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By John R. Spencer

A capillary tube variable volume cell is described, which has operated satisfactorily over a range of 100°F and 3,500 psi to 550°F and 1,500 psi. The cell contents are entirely visible over the length of the capillary with the exception of a space at the top amounting to three per cent of the total volume. Observations on the critical behavior of simple systems have been greatly facilitated by the apparatus, it being possible to establish the critical conditions for a particular mixture in the course of a day's run. INTRODUCTION Many types of apparatus have been designed for obtaining data on the phase relationships of hydrocarbon systems. Such apparatus can in general be subdivided into two classifications; (l), indirect measurement of phase volume, and (2), direct visual observation of phase volume, each of which has outstanding advantages and disadvantages. Indirect measurement of phase volume requires the use of rather elaborate apparatus including internal probes in which are located the device for determining the locus of the interface between phases. Such equipment is by its very nature costly, and is complex from the standpoint of operating technique. Probing techniques can be used, however, over wide ranges of temperature and pressure with a high degree of reproducibility. Apparatus for visual observation of phase behavior obviously has the advantage of enabling the experimenter to see exactly what takes place, but because the material to be tested is contained in a cell constructed of both metal and glass, is limited severely as to the temperature range of operation. Furthermore. the maximum pressure usually is limited by the choice of material used for sealing the glass to the metal, and by the strength of the glass itself. In the interest of increased efficiency of observation, as much of the cell as possible should be visible to the eye. Glass capillary tubes have been used successfully but have always given difficulty at the metal-to-glass seal. An apparatus has been devised to overcome the problems of sealing and resistance to temperature effects that have heretofore been the limiting factor with glass apparatus in the observation of phase volumes at elevated temperature and pressure. APPARATUS The objective which dictated the general arrangement of the apparatus (Figs. 1 and 2) was simplicity of operation. The air bath, A, was constructed of an iron framework to which was attached approximately one inch of glass wool bats which were covered on the outside with "Masonite." A roughly octagonal center piece was installed to provide forced circulation of the air by the fan, B, past the heaters, D, cell, F, and thermoregulator, C, respectively. The entire top of the box is removable to facilitate charging of the cell and to permit easy maintenance. Two windows are provided before and behind the cell to allow the operator to observe the contents against the background fluorescent light, E. The heaters,

Jan 1, 1951

By Nathaniel Arbiter

T. M. Morris (School of Mines and Metallurgy, Rolla, Mo.)—Rate studies promise to help quantify flotation operations. The author's exposition of rate studies is therefore laudable. However his exposition of a second order rate equation rather than a first order rate equation is not convincing. It is important to use the correct equation, otherwise erroneous conclusions may be drawn. The data assembled by the author and plotted according to a second order rate equation can be plotted according to a first order rate equation. As a matter of fact much of the data used reveals that a second order rate equation is not applicable. According to the method used by the author for plotting data, the reciprocal of the slope of the line is the maximum possible recovery. Physically this cannot exceed 100 pct, yet several graphs yield maximum recoveries greater than 100 pct. For example: l—Curve 2, Fig. 1 yields a value of 120 pct; 2—Curve 2, Fig. 2 yields a value of 115 pct; 3—Fig. 7 yields a value of 110 pct. The real test of the graphical method is, as the author points out, whether or not the earliest points agree with a straight line. The second order rate plot does not fulfill this requirement. Fig. 10 shows the data used by the author to obtain Curve 2 in Fig. 1, plotted according to both a second and first order rate equation. Fig. 11 shows the two rate plots made from data published by Ludt and DeWitt.19 In Fig. 10 the first order rate plot gives a very good fit and obeys the boundary condition of passing through the origin. For the second order rate plot a straight line can be drawn through the last three points but the earliest points are not in agreement with this line. The reciprocal of the slope of the straight line gives a value of maximum possible recovery of 112 pct. The maximum possible recovery according to the first order rate plot is 78 pct. In Fig. 11 the first order rate plot again fits all of the points very well and passes through the origin. The second order rate plot shows wide deviation of the earliest point, indicating that the second order rate equation is not applicable. The reason for the fit of data to the second order rate equation during longer flotation times is that R, the cumulative percent recovery, changes slowly toward the end of the flotation operation, so that when t/R is plotted against time, one is, in effect plotting t against t and one would certainly expect a straight line. The author attempts to show that the second order rate equation is correct by citing evidence which shows that recovery is a function of initial concentration. This is a debatable point especially since, in the author's original presentation of this paper at the St. Louis

