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By Walter Harvey Weed

INTRODUCTION. IN a previous paper upon the enrichment of mineral veins by later metallic sulphides,† the writer has shown that certain masses of rich ores, such as are found in many mines, either near the water-line or as bonanzas in depth, are of secondary origin, and are due to a leaching of lean ore and the concentration of the material by reaction between the solution and the unaltered ore below. The geological and mineralogical evidence is believed to form an adequate basis for a chemical and physical explanation of the phenomenon. In the present paper the writer will give a brief synopsis of this theory, and will apply it more particularly to deposits of the precious metals, laying special emphasis upon the dependence of such enrichments upon the presence of iron sulphide (as pyrite, etc.) in the primary ore, and upon structural features which control the circulation of the enriching solutions below the water-level. It is believed that many, though not all, of the bonanzas and pay-shoots of rich sulphide ores, especially those carrying gold and silver, which are encountered in ore-deposits, are of such secondary origin. Apparently it is essential that the occurrence and structural relations of such ore-masses should be understood, as the success of the mine is often dependent upon the finding and extraction of these ores. A legitimate deduction, too, is that such ore-deposits decrease in value with depth. As my own studies have been mainly in Montana, my illustrations must be drawn from the ore-deposits of this and adjacent States, with such as I have noted in hurried visits elsewhere. The literature of ore-deposits doubtless affords also

Jan 1, 1902

By K. A. Johnson, F. H. Ellinger, C. C. Land

The Pu-La alloy systenz has been studied by thertnal, tnzcrographic, and X-ray diffraction methods. It is churacterized by a liquid miscibility gap, a maximum solubility of about 20 ut. pct PM in y lanthunum and 19 at. pct PI* in 0 lanthanum, very little soluibility of lanthanum in the plulonium allotropes, and the absence of intermediate phases. THE existence of immiscible liquids in the Pu-La system has been reported by Schonfeld.1 A tentative phase diagram based on the results of thermal-analysis experiments has been constructed by Poole et a1 2 This diagram shows a liquid immiscibility loop with a monotectic at 77 at. pct La and 846°C. 7 lanthanum is shown to dissolve 20 at. pct Pu and to decompose by an inverse peritectic reaction (y La = L , + p La) at about 82 at, pct La and 833°C. The ß lanthanum solvus was not determined, but the thermal work indicated a maximum solubility of 16 at. pct Pu in ß lanthanum. The present investigation has defined the solubility limits of plutonium in y lanthanum and 0 lanthanum, and, with the exception of minor discrepancies, has verified the results of Poole et al. 1) EXPERIMENTAL The electrolytic plutonium melting stocks were better than 99.9 wt pct pure, the main impurities being 90 ppm Fe and 50 ppm W. The lanthanum melting stocks, supplied by Research Chemicals and the Cerium Metals Corp., were about 99 wt pct pure, the main impurity detected by our spectrochemical analysis being 2000 ppm Fe. The components for each alloy button (-5 g) were weighed on an analytical balance and were melted together in a conventional arc furnace. If no significant weight loss occurred during melting, the as-weighed

Jan 1, 1968

By William H. Shockley

There was an extensive mining and industrial exploitation of Russia, about 20 years ago, by Belgian, French and British capitalists; but the results were discouraging. It is said that the Belgian and French public together lost approximately $400,000,000, chiefly in the coal and iron industry of southern Russia. This loss is largely accounted for by the fact that most of the companies were formed, as usual in " boom" times, to sell stock; and that thorough investigations were not made. I11 1906, renewed interest was taken in Russian mines, especially in those of gold and copper, and a considerable literature is growing on this subject; but as yet I have seen no account of one of the large Russian mining estates. The following notes on such property, where the conditions are so different from those in the mining regions of the United States, should be of interest: This inadequate and probably somewhat inaccurate account is made up, partly from my own notes made on the ground, in the summers of 1904 and 1905, and partly from a volume on the geology and resources of the estate issued several years ago, containing surface- and mine-maps, and from a pamphlet published in 1904, giving a general account of the condition and prospects of the property. This pamphlet includes a report made in 1899 by Arthur L. Pearse, a member of this Institute. Both these books are in Russian, and were prepared by the Bogoslovsk Mining Co., which owns and operates the property. Articles in many other languages have appeared dealing with various matters connected with the estate; but I know of no other general account of it. In numerous books and articles on the Urals and Siberia, however, localities are described in which somewhat similar conditions prevail. Recent papers by

