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By R. F. Burdyn

The inadequate use of centrifugation to economically recover solids from weighted drilling fluids reflects the need for better equipment and techniques for this putpose. Laboratory studies in the development of an improved separator are described in which an operating equation is derived and tested. Results show that the concentric cylinder geometry employed effectively separates bnrite from a suspension and that the operating equation provides a good approxinmtion for scale-up. INTRODUCTION Our current drilling technology frequently requires a high-density drilling fluid obtained by addition of barite. In the course of drilling, formation solids which are too fine to be removed either by screening or settling become suspended in the drilling fluid and gradually the volume of solids in the mud increases. The volume fraction of solids must be limited (if a satisfactory set of rheological parameters are to be maintained). A centrifugal separatorprovidesan economical way of accomplishing this. The barite recovery process can be considered as a separation of two solids. One, the light solids, composed of formation and added solids, has a specific gravity of 2.6 to 2.7; the other, barite, has a specific gravity of 4.2 to 4.3. This density difference, plus the fact that the average light-solids particle size is much smaller than the average barite particle size, permits separation by a centrifuge. In drilling fluids some of the coarse particles of the light-solids-range will settle faster than fine particles of the barite-particle range. As a result a complete separation of the two species is not possible. since the object of the process is not merely recovering the maximum amount of barite but includes as well removing the maximum amount of light solids, an optimum barite recovery efficiency exists. From a practical standpoint this optimum cannot be determined in the field for each drilling fluid system, and in practice the separation is less than optimum, with some sacrifice of barite. Drilling technology has included centrifugal separators for barite recovery for more than a decade. Results have been reported by a number of investigators indicating that the process is practical and economica1. l-4 The decision to use a centrifuge is based on economics in which direct cost savings and the indirect benefits in rig time derived from improvement of the drilling fluid are important factors. One would expect that centrifugal separation of barite from drilling fluids would significantly affect barite consumption; however, this is not the case. The Minerals Yearbook shows an annual domestic barite consumption in the drilling industry of nearly 1 million tons.5 By rough estimate there are perhaps 80 separators presently in field use. Assuming half of these in use at any one time, operating an average of four hours per day, at recovery rates averaging 3,000 Ib of barite per hour, total annual recovery is about 90,000 tons. This is less than 10 per cent of he total barite used. I conservatively estimate that barite consumption in drilling operations can be reduced by 30 per cent through greater utilization of centrifugal separators. To encourage more widespread acceptance of centrifugal separators in the drilling industry, improved equipment and techniques would be very desirable. The present paper, covering theory and results obtained from a laboratory model, is the first in a series on he development of an improved mud separator for field use. THE CONCENTRIC CYLINDER GEOMETRY AS A SEPARATING DEVICE Consider the geometry shown in Fig. 1, consisting of two concentric cylinders separated by an annular space. These are arranged so that the outer cylinder is fixed and the inner one can be rotated about its axis on shafts sealed against the ends of the outer cylinder. If the outer cylinder is fitted with openings at either end, the inner

Jan 1, 1966

By George T. Wickes

(Washington Meeting, May, 1905.) SEVERAL years ago, Mr. Robert A. Cook described and illustrated in our Transactions 1 a mechanical coke-drawer, patented in 1891 by Mr. Thomas Smith of the Thorncliff Iron Works, Sheffield, England, and first introduced in the United States in, 1896, at the coking-plant of the Latrobe Coal Co., Latrobe, Pa. This machine has not received any very extended application in this country, although it was successfully used in two places for a number of years. The present. paper describes a new and simpler machine, containing few wearing-parts capable of withstanding continued rough usage. Anything which tends to prolong the general use of bee-hive ovens will be welcome to those who are interested in cheapen¬ing the cost of producing coke in such ovens, especially if it provides satisfactory mechanical means, replacing the hard labor involved in drawing coke by hand with the old-fashioned ?duck bill.? The difficulty of finding efficient coke-drawers, especially during the summer season, and in the South, is notorious. Yet, notwithstanding the great improvements that have been made in retort coke-ovens, new bee-hive ovens are continually constructed; and a machine which will successfully compete with hand-drawing, and, at the same time, add to the efficiency of the bee-hive oven, seems to deserve notice. The machine here described was put in operation at the Frick Coal and Coke Co.'s plant, known as Continental No. 1, at Uniontown, Pa., in October, 1904, and is reported to have met successfully all the tests to which it has been subjected. This trial has demonstrated that one of these machines, equipped with an electric motor, and operated by one mart with an assistant, besides two men to " water down " the