Jan 1, 1952

By W. J. West, T. D. Mueller, J. E. Warren

Two methods are used to obtain the relatiorlship between ratio of gas to oil permeability and gas saturation. One method is to calculate a curve from field measurements of reservoir behavior: the other is to measure the relationship on a core .sample in the laboratory. The curves resulting from these TWO methods arc often comparer1 and seldom found to agree. The most important reason for the nonagreement is often overlooked. This reason is that the performance k9/k0 curve is calculated with the assumption of uniform pressure and saturution throughout the reservoir. To show the differerence between performance type kg/k0 curves and laboratory type kg/k0 curves. two performance type kg/k0 curves for two different production rates were calculaled from the production perforrnance of a hypothetical reservoir for which a laboratory type curve was assumed. Production performance of the hypothetical reservoir bras calcu- lated by use of international Business Machine's 701 Computer. The perfortnance type kg/k0 curves differed from the laboratory curve for the hypothetical reservoir. The performance type crrrve for the lowest production rate most nearly coincided with the laboratory curve. INTRODUCTION Predictions of oil reservoir performance are often made with the aid of complex numerical calculations. An important quantity required in these calculations is the ratio of gas permeability to oil permeability (kg/k0 )at a particular gas saturation. Two methods arc used to obtain a relationship between this ratio and gas saturation. The curves resulting from these two methods are called performance kg/k0 curves and laboratory kg/k0 curves. The performance curve is obtained from field measurements of reservoir behavior. Particular kg/k0 values are calculated from the producing gas-oil ratio, the cumulative reservoir withdrawals, the original oil in place, the average reservoir pressure, and the PVT properties of the reservoir fluids. The particular kg/k0 values are then plotted against the average rcservoir gas saturations for the entire history period. In order to use this derived kg/k0 relationship for performance predictions, a curve through these points is extrapolated to higher gas saturations. The laboratory kg/k0 curve is obtained from measurements made on core samples. Saturation is maintained uniform throughout the core during these measurements. The kg/k0 curves obtained with these two independent methods are often compared and seldom are found to be the same. Various reasons have been offered for the lack of correlation. One is that insufficient core? were obtained to derive a curve representative of the reservoir rock. Another is that laboratory methods have failed to reproduce reservoir conditions. The most important reason for the noncorrelation has been often overlooked because of the difficulty in evaluating its effect. This reason is that the performance or field kg/k0 curve is calculated with the assumption of uniform pressure and saturation throughout the reservoir. In any

Jan 1, 1956

By Louis A. Panek

THE purpose of this paper is to present a method of designing safe and economical arch structures that are to be constructed of concrete or directly of original earth materials. The experimental data used to illustrate the design method are taken from Bucky and Fentress,1,2 and the application of the ideas presented by them is extended by obtaining an additional set of curves from which arch structures may be designed. This design method is based upon the following principles of similitude: A scalar model made of the same material as that of the full sized structure will behave similarly to its prototype if the density of the model is increased in the same proportion as its linear scale is decreased. Let R represent the scale or model ratio, namely, the ratio of a prototype linear dimension to the corresponding model linear dimension. The effect of increased density may be obtained by rotating the model in a centrifuge at a speed such that the centrifugal field exerts on the model an accelerative force R times the accelerative force of gravity. Under these conditions; (I) model unit stresses are equal to corresponding prototype unit stresses, (2) the ratio of the prototype deformation at a given point to the model deformation at a similar point is equal to the scale ratio, R, and (3) the model and the prototype will behave similarly within and beyond the elastic limits of strain. According to the above relations, such models can be used to solve the following problems: I. The dimensions of the most economical safe arch structure for a given load. 2. The maximum safe roof span underground for given geologic conditions. The procedure is described briefly as follows. Tests are made by rotating in a centrifuge a number of models that repIesent a variety of prototype loads and dimensions. From the experimental data, curves are plotted to show the relations between these loads and dimensions. The curves are used to solve directly the problems stated above. Structural design is based upon the working (safe) stress of the material of construction, which is established by applying a factor of safety to the experimentally determined ultimate strength of the material. In conformity with this principle, each model is gradually loaded until failure occurs. A safety factor is then applied to the results. If a safety factor of 4 is used, a given model at failure represents a safe prototype, the linear dimensions of which are equal to one-fourth the model ratio at failure times the corresponding model dimensions. The safe model ratio is computed from the following formula: [Safe R = (rl 47r2n2r _ 7r2n2r~r~ \4/ gg in which: n = centrifuge revolutions per second at model failure; r = radius of rotation of the model in feet; g = 32.2 ft/sect.]

Jan 1, 1947

US 4,137,751-Aerial geophysical exploration for ore deposits by collecting and analyzing atmospheric particulates The aircraft has an Inlet duct extending outward and including a "shave-off" duct, a cyclone separator located inside the cabin which is coupled to the inlet duct, a clean air exhaust duct, and a receiver for the collected particles incoming air is divided into two fractions. The fraction taken by the "shave-off" duct and containing the bulk of the particles is routed to the cyclone Particulates are gathered on a collector tape for subsequent analysis and correlation with the areas covered J. R Rhodes, R D. Sieberg, M. C Taylor, J. C Westkaemper, and R C. Young, assigned to Columbia Scientific Industries, Inc Feb. 6, 1979 7 pp. (73-28) Filed- 2-28-75 (554,114) Same British 1,446,760, dated Aug. 18, 1976. US 4,156,138-Exploration for subsurface deposits of uranium ore Pairs of dosimeters are placed underground in a grid pattern Each dosimeter contains a phosphor which IS capable of storing the energy of alpha particles. One dosimeter is heavily shielded from alpha particles, while the other in the pair is thinly shielded to exclude dust After a period underground the dosimeters are heated to release the stored energy as light. The amount of light produced from the heavily shielded dosimeter is subtracted from the amount of light produced from the thinly shielded dosimeter to give an indication of the location and quantity of uranium underground This patent is a division of US Patent No 4,053,772, dated Oct 11, 1977 P E Felice, assigned to Westinghouse Electric Corp May 22, 1979 5 pp (250-253) Filed. 8-12-77 (824,203) US 4,180,727-Method for measuring the gamma-gamma density of uranium ore in the vicinity of a borehole A first gamma-ray detector receives only natural gamma rays from the borehole, while a second receives both natural gamma rays and scattered uranium-source gamma rays The value of the uranium-source gamma rays is calculated. W W Givens, assigned to Mob11 011 Corp Dec 25, 1979 6 pp (250- 264) Filed 10-20-77 (843,909) US 4,180,72&A neutron activation probe for determining the location and grade of uranium ore, especially where thorium or other fissionable isotopes are present, includes a pulsed neutron source in series with a plurality of delayed neutron reactors for measuring radioactivity in a well bore- hole together with a Nal(T1) counter for measuring the high energy 2 62 MeV gamma line from thorium The signal from the Nal(T1) counter IS subtracted from the signal from the delayed source detectors to ascertain the amount of uranium present in the ore body N. P Goldstein and R C Smith, assigned to Westinghouse Electric Corp Dec 25,1979 6 pp (250-264) Filed. 4-1 1-78 (895,323)