Jan 1, 1909

By W. Denham Verschoyle

In designing a pocket instrumeut whereby any giver1 horizontal or vertical angle may be closely approximated, the following points should be kept in view, if general utility is aimed at : 1. The instrnment should be light and compact, so that it can be carried in the pocket, or in a sling. 2. It should be capable of observing any angle whatever, horizontal or vertical. 3. Since time is often an important consideration in making a preliminary survey, it should be capable of giving the horizontal and vertical angle at one observation. I do not know of any instrunlent that will fulfill these requirements, except the one here described. Where the depression- or elevation-angle of the distant object, whose bearing is required, exceeds 50 or 60 degrees, it becomes difficult or impossible with a prismatic compass, for instance, to obtain accurate results; and since it frequently happens, particularly in mining, that much work requires to be done beyond that limit, it is obvious that an instrument which can be used to observe a high angle just as easily as a low one, if not absolutely a necessity, will at least be a great convenience. How this a pocket transit" attains to the required degree of universality will be understood from the diagram, Fig. 1, in which B is a beveled, graduated circle, attached to and freely revolving about the center of the magnet A. Light falling on B is reflected through a window in F (the compass-box), along the line AC, and is again reflected back to the eye at D by the prism C. By a simple arrangement, the tight-line BCE call be completely revolved in the vertical plane DE, which is normal to AC. It is clear, then, that no matter through what vertical

Jan 1, 1908

By R. S. Dean

MANY studies have been made of the properties of steel produced by adding varying amounts of sponge iron to the charges used in steel-making furnaces.1-3 The results of these previous studies, however, have failed to disclose a reason for the belief of steelmakers that steel made in this way is definitely different from steel made entirely from scrap or iron melting stock. This paper deals chiefly with the structure of the sponge iron, of the wrought iron made by welding the sponge iron into blooms, and of the steel made by melting the forged and rolled blooms. It is believed that the structure of the final steel is inherited from the ore and that this inherited structure produces marked differences in the properties of the steel and explains the feeling of steelmakers which is based on their experience. Three kinds of sponge iron were used in this investigation: One made from a limonite ore reduced with natural gas, one made from a hematite ore reduced with natural gas, and one made from a magnetite ore reduced with charcoal. The sponge iron made by reduction with natural gas

Jan 1, 1935

By James Gayley

The paper presented to the Institute in 1910, by H. O. Hof-man, on Recent Progress in Blast Roasting,' has called the attention of the iron industry to the adaptability of these processes to the reclamation of by-products such as flue-dust and blue billy, and the better preparation of concentrates and fine ores for use in blast-furnaces. The waste of valuable iron-ore through the production of flue-dust has increased at an enormous rate, and much of it has in

Jan 1, 1912

By L. C. Uren, E. J. Bradshaw

This paper presents the results of a group effort by a number of University of California students and faculty members, and the authors attach their names primarily in the capacity of editors and interpreters of the data thus assembled. In addition to the writers, the following individuals have made substantial contributions in time and effort in the conduct of this research: Dr. A. J. Carlson, Associate Professor of Petroleum Engineering; J. E. Gosline, University Research Assistant; C. F. Bedford, G. W. Mikulasek and H. S. Conder, senior and graduate petroleum engineering students; H. Bachman, G. Spencer and G. W. Gard, mechanicians in the Department of Mining and Metallurgy. Acknowledgment is also due the Research Board of the University, the Department of Mining and Metallurgy, and Prof. F. H. Probert, Dean of the College of Mining, for continued cooperation in securing mechanical assistance and funds for the purchase and assembly of apparatus. Significance of the Pressure Gradient The expulsion of petroleum from its reservoir sand doubtless is due to expanding natural gas intimately associated with the oil, to the hydrostatic pressure of encroaching edge waters, and to gravitational influences. These forces may operate independently or collectively. In any case they subject the fluids stored within the reservoir sands to elevated pressures, thus causing movement of oil and gas through the productive formations toward the lower pressure of the well outlets. This movement is opposed by pore friction, capillarity and adhesion: resisting influences brought to bear by the reservoir sand on the moving fluids. The magnitude of the resisting force is influenced directly by the viscosity, surface tension and density of the oil, as well as by the properties of the gas. The more rapid the rate of flow, the greater will be the resistance offered, and the greater will be the energy consumed.

