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By R. Kossowsky

In the course of a study concerned with structural stability of precipitation hardening nickel base super -alloys after exposures to elevated temperatures, some interesting effects of hydrostatic pressure treatment on Rene were observed. The evidence presented below suggests that hydrostatic pressure treatment of the solution heat-treated alloy can affect the dispersion of the y' (Ni3Al) phase upon subsequent precipitation heat treatment and long time aging. Rene 41 alloy has the following nominal weight percent composition: Al B C Co Cr Fe Mn Mo Ti Ni 1.4 0.006 0.7 11.3 19.2 1.0 0.05 9.4 3.3 balance The effect of successive pressure, precipitation heat treatment, and long time aging on the microstructure of this alloy was determined by subjecting a number of alloy buttons to five different thermopressure treatments. Pressure and precipitation heat-treatment parameters are listed in Table I. Fig. 1 shows y' morphology* of specimens in groups I and 11. The treatment results in a fine dispersion with particle size on the order of 950 and 1350A, respectively, see Table I. Fig. 2 shows the morphology of y' precipitate in

Jan 1, 1967

By J. D. Campbell

"Coal is one of Alberta's major fuel resources, but its distribution, especially in the flat plains region, has been somewhat obscured by surficial deposits. After a period of neglect, easily strippable plains coal is presently approaching a position of dominance in electrical power production, a position it is likely to retain for a number of decades in the face of strong competition from hydro and nuclear power. Accordingly, the Research Council of Alberta has undertaken an inventory survey of the province's supplies of this resource.In the southern part of the province and in the north-central forest-fringe area, some strippable coal is found in the Belly River Formation and its equivalents, but major strippable coal reserves in large areas of central Alberta occur within the Edmonton Formation. The survey is planned on a reconnaissance scale, drilling test holes at 2-mile intervals in selected large areas. It appears to show that, in well-settled regions, large reserves of strippable coal are only to be expected where they have long been known; major presently unknown bodies of coal must be sought in unsettled regions or at depths too great for strip mining. However, such bodies might still be economically competitive with hydro and nuclear power in the production of electric power for some time to come."

Jan 1, 1967

By H. R. Cooper

Beginning from the point of view that process control of ore flotation can be approached by on-line analysis of processing behavior, an equation was developed which has characteristics useful for a multi-variable feedback loop. The application of this equation to optimizing control with a data acquisition system will be discussed in Part 11. OBJECTIVE OF CONTROL The purpose of developing a feedback method for concentrator control is to provide a means for determining ore processing behavior in order that data describing the ore can be used to make appropriate changes in control conditions while the ore continues to flow through the flotation circuit. In absence of simple linear relationships between pairs of variables in the flotation process, attention is directed to the need for a generalized relationship which possibly would incorporate all pertinent variables. It would be possible to apply such an equation to the control of variables in a concentrator in real time according to operational requirements as ore gradually changes in quality and processing behavior. To meet this objective, it is necessary to define relationships describing flotation performance in terms of performance variables capable of being measured on-line, either with on-line instruments and analyzers or with manual methods lending themselves to quick determination of meaningful information. Relationships derived to meet this objective form a model for the flotation process. The evaluation of flotation parameters of the ore and the execution of control on the basis of the derived information while the ore is continuing through the process would constitute a feedback control system. Data for the following control and performance variables can be made available: 1) ore feed rate, 2) collector addition rate, 3) lime addition rate, 4) pulp density, 5) assay or multiple assays in feed, tails, or concentrate sufficient for material balancing, 6) particle size distribution in flotation feed, 7) froth height, and 8) frother addition rate. Other process variables, such as flotation air input and mechanical agitation intensity, are usually not considered as control variables and were not taken into account in this analysis. Other data, such as that describing the ore, would be useful for concentrator process control. However, information of this type (such as ore hardness, grain size of the mineral, chemical species of the mineral, and ore surface properties) being not presently measurable in the on-line sense, has the effect of causing disturbances in the system which can be detected only indirectly. The process control system being sought must recognize disturbances by their effect on measured performance followed by determining control changes to compensate for them in meeting the objectives of improved performance (perhaps higher throughput, maximum return, etc.). A suitable model for the process having capability of recognizing the effects of ore disturbances should provide the means for introducing proper compensation through control changes. This would be done by processing on-line data with the model to calculate coefficients reflecting ore characteristics. This procedure can only be applied in a typical flotation system when on-line data can be processed at faster rates than the usual rate at which the ore in flotation feed takes on significantly different characteristics. For example, material balance data can be accumulated in approximately 5-min intervals using on-line X-ray fluorescence analysis. The flotation system time constant might be 15 min including grinding. Ore changes having time constants longer than 1 hr could be accommodated using on-line feedback control by this procedure. FORM OF A FLOTATION MODEL A suitable form for mathematical expression of the flotation process is an equation involving rates, when each of the components entering into the separation can be treated independently by a rate equation. A first-order, kinetic rate equation can be written on

