in Figs. 1 and 2, which show the "static" friction coefficient vs hardness for the nitrided and oxidized specimens, respectively. A separate measurement of the friction coefficient of clean copper vs iodide titanium also was made. From results reported in the literature' giving the oxygen and nitrogen contents as functions of the hardness, cross plots were made showing the friction coefficients as functions of the amount of interstitial solute. These plots are given in Figs. 3 and 4. From micrographs of the diffusion layers and the phase diagrams, it was deduced that the data in Figs. l through 4 correspond to the single phase a region. The points observed on the compound regions have been excluded from the figures. It is apparent that nitrogen or oxygen in solution in the a titanium markedly affects the friction coefficient against a softer mating metal. Discussion of Results These results are extremely interesting from both a practical and theoretical viewpoint. The theoretical implications will be discussed first. According to Bowden, the friction coefficient should be given to a good approximation by the relation where a is the fraction of contact area that has welded, a is the shear strength of weaker component, and H is the hardness of softer component. Using this relation alone, it is difficult to understand the results because none of the terms should be affected by a variation in the oxygen or nitrogen content of the harder and stronger metal, titanium. Even if the ratio of S/H for titanium is used in Eq. 1, the ratio has been shown to be independent of oxy-gen or nitrogen content.' If a more rigorous equa-tion is used combining Eq. 1 and a result given pre-viously" for the case where welding is absent, then the relation obtained is µ = a S/H + (1-a) a W aß/H where a is constant and Waß is the work of adhesion between the two metals comprising the friction couple. This relation states that if a is less than 1/2 or so, variation in the work of adhesion Waß between copper and the titanium should affect the friction coefficient markedly. It is reasonable to expect that the work of adhesion will depend on the oxygen or nitrogen content of the titanium. Available data4 show that clean metals and oxides have much lower works of adhesion than the same metals against the

Jan 1, 1955

By R. H. Smith, A. C. Polk

The physical properties of the materials are listed, together with a short explanation of how this material binds the sand grains together without materially reducing the effective permeability of the sand. The chemical can be used in wells with bottom-hole temperatures ranging from 105°F to more than 350°F A description of the equipment required and the techniques used for applying these plastics to the wells is included. Introduction Recovering oil and gas from unconsoli-dated sand formations offers one of the most troublesome of all production problems. These sands generally present no particular trouble while drilling is in progress, but after the well has been completed and a pressure differential has been established across the face of the producing zone, the formation begins to L'slough," resulting in "sanding up" of the well. The term "sanding up" means that sufficient volumes of sand have moved into the well bore or casing to cause a serious reduction or complete halt of all flow of oil, water or gas. In rare cases a well may produce only a small amount of sand and still continue to flow or pump, the sand being carried to the surface in the fluid stream. However, in such instances, the result may be a costly repair bill due to the effect of the sand on surface and pumping equipment. The difficulty of producing petroleum from sands that are loosely cemented has long been recognized by petroleum engineers but only within the last few years has any new approach to the problem been undertaken. This involves the use of plastics that are capable of bonding the individual sand grains in place without materially reducing the effective permeability of a formation. The successful application of plastics for the consolidation of poorly cemented sands is relatively recent but now it is widely used in many of the more difficult areas on the Gulf Coast of Texas and Louisiana. This relatively new use of plastics1 in the oil fields has been preceded by much laboratory and field research on the use of various chemicals2,3 for solving numerous well-completion and work-over problems. Plastics now are being used successfully to control gas-oil and water-oil ratios,4'6 in zone isolation, the repair of casing leaks, the elimination of caving in cable-tool drilling wells6'7 and in the setting of linerss and casing.9 Sand-consolidating plastics, however, are basically different from all others in that they must not form an impervious seal. Field Practices The approach to the sanding-up problem usually has been the mechanical obstruction of the movement of the sand grains.

Jan 1, 1947

By A. C. Polk, R. H. Smith

The physical properties of the materials are listed, together with a short explanation of how this material binds the sand grains together without materially reducing the effective permeability of the sand. The chemical can be used in wells with bottom-hole temperatures ranging from 105°F to more than 350°F A description of the equipment required and the techniques used for applying these plastics to the wells is included. Introduction Recovering oil and gas from unconsoli-dated sand formations offers one of the most troublesome of all production problems. These sands generally present no particular trouble while drilling is in progress, but after the well has been completed and a pressure differential has been established across the face of the producing zone, the formation begins to L'slough," resulting in "sanding up" of the well. The term "sanding up" means that sufficient volumes of sand have moved into the well bore or casing to cause a serious reduction or complete halt of all flow of oil, water or gas. In rare cases a well may produce only a small amount of sand and still continue to flow or pump, the sand being carried to the surface in the fluid stream. However, in such instances, the result may be a costly repair bill due to the effect of the sand on surface and pumping equipment. The difficulty of producing petroleum from sands that are loosely cemented has long been recognized by petroleum engineers but only within the last few years has any new approach to the problem been undertaken. This involves the use of plastics that are capable of bonding the individual sand grains in place without materially reducing the effective permeability of a formation. The successful application of plastics for the consolidation of poorly cemented sands is relatively recent but now it is widely used in many of the more difficult areas on the Gulf Coast of Texas and Louisiana. This relatively new use of plastics1 in the oil fields has been preceded by much laboratory and field research on the use of various chemicals2,3 for solving numerous well-completion and work-over problems. Plastics now are being used successfully to control gas-oil and water-oil ratios,4'6 in zone isolation, the repair of casing leaks, the elimination of caving in cable-tool drilling wells6'7 and in the setting of linerss and casing.9 Sand-consolidating plastics, however, are basically different from all others in that they must not form an impervious seal. Field Practices The approach to the sanding-up problem usually has been the mechanical obstruction of the movement of the sand grains.

