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In 1934 the Southern Experiment Station of the U.S. Bureau of Mines in. cooperation with the University of Alabama began an investiga-tion of the availability of kyanite ores as a source of raw material for the manufacture of refractories. Under this program, gravity concentration and flotation tests have been made on two varieties of Georgia kyanite ore, mica schist and massive. Most of the attention has been directed to the mica schist ores, as they are more widely distributed and seem to offer greater economic possibilities than the massive ores. It is evident that the preparation of kyanite for use as a refractory material involves other considerations than the mere elimination of impurities. A concentration process that eliminates impurities satisfactorily may have to be followed by some additional treatment, since the final product must be of a coarse-ness and size ratio that will make it suitable for refractories manufacture. So far in the investigation at the Southern Experiment Station of the U.S. Bureau of Mines only the concentration problem has been considered, and this paper is intended as an interim report.

Jan 1, 1936

By L. S. Castleman, R. Resnick

The self-diffusion coefficient of columbium has been measured over the temperature range 1535o to 2120°C, using the radioactive isotope Nb95 as the tracer. The data for the temperature dependence of the self-diffusion coefficient are best fitted by the equation D = (12.4 ± 0.8) exp [(-105,000 ± 3000)/RT] cm2/sec. THE increasing need for high-temperature structural materials has stimulated considerable interest in the properties of columbium, since it is a strong, ductile metal with a high melting point—in the vicin- ity of 2450oc.l One fundamental property which has not heretofore been measured is the self-diffusion coefficient. The self-diffusion coefficient plays an important role in theories of oxidatioq2 creep,' sintering4 and other phenomena. Accordingly, the investigation reported in this paper was undertaken to determine the value of the self-diffusion coefficient and its temperature dependence by the use of Mb95.

Jan 1, 1961

By K. Sallmann

Spurred by a variety of factors, coal flotation is making headway among the preparation plants of West Germany. Mr. Sallmann provides a general view of flotation practices being employed in his country, with special emphasis on the many-sided problems that confront German coal preparation engineers.

Jan 9, 1961

By Charles Will Wright

DESPITE the war, the First Pan American Mining Congress, held in Santiago, Chile, Jan. 15-23, was attended by about 300 persons including the official delegates from sixteen of the American republics. The United States delegation consisted of Elmer Pehrson, of the U. S. Bureau of Mines; D. F. Hewett, of the U. S. Geological Survey; William H. Hobbs, of the Carnegie Foundation; and C. W. Wright, delegate of the Board of Economic Warfare and of the A.I.M.E. Mr. Wright was elected to head the delegation. Among the other members were Edward Steidle, of Pennsylvania State College and also an official A.I.M.E. delegate; John Huttl, of Engineering and Mining Journal; W. 0. Vanderburg, foreign mineral specialist from Lima, Peru; O. B. Hundley, of the American Cyanamid Co.; Horace Graham, of the Anglo-Chilean Nitrate Co.; and several officials and engineers from the Anaconda, Kennecott, and Bethlehem Steel companies' mines in Chile.

Jan 1, 1942

By Frank Firmstone

Discussion of the paper of John B. Dilworth, presented at the Pittsburg meeting, March, 1910, and printed in Bulletin No. 35, November, 1909, pp. 1041 to 1043. FRANK FIRMSTONE, Easton, Pa. (communication to the Secretary*) :-Mr. Dilworth's formulas and tables are of course correct, and the extinction will occur as calculated, provided the money periodically set aside for sinking-fund be really invested. and the interest compounded as assumed in the calculation. Actually, in almost all cases, such funds are used "in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must be made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varying and continually increasing one until the date of extinction. On many accounts it seems more natural and convenient to make the extinction by a fixed periodical charge under the legal rule for partial payments, namely, that each payment should apply first to the interest due at the date of payment;: and any remainder, after this is satisfied, be deducted from the principal before the interest for the next period is calculated. The formula below is convenient for such calculations S, Principal to be extinguished. Q, Periodical payment or charge for sinking-fund. B, Balance unpaid at date of nth payment, but before that payment is made. r, Rate of interest per period per cent. n, Number of payments or periods. Then, B=S(1+r)n-Q(1+ r)n-(1+r) Received July 27, 1910.