Jul 1, 1905

By David R. Mitchell, B. M. Bird

DENSE-MEDIA processes utilize the familiar laboratory float-and-sink procedure on a commercial scale. Just as wood chips float on water and sand sinks, so coal floats and refuse sinks when placed in a medium intermediate in specific gravity between the coal and refuse. Liquids intermediate in specific gravity between coal and refuse used in commercial plants are of four types: (1) organic liquids of high specific gravity-halogenated hydrocarbons; (2) dissolved salts in water; (3) pseudo liquids obtained by suspending solids, such as sand or magnetite, in water, and, (4) fluidizing a mass of sand or other solids by air currents. Those most widely used for cleaning coal are solutions of calcium chloride in water and a suspended sand or magnetite pseudo liquid. Laboratory float-and-sink testing is an intermittent operation during which every opportunity is given for particles lighter than the medium to float and particles heavier to sink. Commercial processes are continuous; vertical and horizontal currents of the separating medium occur as either part of the process or unavoidedly produced by the introduction of feed and withdrawal of products, 'so that the exact separation of the laboratory technique is not duplicated by commercial processes. However, separations close to the theoretical are obtained in commercial machines by careful technical control of the process. Most machines in commercial installations are crowded to get as much out of the equipment as possible, so that careful technical control is necessary is get the recoveries and grade of product desired. Sizes usually cleaned are plus ¼ in. or plus 1/8 -in. in the United States and plus 1/16-in. in Great Britain. Coal as small as 1 mm. has been cleaned in some experimental installations. The separation of coal from refuse in sizes finer than about 1/8-in. is made difficult by viscosity effects and hence at the present time cleaning is confined to the coarser sizes. Technical advances in the art of cleaning coal by dense-media processes is progressing rapidly and it is likely that equipment, media, and procedures will be developed to clean sizes down to 0.5 mm. efficiently and at low cost.

Jan 1, 1950

By Theodore B. Comstock

The existing topographical features of the United States present many points of interest to the student of dynamical geology, but there is, perhaps, no subject which offers a more promising field for investigation than the relations between the geological structure and the mineralogical characteristics of the principal mining districts. There are seven prominent culminating points in the relief of North America, each one of which can be used as a type of the physical features of all the others. Again, if we divide these seven elevated districts into two sets, we shall discover a still more striking parallelism between the individual members of each group. But the most remarkable revelation is the fact that each one of these points is more or less closely the centre of an area of economically important mineral resources. It is interesting to note in this connection that six of these mineral tracts lie mainly within the borders of the United States, three of them being almost wholly in our territory. For

Jan 1, 1883

By Persifor Frazer

The mines which I am about to describe are all situated in the northern part of the States of Nuevo Leon and Coahuila, Mexico, between the twenty-sixth and twenty-seventh degrees of latitude. They might be grouped, orographically, into four classes: 1. Those in the Sierra de la Ygnana chain; 2. Those in the Sierra de Gomez chain; 3. Those in the Cerro Mercado; 4. Those in the Sierra de San Marcos chain. (See large map.) The first two of these may be further arranged in one geographical district, to which the name, "the Villaldatna. district," may be applied, and the last may be ascribed to the geographical district of " Monclova." Geologically described, the country rock, in which four of the six mines occnr, is a limestone, concerning which a few words will be said further on, to wit.: The Arroyo (gulch), the Montanos and the Pinitos (pines), in the Villaldama district, and La Paloma (the dove), or Iron Mine, in the Monclova district. The San Rafael appears to lie in granite, or a heavy-bedded gneiss, presenting most of the characteristics of the latter, though the contact plane of the limestone is not far off. It is certainly worthy of attention that the ore occurs in that portion of the crystalline rock, which is nearest to the limestone, and it has been thought by some observers to be a true contact vein. It is well known that veins of this character are very often distinguished for constancy and richness. Although the undersigned cannot entirely free himself from the impression that this proximity of different formations has had an important influence in the origin of the part of the vein on which this mine is situated; still he was unable to establish it actually at the contact of the limestone and granite, but rather a short distance within the latter. Two openings of the Riojas vein were respectively in limestone and in rotten whitish granite, but this fact, if established (as by the correspondence of the strike line of the vein in direction with that of a line joining the