Jan 1, 1967

Jan 1, 1967

By Merton C. Flemings, Harold D. Brody

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses are based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a plate-like dendrite morphology. The classical nonequilibrium freezing equation, Cs = kCo(I - fS)k-l accurately describes solute redistribution between dendrite arms for the solidification processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar inform to the classical expression. 172 addition, a numerical-analysis procedure is etnployed to examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of ternperatcre within the solidifying casting or ingol. SOLUTE redistribution in cellular and dendritic solidification has been discussed quantitatively in recent papers'-3 and in a series of earlier work.4-6 However, none of the analyses developed have permitted close correlation of theory with final solute distribution (microsegregation) observed in castings and ingots. In this paper, discussion is given of approximations which may reasonably be made in mathematical treatment of microsegregation, and analyses are presented based on these approximations. Numerical results are given for Al-Cu alloys. In a second paper the analyses will be compared with exeriment.7 CLASSICAL ANALYSIS The classical quantitative treatment of solute redistribution within a closed "volume element" has been derived repeatedly, for example by Gulliver,4 Scheil,' and Pfann.' This "classical nonequilibrium solidification equation" is written for constant partition ratio: where Cs = interface composition of the solid when the weight-fraction solid within the "volume element" is fs (weight fraction, wt pct); k = equilibrium partition ratio; Co = initial alloy composition within the volume element (weight fraction, wt pct). Assumptions of Eq. [11 are: 1) There is negligible undercooling before nuclea-tion, or from curvature or kinetic effects. 2) There is no mass flow in or out of the volume

Jan 1, 1967

By D. R. Uhlmann, T. P. Seward, K. A. Jackson, J. D. Hunt

microscopic ohservations on alloys of organic trzaterials show that dendrite arms can melt off under normal conditiorzs of growth. This occurs because of the interactiorz of' heat and matter fluxes during dendritic growth. The re melting occurs where the den-drite arms are joined onto the main deizclrite sterrz. Many detached crystals can be produced in this fashion. It is postulated that this remelting phenornenon occurs in metal alloys, giving rise to the equi-axed region in castings. Experiments peyformed orr castings of transparent materials support remelting as a primary source of detached crystals. Ob~ervations an equiaxed tones in metal castings are discussed in terms of this and other mechanisms. It is concluded that the partial remelting of dendrites is on important mechanisnl for producing the equiaxed regions in castings. THE freezing of a casting can be divided into three regions: a chill zone formed near the mold wall, a columnar region, and a third region, at the center of the casting, which is called the equiaxed zone. The origin of the grains that comprise the equiaxed region is the subject of this paper. We will first outline the mechanisms which have been proposed to account for the origin of the equiaxed region and discuss some recent experiments which cannot be explained by these theories. We will then present some microscopic observations of dendritic growth which have led us to conclude that the equiaxed zone in castings can arise from partial remelting of dendrites. This proposal is supported by observations on transparent castings. Finally, we will discuss several observations on metal castings which could not be explained previously, and which can be accounted for by the present proposal. Previous Mechanisms. Winegard and Chalmers3 pointed out that the molten central region of an ingot could be constitutionally supercooled, because of the solute layer at the growing interface. In this supercooled region, nucleation on particles could occur, giving rise to the equiaxed crystals. Another mechanism has also been suggested,4y5 that the nuclei originate in the chill zone then float or are carried by convection to the center of the casting, where they grow to produce equiaxed crystals. In this case, all the crystals nucleate immediately on casting, so this mechanism will be termed "big-bang" nucleation. Walker's Experiments. J. L. Walker has made observations on the solidification of nickel and Ni-Cu alloys which cannot be accounted for by either of the above mechanisms. In studying the grain size resulting from freezing of nickel at various undercoolings, walker6 found that at large undercoolings the grain size was small, due to mechanical nucleation, as discussed by walker7 and Horvay.' At small undercoolings, the grain size was large, and the growth dendritic. In Ni-Cu alloys, however, for initial undercoolings starting from just below the melting point and extending for a hundred or so degrees of undercooling, fine grains were also observed. Samples were undercooled 200 Centigrade degrees without nucleating, and were then heated 130 Centigrade degrees so that the undercooling was 70 Centigrade degrees, and nucleated. The samples had a small grain size, indicating multiple nucleation. There were no heterogeneous nuclei in the liquid which could operate at the temperature of growth. Constitutional supercooling could not have been greater than the supercooling of the initial melt, since the temperature rose as the freezing continued. walker -as also shown that a Ni-Cu alloy which can be undercooled to below its solidus will produce typical columnar and equiaxed regions when cast into a cold mold. This alloy could not reach a temperature below its solidus by constitutional supercooling. It could not, therefore, have nucleated heterogeneously. Neither the big-bang mechanism nor the Winegard-Chalmers mechanism can account for the fine grain