Jan 1, 1932

Discussion of the paper of CHESTER W. WASHBURNE, presented at the New York meeting, February, 1915, and printed in Bulletin No. 9S, February, 1915, pp. 469 to 471. ROSWELL H. JOHNSON, Pittsburgh, Pa.-I hope that this contribution of Mr. Washburne's is only the first of a series dealing more in detail with the very important problems involved. Pores are of two kinds: Those which are entirely inclosed, so that they do not belong to a system of communicating pores tapped by the bore hole or shot hole; second, those which do so communicate. Porosity, of course, includes both. But since pores of the first class are valueless to us, we should confine our attention to the latter, for which I propose the term "effective porosity." This should be measured by the Wisconsin method, based on the quantity of fluid that can be introduced by the aid of vacuum. Another factor which requires attention in this connection is the dependence of the extractability upon the rate of loss of pressure, as affected by the number of holes, and the rapidity of their completion, the existence of uncontrolled wells, the use by other operators of vacuum pumps upon the casing head, the exhaustion of a gas field in the same reservoir prior to the discovery of the oil, etc. The extractability depends upon the pressure available for the exclusion of the oil from the reservoir into the hole. The action of gravity in bringing oil into the hole is relatively small where the pores are very small, as is so frequently the case.

Jan 5, 1915

The early history of a country is linked with its topographic features. Mountains are barriers, rivers are avenues, the sea is a highway. The first Europeans to reach the northwestern corner of the American continent, now known as Alaska, came from Asia, for the Pacific Ocean provided an approach by means of the islands that like stepping-stones stretch far westward from the inhospitable shore of the mainland. The Russians crossed Siberia and explored the Arctic coast of Asia. In 1728 a band of Cossacks was driven by a storm eastward from Kamchatka, and landed in Norton Sound.* Others followed them, and settled on the islands and peninsulas of southeastern Alaska. The mountains guarding the coast discouraged any advance into the interior. Another range, the northern extension of the Rocky Mountains, barred the westward progress of the French voyageurs and the English fur-traders of the Hudson's Bay Company. After the Russians had obtained a foothold among the Indians, the viceroys of Mexico sent successive expeditions up the coast, such as that of Pérez in 1774 and of Heceta in 1775. If the English fur-traders had not interfered, the Spanish and Russian spheres of influence would have conflicted, and the contest for control might have ended in establishing a line of demarkation somewhere near the mouth of the Columbia river. The British navigator Captain James Cook landed near Sitka in 1778 while seeking a way by water to Hudson Bay. Fifteen years later his midshipman, George Vancouver, in command of another British expedition, surveyed the coast

Jan 1, 1932

By Samuel B. Christy

" The man is always greater than his work." The training of the men who are to develop the mineral resources of the world is the most important problem connected with mining engineering. It becomes ever more important to civilization as the mineral wealth of the earth approaches exhaustion. I have therefore decided to consider a few of the more important problems arising in the training of the mining engineer, and especially those arising in America. , The Peculiar Nature of Mineral Wealth. Mining and Agriculture are the two fundamental arts. Without the latter our existence would be precarious; without the former, our civilization impossible. Agriculture furnishes that regular supply of food and raiment which leads to the growth of large communities in which cultivated leisure first becomes possible; while mining furnishes the metallic thread from which is woven that complex fabric we call civilization. But in these two arts the conditions for success are widely different. Most of the crops that the farmer reaps may be harvested year after year, and the proper fertilizers being added, he may continue the annual harvest indefinitely, while, as a result of cultivation, his farm becomes yearly more valuable. But the crop the miner reaps can be harvested but once in the history of the race. Our mineral wealth has taken unknown ages to mature in the bosom of the earth. The ripened fruit can be plucked but once. There are no fertilizers for worked-out mines. It never pays to work over a mine that has been