Apr 1, 1911

•Mineral Development Corp. of Salt Lake City, Utah purchased the Somerset and Oliver coal mines from the Kaiser Steel Corp. The mines are located at Somerset, Colo., about 75 miles east of Grand Junction, Colo. Somerset Town, with housing for 600 persons was included in the transaction. The mines employ 115 miners and have a combined capacity of 1750 tons per day. The Minerals Development Corp. is headed by Claude P. Heiner and is controlled by Godfrey L. Cabot, Inc. of New York and Boston. The Cabot Company is a major producer of carbon black. • The Dept. of Interior has announced that the name of the Defense Minerals Administration will be changed to Defense Minerals Exploration Administration. The new name of this defense agency more nearly describes its duties, since the mineral programming, procurement and claimant functions of the former DMA have been transferred to the Defense Minerals Procurement Agency. C. O. Mittendorf, formerly acting administrator of DMA, is serving as acting administrator of the new DMEA.

Jan 1, 1952

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.' and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By B. F. Tillson

Mining may be defined as a general term for the working of valuable deposits of minerals, either organic or inorganic in origin, for their removal from the crust of the earth. Besides subsurface excavations, mining generically includes opencuts, clay pits and stone quarries, oil wells, sulphur wells, salt wells, placers, coal stripping, and the leaching of ore bodies. The origin of the word "mine" or "mining" is a matter of conjecture. A Celtic origin has been suggested since the Irish word mein, or the mwyn, meant ore, but it seems to have come from an olf French verb mineor, which meant to excavate, to make an underground passage as in the military appraoch to a fortification, sometimes called ?sapping.?

Jan 1, 1949

By J. C. McCarthy, J. B. Stone

AT Fresnillo a series of veins that has yielded very large quantities of silver and other metals has been developed over a length of 6500 ft. and to a depth of over 3000 ft. In the course of this work striking changes in the mineralogy and metal content of the principal veins have been disclosed and are well illustrated by assay data and ore reserve calculations. This paper describes those changes and suggests their bearing on theories of ore deposition. LOCATION The Fresnillo mines and the adjacent city of Fresnillo are in the central part of the state of Zacatecas, 35 miles northwest of the capitol city of Zacatecas, once a great silver-mining center whose total production is said to place it fourth in the world. Another famous old silver district, Sombrerete, lies northwest of Fresnillo. Fresnillo is connected by a 5-mile branch with Fresnillo station on the Mexican National Railways line from Juarez to Mexico City. Lying near the southwestern edge of the central plateau of Mexico, Fresnillo is surrounded by a semi-arid rolling plain from which rise widely scattered low hills. One of these is Proano hill, an inconspicuous elevation rising barely 300 ft. above the plain, but in and around Proa[n]o hill are the Fresnillo mines, and it is marked now by a great gash cut by gloryhole mining. HISTORY According to an account written in 1834 by Francisco García, then Governor of the state of Zacatecas, Fresnillo was discovered in 1554, and a presidio was established there in 1568 to protect travelers on the road between Zacatecas and Sombrerete. Little is known of the earliest mining at Fresnillo. which seemingly began soon after its discovery, but by piecing together various accounts, it appears that mines there were working in 1717 and were notable active in 1751 under an administrator named Murguía, who left detailed notes describing them. In 1757, however, the mines became inactive because of difficulties with creditors and no doubt also because of increasing water troubles, and they remained abandoned until 1830. In 1830 the mines at Fresnillo became the property of the State of Zacatecas because the interest of Governor García had been aroused by the long disregarded notes of Murguía. Under Garcia's energetic leadership the mines were reopened, and silver production began in 1832 in spite of serious difficulties, including abnormal rains and an epidemic of cholera. In 1833 English capital was sought to allow installation of steam-driven Cornish pumps at the two principal shafts and to build the great hacienda de benefacio (the present Proano hacienda). The company formed in 1835 (Cia. Zacatecano-Mexicana) operated successfully until 1872, when its career was brought to an end by the political and economic disturbances

