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By C. S. Land

Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water - wet rocks for both two- and three - phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. INTRODUCTION Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. 1 and by Osaba et a1.2 Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems.3 Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by snel14 as 11, ID, DI and DD. I and D refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis5 published three-phase curves for unconsolidated sand, and Snell4 reported results of several English authors for both drairrage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et a1.3 for increasing water and gas saturations (ID). Corey et a1.6 reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean7 and Sarem8 calculated three-phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three-phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (11) are those of Naar and Wygal.9 These curves are based on a theoretical study of the model of Wyllie and Gardner 10 as modified by Naar and Henderson.11 Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids.12 Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term.13 The works of Purcell and Burdine were combined by Corey14 into a form that has

Jan 1, 1969

By B. Yu, H. M. Lee, R. P. Gardner

Some preliminary results are given on the use of radioactive tracers for implementing the mechanistic approach to flotation. The process studied is an industrial one for the cleaning of sand for the production of glass. The radioactive tracers employed are those produced from intrinsic elements in the sand by neutron irradiation in a nuclear reactor. The results indicate that the technique will be useful for the determination of flotation simulation mechanistic model parameters on operating industrial processes without interruption of their normal operation.

Jan 1, 1980

By John E. Hagni, Richard D. Hagni

ORE.ID, a microcomputer program, rapidly searches a database of the principal properties for 573 ore minerals. Searches may be performed on any or all of the following properties: mean Vickers hardness, Talmage hardness, mean reflectance, strength of anisotropism, and colors and tints of the mineral and its internal reflections. Data from the International Mineralogical Association - Commission on Ore Microscopy data card file have been used when available. The program displays the number and type of data matches for each mineral found, displays their chemical components, and allows the range to be narrowed or widened for each of the identification properties for repeated searches, if desired. ORE.ID is much more rapid, allows for the use of more identification properties, and involves more ore minerals than any previous identification system.

Jan 1, 1985

By M. S. Seltzer

In a previous paper1 it was shown that activation energies for steady-state creep in lead sulfide single crystals varied with the concentration of electronic defects. For n-type lead-excess crystals, values for the creep activation energy, Qc, decreased from 2.9 to 2.2 ev as the carrier concentration increased from 1017 to 1017 electrons per cu cm, while Q, increased from 1.6 to 2.3 ev for p-type sulfur-excess crystals as the concentration of holes increased from 6 X 1017 to 1018 per cu cm. It was also shown in Ref. 1 that the Q, values could best be correlated with the sum of the self-diffusion activation energies in PbS, i.e., for a given concentration of electrons or holes Q, = QPb + Qs, where Qpb and QS are the activation energies for diffusion of pb210 and s35 in PbS. This result suggests that creep rates are controlled by at least two atomic defects, one for lead migration and one controlling sulfur transport. It would be most desirable to interpret these creep energies in terms of an atomic defect disorder model for lead sulfide. Studies of creep rates as a function of sulfur pressure2 indicate that the defects controlling creep rates are singly ionized lead and sulfur vacancies, VPb and Vs. This hypothesis can be more firmly established by determination of Q, under conditions of constant atomic defect concentration rather than constant electronic defect concentration as has been previously done. Therefore, several measurements have been made of Q, on crystals whose con- centration of lead vacancies or sulfur vacancies has been fixed by equilibration under appropriate sulfur pressure and temperature. It was indicated in Ref. 2 that high-temperature isotherms are available which show how the concentrations of various atomic point defects in PbS vary with composition over the entire homogeneity range for the compound. Two such isotherms are shown in Fig. 1 for 900" and 1000°K. Utilizing these isotherms the concentration of a given defect, say Vbb, may be held constant over a particular temperature range by adjusting the sulfur pressure as the temperature is changed. Thus the concentration of one defect suspected of controlling creep rates may be held constant while other defect concentrations vary. The apparent activation energy for formation of these defects can be obtained from the isotherms giving their concentration as a function of sulfur pressure. Activation energies for creep obtained under conditions of constant defect concentration can then be compared with defect formation energies and certain possible atomic defects can be eliminated as creep-controlling species. We have performed creep experiments as a function of temperature at a stress of 244 g per sq mm under conditions which fixed the lead vacancy concentration, V', at 1016, 3.2 x 1016, and 3.2 x 1017 cm-3, and one were the sulfur vacancy concentration, Vs, was held at lo17 cm-3. The results are presented in Fig. 2 as creep rate, k, vs reciprocal of absolute temperature, 1/T. Specimens 34, 35, and 36 were deformed under constant lead vacancy concentration while specimen