Jan 1, 1906

By Richard Amberg

While the old-time melter was satisfied to bring his metal out in the desired condition, and therefore took care to have the slag liquid enough, the importance of a thorough knowledge of the slag is at present recognized in all up-to-date melting-shops. Formerly slag or cinder was considered a necessary evil, accumulating in some mysterious way wherever a man was striving to produce a clean metal. Nowadays we deliberately aim at a well-defined slag, which varies with the nature of the process and the product. In steel-making we need slag for two main purposes, namely, refining and protecting the metal. To refine metal, essentially oxidizing and reducing processes are required, while to protect the metal we need a reducing or, still better, a neutral atmosphere. Although an absolutely neutral condition between steel, on one side, and the containing vessel and the slag, on the other, is an imaginary conception, the various furnaces in use for the production of liquid steel maybe arranged with respect to the attainment of this ideal in about the following order of merit: converter, open-hearth, crucible, and electric furnace. In dealing with the subject we will find it convenient to avail ourselves of the terms of physical chemistry, which yield a simple conception of the matter and an expedient way of expression. Slag and metal at large are not mixable with each other, and we will therefore call them the two " immiscible phases," though there are certain compounds which dissolve in both phases under conditions to be considered later. Reactions be-

Jan 1, 1913

By W. J. Keep, Edward Orton

During the past two or three years consumers of pig-iron have been seeking more knowledge regarding the chemical questions involved in foundry-practice. This desire has been increased by the papers of Professor Thomas Turner, of Mason College, Birmingham, reporting a series of tests made to show that silicon is a useful, rather than a damaging element when present in proper quantities in cast iron, and that by its use pig-irons and scrap, which when used alone are totally unfit for foundry purposes, may be made to give satisfactory results. Professor Turner has shown that the strength of a cast-iron depends on : 1. The amount of weakening impurities present; 2. The proportion existing between the combined and the graphitic carbon in the cast-iron. He says that the tendency of combined carbon is to increase hardness and brittleness, while graphitic carbon makes iron soft, malleable and tough; too much of either form is a disadvantage; the strength depends on the proportion. Strength being the thing most desired, irons having an excess of weakening impurities will not find a market, and therefore the only thing to provide for is the proper proportion between combined and graphitic carbon. Professor Turner shows that by a judicious use of silicon this proportioning can be accomplished exactly according to the wish of the founder; an increase of silicon changing combined carbon to graphitic, and vice versa. When the founder understands its use he may soften and toughen, or harden and strengthen his

Jan 1, 1889

By R. W. Raymond

I have the pleasure of exhibiting samples of the rock in which the South African diamonds are said to occur, for which I am indebted to Mr. Franz Groeger, of Vienna, formerly an assistant of the Royal Imperial Geological Institution, whose account of the general geology of Southern Africa was contained in a recent number of the proceedings of that Institution. The rock is apparently a sort. of tufa, evidently of volcanic origin. Mr. Groeger assured me that it could be seen in situ, bounded by uplifted stratified rocks; and that diamonds had been mined from it, by means of shafts, some distance below the surface. Groeger calls it " greenstone-tufa," and says of it, in the proceedings of the Geological Institution, " it breaks through the younger members of Group III [lower Trias and Jura], .... and crops out in oval masses, filling fissures.....The occurrence of this tufa is not locally limited, but has been traced and proved already over a large territory." Dr. Hunt remarked that the material looked like the trass of the Rhine region. He thought it a new occurrence for diamonds. He believed diamonds to belong to ancient crystalline rocks, although these materials might be brought up by volcanic agency, and the diamonds remain unaltered. In the volcanic rooks of Auvergne, crystals of sapphire, zircon, and spinel are found; and yet no one supposes that these minerals have been generated by volcanic agency. He had had a conversation with Bertrand de Lorn on this subject, who agreed with him that these minerals, being hard and resistant,

Jan 1, 1886

By Zay Jeffries

IMAGINE a spinning sphere of hot matter about 8000 miles in diameter, rushing through space at a velocity measured in miles per second, and you have a rough idea of what our earth is supposed to have been like about two to four billion years ago. By applying all of the science known to man and, more especially, by determining the velocity of earthquake waves at different depths, making comparisons with meteorites, studying densities, compressibility of rocks and the nature of surface rocks, a fairly definite conception of the general constitution of the earth has been obtained.1 The earth is supposed to have a central core rich in iron containing a substantial amount of nickel and small percentages of several other elements. The density of the core is assumed to be about ten times that of water and the diameter about 4200 miles. An intermediate shell of density about 4, and thickness of about 1800 miles, is sup- posed to consist of heavy rocks including sulfides, oxides, and silicates. The outer rock shell, probably about 100 miles thick and with a density around 2.8, is thought to be composed mostly of silicates, becoming in general more siliceous as the earth's surface is approached. NATURE'S SMELTING OPERATION Nature seems to have subjected the earth to a stupendous smelting operation, burying beyond reach much of the metal that man recovers in his smelting practices. We live on the surface of Nature's "slag dump" and must be content, for the near term, to recover for man's