Jan 1, 1967

By A. Gene Collins

The Bureau of Mines undertook research to determine the bromide and iodide content of Mississippi and Alabama oilfield waters of the Tertiary and Cretaceous Period to determine genetic relationships of the ions, to determine their origin, and to determine their genetic relation to petroleum. The 280 samples were analyzed after a pretreatment to remove interferences. The iodide was oxidized to iodate and was titrated with thiosulfate. The bromide was oxidized to bromate and was determined iodometrically. A computer was used to calculate the correlation coefficients of iodide to bromide and to other ions. The other ions are sodium plus potassium, calcium, magnesium, chloride, bicarbonate, and sulfate. The mineral content of the samples ranged from 52 to 1,760 mg/l for bromide and from 2 to 65 mg/l for iodide. The mean bromide-to-chloride and iodide-to-chloride ratios were 0.0065 and 0.0002. The correlation coefficient matrix and linear plots indicated a definite bromide-to-calcium relationship for the brines investigated.

Jan 1, 1967

The mineralogy, maero- and micro-textures of Thackaringa ore are simple and have many counterparts among base metal-quartz-siderite vein type deposits elsewhere.The ore consists predominantly of galena, sphalerlte, chalcopyrite, tetrahedrite, and arsenopyrite in a quartz and siderite gangue. Silver minerals, as such, appear to be lacking and silver values are no higher than in other sulphide ores of this type. These features contrast very markedly with those of the A.B.H. Consols Lode which appears to have emanated from the north end of the Broken Hill Main Lode Horizon during high grade regional metamorphism. The Consols Lode has been regarded as of Thackaringa type, and both are regarded as possibly arising from the remobilization of Main Lode Horizon ore. Whilst this may yet prove to be so it appears that the marked differences in mineral composition between the Consols and the Thackaringa types, would require somewhat different modes of regeneration.Thackaringa ore, as well as A.B.H. Consols ore, on this basis, would necessitate the development of a metahydrothermal ore fluid to account for their present apparently hydrothermal (or pseudo-hydrothermal) constitution...

Jan 1, 1967

By Rodney P. Smith

The solubility of niobium carbide in y iron has been determined for the temperature range 1000" to 1300°C from the carbon content of a series of Fe-Nb alloys equilibrated with hydrogen-methane mixtures. The method is similar to that used by Darken, Smith, and Filer 1 to determine the solubility of aluminum nitride in y iron and by smith2 to determine the solubility of niobium nitride in y iron. The samples* were strips 1.2 by 3 by 0.035 cm. The niobium oxide.* For samples of composition slightly

Jan 1, 1967

By Warren E. Morrison

Demand for energy in the United States in 1965 was stimulated by the continuing expansion of the economy. A gain of 5.9 percent in gross national product for the year was accompanied by a 4.4-percent rise in energy consumption. Domestic energy resources met about 93 percent of the nation's requirements. The remaining 7 percent consisted of imported fuels, mainly of crude petroleum and residual fuel oil. The major fossil fuels-natural gas, crude petroleum, and coal, in that order-contributed 96 percent of all commerical energy utilized, with the balance of 4 percent being primary electricity from hydropower and nuclear power plants. Production was up for all of the major mineral energy resources in 1965, with the single exception of anthracite, output of which continued to decline. Bituminous coal output for the year was 512 million tons; marketed production of natural gas, 16,039 billion cubic feet; and crude petroleum output, 2,848 million barrels. Among the secondary products processed from primary energy resources, the most significant gains were in coal carbonized for coke which increased 6.7 percent to 95 million tons, and in the output of liquefied gases from natural gas which rose 4.8 percent to 11,257 million gallons (268 million barrels). Within the latter category, the off? take for petrochemical feedstocks continued to rise at a very rapid pace.