Jan 1, 1969

By J. L. Zakin, G. K. Patterson, J. M. Rodriguez

Correlation has been obtained between drag-reducing characteristics for turbulent flow in a pipe and measurable properties of several polymer solutions. Several concentrations of high molecular weight polymethyl methacrylate in toluene, high molecular weight polyisobutylene in both toluene and cyclohexane, medium molecular weight polyisobutylene in cyclohexane and benzene and low molecular weight polystyrene in toluene were studied. Data obtained in these nonpolar solvents and literature data for more polar solvents were successfully correlated as the ratio of measured friction factor to purely viscous friction factor vs the modified Deborah number vrl/D0.2 where 71 is the first-mode relaxation time of the solution estimated by the Zimm theory. A shift factor which is a function of intrinsic viscosity 1/(4[?] - 1) allowed all the data obtained with nonpolar solvents to be correlated as a single function. For these systems, most of the data fit a single curve to within + 5 percent of the average friction factor ratio. The shift factor did not give a unique function of the data for the more polar systems. INTRODUCTION The phenomenon of drag reduction in polymer solutions was first studied by Toms1 in dilute solutions of polymethyl methacrylate in mono-chlorobenzene. The drag ratio for flow through circular tubes has been defined2 as the ratio of the pressure. drop of the solution to the pressure drop of the solvent at the same flow rate. The drag ratio is less than 1.0 for a drag-reducing fluid. Practical use of drag reduction is being made in fracturing operations in the petroleum industry.3 A more fundamental quantity is the friction factor ratio, defined as the ratio of the observed pressure drop to that predicted for a solution of the same viscosity characteristics and density at equal flow rates using the Dodge-Metzner friction factor equation4 Viscous solutions with drag ratios greater than 1.0 can have friction factor ratios less than 1.0. For practical applications, it is drag reduction which is of interest. However, for correlation the fundamental ratio is the friction factor ratio. In recent years, drag reduction has been studied extensively. Recent studies have shown that reasonable predictions of the incipience of drag reduction in polymer solutions can be made from the properties of the solutions and the flow Variables.5 However, it has not been possible to predict accurately the amount of drag reduction to be expected for a given polymer solution without any drag-reducing turbulent flow data on the same solution.6 For flow through circular tubes it is well established that there is a concentration effect and a diameter effect on drag reduction. Toms1 observed that drag reduction increases with an increase in the concentration of the solution up to an optimum concentration beyond which, due to the increased viscosity of the solutions, the drag ratio increased with an increase in concentration. Hershey 7 observed that for dilute Newtonian polymer solutions in nonpolar hydrocarbon solvents, a normal transition region may be obtained followed by a departure from the von Karman equation (on a friction factor-generalized Reynolds number chart). The point of departure is a function of diameter: the smaller tubes depart at the lower Reynolds numbers. Concentrated solutions may show no abrupt transition region, but merely an

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By Albert F. J. Bordeaux

INTRODUCTION. THE following general survey of the character and present condition of the silver-mines of Mexico, though not offered as a detailed treatise, has been prepared with care, is believed to he generally up-to-date, and is offered as a summary which may be found useful by mining engineers. Mexico has ranked for several centuries first among the silver-producing countries. It is now second as copper-producer, and seventh as gold-producer, with a fast-increasing output every year. The total amount of capital invested in its mining- and smelting-works is more than $250,000,000, while the yearly metallic production is $160,000,000. There are more than 20,000 recorded mining properties. The silver-mines of Mexico represent deposits of three principal classes: (1) veins and stock-works in eruptive rocks; (2) fissure-veins crossing the crystalline schists, granite, diorite, etc. ; and (3) veins and replacement-deposits in limestone. The true fissure-veins in some districts contain (in value) more gold than silver. In other deposits, the silver is decreasing in depth, leaving galena and zinc-blende as the principal ores.