Jan 1, 1953

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.'" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase 'Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By Frank Van Horn

IT is customary to ascribe two general modes of occurrence to natural gas, namely shale. gas which, as the name indicates, is found in' shale, and reservoir gas, which occurs ill sandstone, conglomerate and dolomitic limestone. Both of these types are found in the Cleveland district. The shale gas has been produced on a small scale for a long period of years, probably dating back as far as 1883. Shale gas is a low-pressure gas, small in volume with variable pressure, and is limited to no definite horizon. It is generally independent of oil, may last for a long time, and is not dependent to any great extent on the structure of the rocks. There are many such wells in the district which range from 400 to 1,840 ft. in depth, although most have been completed at about 800 ft. This indicates that the wells pass through the Cleveland and Chagrin shales into the Huron or Portage shale of the Upper Devonian. During the last 2 years great interest has developed in a deeper-seated reservoir gas. What is commonly called reservoir gas is generally a high-pressure gas occurring in large volume at a definite horizon. Oil may, or may not, be associated with the gas, and in most regions in which reservoir gas is found, the geological structure is of great importance. This type of gas occurs in all large fields such as those of West Virginia which have been supplying Cleveland until the recent discovery of local gas at great depths in commercial amounts.

Jan 1, 1917

By H. W. Knott, M. H. Mueller

The crystal structures of Ti2Cu, Ti2Ni, Ti4Ni2O, and Ti4Cu20 have been determined using powder specimens examined by X-ray and neutron diffraction. Lattice constants have been determined for all four phases using X-ray powder diffraction films. Atom positional parameters of all four phases have been determined from observed neutron intensities. X-ray diffraction calculated intensity data have been presented also for the phase Ti2Cu to point out the particular suitability of neutron diffraction in this case. Interatomic distances have been determined using the positional parameters obtained from neutron diffraction. ALTHOUGH some investigations of the crystal structures have been made of these four compounds previously,'-13 it was the purpose of the present investigation to expand the previous work in order to locate the various atoms, determine their coordinates, and to confirm or to correct some of the previous work. It was convenient to group these four compounds together since they are related chemicallv and/or structurally. The compound Ti2Cu is tetragonil; and Ti2Ni, Ti4Ni2O, and Ti4CU2O are all large fees of the same space group. Ti2Cu has been previously reported as a fee phase by Laves and Wallbaum;1 and Rostoker2 which was possibly the oxide phase, Ti4Cu20. Joukainen, Grant, and Floe;3 and Trzebiatowski, Berak, and Ramotow-ski4 have also reported a phase of this composition. karlsson5 has reported a small fct phase of the composition Ti3Cu which may be the presently discussed Ti2Cu phase. More recently Ence and Margolin6 have reported a small fct phase for Ti2Cu and the present authors7 together with Nevitt8 have briefly reported it to be a bet related to the fct with a co three times the length of the co of the fct and have also reported that this phase has a very limited composition. Further refinements will be reported which have varied some of the parameters of this bct structure slightly. Ti2Ni has been reported as a fee phase by Laves and wallbaum;1 Duwez and taylor;9 Rostoker;2 Poole and Hume-Rothery;10 and Yurko, Barton, and parr.11 In a later paper Yurko, Barton, and parr12 have given the complete structure of this phase based on an X-ray diffraction study which was independently confirmed with neutron diffraction by Mueller and knott.7 Additional crystal structure information will be given. Ti4Ti2O, Ti4Cu2O, and a number of other compounds including Ti4Fe2O have been reported as fcc phases by Rostoker,2 and more recently Nevitt13 has confirmed the Ti4Ti2O phase. Rostoker,2 however has reported diffraction lines for Ti4Fe2O which do not have all odd or all even indices. These lines, therefore, cannot be observed if this compound has a fee structure. This same error has crept into the diffraction results reported for TiNi2O and Ti4Cu20 in the ASTM powder data which has been credited from Rostoker's data. Complete crystal structures of these two phases will be presented. Although all four of these structures have large unit cells and hence do not lend themselves for completely resolved neutron powder patterns, a sufficient number of individual reflections was observed for solving the structure. They also serve as good examples of some of the advantages to be gained by using both neutron and X-ray diffraction techniques. EXPERIMENTAL PROCEDURE All of the alloys were prepared by arc melting. The starting metals had the following purity: Cu 99.999 pct, Ni 99.83 pct, and Ti 99.92 pct. Oxygen was introduced into the two oxide phases as chemically pure TiO2, with the remainder of the titanium coming from the above mentioned metal. All of the sample buttons were annealed in evacuated Vycor tubes, the two binary phases for 5 days at 700°C and the two oxide phases for 3 days at 900°C. Oxygen analyses were performed on all four phases by two independent laboratories with the following amounts of oxygen present in atomic percent; Ti2Cu-0.06, Ti2Ni-1.03, Ti4Ni2O-13.95, and Ti4Cu20-13.87. The stoichiometric amount for the oxide phases is 14.29 at. pct. Since all of the samples were very brittle they were easily reduced to a powder for diffraction measurements. The lattice constants given in Table I were determined for the four compounds from X-ray diffraction patterns of powder samples exposed to filtered copper radiation using a 114.59 mm diam Debye-Scherrer type camera using the Straumanis loading. None of the patterns showed a detectable amount of a second phase. The lattice constants were obtained from an IBM 704 computer program employing a least squares treatment with systematic correction terms as previously reported.14