Jan 1, 1980

By A. D. Dorenfeld

Factorial design is a mathematical method of drawing valid conclusions from a series of tests made in a predetermined pattern. It is applied to flotation ore testing using, in this case, five variables, each varied twice, requiring a total of 32 tests. Representative conclusions are checked by repeat testing. THE factorial design method of testing is particu-J- larly applicable to mill-scale plant tests because 1—the conclusions take into consideration all variabilities of the plant, 2—there are no subjective guesses as to the conclusions, 3—the number of tests necessary to check large numbers of variables are at a minimum, and 4—interactions between variables can be discerned. It is equally applicable to laboratory testing because once the variables to be investigated have been decided upon, as well as the number of levels for each variable, a well-trained assistant can run the tests, since the test work follows a predetermined mathematical pattern, leaving the conclusions to be found by the person in charge. The conclusion takes into consideration all errors of the tests. To illustrate the use of factorial design, a sample of copper porphyry ore was tested, the copper content of the batches not being uniform. Five variables were investigated, each at two levels, requiring only 32 tests. After suitable arithmetical analysis, conclusions for copper recovery and concentrate grade are arrived at. Four cases of these conclusions are checked by repeat testing. Testing Methods Reproducibility of flotation tests varies widely, depending on the experimenter, the process, the equipment, and probably a host of unknown and perhaps interacting variables. If the reproducibility of tests is good, let us say to 0.2 pct recovery of a certain metal, and the minimum difference between tests upon the variation of the interested variables is, say 1 pct, then simple averaging and inspection is ample in interpreting results. However, often such a happy situation is not the case. This is particularly true in mill-scale operations where the ores are variable, and a host of minor operating fluctuations common to most milling, and familiar to all mill operators, is the normal state of affairs. Yet, mill scale tests are run, the results averaged, and conclusions drawn therefrom. The trustworthiness of such results should be measured by comparison to the experimental error—the measure of the degree of reproducibility of the results. This comparison is a test of significance. Thus, if daily results of recoveries average 80.0 pct, and a spread of 78.0 pct to 82.0 pct, is recorded, then, clearly, on changing mill operations, an 81 pct recovery cannot be construed as significant by using averages, since it is well within the previous test limits. By using rigorous statistical tests of significance, conclusions arrived at by inspection or simple averaging may be shown to be based on inadequate evidence or even wrong. In any event, a plant super-

Jan 1, 1952

By M. H. Cullender

The performance characteristics 01 gas wells producing from formations which fail to stabilize within a relatively short period of time are obscured by the interrelation of the coefficient (C) and the slope "n" of the conventional back-pressure curve q = C(P2 f- p2s)n An empirical method is presented whereby the characteristic or true slope (11) of the back-pressure curve may be determined for a particular gas well. For those gas wells which do not stabilize within a relatively short period of time, the coefficient (C) is considered as a variable with respect to time and as a constant only with respect to a specific time. Thus, the back-presrure performance of such a well is presented as a series of parallel curve5, each curve representing the performance of the well at the end of a given time interval. Through use of the method presented, a simple presture gradient is developed and maintained within the drainage area around a producing gas well during the test period in order that the variation of the coefficient (C) with respect to time does not obscure the true value of the lope. INTRODUCTION The back-pressure method of testing gas wells as set forth by Schellhardt and Rawlins1 is dependent upon the requirement that a series of flow rates and corresponding pressure data be obtained under stabilized conditions. These data arc then plotted on logarithmic coordinates of flow rate (Q) vs difference in squared pressures (P2f — P2s) in order to determine the constants (C) and (n) for Equation 1. With respect to this method of presenting the performance characteristics of a gas well, it should be pointed out that although Equation 1 is an empirical relationship, the form of the equation was justified to a considerable extent by an independent development by Muskat and Botset.2 This development was theoretical in nature; however, certain assumptions with respect to the type of flow existing (viscous vs non-viscous) were madc which may or may not be correct. As the use of the method presented by Schellhardt and Rawlins spread through the industry, it became evident that the method of testing was applicable for those wells which approached stabilized prbducing conditions within a relatively short period of time. Performance characteristics could not be determined by this method, however, for wells which approached stabilized protlucing conditions slowly over a considerable period of time. This characteristic of "slow stabilization" has generally been associated with gas wells producing frorn reservoirs of low permeability. As the demand for natural gas continued to grow through the years, a great number of wells were completed in reservoirs of low permeability which exhibited "slow stabiliz:~tion" characteristics. Consequently, the problem of determining the true performancc characteristics of these wells became more apparent. It is with this problem in mind that the isochronal performance method of determining the flow characteristics of gas wells is presented.