Jan 1, 1967

By Witold J. S. Ostrowski

Stabilization of water-bearing sediments by the freezing method for shaft sinking has been used for over 80 years on the European Continent. The real application of this method in Canada started with the development of the potash mines in Saskatchewan during the past fifteen years. The great depth to which it is applied creates a number of problems which have to be seriously considered by engineers in order to produce a safe and economical design. Freezing depth, thickness of the ice wall, number of the freeze holes, capacity of the freezing plant, pre-freezing time, etc., are the most important points which have to be established. Recent field experience in freezing to great depth in the Saskatchewan area is immensely interesting and important for further development of our potash mining and the application of the freezing method.

Jan 1, 1967

Jan 1, 1967

By J. E. Cannaday, R. J. Austin, R. K. Saxer

PREVIOUS investigators have determined activation energies and have postulated various controlling mechanisms for creep.'-' Recently Barrett et 01.I5 have suggested, as the result of their work with cadmium, that the apparent activation energies for creep (AHc) above 0.5 T, could be correlated by means of activation energies for self-diffusion (AHSD) and modulus of elasticity functions: AHC = AHSD - (5RT/E) dE/dT. The wide disparity of apparent activation energies previously obtained with nickel compared to those reported for other fcc metals and the desire to test the postulate of Barrett el al. prompted this study. The as-received 17.5-mil nickel wire used during this work assayed 99.87 pct pure, Table I. X-ray analysis indicated that the wire was in a stress-re- lieved state and metallographic examination revealed an equiaxed grain size of approximately 0.01 mm. Specimens degreased in acetone and cut to 1-1/2 in. lengths were tested in a cam-mechanized constant-stress creep machine. A vacuum of at least lo-5 mm Hg was maintained during all tests. Stresses were applied when thermal equilibrium was established. When a measurable (at least 0.5 pct) secondary creep was observed, the temperature was pulsed to a higher temperature. Pulsing time varied from 30 sec at 480°C to 2 min at 1300'C and above. Slopes of creep curves were determined after the initial acceleration in the strain rate had subsided and steady-state creep was achieved. To confirm the results obtained, additional tests were performed incorporating a temperature pulsing method suggested by sherby. In this method the load was removed during temperature pulsing and reapplied after thermal expansion had occurred. No appreciable differences in results were obtained. Tests were performed over a wide range of temperature (470" to 1310°C) and stresses (250 to 17,000 psi). The expression was used to calculate activation energies. In this expression T1 and T2 are the initial and final temperatures, and el and i2 are the creep rates at T, and T2. The variation of the apparent activation energies with the mean test temperature calculated by means of Eq. [I] are shown in Fig. 1. The mean test temperature (Tmean) was calculated from the relationship

Jan 1, 1967

By V. R. Miller

The Bureau of Mines investigated methods for testing the tensile and sheer strength of cast specimens of bulk solder and of soldered joints in order to increase the strength and extend the useful temperature range of soft solders. A spread-area test for determining the wettability of solder on copper surfaces was developed. Mannitol was used as a flux in spread tests to control spreading and to avoid plating, etching, and other side effects of regular fluxes. Data on commercial and high-purity solders obtained by these methods show more consistency than those reported by others from similar tests.

Jan 1, 1967

By R. O. Pynnonen

This publication is an analysis of reports to the Bureau of Mines of 44 fatal accidents that occurred during the operation of rubber-tired, front-end loaders in the mineral industry. The causes of the accidents, the nature of the work being performed, and recommendations for preventing similar accidents are included.

Jan 1, 1967

By R. V. Higgins

This report presents computer instructions for calculating the performance of three-phase flow of gas, oil, and water. The calculated results for an illustrative example are presented. The example is the waterflood of a reservoir containing free gas in the reservoir as a result of the partial depletion of the oil by the expansion of the gas initially in solution. The flood pattern for the example is a 5-spot.