Jan 9, 1908

By R. V. Smith, M. H. Cullender

Rigorous equations for calculating subsurface pres.tures in flowing and static gas wells, and pressures along horizontal pipelines are presented in this paper. These general equations, based on the mechanical encrgy balance, contain no assumptions regarding temperature and can be used with either straight-line or curved temperature gradients. The friction factors recommended in this report are based on an absolute roughness of 0.0006 in. Flow is always considered to he turbulent. Although these general flow equations are solved by numerical means, the methods are as convenient as many of those used today to calculate pressures in gas wells and pipelines. These numerical methods are illustrated for flowing and static columns of gas in wells and for flow in pipelines. The authors believe that the use of these methods will result in more accurately calculated pressures in gas wells and pipelines and that [he methods are more flexible than any in use at the present time. Also, the methods are easily adaptable to automatic computers. INTRODUCTION The problem of calculating subsurface pressures in gas wells and along flowing pipelines has been studied by many investigators with the results that two widely-used methods have been presented in technical literature. One approximates conditions in a gas well or pipeline by assuming that temperature and compressi- bility are constants tor the entire gas column. The other method assumes that temperature is constant at some average value but permits compressibility to vary with pressure at the constant temperature. While these approximations may be justified for relatively shallow and low-pressure wells, they become more and more unrealistic as the calculations are applied to the deeper high-pressure wells. In wells or pipelines where there is an appreciable change in temperature between the inlet and outlet ends of the flow string, it is equally as important to consider the change in compressibility with temperature as it is to consider the change with pressure. Consequently, the methods presented in this paper were developed to provide a workable procedure for calculating pressures in gas wells and pipelines which makes no assumptions regarding either temperature or compressibility. The friction factors recommended for use with the equations were the result of study of published literature and extensive experimental work with gas wells. The F,. values in Appendix IV which contain the friction factor are equivalent to an absolute roughness of 0.0006 in. as calculated by the Nikuradse equation. The absolute roughness of 0.0006 in. was previously published by Cullender and Binckley2 for gas wells; it is in agreement with 0.00065 in. of Smith, Dewees, and Williams1 for gas wells and 0.00065 in. of Baker and Swerdloff4 for pipelines; it is in reasonable agreement with 0.0007 in. reported by the Bureau of Mines and the American Gas Assn.5 for large transmission lines. However, any type of friction factors may be used in the equations by a change in the F, values in Appendix [V].

Jan 1, 1957

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the lengt of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel-per-day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel-per-day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable-yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from she commonly understood barrel-per-day value, in that the conditions turrounding the sale of one lease or property at a fair market value may

Jan 1, 1923

By W. Irwin Moyer

Two methods for the rapid valuation of oil properties are in common use. The one best known and most widely used is the "per barrel" value, based on the present daily production of the well, without regard to its past performance or the history of the sand or pool from which it produces. The second method is the "time to pay out," or the lengt of time required for a well to place itself upon the credit side of the ledger, from which time the returns from its production (less the operating expenses) will be clear profit. The time basis for valuation is also commonly used in the appraisal of an undeveloped lease. In most oil fields, it is not thought good business to invest in production that will not pay out in at least 4 to 5 years. Nearly all buyers (except in certain regions of very persistent production like the deep-sand territory of the Appalachian field) expect wells to pay out in considerably less time than this. Like the barrel-per-day price, the time necessary for a well to pay out has been determined for each field, so that one frequently hears a field or district referred to as having a certain time to pay out. This is considered the norm for that field or district and the buyer and seller base their value, to greater or less extent, on their belief in the accuracy of this time. The writer long ago became convinced of the inaccuracy of the barrel-per-day method, except when greatly modified for local conditions, such as the age of the wells, their economic limit, operating conditions in the field, the future price of oil, and the persistence of the sand as a producer. When so modified, this method becomes more of an analytic or predicted probable-yield valuation. While the appraiser may not go through each step in a valuation based on future returnable revenue, his knowledge of the field and the local conditions surrounding his leases make it possible for him to estimate a fair sales value that, in many cases, will be a close approximation to the truth. This is quite different from she commonly understood barrel-per-day value, in that the conditions turrounding the sale of one lease or property at a fair market value may