Jan 1, 1942

By Karl Eilers

This process, invented by Messrs. Hanisch and Schroder, of Rosdzin, was patented in 1883. It has attracted considerable attention in Germany, as a very neat and simple method of extracting sulphurous acid from the gases produced by roasting, and of condensing this acid so as to obtain it in the very compact anhydrous liquid form. The special importance which such a process may have at this time in the United States is suggested by the growing inconvenience, amounting to distress, experienced in such localities as Butte, Mont., where the sulphurous gases from large roast-plants have proved not only fatal to vegetation but injurious to human health. It is reported that the authorities of Butte are earnestly considering the enterprise of removing, if practicable, the dense and suffocating cloud which now hangs over that city, and of which sulphurous acid undoubtedly forms the greater and most oppressive, if not the most poisonous, part. May it not be that the solution of this problem is furnished by a

Jan 1, 1892

By Richard V. Ageton

Salt bodies in the form of rolls, horses (sometimes called horsebacks), folds, wants and pinches1 have been encountered while driving entries and mining out rooms during the development of the potash mines in New Mexico. Superficially these sporadic salt occurrences appear to be much alike, but closer examination reveals individual characteristics, and after four years of observation it seems possible to divide them into three general groups that may tentatively be called "depositional," "erosional," and "structural." The data collected are not yet sufficient to permit forecasts of their probable location, so that the annoyance of having to mine salt instead of potash could be avoided or lessened. However, the information so far available appears to throw some light on the occurrence of the sylvite2 bed now being mined, and it is as a progress report that the writer presents the results of his observations. The mines of the United States Potash Co. and the Potash Company of America are about 20 miles northeast of Carlsbad, in Eddy County, N. M. They are on the southwestern flank of the Permian salt basin, which underlies western Texas, Oklahoma and Kansas, south-central Nebraska, southeastern Colorado and eastern New Mexico. The cuttings from many oil wells and the cores from the potash tests drilled in this basin indicate that this salt series approached its greatest thickness (about 4000 ft.) in the southeastern part of New Mexico and the adjoining portions of Texas, and that the most advanced stages of

Jan 1, 1938

By Richard V. Ageton

Salt bodies in the form of rolls, horses (sometimes called horsebacks), folds, wants and pinches1 have been encountered while driving entries and mining out rooms during the development of the potash mines in New Mexico. Superficially these sporadic salt occurrences appear to be much alike, but closer examination reveals individual characteristics, and after four years of observation it seems possible to divide them into three general groups that may tentatively be called "depositional," "erosional," and "structural." The data collected are not yet sufficient to permit forecasts of their probable location, so that the annoyance of having to mine salt instead of potash could be avoided or lessened. However, the information so far available appears to throw some light on the occurrence of the sylvite2 bed now being mined, and it is as a progress report that the writer presents the results of his observations. The mines of the United States Potash Co. and the Potash Company of America are about 20 miles northeast of Carlsbad, in Eddy County, N. M. They are on the southwestern flank of the Permian salt basin, which underlies western Texas, Oklahoma and Kansas, south-central Nebraska, southeastern Colorado and eastern New Mexico. The cuttings from many oil wells and the cores from the potash tests drilled in this basin indicate that this salt series approached its greatest thickness (about 4000 ft.) in the southeastern part of New Mexico and the adjoining portions of Texas, and that the most advanced stages of