Jan 1, 1967

By T. E. Scott, O. G. Koepke

DURING research currently in progress the need arose for interplanar angles and planar spacings to analyze crystallographic data obtained from hcp yttrium. In the absence of such existing information, a program was written in Fortran-11 language and processed on an IBM 7074 computer. The program and results have been assembled in report form to make them generally available.' Of the possible combinations of, only those most frequently encountered were employed. The ranges of h, k, and 1 involved were: However, not all combinations and permutations of the above appear in the tabulation because redundancies occur in several cases. Nevertheless, fifteen types of planes and all their equivalent planes have been included, giving a total of 109 sets of Miller-Bravais indices.

Jan 1, 1967

By W. W. Krech, T. E. Perkins

As fractures are propagated through rocks, energy is absorbed near the extending crack tip. Apparent surface energies for several rocks have been measured by cleavage under dynamic con-ditions. At nominal crack velocities from 0.5 to 500 in (min, measurements showed that fractures propagated in discrete jumps. Calculated surface energies and moduli were relatively insensitive to nominal rate of cleavage. in another set of experiments, rocks were cleaved under high confining stresses. The rocks were submerged in low leak-off fluids which formed a filter cake on the freshly cleaved surfaces (similar to the hydraulic lracturing process). Apparent surface energies were increased substantially as the surrounding fluid pressure was increased. Moduli in bending increased significantly upon application of the first 1,000 psi but were insensitive to stress level at greater pressures. INTRODUCTION For almost 20 years, hydraulic fracturing processes have been utilized effectively to stimulate oil and gas wells. During this period, some process improvements have resulted from studies of fracture orientation, mechanics of fracturing, areas generated, conductivities of cracks, etc. Yet many questions remain concerning the conditions and pressures needed during fracture propagation. In this paper we will report additional studies of the mechanics of fracture extension. It was shown previously3 that large rock samples could be cleaved under controlled conditions so as to measure the apparent surface energy (that amount of energy absorbed per unit area of new surface created). In this paper we consider the effects of two additional factors on surface energies, viz.: (1) effect of cleavage rate and (2) effect of confining stress level. THEORY Cleavage experiments were conducted on rock samples similar to that illustrated in Fig. 1. Blocks of rock several inches wide, 2- to 3-in. thick, and up to 3 ft in length were grooved longitudinally with shallow guide slots. A crack was initiated and allowed to extend along the web as the top of the rock specimen was pulled (or pushed) apart. Auxiliary equipment permits the measurement of (1) force applied at the top, (2) separation at the top and (3) crack length. (Further experimental details will be given in the next section.) The rock beams created by the crack are considered ton be cantilever beams. The deflection (or separation of the rock beams) at any point is calculated 4,5 by the beam Eq. 1.

Jan 1, 1967

By N. Mungan

A study was made of the effects of wettability and interfacial tension on the immiscible displacement of a Iiquid by another Iiquid from porous media. The influence of viscosity ratio was also investigated. Porous media used were polytetrafluoroethylene (TFE) cores prepared by compressing TFE powder under different pressures. lt is shown that displacement of a wetting by a nonwetting Iiquid is always less efficient than the displacement of a nonwetting by a wetting fluid, all other things being equal. In the former case, the recovery efficiency can be increased substantially by either reducing the interfacial tension or increasing the viscosity of the displacing fluid. A qualitative discussion is given on the implications of this work to the recovery of crude oil by water flooding. INTRODUCTION The high cost of oil exploration and new recovery schemes makes it imperative that waterflooding be conducted under conditions favoring most efficient oil recovery. To improve oil recovery by waterflooding, it is essential that the role played by interfacial forces in the entrapment of residual oil be studied and understood. Interfacial phenomena in natural rock, connate water and crude oil systems are very complicated because of the complexity of the natural liquids found in petroleum reservoirs, because of our inability to adequately describe the geometrical structure of the porous media and because of a lack of understanding of physical and chemical interactions between the liquids and surface of the pores. The problem becomes further complicated when one tries to elucidate the role of interfacial phenomena in fluid flow. Numerous studies of the displacement of oil by water under different interfacial tension or wet-tability conditions have been made.lm3 These studies have been performed in silica, alundum or sandstone systems using water and paraffin oil and also some surface active material to control the interfacial tension s and the contact angle 0. Unfortunately, the high energies of various interfaces involved favor adsorption and orientation of the surface active material at the interfaces. Also the surface active material concentration at the interfaces exceeds that in the bulk of the liquid phases. Such surface excess may cause the surfactant distribution, the contact angle and the interfacial tension to differ from their measured static equilibrium values and makes interpretation of the displacement experiments difficult. Furthermore, as changes in s also lead to changes in cos 0, the role played individually by one of these parameters in the displacement becomes obscured by the effect of the other. To circumvent these difficulties, a low surface energy solid and true solutions or pure liquids should be used. Use of a low surface energy solid minimizes adsorption and orientation effects at the solid-liquid interfaces. By controlling s and cos 0 through use of selected pairs of pure liquids or true solutions rather than by surfactants, the adsorption effects at liquid-liquid interfaces are eliminated. In the present study TFE cores were used as the porous media. Liquids used were water, sucrose solutions, paraffin oils and benzyl, n-butyl and isobutyl alcohols. The interfacial tension was varied from 40 to 1.1 dynes/cm by suitably choosing the liquid pair. A surface active material was added to the water-oil system only in the case where interfacial tension of 0.5 dyne/ cm was desired. No precise changes of cos 0 were attempted. However, either the displaced or the displacing liquid could be made the one which preferentially wets the TFE surface. Using sucrose solutions and blends of paraffin oils proved to be a convenient way of changing the viscosity ratio between the displaced and displacing liquids. The present investigation examines the effect of interfacial tension, wettability and viscosity ratio on the immiscible liquid-liquid displacement from porous media. Observed data permit a