Jan 1, 1884

By A. J. Hendron, D. U. Deere, F. D. Patton, E. J. Cording

In the design of structures founded in the near-surface rock, a distinction may be made between those problems that are related to the strength of the rock mass, and those that are related primarily to the compressibility of the rock mass. The mining engineer deals almost exclusively with problems involving strength in the design of open-pit slopes and underground openings. The civil engineer is similarly concerned with strength problems in the design of vehicular and water tunnels; underground power plants; cut slopes in rock for highways, canals, and spillways; and in the study of the sliding resistance of the foundations of gravity dams and the abutments of arch dams. Moreover, the civil engineer encounters problems in which the compressibility of the rock becomes the key element in the design. These problems include settlement of heavy structures supported on rock, deformation of the abutments of arch dams, and deflection of pressure tunnel linings. The design problems listed above are still solved largely on the basis of experience and rule-of-thumb. However, recent developments in rock mechanics give promise of providing more realistic approaches to certain aspects of the design. This paper, presents some of the more important recent developments which contribute to an understanding of rock behavior and which aid in design of rock structures. Typically, four steps are involved in the design of a structure, whether it be a machine element, a structural member of a building, or a structure in rock. These steps are listed below:

Jan 1, 1967

By H. Rush Spedden, A. M. Gaudin

IN the belief that a critical study of its operating problems might be a sound investment, the Cuban American Manganese Corporation initiated an ore-treatment research in cooperation with the Massachusetts Institute of Technology. One of the early objectives of this research naturally became the relationship of the microscopy of the Cuban ores of the Corporation to their flotation treatment. The operations in Cuba have already been described by F. S. Norcross, Jr.7 and the laboratory study of manganese oxide flotation goes back a number of years .4 Broadly speaking, the difficulties encountered in the flotation of manganese ores are that the consumption of reagents is extremely high, the concentrate contains more silica than is desirable and the tailing losses are relatively high. An appreciable betterment on any of these scores would achieve a definite betterment in costs, quantity of minable ores, and quality of product. The microscope study discussed in this paper was made on samples from the Quinto mine, from the Ponupo mine, and from mill products at various stages of passage of the ore through the mill. The writers have had access to Company records and in particular to the petro¬graphic studies made on thin sections of ore by the late Professors R. J. Colony and Philip Krieger, of Columbia University. They acknowledge their debt to both of these men for the help derived from the reports. Manganese oxides are black, friable, smudging. It is, therefore, very difficult to judge operations by inspection. The mineralogy of manganese compounds seems to be confused, and the authors believe that many more minerals have been described than actually exist. Much of this difficulty is due to the prevalence of the structural conditions that will be discussed further in this paper; namely, the porosity and the friability of the ores, and the extremely intimate association of minute manganiferous mineral crystals with impurities of various sorts. By all odds the most important manganese mineral in Cuba is the one that in this paper is called "psilomelane." The name "psilomelane" has been used in so many different ways that the choice of it for this ore may not be approved by all. However, it seems to be the best under the circumstances. This mineral accounts for about 97 per cent of the manganese in the ores of the Quinto and Ponupo mines and in the mill feed. The remaining odd 3 per cent consists mostly of pyrolusite together with minor amounts of other manganese oxide minerals. DESCRIPTION OF PSILOMELANE Aggregate Structure In grains or lumps, psilomelane has a characteristic fibrous appearance and seems