Jan 1, 1947

By Shiou-Chuan Sun

SHIOU-CHUAN SUN (author's reply).-Thanks are extended to Professor Hassialis for his recognition of the usefulness of a new tool, the cataphoretic cell, as an adjunct to the bubble machine and the abstraction test. His questions concerning adsorption, dielectric constant, floatability, activation, and depression are interesting and worthy of discussion. I According to Mueller,28 it is questionable that any of the present formulas gives absolute values of zeta potentials which are completely accurate. The problem is further complicated by the question" of whether the "dielectric constant" has any meaning at all for such a microscopically thin layer. With these in mind, the results in this paper should be considered in the relative sense as a first approximation and not as absolute quantities. Adsorption Referring to item a of Fig. 8, the dielectric constant and the viscosity of the xanthate solutions are the same for galena, sphalerite and quartz. If dielectric constant and viscosity (but not the adsorption) were the first-order variable of the cataphoretic system, as claimed by Professor Hassialis, then the magnitudes of zeta coefficient of galena, spha)erite and quartz would have been similar to each other. These are not. The big difference of zeta coefficient of these three minerals in the same xanthate solutions is not altogether unjustified to be attributed to their difference in adsorption of xanthate ions. This is supported by the results of chemical abstraction tests reported by Ince.14 Again, the big difference of zeta coefficient between wollastonite, calcite, and fluorite in the same laurylamine hydrochloride solutions (p. 118, Figs. 58, 59, and 60 of ref. r5) also indicates that the cataphoretic system is not governed chiefly by the dielectric constant. Beside the data shown in Fig. 8, other experimental evidences15 which support the idea of correlation between adsorption and zeta coefficient are: (I) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of various concentrations of sodium cyanide, (2) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of constant concentration of copper sulphate at different pH values, and (3) there is a qualitative parallelism between zeta coefficient curve and chemical abstraction curve of quartz in solutions with constant concentration of barium chloride at different pH values. The above mentioned experimental results are generally in agreement with Gouy's double layer theory,1-5 and support this idea that the concentration and the kind of ions adsorbed at the mineral surface and in the adjacent surrounding liquid chiefly govern the electrokinetic phenomena. Dielectric constant and viscosity of the liquid medium may be of somewhat lesser importance. It follows that the correlation between the coefficient and adsorption as claimed in this paper is justified. Dielectric Constant The term "dielectric constant " was first introduced into the electrokinetic equations by Perrin.30 In a footnote of his publication he states that Holmheltz has forgotten to include the dielectric constant. The conversion of the moment29 to the zeta potential involves an additional difficulty and confusion not involved for the moment, namely, assigning a value to the dielectric coefficient. This is conventionally assumed to be constant and equal to the dielectric constant of the bulk liquid. 21 The published literature 10, 12 indicates that the values of dielectric constant for dilute chemical solutions have been assumed as those of pure water.

Jan 1, 1947

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.

By Jonathan G. Price

Silver-copper-lead deposits In Precambrian, Permian, and Cretaceous red-bed sequences near Van Horn, Texas, have the following features In common: (1) mineralization controlled by steeply dipping fractures in sandstones, (2) lack of ore in overlying and interbedded limestones, (3) absence of igneous intrusions, (4) sulflide ores without typical hydrothermal gangue minerals, and (5) associated arsenic, molybdenum, zinc, and cadmium but not gold. Ore was probably deposited along fractures by reaction between low-temperature, oxidizing, metal-rich ground waters and sulfide-bearing waters or rocks. Detailed mapping and studies of fracture patterns indicate that mineralization occurred during Basin and Range extensional deformation, thereby postdating major Trans-Pecos igneous activity.

Jan 1, 1984

By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts'2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