Jan 1, 1938

By P. Chiotti, G. R. Kilp

IN the study of zinc-zirconium1 and zinc-uranium2 systems, vapor-pressure measurements were made in order to establish the equilibrium phase diagrams for a pressure of 1 atm. In each of these systems, only zinc has an appreciable vapor pressure over the temperature range investigated. The zinc pressure was measured over a sufficiently wide temperature and composition range to permit calculation of the standard free energy, enthalpy, and entropy of formation for the compounds ZrZn, ZrZn2, ZrZn3, ZrZn6, ZrZn14 , and U2Zn17. In these calculations the compounds were treated as line compounds. Although the exact composition range was not determined, metallographic and thermal data indicate that the solubility range for these compounds is small. It is to be noted that the compound initially reported to correspond to the formula UZn9, 2 has been shown by the crystal structure work of Makarov and vinogradov3 to correspond to the formula U2Zn17,. The crystal structure is similar to that for the compounds Th2M17, investigated by Florio,4 et al; here M represents iron, cobalt, or nickel. Therefore, thermodynamic calculations are based on the formpla U2Zn17 EXPERIMENTAL The dew-point method employed to measure the vapor pressure of zinc over uranium-zinc alloys has been described previously.2 The same procedure and apparatus were used in measuring the zinc pressure over zinc-zirconium alloys. In the case of alloys in the two-phase region consisting of a zirconium and the compound ZrZn, the Knudsen effusion method was employed to obtain a few values in the temperature range 600" to 560°C. In most cases, tantalum crucibles were used to contain the zirconium alloys. THERMODYNAMIC PROPERTIES OFU2Zn17 A least-squares treatment of the vapor-pressure data obtained for 35 and 65 wt pct U alloys in the temperature range 650° to 940°C gave lOg10PAtm = 7,713/T + 6.33 Here, as in following equations, T represents degrees kelvin and P represents the zinc vapor pressure in atmospheres. The probable errors for the two constants were calculated to be 60.68 and 0.0563, respectively. This relation represents the equilibrium dissociation pressure for the reaction U2Zn17 (s) - 2U(s) + 17Zn(v) The solubility of zinc in solid uranium is negligible and the only additional information required to calculate the free energy of formation of U2Zn17 is the free energy of vaporization of pure zinc. K. K. Kelley5 gives the relations, AF°= 30,902 + 6.03Tlog T + 0.275 X 10-3T2 - 45.03T

Jan 1, 1961

By R. M. Board

This paper will focus on measurement and control of four main aspects of crushing, namely horsepower, bowl level, mantle position and feed rate, and will discuss related sensors and control techniques, some of them designed specifically for crusher control, that have proven successful and reliable in many installations.

Jan 1, 1982

By John E. Conley

THE slate industry of the United States has shown a marked decline in value of products made annually since the peak year 1925, although there has been moderate improvement over the lean years 1932 to 1934. In 1940, the value of all slate products sold was approximately 5 3/4 million dollars for a total output of 473,450 short tons. The quantity sold was a little less and the value a great deal lower than the annual averages for the past two decades. Enormous quantities of waste materials result from the quarrying, splitting and milling of slate. Obviously, utilization of such waste material is desirable, not only from the viewpoint of economical operation but also for the purpose of conserving natural resources. One possible use is to produce expanded or puffed lightweight aggregate for use in concretes. Such concretes are strong enough for specific uses, and the advantage of lightness could be obtained in such structures as the walls and roofs of buildings, suspension-bridge roadways and various other applications where weight is a factor. Conceivably, these uses could consume an appreciable annual tonnage. USE OF WASTE SLATES FOR MAKING AGGREGATES The lightweight-aggregate industry has been discussed elsewhere4.5 and need not be covered in detail in this paper. The materials commonly utilized are naturally occurring aggregates such as volcanic cinder, tuff and pumice; by-product materials, such as ordinary cinders and air-cooled slags; and the specially manufactured products, including Haydite, Pottsco, Gravelite, Cel-seal, Superock and Waylite. Slates, however, have not been given the consideration they merit, especially in the United States. In the British Isles, some work has been done' on certain Welsh slates by the Building Research Station to stimulate the use of these wastes. REQUIREMENTS FOR RAW MATERIALS As pointed out by Hughes,4 the lightweight-aggregate industry is segregated in regions adjacent to large cities in order to localize the market and avoid the necessity of long freight haulage. Waste slate from the deposits of eastern Pennsylvania, northern Maryland, and Virginia would meet the basic requirement of any low-priced structural raw material. One apparent advantage is attained when slate waste, normally discarded, is utilized in the manufacture of a by-product. Mining or quarrying costs usually have been assessed against the main product. Some additional grinding might be desirable, but this operation would be relatively cheap, as most slates grind easily. It is believed that virtually all slates, when properly heated, will expand to some degree. However, types that will expand from 3 to 7 times their original volume are preferred. Fig. I illustrates the expansion of a Pennsylvania slate. The cube originally

Jan 1, 1942

By U. C. Tainton

IN reviewing progress in zinc metallurgy during the last year or so one is reminded of the premise on which H. G. Wells based his "Food. of the Gods," namely that growth does not and cannot take place smoothly and steadily, but occurs in a series of bursts and intermissions: "It is as if every living thing has to accumulate force to grow, grows with vigor only for a time, and then has to wait for a space before it can go on growing again."