Jan 1, 1956

By Dorsey Hager

North Central Texas has recently become a center of interest for the oil men of America. The bringing in of the McClosky well at Ranger, Eastland County, and the shallow pool at Brownwood, Brown County, in 1917, has stimulated interest in this area to fever pitch. Oil men from all over the United States are now investing there. The area of present interest is shown by the accompanying map (Fig. 1). The money spent in leases runs into millions of dollars. It is no exaggeration to say that a strip of country 200 miles (321 km.) long and 125 miles (201 km.) wide, comprising some 15,000,000 acres (6,070,310 ha.), has been leased practically solid at a cost for rentals and bonuses of at least $1 per acre. The test holes contracted for will certainly number 400, at a cost of at least $5,000,000. From what has been done in the past six months, $20,000,000 at least will be spent. To pay returns on this amount of money, new production to the extent of at least 12,000,000 bbl. must be obtained. At present, the production from new fields will not average over 5000 bbl. per day; three wells at Ranger are producing 3000 bbl.; 250 wells at Brownwood produce 1000 bbl.; and the Gray well, Coleman County, is as yet an unknown factor. However, at Ranger there is every indication of developing a good pool covering from 1500 to 2000 acres (607 to 809 ha.), more or less, but the wells are deep, 3400 to 3800 ft. (1036 to 1158 m.), and cost $35,000 to $40,000 to drill. Large wells are necessary to pay for such expensive holes. As new wells are drilled, the gas pressure will be lowered rapidly, and large production need not be expected. For those oil men who expect a second Cushing or an Eldorado, Ranger holds little of promise. At Brownwood, Brown County, there are some 250 shallow wells (depths from 200 to 350 ft.) averaging 4 to 7 bbl. per day. There is a chance of an extensive producing area for these shallow sands to the southwest, and the opening of several thousand acres of shallow oil territory, and also some promise of deeper oil horizons in the Ranger horizon, but probably all under 2500 ft. At present, the lease brokers and speculators, and only a handful of oil men, have made any money. More fields must be developed, and it is more particularly with these possibilities that this paper deals. Lack of water for drilling purposes has undoubtedly held back development so far this year; this part of Texas has had a drouth for two years and there is an actual scarcity of water. Geological investigations so far undertaken cover nearly all the area outlined, and while pakt of the

Jan 1, 1920

By J. E. Lawrence

Copper-decorated lattice disorders in silicon have been analyzed by electron transmission microscopy, chemical etching, and P-N junction reverse current measurements before and following different gettering treatments. Lattice disorders acted as the nucleating sites for copper precipitation. Copper precipitates in silicon resist chemical etching, absorb electron beams more than silicon, and cause excess reverse currents. Totally gettered disorders will chemically etch rapidly, be transparent to electron beams at extinction contrast, and not contribute to excess reverse currents. Three different gettering procedures were performed to determine the effectiveness of different EXTRANEOUS metal contamination can alter the minority carrier lifetime and resistivity of bulk silicon as well as cause excessive reverse currents in semiconductor devices. Previous workers have reported such activity for gold,1,2 copper,'-* iron,' and rnanganese.2,5 Gettering is a method employed to render these impurities electrically inactive. However, some property of the junction-degrading metals prevents gettering procedures from being wholly reliable. The comparative effectiveness of gettering with different agents has been the topic of earlier publications.2,3,6-11 Two mechanisms for gettering metallic impurities have been proposed: the distribution coefficient mechanism by Thurmond and Logan7 and the compound formation mechanism by Goetzberger and Shockley.2 Both of these models evolved from data gettering mechanisms. First, phosphorus was allowed to enter a protective SiO2 film but remain away from the Si-SiO2 interface to test the effectiveness of the compound formation gettering mechanism. Second, phosphorus was allowed to enter the backside of silicon wafers to test the effectiveness of the lattice strain gettering mechanism. Finally, nickel was diffused into the backside of silicon wafers to test the effectiveness of the distribution coefficient gettering mechanism. In each case, copper precipitates dissolved as a result of the gettering treatment. Tightly packed precipitates will resist gettering more than loosely packed copper precipitates. acquired by the electrical analyses of gettered semiconductor materials. An electrical analysis, however, cannot identify the fate of the gettered metals. The radiotracer technique has recently been applied to determine the redistribution of metals following different gettering treatments.3,9,10 The spatial resolu tion of the radiotracer technique prevented the analysis of metal precipitates which contribute to the excessive reverse currents of P-N junctions. The gettering processes employed by the earlier workers, almost without exception, allowed the gettering agent to enter the silicon lattice. This procedure makes it quite difficult to differentiate between the distribution coefficient and the compound formation mechanisms. The metallographic analysis of gettered copper precipitates discussed in this work supplements the earlier work by obtaining direct evidence of silicon lattice defects decorated with copper before and following different gettering treatments. The effectiveness of a process which restricts the gettering agent, phosphorus, to a dielectric film and thus away from the silicon lattice is discussed in addition to the ef-