Jan 1, 1942

By Ellis Clark

THE mining town of Pribram is situated in Central Bohemia, on the western slope of the Heiliger Berg, 30 miles southwest from Prague. Birkenberg, the village in which most of the shafts and ore-dressing establishments are situated, is built on a mountain of the same name. It is about a mile from Pribram, is 1700 feet above the sea, and is surrounded by graywacke rocks of Silurian origin, which are intersected by greenstone dikes, and in the southerly, southeasterly, and southwesterly direction are bounded by granite. The graywacke formations consist on one side of graywacke sandstone and quartzite, and on the other of graywacke slates. These last are separated from the first in the immediate vicinity of the mines by a graywacke seam converted into clay. For many years this so-cal led clay seam (lettenkkluft) was considered as a boundary of the ore deposits in both zones of graywacke. The graywacke formation is divided according to its hardness, structure, texture, and color, into fine, coarse, compact, slaty, whitish-gray, reddish-gray, and black graywacke. The, miner divides the formation into four divisions. The first or lowest division, which is in contact with the granite, consists of a fine-grained dirty gray slate; the -second is a very fine to a very coarse schist, white to reddish-gray in color, and rich in quartz, but containing little mica; the third consists of a slate with a contused cleavage, which has a dirty gray, dark gray, and very often black color and is often graphitic in its composition ; the fourth consists of a fine to coarse-grained graywacke schist, of a grayish-white or reddish-gray color, and rich in quartz. The cleavage in all four divisions strikes from northeast to southwest, and the dip is sometimes northwesterly, sometimes southerly, and often vertical. All four zones are cut through by a great number of diorite and greenstone dikes and chimneys. The thickness of these dikes, which are of

Jan 1, 1881

By Chandler Morse

RENEWABLE VS. NONRENEWABLE NATURAL RESOURCES Nonrenewable resources, such as minerals, are the inevitable center of attention in discussions of depletion and exhaustion. Nevertheless, it may well be proper to regard some nonrenewable resources as not subject to exhaustion, and renewable resources may sometimes be treated as if they were finite stocks. Thus, the availability of nonrenewable resources is not and probably never will be known completely Chap. 2.5A, and therefore is not subject to firm predictions concerning exhaustibility. Moreover, because exploration and discovery are more or less continuous processes it is often appropriate to regard mineral supplies as flows, and to treat the estimated reserves as working capital, an inventory, continually depleted by use and augmented by discoveries.23 The aggregate economically exploitable stocks of a given mineral are seldom estimated (or estimatable) with precision, as Chap. 2.5A shows, and even when they are, forecasts concerning years of remaining life can be and often are falsified by changes in one or more of the multidimensional conditions of supply and demand; or the productive services formerly derived from an exhausted stock may continue to provided without material impairment by one or more substitutes b Conversely, the renewable resources are all subject to depletion when the rate of use exceeds the natural or induced rate of replenishment, and cases of exhaustion or near exhaustion, as through soil erosion, overcuttmg of forest lands, and overfishing, are rather common c Where exhaustion is a clear possibility the resource may either be exploited on a consciously adopted "sustainable yield" basis or be treated as an exhausting asset." In some cases, conscious treatment

Jan 1, 1976

By Charles S. Barrett, Robert F. Mehl

A study of the structures arising from the decomposition of the ß solid solutions in the Cu-Zn and the Cu-A1 systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution— the Widmanstätten structure—-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the ? phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series—that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-—which at present seems the only a1ternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the ß and in the precipit'at.ion of the y phase from the y in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point, of view.