Jan 1, 1923

By F. Lynwood Garrison

There is probably no subject for study in the metallurgy of iron and steel of greater interest than the effect of manganese upon the properties of iron. Some of the peculiarities of iron and steel containing appreciable quantities of manganese were observed many years ago by Heath, Robert Mushet, and others; but it was not until the introduction of the Bessemer process, when a demand was created for large quantities of iron-manganese alloys, that such compounds of iron and manganese became articles of commerce. Since that time the demand for these alloys has steadily increased, the use of ferro-manganese not only becoming an absolute necessity in the ordinary Bessemer practice, but also essential to the manufacture of open-hearth, crucible steel and steel castings; in fact it is the only source of supply for all the manganese used in metallurgical opera-

Jan 1, 1893

By Vernon F. Swanson

An equation has been developed which will permit the direct determination of free settling velocity of any sized particle encountered in mineral benefici-ation. The equation is based on Newton's Law with the friction factor defined as a function of the laminar boundary layer. Development of the equation is described first from an empirical trial-and-error approach. Examples are given of actual settling data from the literature versus calculated data to prove the validity of the new equation. Newton's law of resistance of a fluid to flow around a sphere is expressed in Eq. 1. Free settling velocities can be determined by setting Eq. 1 equal to the gravitational force on a particle and solving for V. Experience has shown that when the solids are greater than 1 mm in diam, or when Reynold's number for the system is greater than 800-1000, the friction factor term, fD, essentially becomes a constant, and Eq. 2-b becomes Newton's equation for free-settling and is applicable under the conditions stated. Another special condition exists for particles smaller than 0.05 mm or when Reynold's number for the system is less than three. In this case fD=24/NRor24µ/pL,dV,. Eq. 2-b can then be rewritten as

Jan 1, 1968

By R. Simon, D. J. Graue

This paper presents correlations for predicting the solu-lility, swelling and viscosity behavior of CO2-crude oil sys8i.m~. The correlations were developed from experimental data obtained by the authors. These data are also presented. The data were determined by measuring the properties of mixtures of CO, and nine different oils. Experiinental conditions covered a range of 100 to 250°F and pressures up to 2,300 psia. Properties predicted by the correlations have average deviations, expressed as per cent of experimental value, of 2 per cent for solubility, 0.5 per cent for swelling and 12 per cent for viscosity. INTRODUCTION Interest in CO2 injection as an oil recovery process has led to the development of performance prediction methods which can be applied to specific reservoirs.1 iS To use these performance prediction methods, it is necessary to know the solubility, swelling and viscosity properties of CO2-crude oil mixtures at reservoir conditions. Some information on these properties has appeared in the literature; however, this information did not cover the range of different oils and conditions needed to prepare generalized correlations for reservoir engineering purposes. Consequently, an experimental program was undertaken to collect the data needed. The data obtained and the correlations developed from the data are described in the following sections of this paper. SOLUBILITY OF CO2 IN CRUDE OILS CO2 solubility data in the literature come from six principal sources. The solubility prediction method of Welker and Dunlop3 is limited to 80F. The information in Ref. 4 is of two types: the first includes binary and ternary mixtures of CO, and light hydrocarbons (C1 to C6), and the second gives data for CO1 and heavy hydrocarbons for a temperature range of 40 to 90F. Ref. 5 contains a KCO2 chart for systems whose convergence pressure is 4,000 psia. The KCO2's are based mainly on CO2-natural gas mixtures. Poettmann's work covered CO2 solubility in one condensate and one crude oil6,7 Ja-coby and Rzasa measured CO? solubilities as a function of pressure and temperature for two natural gas-absorber oil mixtures and two natural gas-crude oil mixtures.'8 CO, concentration in these four systems was fixed at 5 mol per cent. The work reported in this paper extends CO, solubility data to a variety of different crude oil types in a temperature range from 110 to 250F and pressures up to 2,300 psia. The experimental procedure used by the authors to obtain the solubility data consisted of combining known amounts of pure CO, and crude oil in a visual cell at a fixed temperature and measuring the bubble point of the mixture. Measurements were made for a total of 40 different CO2-oil mixtures and the results are shown in Table 2. The mixtures included nine different oils (seven crude oils and two refined oils) whose properties are listed in Table 1. All nine oils had vapor pressures less than 1 atm at the experimental temperatures. Consequently, analysis of the bubble-point vapor showed a CO, concentration over 99 mol per cent. At no time during these experiments was a second, more dense, liquid phase observed. The solubility correlation which was developed from the data in Table 2 is presented in Figs. 1, 2 and 3. In these figures, solubility is expressed as xco2 the mol fraction of CO, in the CO2-oil mixture. Fig. 1 shows solubility as a function of CO2 fugacity6 and temperature. Fig. 2 shows the same solubility data expressed as a function of saturation pressure and temperature. The solubility shown in Figs. 1 and 2 is for an oil whose UOP characterization factor is 11.7. UOP characterization factors of crude oils can be determined from Ref. 10 if the viscosity and APT gravity of the oil are known. Fig. 3 gives the solubility correction factor for oils whose UOP characterization factors differ from 11.7. The solubility correlation in Figs. 1, 2 and 3 predicted