Jan 1, 1969

By Edward W. Mehal

This paper presents a review of the technologies which have been used in the application of III-V compound semiconductors to integrated circuits and arrays. These materials have properties which make them useful for various devices such as: light emitters, sensors, microwave sources, and microwave diodes. Technologies for incorporating these devices into integrated circuits have been reported and processes developed for fabricating planar devices using selective epitaxial deposition or selective diffusions. Isolation methods utilizing semi-insulating GaAs, oxide isolation, and ceramic insulation have also been reported. These techniques, and the devices and circuits produced or proposed are discussed. AFTER the invention of the silicon-integrated circuit, methods for utilizing compound semiconductors for integrated circuit applications were proposed. The scope of applications was potentially much broader because of the range of properties available from these materials. There also was the opportunity of coupling these properties with germanium and silicon devices to realize functions and circuits which could not be produced with silicon monolithic circuits. Table I exemplifies the range of electrical properties available in III-V compound semiconductor materials which are currently being widely used. A wide range of sensor and emitter applications result from the range of band gap. The band structure of GaAs and GaAsxP1-x permits their use as microwave oscillator source, and the high electron mobilities further facilitate their utility in microwave devices. The concept of "integrated functions"1 results from the availability of these materials and methods for utilizing their special properties. Heteroepitaxial growth allows the fabrication of a monolithic block of these materials. Semi-insulating GaAs permits the attainment of electrical isolation between components in a monolithic block without resorting to p-n junction biasing or oxide isolation methods. An "integrated function" is a unit which can perform a system or subsystem role and perform a number of electromagnetic functions. These functions could include sensor or input transducer, signal processing, interconnections, and control or output function. Two examples which demonstrate this concept are an optoelectric processor and a microwave receiver front end. The optoelectronic processor, Fig. 1(a), would consist of a light sensor, signal processor, and output emitter. The sensor could be InSb or InAs which would be IR-sensitive. The signal from this sensor would then be amplified and transmitted to the light emitter. The amplifier could utilize GaAs bipolar or field effect transistors. A Gap emitter would then produce visible radiation. The microwave receiver front end, Fig. l(b), would consist of a local oscillator section and a mixer section. A signal input from an antenna is mixed with the signal from the local oscillator. The local oscillator signal is produced by a Gunn oscillator. The single-ended mixer utilizes one Schottky barrier mixer diode. The IF signal would then be amplified further and suitably displayed. A further extension of the capability of utilizing the

Jan 1, 1969

By C. W. Spencer, F. G. Hochgraf, R. F. Cheney

Columnar grained specimens of nickel, containing 0.25 pct Si and 0.22 pct Mn, have been exposed to liquid bismuth in the temperature range 670° to 1050°C. Under isothermal conditions the liquid penetration rate is constant. The activation energy for the process is 22,000 cal per g-atom. Small amounts of plastic deformation, introduced into specimens prior to exposure, increase the penetration rate. The slou. step in liquid film penetration is associated with a reaction which occurs at or near the leading edge of the film. Either transfer of nickel across the liquid-solid inteqace or diffusion in the grain boundary ahead of the liquid film is suggested. Aliquid metal, if brought into contact with the surface of an unstrained solid metal, will usually penetrate to some extent into the grain boundaries of the solid. Under isothermal conditions the extent of penetration after any particular time of exposure is related to the relative magnitudes of the interfacial tensions concerned.1,2 If the liquid-solid interfacial tension is less than one-half the grain boundary tension the liquid may penetrate at a relatively rapid rate for an indefinite distance into the grain boundary surfaces. If the liquid-solid interfacial tension is greater than one-half the grain boundary energy, liquid penetration occurs at a continually decreasing rate so that after the liquid has penetrated to a relatively short distance below the surface the process essentially ceases.3 Many observations of a qualitative nature concerning inter crystalline attack by liquid metals have been reported, for example, liquid bismuth upon copper,' liquid mercury upon brass,4 and liquid mercury upon nickel.' Scheil and Schessl determined the rate of penetration of liquid bismuth into the grain boundaries of hot rolled copper rod? At constant temperature, penetration rate was found to be independent of the depth penetrated, the rate in- creasing with increasing temperature corresponding to an activation energy of 20,000 cal per g-atom for the process. It was suggested that at lower temperatures the liquid travelled mainly along lines of three grain intersections while at temperatures greater than 1000°C essentially all grain boundary surfaces were covered. Recently, in a study of copper bicrystals having a common [loo] axis it was found that at 649°C bismuth penetrated 22, 25, and 63 deg boundaries while it did not penetrate 2, 12, 15, and 72 deg boundaries.' Elbaum reported that liquid gallium penetrates aluminum grain boundaries to a depth of 0.6 cm after 11 hr at 27°c.8 Assuming that the rate controlling step in the process was diffusion down the liquid film to the specimen surface, a diffusion coefficient of 10-5 cm2 per sec was calculated. This paper reports a study of the penetration of bismuth-nickel liquids into the grain boundaries of a nickel alloy, containing 0.25 pct Si and 0.22 pct Mn as principal alloying elements. The phase diagram