Jan 1, 1963

By J. Jones-Parra, J. C. Calhoun

INTRODUCTION The purpose of this paper is to present the results obtained by solving the fractional flow' and frontal advance' equations to obtain oil recovery at water breakthrough as a function of the length of the system being flooded, the linear velocity of injection and the displacing phase viscosity. The method of solution makes use of the stabilized zone concept first presented by Terwilliger, et al3 when calculating saturation distributions in a gravity drainage system. In order to check the calculated results, the equations and method of solution were applied to the system on which Rapoport and Leas' reported experimental data. METHOD OF SOLUTION The solution of the fractional flow equation and the frontal advance equation is obtained by assuming that a water front forms to sweep the oil out ahead of it. There is ample evidence that under the proper conditions a water 'front does form. If this water front is not to dissipate, the water saturations which comprise it must have equal linear velocities. These water saturations are said to comprise the stabilized zone. Equation (2) indicates that for all these saturations and hence fw must plot as a straight line against saturation for those water saturations comprising the stabilized zone. The water saturations lying between the highest in the stabilized zone and the highest that can be achieved in the porous medium comprise the variable zone. Regardless of the numerical value of the length of the system, the variable zone must eventually span all of it, so that for long enough systems in Equation (1) will be small enough to be neglected. Hence, for the saturations in the variable zone Equation (1) can be simplified to In order to determine the composite fw function applicable to the entire range of saturations in the porous medium, it is necessary to find the water saturation which separates the stabilized zone from the variable zone. This dividing saturation must be on the curve defined by Equation (4), and a tangent curve at that point must pass through the initial water saturation to satisfy Equation (3). Hence, the valid fw curve is given by a straight line starting at the initial water saturation, tangent to the curve of Equation (4): and along the curve of Equation (4) from the point of tangency on. The point of tangency determines the water saturation dividing the zones. The length and shape of the stabilized zone can be found by solving Equation (1) for Integrating this expression numerically between any two saturations in the stabilized zone gives the distance separating these two saturations. By repeated integration, the saturation distribution of the stabilized zone can be determined. The total length of the stabilized zone is given by The integral appearing in Equation (5) is a function of the viscosity ratio, the capillary properties of the rockfluid system, the relative permeabilities, and the initial water saturation. Considering these variables fixed and designating the value of the integral by writing caw for and v/60 for q/A; Equation (5) becomes The saturation distribution of the stabilized zone can be integrated over its length and divided by the length to obtain the average water saturation The volume of water in the stabilized zone is then given by The average water saturation in the variable zone can be found by extending the straight line segment of (the segment joining Sw and Sw) until it intersects fw = 1.00. The saturation at the intersection is. This method of finding is nothing more than the graphical solution of the equation The volume of water in the variable zone at breakthrough is then given by Assuming no initial water saturation, the recovery at breakthrough expressed as percent pore volume is given by

Jan 1, 1953

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949