Jan 1, 1931

By J. B. Morrow, D. H. Davis

THERE are two general approaches to the problem of increasing profits from an operation. One is to lower expense; the other is to raise income. Mechanical preparation of coal may be used for either purpose but a prudent consideration of many details must precede any decision lest the results be negative instead of positive. It is quite possible that any net gain will result from a combination of the two. Since mechanically prepared coal invariably is a better product qualitatively than a hand-picked coal from the same mine, it is a reason- able expectation that the customer will be willing to increase the producer's income by paying a higher price. Or there may be the possibility that a combination of mechanical mining plus mechanical cleaning will give a lower over-all production cost for the coal in the railroad car. More likely, there will be found a combination of these two factors. From the customer's point of view, the competitive delivered cost per B.t.u. considered in relation to such incidental factors as dust nuisance, handling properties, ash disposal, and ash fusibility determines what he will pay. In a bulk tonnage product such as coal, freight is a very considerable part of the delivered fuel cost, and obviously freight paid on incombustible ash has no economic attractions. INCENTIVE FOR CLEANING Coal is prepared in four major ways: 1 (I) by screening or sizing, (a) by mixing or blending, (3) by cleaning, including hand picking and mechanical cleaning, (4) by dustless treatment. By a combination of any or all of these methods, coal can be prepared to standard specifications. It is easily possible to have good cleaning and still get a poor final product because of faulty screening or mixing,

Jan 1, 1943

By Norman Goss

IT is generally agreed that cold-working mechanically refines the grains into smaller fragments and with continued working these are oriented with certain crystallographic directions bearing a relation to the direction in which the metal is worked. Some of the energy expended on the metal during plastic deformation appears in the form of heat, but a very small portion remains in the metal as stored energy. The entropy, specific heat capacity, temperature at which recrystallization will just begin, density, ductility, elasticity, tensile strength, and resistance to corrosion are affected. These properties have been studied extensively and some of the changes in the physical properties due to cold-working were attributed to lattice distortion.1-8 The broadening of the K. lines on the X-ray diffraction diagrams of plastically deformed metals is believed to indicate lattice distortion, and consequently the existence of internal stresses. The evidence supporting this theory rests solely upon the observed experimental fact that the dif-fraction lines are broadened and the K a doublets are completely diffused. Elam9 has reviewed the matter of lattice distortion in relationship to the hardening of metals by plastic deformation. The X-ray diagrams of plastically deformed metals differ in general from annealed metals. The hardening of a metal was believed due to lattice distortion.9 The resolu-tion of the doublet is lost when a metal is cold-worked and the Lane spots are elongated. At one time this elongation was thought to indicate the elastic bending of the crystal planes. However, more careful work showed that the asterism was due to new orientations developed within the fragmented grains during plastic deformation. Some theories attrib-uted the hardening to fragmentation of the grains into smaller units.

Jan 1, 1940

Alfred Noble Joint Prize Committee F B Foley, '56 American Documentation Institute F B Foley, '56 American Geological Institute J L Gillson, Nov '56, H A Meyerhoff, Nov '57 Committee on Government Relations J L Gillson, '56 American Power Conference Paul R Nichols, '56 American Standards Association Mining Standards Board E R Borcherdt, Jan '58, Otto Herres, Jan '58 Alternates E W Bullard, Dec '56, and J K Richardson, Dec '56

Jan 1, 1956

By H. F. Yancey

Various criteria for evaluating the performance of coal washeries are discussed critically, with particular reference to ideas developed at the First International Conference on Coal Preparation held in Paris in June 1950. Criteria that relate only to the sharpness with which a cleaning unit separates coal from impurity are compared with those that reflect loss of coal or quality of products.

Jan 6, 1951

By Hugh Henton

THIS paper is the result of an investigation made in association with Dr. Charles H. Fulton. Early in 1918 a search was started for methods of utilizing, in the manufacture of basic refractories, certain domestic resources in magnesites, dolomites, and magnesian limestones. Much information was collected during that year and during 1919 regarding magnesite and dolomite deposits. During 1920 and 1921 a research was made into methods of calcining dolomite and separating magnesia therefrom. Some success was attained and many new ideas were brought out in connection with the preparation and utilization of magnesia in the form of "caustic" or light-burned material as well as in the form of refractory or "dead-burned" material. Stimulated by this success, much advance has been made in manufacturing processes for the "plastic magnesia," so called, used for magnesia cement, stucco, flooring and otherwise in the structural industries.