Jan 1, 1962

By C. D. Michaelson

Bridging the gap between have and have-not nations is one of the necessities of the present era. The responsibility for accomplishing this must be assumed by the affluent industrial societies of the world, both through their governments and through private enterprise. Despite a discouraging number of instances where companies established in underdeveloped countries have been expropriated, U.S. industry must not abandon such ventures. Instead, it should tailor them to the needs and aspirations of the host nations. One way in which industry can minimize the danger of expropnation is to enter into partnership with the government of the host nation. Kennecott Copper has recently done this in Chile, becoming 49% owner of a company formed to expand and operate the El Teniente mine. So far, the partnership has produced marked benefits not only for Chile, but also for Kennecott. The memory of D.C. Jackling serves chiefly to remind us how much we owe to the pioneers of our industry. Jackling was one of the giants. Orphaned at the age of two, he made his way through sheer persistence and plain hard work. His brilliance gave rise to a vision, and his tenacity made his vision a reality. Foreseeing that economies of scale would make the handling of low-grade ore profitable, he introduced the revolutionary concept of open-pit copper mining. During World War I, the defense effort of the United States was irnrneasurably strengthened by the tremendous supplies of copper from the western mines that Jackling had made possible. Again in World War 11, the demands for copper were supplied, and the nation once more had profound reason to be grateful to this rugged, stubborn man who had long ago ventured into the mountains and unlocked their wealth. We are now embarked upon another great era of change, and we must devise new concepts to meet it. The task is not only to create new techniques of mining, but to forge better ties between men and institutions which will let us work in harmony with the techniques we have. We might recall that while Jackling was a man of towering pride and formidable will, he was also adept at getting others to share his vision and join his purpose. Today our reach for cooperative endeavor must go far beyond our own shores as we seek to develop the buried riches of distant lands. And we would do well to remember that Jackling's remarkable insight would have come to nothing had not British investors been willing to provide much of the initial capital. As was true of so many early enterprises in America, European capital was absolutely essential. CORPORATIONS ABROAD - AN EXPANDING ROLE Today the situation is quite different. The United States is now a capital-surpIus nation and looks abroad for opportunities to employ its capital profitably. On the other hand, we have become dependent on foreign sources for supplies of vital raw materials, while we seek

Jan 1, 1970

By W. S. Potter

The proportions of manganese and carbon in manganese steel are familiar to all…

Jan 1, 1915

By H. L. Teichman, E. M. Sipprelle

ENACTMENT' of Public Law 290 by the 78th Congress authorized the U. S. Department of the Interior, Bureau of Mines, to conduct an experimental program to develop the technology for obtaining oil from oil shale. In adopting and later extending this legislation, the Congress recognized the impending necessity of supplementing ground petroleum reserves with synthetic fuels. Under the provisions of this legislation, the Bureau of Mines, among other things, was charged with the responsibility of developing mining techniques, methods, and equipment for mining the oil shales of the Green River formation of Colorado, Utah, and Wyoming. The oil shales of western Colorado are apparently richer, more accessible, and more amenable to exploitation than elsewhere in the Rocky Mountain region. The site chosen for the Bureau's Experimental mine is about 10 miles west of Rifle in northwestern Colorado. It is within a 1000-sq-mile area from which, it has been estimated, 300 billion barrels of shale oil could be produced from a 500-ft measure near the top of the formation. One hundred billion barrels of this amount could be produced from the Mahogany ledge, a 60 to 100-ft section near the bottom of the 500-ft measure. This ledge is considered to have economic importance at present. The Green River formation was laid down as sediment in the bottom of vast, shallow inland lakes during Eocene time. The deposit is flat-lying, and there are no faults, fissures, or local rolls. Oil shale is actually a strong, tough magnesium marlstone, which will stand unsupported over relatively wide spans. These and other natural physical characteristics favor mechanized, low-cost mining, which is essential for establishment of an oil-shale industry. It was realized from the outset that an extensive research program would be necessary to develop mining methods, equipment, and techniques for a mechanized, low-cost operation. The program was designed to include research. into all the productive phases of mining, such as drilling, blasting, loading, transportation, and maintenance of the mine structure. The methods, equipment, and techniques developed as a result of this research have established a production of 116 tons per man-shift total labor at a direct cost of $0,292 per ton. Another important phase of the research program that has received little publicity because of its theoretical nature is study of the roofstone behavior and determination of mine structure stresses. This paper purposes to discuss this phase of the research program. Preliminary studies of the physical properties of the Green River oil-shale formation were made in the Barodyramics Laboratory at Columbia University during the latter part of 1945 and the early part of 1946.* The purpose of these studies was to determine the maximum size of unsupported underground openings that would be commensurate with safety and still permit the use of large, efficient mining equipment. Also to be determined were the pillar support to extraction ratio and the shape, size, and spacing of supporting pillars. Selected samples of possible roofstones near the top of the Mahogany ledge, as well as representative samples of different rock types found within the ledge, were obtained from the Bureau's oil-shale mine for these studies. The maximum safe unsupported roof span calculated from this work was 200 ft. Using a safety factor of four, it was theoretically determined that openings 60 ft wide could be advanced under a roofstone at the top of the Mahogany ledge. To support the overburden, 60-ft-sq pillars would be left in a checkerboard pattern. From visual observations made of core samples through the selected roofstone at the oil-shale mine, it was determined that the roofstone was actually a plate 6 to 8 ft thick. Because the calculations were theoretical and allowance had to be made for unknown cracks and fractures in the formation, openings 50 ft wide and pillars 60 ft sq were originally contemplated in the Bureau's Experimental mine. This would be the minimum allowable width that would permit use of large underground mining equipment. For lower mining costs and greater efficiency larger openings were desirable. Different but analogous approaches were made to the problem at the Bureau of Mines Applied Physics