Jan 1, 1966

By S. Gilbert, G. R. Bailey

A further evaluation of the bomb-sampling method for determining the oxygen content of liquid steel is presented. The results of this study and their close agreement with the results of an earlier evaluation confirm the conclusion that the bomb-sampling method is valid for obtaining representative samples for the determination of the oxygen content of a liquid steel bath. WHAT constitutes the most desirable procedure for obtaining a sample suitable for determining the oxygen content of a liquid steel bath has been a controversial subject for several years. In 1952 Huff, Bailey, and Richards' described a modification of the bomb-sampling technique originated by McCutcheon and Rautio.' In both the modified and original techniques, a small cast-iron or steel mold containing aluminum wire and appropriately covered is inserted into the furnace, coated with slag, and then plunged into the metal bath. Upon entering the metal, the cover melts and a sample of the steel bath enters the mold. The data presented by Huff, Bailey, and Richards' indicated that reproducible samples could be obtained by their method. Furthermore, the oxygen analyses from samples obtained by their method agreed better with those from controlled laboratory experiments than did analyses from samples obtained by methods previously suggested for sampling large liquid-metal baths. Most techniques, other than bomb-sampling, require that a sample of liquid steel be removed from the furnace in a well slagged spoon and poured into an iron mold containing aluminum or into a massive copper mold for rapid chilling. Pouring in this manner requires that the sample pass through the air. The controversy, then, is somewhat as follows: Proponents of the spoon-sampling method and similar dip-and-pour methods feel that the introduction of a cold steel mold into a molten steel bath may result in a localized boiling condition that may deplete the steel of oxygen to a significant degree in the area where the bomb is introduced. Conceivably this boil could cause results that are, on the average, too low and nonrepresentative of the bath composition. On the other hand, samples that are spooned and then poured through the air may also be nonrepresentative because of oxidation by the atmosphere. The restrictions imposed in sampling with a spoon are much more stringent than those imposed when sampling with the bomb-type mold within the furnace. The spoon sample must be taken in a well slagged spoon, a requirement that depends on the condition of the slag in the furnace. Also, the samples must be poured as quickly as possible, without shaking the spoon and without allowing slag to enter the mold. The necessity of fulfill-

Jan 1, 1955

By B. M. Larsen, W. E. Shenk, T. E. Brower

Shortly after our previous paper on this subject was printed1 we located a source of uncertainty in the results arising from the unexpected fact that hydrogen slowly reduces silica at 1100" C. in presence of iron, even when the iron nowhere touches the silica, although in absence of iron it does not do so. This difficulty has been completely obviated by the use of a small high-frequency furnace, which enables us to heat the specimen for analysis without raising the temperature of the silica vessel to a point at which any appreciable reduction of the silica glass occurs. We now describe this modification of procedure, and present some typical results obtained with it. For any given specimen of steel, the results are entirely definite and reproducible, but their precise significance is still open to some question, as indeed is true of all methods of oxygen determination SO far developed. Further elucidation of this question is to be expected from the cooperative comparison of the several methods now under way under the auspices of the Bureau of Standards at the instance of the Iron and Steel Division of the A.I.M.E. Apparatus The final form of apparatus we have used is identical with that described and illustrated in our previous paper, except for the substitution for the Globar furnace of a small high-frequency furnace actuated by a vacuum tube oscillator2 0f about 1.5 kw. capacity, and for a slight modification of the containing vessel. This transparent silica vessel is illustrated in Fig. 1 of this paper. Its enlarged portion is about 5 cm. in diameter and 13 cm. long. The silica tube for inlet of hydrogen is fused into this bulb and ends beneath the metal "bucket" holding the steel sample. This sample is in the form of fine millings. The "bucket" is suspended by a platinum wire from the cap of Pyrex glass. The high-frequency