Jan 3, 1926

By JAS. F. McCARTHY

THE present Hecla Co. is a Washington corporation; the Hecla Co. of Idaho was the old company. The older corporation owned two claims, the Hecla and the Katie May, and was incorporated for 500,000 shares of one dollar par value. The principal shareholders and officials of the older company were among the early mining men of the camp. Among the active officials were John A. Finch and A. B. Campbell. Among the directors and share- holders were Patrick Clark, J. R. Smith, Frank Upman, F. J, Kipp, Chas. Kipp, B. A. Kipp and Carl Landsee. F. J. Kipp and Carl Landsee are now directors of the Company. All of the others mentioned have died, but the surviving members of their families retain their ownership in the Company's shareholders. B. A. ,Kipp, who recently died, was the largest shareholder at the time of incorporation and Patrick Clark was the second largest shareholder. B. A. Kipp is a brother 'of F. J. Kipp, director of the Company.

Jan 1, 1924

By ALFRED D. FLIWN

ENGINEERING COUNCIL is not "about to die," as some persons are saying. Through a natural and foreseen reorganization, Council is entering a new stage of existence with enlarged power for usefulness. Its early constituents have made it possible for many more of their fellow engineers and men of other technical vocations -to take a- share in its activities, responsibilities and support. A new organization is being set up, but it is really a new embodiment of the same spirit of service. Another step is being taken toward the full acceptance by the technical professions of their obligation to the public and to one another for those services which can -be rendered only through effective organization. A brief retrospect is timely. Engineering Council was established in the spring of 1917, as a department of United Engineering Society in response to requests of its Founder Societies. .It followed various attempts of these societies to deal through joint committees with public questions affect¬ing engineers -and with inter-society affairs. These attempts had very limited results. In the new by-laws adopted by United Engineering Society, the purposes and-powers d-powers of Engineering Council were thus defined: "To provide for convenient cooperation between the four Founder Societies, for the proper consideration of questions- of general interest to engineers and to the public, and to provide the means for united , action upon questions of common-concern to engineers.

Jan 1, 1920

By R. H. Hadfield

Professor ArnolD, of the Sheffield Technical School, who has done so much excellent work in metallurgical research, recently produced, with the aid of aluminum, a sound ingot and bar from the purest known Swedish brand containing 99.8 per cent. of pure iron. Table 1. shows the physical quantities of this metal. TABLE I.— Tests of a Sample of Almost Pure Iron Prepared by Professor Arnold from D. v Ewedish Bar, Containing Before Fusion 0.04 Per Cent. of Carbon. I. II.+ III. Series mark,.. 136 1.371F ...... C, 0.07 0.07 Si, 0.04 0.04 8, 0.02 0.03 ...... Analysis, per cent,. .. P, 0.02 0.015 ...... Mn, 0.06 0.07 Al, 003 ............ Fe, 99.76 99.81 ...... Specific gravity,........... 7.863 ...... Original diameter, inches,. .. 0.564 0.798 0.798 Original area, square inches,. . 0.25 0.50 0.50 Limit of elasticity, tons per square inch,...... 18. 3.8 Breaking-load, tons per square inch,. 21. 23. 14.75 Total elongation, per cent., measured on 2 in.,...... 50. 49.25 61. Total reduction of area, per cent.,. 80. 69.60 61.20 Extension at permanent set, per cent.,...... 0.007 ...... silky and Appearance of fracture,. .. . silky i granular in parts.

Jan 1, 1894

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By V. Apraxine, J. Lakaye, J. J. Saquet, P. Troch

Union Minière du Haut-Katanga owns concessions for extracting copper and associated metals in the high plateau region of Katanga. The concession is about 188 miles long by 44 miles wide and has three principal areas: Southern area-The Prince Leopold mine is an underground operation from which a copper-zinc sulfide ore is extracted. The mine and associated concentrator are at Kipushi. Copper concentrates are smelted and converted to blister copper at the Lubumbashi smelter at Elizabethville.

Jan 12, 1962