Jan 1, 1951

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By H. L. Teichman, E. M. Sipprelle

ENACTMENT' of Public Law 290 by the 78th Congress authorized the U. S. Department of the Interior, Bureau of Mines, to conduct an experimental program to develop the technology for obtaining oil from oil shale. In adopting and later extending this legislation, the Congress recognized the impending necessity of supplementing ground petroleum reserves with synthetic fuels. Under the provisions of this legislation, the Bureau of Mines, among other things, was charged with the responsibility of developing mining techniques, methods, and equipment for mining the oil shales of the Green River formation of Colorado, Utah, and Wyoming. The oil shales of western Colorado are apparently richer, more accessible, and more amenable to exploitation than elsewhere in the Rocky Mountain region. The site chosen for the Bureau's Experimental mine is about 10 miles west of Rifle in northwestern Colorado. It is within a 1000-sq-mile area from which, it has been estimated, 300 billion barrels of shale oil could be produced from a 500-ft measure near the top of the formation. One hundred billion barrels of this amount could be produced from the Mahogany ledge, a 60 to 100-ft section near the bottom of the 500-ft measure. This ledge is considered to have economic importance at present. The Green River formation was laid down as sediment in the bottom of vast, shallow inland lakes during Eocene time. The deposit is flat-lying, and there are no faults, fissures, or local rolls. Oil shale is actually a strong, tough magnesium marlstone, which will stand unsupported over relatively wide spans. These and other natural physical characteristics favor mechanized, low-cost mining, which is essential for establishment of an oil-shale industry. It was realized from the outset that an extensive research program would be necessary to develop mining methods, equipment, and techniques for a mechanized, low-cost operation. The program was designed to include research. into all the productive phases of mining, such as drilling, blasting, loading, transportation, and maintenance of the mine structure. The methods, equipment, and techniques developed as a result of this research have established a production of 116 tons per man-shift total labor at a direct cost of $0,292 per ton. Another important phase of the research program that has received little publicity because of its theoretical nature is study of the roofstone behavior and determination of mine structure stresses. This paper purposes to discuss this phase of the research program. Preliminary studies of the physical properties of the Green River oil-shale formation were made in the Barodyramics Laboratory at Columbia University during the latter part of 1945 and the early part of 1946.* The purpose of these studies was to determine the maximum size of unsupported underground openings that would be commensurate with safety and still permit the use of large, efficient mining equipment. Also to be determined were the pillar support to extraction ratio and the shape, size, and spacing of supporting pillars. Selected samples of possible roofstones near the top of the Mahogany ledge, as well as representative samples of different rock types found within the ledge, were obtained from the Bureau's oil-shale mine for these studies. The maximum safe unsupported roof span calculated from this work was 200 ft. Using a safety factor of four, it was theoretically determined that openings 60 ft wide could be advanced under a roofstone at the top of the Mahogany ledge. To support the overburden, 60-ft-sq pillars would be left in a checkerboard pattern. From visual observations made of core samples through the selected roofstone at the oil-shale mine, it was determined that the roofstone was actually a plate 6 to 8 ft thick. Because the calculations were theoretical and allowance had to be made for unknown cracks and fractures in the formation, openings 50 ft wide and pillars 60 ft sq were originally contemplated in the Bureau's Experimental mine. This would be the minimum allowable width that would permit use of large underground mining equipment. For lower mining costs and greater efficiency larger openings were desirable. Different but analogous approaches were made to the problem at the Bureau of Mines Applied Physics