Jan 1, 1934

By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

By F. S. Pettit

The oxidation of Ni-3 to 25 wt pd Al alloys has been studied in 0. 1 atm of oxygen at temperatures between 900° and 1300°C. These alloys have been found to oxidize by three different mechanisms which depend on the temperature of- oxidation and the alloy composition. Two of the three mechanisms do not permit a continuous layer of Al,0, to be formed on the alloy surface and the oxidation rates are greater than that for pure nickel. The third mechanism results in the formation of an external A1203 scale and lke oxidation rates are about three orders of magnitude smaller than those for pure nickel. The minimum amount of aluminum required for the formation of external scales of A L,0, has been determined. NICKEL-base alloys are currently the main source of materials for use at elevated temperatures in gas turbine engines. These alloys are usually coated to obtain oxidation resistance. Coatings on nickel-base alloys are frequently formed by reaction of the alloy with aluminum whereby alloyed nickel aluminides are formed. The alloyed nickel aluminides provide protection to the nickel base alloy because external scales of A1203 (alumina) are formed during oxidation and mass transport through A120, is slow in comparison to mass transport through most other oxides. In view of the protective properties of A1203, it is important to know how much aluminum is required in these alloys in order to form external scales of AlzO,. The present paper is concerned with the oxidation kinetics and the oxidation mechanisms of Ni-A1 alloys and the minimum amount of aluminum required in these alloys for the formation of external scales of Alz03. THEORETICAL CONSIDERATIONS When a Ni-A1 alloy is heated in oxygen at elevated temperatures, the following reactions can take place on the surface of the alloy where the oxide phases are assumed to be virtually pure: These oxide phases are in the form of nuclei scattered over the surface of the alloy and, in view of their rapid formation, they need not be in equilibrium with the alloy. As the oxidation process continues, equilibrium between the alloy surface and the oxide phases is approached and the stability of the oxide nuclei is determined by the composition of the alloy at the alloy/oxide interface because of the following reactions: 3NiA1204 + 2A1 (alloy) = 4AlzO3 + 3Ni (alloy) [41 4Ni0 + 2Al (alloy) = NiA120, + 3Ni (alloy) [ 5 1 Application of the mass-action law to Eqs. [4J and [5J yields the following equilibrium conditions for these reactions: where aA1 and aNi are the activities of aluminum and nickel, are the standard free energies of formation of NiO, A1203, and NA1204, respectively, R is the gas constant, and T is the absolute temperature. If the composition of the alloy at the alloy/oxide interface is such that (akl/ahi) is greater than the equilibrium values defined by Eqs. [6] and [7], then Reactions (41 and [5] will go to the right as written. Conversely, if the alloy composition is such that the activity ratio (aLl,/aki) at the alloy/oxide interface is less than the equilibrium values, then Reactions [4] and [5] will proceed to the left. The equilibrium activity ratios in Eqs. [6] and 171 can be calculated since values for the standard free energies of formation of the oxide phases are available. Standard free energies of formation for NiO and A1203 have been tabulated by Elliott and ~leiser.' The standard free energy of formation for NiA1204 can be obtained from the data of Tretjakow and Schmalzried.' The results of these calculations are tabulated in Table I. Table I shows that the following inequality is valid over the temperature interval 900" to 1300°C: (Reaction [5]) (Reaction [4]) « 1and therefore the aluminum activity for these compositions can be taken as equal to the square root of the activity ratios (i.e., aNi = 1). If equilibrium is estab-

Jan 1, 1968

By R. V. Ramani, C. J. Bise

The potential of deep-mineable coal reserves in the western United States for meeting future energy needs has been recognized for quite some time. However, two of the major constraints tending to limit the development of these underground reserves are the great thicknesses of the coal seams encountered and their high pitch. Although new mining methods may need to be developed to recover these reserves, at least in the short-term the industry has to incorporate presently available equipment not originally designed for thick-seam mining. The purpose of this paper is to present an analysis of the various equipment in use today and their possible application to thick-seam mining. The paper also addresses various ground control and safety considerations unique to thick-seam extraction.