SMALL things are customarily moulded in two ways (unless they have undercut parts which hold them in the moulds); that is in clay, or with natural or which artificial earthern powder made in halves in either wooden boxes or bronze frames. This also depends on whether the object is larger or smaller. Now if you wish to mould with moist clay, you must grease your relief with oil or pig fat; apply a dusting of charcoal, ashes, or cuttlebone on it; or gild or silver it dry with gold, silver, or tin foil. Then, first make with moist and somewhat firm clay a plate as, thick and large as can conveniently hold your relief, and carefully set the latter halfway into this and let it dry. Then, greasing or dusting it again, make the other half. When both are well dried, take out your relief and at the top make its gates and vents. If plastering is needed, do it. Finally, bake the halves, fit them together, and tie them well, as you wish, using the procedure that I taught you in the discussion of brass. But if one has to make a large quantity of works of one kind, he should for the sake of convenience use the method with powder [120] because it is short and requires less time and expense. Therefore if you wish to do this, you need to have several pairs of bronze frames or wooden boxes, higher than half the relief that you wish to mould, and of convenient length. On a flat board always keep half of one of these frames full of powder that has been slightly moistened for moulding, as I told you, so that by pressing with the ends of the fingers and with the hand it holds together as well as possible. Level it off with a cutting tool and when leveled put a flat board over it and turn it over. Turn it on to a dusting of ashes so that it will not stick, dust it on the other side, and remove the excess by blowing it off Then mould the thing that you wish to mould, pressing it halfway in once or twice, always taking it out and putting it back again. Then the other frame is fitted in its place and filled with earth by pressing and squeezing it carefully. Then it is leveled off on the outside with a sharp tool as you did with the other part, and then one of the parts of the frames is lifted up with the point of a knife or some other tool and,

Jan 1, 1942

By C. H. Herty

During the past few years frequent reference has been made to a certain type of iron known generally as "bad iron," "dirty iron," etc., both by steelmakers and producers of iron castings.' Open-hearth operators have claimed that such iron was entirely within the specified limits as to ordinary analysis but it was difficult to make good steel from it. It has been suggested that unreduced material in the iron is responsible, also that most trouble is experienced with the iron when the blast furnace is delivering a product whose analysis is more or less variable. Other reasons suggested are the use of scrap or borings, unsintered flue dust in the burden, a cold hearth, too high a proportion of unsuitable grade of ore, or the form of the carbon in the iron. Accordingly, a subcommittee was appoint at the fall meeting of the Open-hearth Committee of the Americ m Institute of Mining and Metallurgical Engineers held in Pittsburgh in October, 1926, to investigate the reasons for the occurrence of this bad iron and suggest methods for preventing its appearance. This committee enlisted the cooperation of the U. S. Bureau of Mines Experiment Station at Pittsburgh in undertaking a study of pig-iron quality as affecting the open hearth. The following is a report of the findings to date: Method of Testing Inasmuch as a "spell" of dirty iron occurs without warning and may be of short duration, it was deemed advisable to attempt to simulate the conditions existing before and during such a period and compare the quality of the steel made with the normal and with the dirty iron. The Bourne-Fuller Co., of Cleveland, which has a single furnace that supplies

Jan 1, 1929

By K. U. Snowden, J. N. Greenwood

EARLY studies by Gough and sopwith' have shown that the fatigue resistance of certain metals increased when the test was carried out in a partial vacuum; lead showed this effect to a marked degree. This communication describes surface deformation differences between high-purity lead fatigued in air and in a vacuum of approximately 5 X l0-3 mm Hg. Both air and vacuum tests were carried out by the same alternating flexure machine at a frequency of 500 cpm. Flat cantilever-bend specimens with tapered sides were cut from strip, annealed at 100°C, and chemically polished.

Jan 1, 1959

By E. T. Dumble

Discussion of the paper of E. T. DUMBLE, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 104, August, 1915, pp. .1623 to 1638. E. L. DEGOLYER, Norman, Okla. (communIcatIon to the Secretary*).-Referring to Mr. Dumble's description of the stratigraphy of eastern Mexico, I should like to question the classification of the ?Papagallos? or ?Mendez? shales as being of Cretaceous age and the so-called overlapping of the Papagallos or Mendez shales by the Alazan shales; the classification of the San Felipe series as Cretaceous, and the correlation of the San Felipe series with the San Juan limestones. Mr. Durable apparently recognizes the continuity of the great shale formation by his use of the terms "Papagallos" and "Mendez," as equivalent and interchangeable, since the Papagallos Hills in the State of Nuevo Leon and Mendez Station in Northern Vera Cruz, localities at which the shale formation outcrops, and from which the formation names are taken, are approximately 250 miles apart and on opposite sides of the Tamaulipas barrier. The Papagallos shales (evidently referring here to the northern extension only) are said to be non-fossiliferous and no reason for .their Cretaceous classification is given, though in a previous article' they are classified as Cretaceous because at their northernmost outcrop they "have the same relation toward the overlying Tertiary that the Escondido (Cretaceous) has through its whole extent." The Alazan fossil locality was found by me and the first collections from it were sent to Dr. Dall; about 17 species of marine invertebrates were recognized by him, the fauna noted as having a distinct Pacific tincture, and the age of the formation from which they cause pronounced lower Eocene. The outcrop of the shale formation has been traced continuously from this point by me and my assistants into the Panuco River region, where Eocene fossils are reported at a depth of 1,810 ft. in a well at Topila.2 From Topila the formation has been traced continuously north to the Padilla-Jiminez region in Central Tamaulipas. Lithologically, the formation is fairly constant and though I am only generally acquainted with it north of the Padilla-Jiminez region, until definite evidence of the Cretaceous age of the Papagallos shale in its type localities, or of an overlap, is available, it seems to me more logical to consider the shale formation a single stratigraphic unit of Eocene age.

Jan 12, 1915