Jan 1, 1951

By executive order of the President, dated June 25, 1918, the investigation of matters relating to gas warfare, which had been initiated by the Director of the U. S. Bureau of Mines early in 1917, and had been continuously maintained and improved since, that time, was transferred to the recently created Division of Gas Warfare of the War Department. On the occasion of this transfer, both the President and the Secretary of War took occasion to speak most highly of the efficient service that had been rendered by the Bureau of Mines. It gives us great pleasure to reproduce here a letter from the President and from the Secretary of War, bearing on this subject and also to append a brief review of the work of the Bureau of Mines, prepared by its Director, Mr. Van H. Manning. The White House, Washington. June 26, 1918. MY DEAR MR. MANNING: I have had before me for some days the-question presented by the Secretary of War involving the transfer of the chemical section established by you at the American University from the Bureau of Mines to the newly organized Division-of Gas Warfare in which the War Department is now concentrating all the various facilities for offensive and defensive gas operations. I am satisfied that a more efficient organization can he effected by having these various activities under one direction and control, and my hesitation about acting in the matter has grown only out of a reluctance to take away from the Bureau of Mines a piece of work which thus far it has so effectively performed. The Secretary of War has assured me of his own recognition of the splendid work you have been able to do, and I am taking the liberty of enclosing a letter which I have received from him, in order that you may-see how fully the War Department recognizes the value of the services. I am to-day signing the order directing the transfer. I want, however, to express to you my own-appreciation of the fine and helpful piece of work which you-have-done, and to. say that this sort of team work by the bureaus outside of the direct war-making agency is one of the cheering and gratifying evidences of the way our official forces are inspired by the presence of a great national task. Cordially yours, Dr. Van. H. Manning, WOODROW WILSON. Chief, Bureau of Mines, Department of the Interior. War Department, Washington, June 25, 1918. MY DEAR MR. PRESIDENT: In connection with the proposed transfer of the chemical section at. American University from the Bureau of Mines to the newly constituted and consolidated Gas Service of the War Department, which you are considering, I am specially concerned to have you know how much the War Department appreciates the splendid services which have been rendered to the country and to the Army by the Department of the Interior, and especially by the Bureau of Mines under the direction of Dr. Manning. In the early days of preparation and organization, Dr. Manning's contact with scientific men throughout the country was indispensably valuable. He was able to summon from the universities and the technical laboratories of the country men of the highest quality and to inspire them with enthusiastic zeal in attacking new and difficult problems which had to be solved with the utmost speed. I do not see how the work could have been better done than he did it, and the present suggestion that the section now pass under the direction and control of the War Department grows out of the fact that the whole subject of gas warfare has assumed a fresh pressure and intensity, and the director of it must have the widest control so as to be able to use the resources at his command in the most effective way possible. The proposal does not involve the disruption of the fine group of scientific men Dr. Manning has brought together, but merely their transfer to General Sibert's direction. Respectfully yours, NEWTON D. BAKER.

Jan 9, 1918

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965

By Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.' Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:' where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

By J. K. Elliott, P. H. Kelly

Many engineering functions such as surface metering work and laboratory compressibility check points involve the use of liquid densities of light hydrocarbon mixtures at various pressures and temperatures. However, at the present time, no simple reliable method exists for determining density variation, particularly if the composition of the liquid is unknown. Consequently, a study was undertaken to develop and present a simple and accurate method of predicting density variation of a light hydrocarbon liquid with pressure and temperature, knowing only the density of the liquid at some condition. The experimental liquid compressibility data from API Project 37 by Sage and Lacey' have been considered to be accurate within 0.5 per cent and cover a wide range of pressure (14.7 to 10,000 psia), temperature (100" to 400°F) and molecular weight (up to 150). From these data, a set of liquid density curves, which relate density to pressure, temperature and molecular weight, was developed. These curves make it possible to predict density variation with pressure and temperature. Compared to extensive laboratory compressibility data on a complex, light hydrocarbon liquid, the use of the liquid density curves resulted in an average error of less than 0.5 per cent. Based on the results of this analysis, it is concluded that the set of liquid density curves developed from the data of Sage and Lacey provides an accurate and simple method for predicting the density variation of light hydrocarbon liquids when the density at some condition is known. These curves should be very helpful in many engineering calculations, particularly in the surface metering of light hydrocarbon liquids. INTRODUCTION Many situations arise in field and engineering laboratory work, such as reservoir engineering studies, check of experimentally determined laboratory data and orifice flow-meter formulas, where liquid density factors at various pressure-temperature conditions are required. Also, the need for accurate light hydrocarbon liquid information has become more important with the advent of miscible-type displacements for secondary recovery purposes in oilfield operations. Several reliable methods are available1 - "or determining the density of liquid hydrocarbons if the composition of the liquid is known. However, there is a definite lack of methods for accurately determining the variation of density when the composition of the liquid is unknown. The purpose of this study is to review the various methods for determining hydrocarbon liquid densities and to develop a simple and reliable method of determining variation in density of light hydrocarbon liquids with pressure and temperature when the compositio~n of the liquid is unknown. METHODS FOR DETERMINING DENSITY OF LIQUIDS OF KNOWN COMPOSITION Sage, Lacey and Hicks' have proposed a method to predict the density of light liquid hydrocarbons by using partial molal volumes. Data are available on experimentally developed partial liquid volumes of hydrocarbons over a rather limited range of temperature, pressure and composition. The partial mold volume method has proved satisfactory for determining the density of some hydrocarbon liquids when the composition is known. Within the range covered in the Sage, Lacey and Hicks1 data, the results agree within about 3 per cent of the experimental values. Hanson mentions the limitation of this method to a composition range of approximately 10 per cent by weight of methane, which will not allow this correction to cover most low molecular weight-light hydrocarbon liquids. Standing and Katz2 studied data on light hydrocarbon-liquid systems containing methane and ethane at high temperature and pressure and have presented a method for determining liquid densities, assuming additive volumes for all components less volatile than ethane and using apparent densities for methane and ethane. The compressibility and thermal-expansion curves used by Standing are based on assumptions that compressibility of a hydrocarbon liquid at temperatures below 300°F is a function of the liquid density at 60°F and that thermal expansion of the liquid is affected little by pressure. The information required to use this technique with an example problem is furnished by Standing.' Hanson eports an average error of - 0.5 per cent using the method of apparent densities in calculating liquid densities of several volatile hydrocarbon mixtures. However, as implied, the apparent density method is not applicable for liquid density calculations when the composition of the liquid is unknown. Watson- as presented a method