Jan 1, 1967

By B. E. Eakin, A. L. Lee, M. H. Gonzalez

Expeximental viscosity and density data of lour natural gases are presented for temperatures from WO to 340F and pressures from 100 to 8.000 psia. A correlation is also discussed and results reported. INTRODUCTION This investigation is one of several efforts by the authors to provide viscosity data for pure hydrocarbons and mixtures. Results of some pure hydrocarbons and their mix tures have been presented." Several predictive methods and correlations have also been reported.'," This paper presents the experimental viscosity and density data of four natural gases and confirms a correlation in a previous study. APPARATUS The viscometer was described previously. 2,6 A bank of stainless steel pycnometers was included to determine density in conjunction with the viscosity measurements (Fig. I). DATA AND MATERIALS The natural gases were furnished by the Atlantic Richfield Co. (Samples 1 and 21, the Continental Oil Co. (Sample 3) and the Pan American Petroleum Corp. (Sample 4). Table 1 shows the composition of these gases obtained by mass spectrometer analysis. The pure component viscosity data used in the correlation have been published."".'"', '" Experimental and calculated viscosity data for the natural gases are presented in Tables 2 through 5. CORRELATION Starling and Ellington"' have reported several semi-empirical expressions based to a certain extent on the theory of viscosity advanced by Born and Green.' The final expression presented by Starling and Ellingto'n is: i'. (micropoise) -- /t,, exp rX(7') p ..... (I) Eq. 1 was modified by Lee et 01." to represent mixture and pure component data simultaneously. This equation has the form: F = K exp [XpY] :.........(2) where K=- (7.77 i 0.0063M)Ti 122.4 + 12.9M +T .................(3) ' ' ' X= 2.57 + ---1914.5+ 0.0095M .... (4) Y = 1.11 -r 0.04 X ........(5) Over the pressure and temperature range studied in this investigation, this equation represents the data on methane, ethane, propane, n-butane and four methane-n-butane mixtures with a standard deviation* of ? 1.89 per cent. Density data by Sage and Lacey" were used to fit the equations. Eq. 2 gives reliable values of the viscosity of light hydrocarbons without prior knowledge of experimental viscosity values, but accurate density data must be available. Eq. 2 was used to predict viscosity values for the natural gases studied in this paper. The particular set of parameters contained in Eqs. 3 through 5 gave values that reproduced experimental data within 25 per cent. Needless to say, in using Eq. 2 better density values will give better viscosity results. However, those engineers who do not have accurate density values at hand or the time, or such facilities as a library, computer, etc. readily available, may feel uneasy in using Eq. 2. Therefore, the authors sought the easiest but by no means best density prediction method, which was reported by Kaf 30 years ago. A set of density values, which were calculated based on Kay's method, and a generalized compressibility factor chart were used to fit Eq. 2. The results are:

Jan 1, 1967