Jan 1, 1984

By Theodore Simons

(Butte Meeting, August, 1913.) DURING the last half century a great amount, of ingenuity and energy has been devoted to the invention of appliances for the recovery of valuable minerals from very fine sands and-slimes. The reason for this is that in almost every, dressing plant the greatest losses of values, considered relatively as well as absolutely, occur in the treatment of slimes. The natural aim of mill operators to minimize these losses has in recent years received another impetus,, from the fact that the gradually diminishing occurrence of high-grade ores makes a more intense recovery of values from existing resources absolutely necessary for profitable operation. The results of such attempts are found in the appearance of a great number of machines and appliances which make it profitable to-day to rework old dumps, containing the tailings of older processes. A constantly growing difficulty of obtaining skilled labor and the increase in wages made it prohibitory to employ those types of machines which required much attention, and in the middle of the nineteenth century the various concentrating tables of the percussion type, which automatically discharge their products, began to take the .place of the intermittent tables, on which, when the bed had reached a certain thickness, operation had to be stopped in order to allow the skimming by hand of the separate layers formed on the table. In the course of. years, two general types of machines evolved for the treatment of fine sands and slimes :- The so-called concentrators and vanners, on the one hand, and the huddles and round tables on . the other.1 For the profitable treatment of the very finest slimes, round tables have as a last resort proved more satisfactory and economical than other machines.

Jan 7, 1913

By R. M. Leibrock, C. W. Ziemer, R. P. Vincent

The Stanolind flowmeter, which employs a hot-wire anemometer connected in a Wheat-stone bridge circuit, has proved useful for determining the relative productive ability of individual sand members of gas wells. The operation of this instrument in measuring gas velocities in the well bore above each producing member has provided both a direct and accurate means of analyzing reservoir performance. Results of tests conducted with the well flowmeter in the Hugoton gas field of western Kansas have indicated some rather unusual production characteristics. In two cases it was found that all or the greater part of the total gas produced was coming from one section in wells where four "pay" sections had been perforated individually. These actual measurements contradict in many instances the indications of data obtained from electric logs and from core analysis; the fact that these latter sources often give incorrect results, demonstrates the necessity of a method, such as is provided by the well flowmeter, for accurately determining the amount of gas coming from each producing member. Introduction In any gas well where a number of pay sections have been perforated individually and are producing to a common outlet, the question arises as to the relative amounts of gas being passed through each set of perforations. In the past it has been the policy to depend on core analysis to estimate relative productivities, or, where the sections were not cored, to obtain some idea of production characteristics from electric-log studies. The weaknesses in these methods are readily apparent and indicate the need for more reliable means of measuring gas flow from each zone. The Stano-lind flowmeter* was developed for this purpose. Preliminary tests were made with the instrument in the Katy gas field near Houston; however, the bulk of the routine work with the well flowmeter has been confined to the Hugoton gas field in western Kansas, where results obtained have been encouraging. A description of the instrument, the field technique employed in testing, and a few of the results obtained in the Hugoton area are discussed in this paper. Description or Instrument The well flowmeter is 1¾ in. od and 7 ft long; it is entirely self-contained, can be run through tubing as small as 2 in. id in wells with high pressure (4500 psi) and temperature (210°F) and is lowered on a wire line commonly used for other instruments of the bottom-hole type at falling rates up to 500 ft per minute. It will detect gas flow as low as 10 ft per minute linear velocity, and yet withstand and record velocities of 1000 ft per minute without damage to the detecting element. Killing the well is not required nor desirable for running a production profile when using the instrument, and it is necessary to stop flow for only a short time. The detecting element of the instrument is a hot-wire anemometer connected in a

Jan 1, 1948