Jan 1, 1937

By Anderson, Burton E.

FOR several centuries diamond mining has been an adventurous, profitable and enticing industry in Brazil. Some of the world's most valuable diamonds have been found in this country. Two of the most famous stones are the "Estrella do Sul" (Southern Star), weighing 2541/ karats, and the "Branganca," weighing 1680 karats in the rough and 367 karats cut. For a great number of years the stones extracted and sold were mostly the white diamonds used for jewelry. Within the last thirty years black diamonds have been developed as an abrasive cutting material and in these black diamonds the State of Bahia, Brazil, has a monopoly of the world supply. Carbons, as they are commonly called, are being used for core-drilling, polishing, cutting, wire-drawing, and vari-ous other applications in which such a hard substance is required. Bernard Bandler & Sons, of New York City, have selected, graded and delivered these carbons to the United States markets.

Jan 1, 1932

By Clarence Woods

ONCE a millionaire's plaything, the Santo Domingo mine, in Peru, is now, because of its metallurgical problem, an engineer's nightmare. It is deep in the montaña jungles of the Amazon basin, 140 mi. northeast of Tirapata, which is a rail- way station between Puno and Cuzco, and about 250 mi. east of Mollendo on the Pacific. The discovery was 111ade by Marian(-) Quispe, an Indian, who, while searching for quinine bark, was attracted by a slab of gold quartz 1x1 the rock wall of a narrow canyon. He broke off a piece, weighing 47 Spanish ounces and, that time, worth approximately $900. This he took to Francisco Velasco and Manuel Estrada, merchants of Coaza, who persuaded Quispe to lead them to the place, five days' journey on foot through a tangled wilderness. Velasco ' and Estrada denounced the claim

Jan 1, 1938

By M. J. Pool, P. J. Spencer, J. R. Guadagno

THE present work was carried out as part of a general program to study the magnitude and concentration dependence of exothermic heats of solution of various metals in liquid tin. Thermodynamic data for the Te-Sn system are very limited, particularly for dilute alloys. Indeed, apart from the prior heat of solution determinations of Pool,1 the only other published values are those of McAteer and seltz2 who carried out electromotive force measurements on solid alloys of compositions from 75 to 95 at. pct Te at temperatures between 543° and 668° K, of Colin and Dro-wart3 who made mass-spectrometric studies of the vapor in equilibrium with solid SnTe, and of Robinson and Bever4 who determined the heat of formation of SnTe by solution calorimetry. The present work thus provides further thermodynamic information for this system, specifically in a temperature range where the solubility of tellurium is very limited. The liquid metal solution calorimeter used in this investigation has been described previously.' No further discussion of its design or operation will therefore be given here. For each series of measurements a tin bath consisting of approximately 70 g of 99.99 pct pure Sn was carefully weighed out and inserted in the calorimeter which was maintained at the desired temperature to within ± 1/4°c. Tellurium, of 99.999 pct purity, was supplied by Atomergic Chemetals Co., a division of Gallard-Schlesinger Chemical Manufacturing Corp. Approximately 0.0006 to 0.001 g-atom specimens of tellurium were used for each experimental run and these were added to the calorimeter from a temperature of 273" K. Heat of solution values were calculated by analysis of a strip-chart recorder plot of the heat effect accompanying the solution of each sample in the tin bath. The heat capacity of the latter was determined at regular intervals during a series of tellurium drops by using pure tin or tungsten calibration samples, the heat contents of which were obtained from the standard compilation of Hultgren et al5 The composition of the bath was calculated after each drop from a knowledge of the weights of tin and tellurium added. Values of the heat of solution of tellurium at 725" and 775° K are listed in Table I together with the corresponding tellurium contents of the alloys. The data are also plotted as a function of tellurium concentration in Fig. 1, which includes the equivalent data obtained by pool' at 750° K. It can be seen that the heat of solution remains

Jan 1, 1969

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957