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By David F. Machuca-Mory

Modelling the geometry of a vein is a crucial step in resources estimation. The resulting models are used as mineralization domain boundaries and have a direct impact on the tonnage of estimated resources. Deterministic models are often built using time consuming wireframing techniques usually based on hand interpretation of the drillhole intercepts. Another approach consists in coding the drillhole samples by a function of their distance to the veins contacts. The coding is subsequently used for modelling the vein contacts away from drillholes. This is a more efficient approach and is able to provide a measure of tonnage uncertainty. The use of location-dependent variograms improves the modelling by incorporating local changes in the anisotropy of the vein structure. This combined approach results in more realistic vein models, particularly when the geometry of the vein has been are altered by folding, shearing and other structural processes. The approach is illustrated on a realistic case study.

Oct 1, 2009

By J. -M. Chautru

A geostatistical simulation of a typical mining site for polymetallic nodules in the North Pacific Ocean is presented. This is the first stage in the design of an industrial mining system. Two variables which have a major effect on the orebody's economic potential are considered, namely: the maximum slope of the ground inside a mining block of 50 x 100 m; and the average quantity of nodules on the same support. Two geostatistical problems have emerged in this study. The first is due to the lack of a change of support model for the maximum of a variable. A provisional solution, considering an experimentally accessible 'equivalent' support, is proposed. The second is due to a non-linear link between the two variables. To be able to take this into account in the simulation, we propose a new method based on the decomposition: X = E(X/Y) + Residue (X). Satisfactory results were obtained with this approach.

Jan 1, 1987

As discussed previously, total cost is the sum of the direct materials, direct labor, and production overhead costs. The assignment of direct materials and direct labor costs to individual activities is generally straightforward. The assignment of overhead often is not. Overhead costs frequently contain allocations that only approximate the demand the activity has made o; the overhead resources. The inaccuracy of the overhead calculation can create erroneous production cost information and lead to suboptimal management of the operation. This problem is particularly acute when determining the production cost of individual products in multiproduct firms. Pricing, process management, and product mix decisions are especially susceptible to errors in product costing. The problem of properly determining production cost is complicated by the fact that few if any alternative methods exist to identify the inaccuracies in overhead allocation. To avoid errors, some firms simply ignore overhead costs in their product cost calculations, particularly those resulting from marketing and distribution of the final product.

Jan 1, 1999

By Paul A. Beck

IN several recent investigations1 ' considerable evidence was accumulated to show the predominance in various face-centered cubic metals of a certain relative orientation, corresponding to a rotation of 30" to, 40" around a [111] axis, between a matrix with a strong single orientation texture and grains growing in this matrix." This relative orientation was found to occur both in recrystallization and in coarsening, "secondary recrystallization", so that one is inclined to look for an explanation applicable in both cases. The abundance of growing grains in the described orientations proves that suitable "nuclei" are present in the matrix material and that they have the capacity to grow. The scarcity of growing grains in other orientations may be explained in one 'of two ways. Either the number of nuclei or the rate of growth must decrease strongly for orientations deviating from that predominating among the growing grains, Fig. 1. Both the "oriented nucleation" and the "oriented growth" theory found support in the literature. Because the frequency of nuclei as a function of orientation is in most instances not amenable to direct experimental investigation, a definitive decision is difficult to achieve. However, it is now known with great certainty that the rate of boundary migration is strongly dependent on the relative orientation of the two grains meeting at the boundary and that the orientation favored by high boundary mobility closely corresponds to that predominating in most cases of recrystallization and coarsening. Thus, it was found that, in general, the mobility is very low for boundaries between grains of nearly identical orientation, or for coherent twin boundaries. On the other hand, the boundaries between two grains of a relative orientation correspending to a [1111 rotation of 30" to 40" have the highest mobility in face-centered cubic metals. If a large variety of nucleus orientations are produced grow- by means of a highly inhomogeneous local deformation, nuclei close to the above orientation are found to grow fastest.z4 In view of this evidence and of the fact that the preferred orientation relationship is the same in recrystallization and in coarsening, the oriented growth theory appears by far the more promising one. Since the origin of nuclei in primary recrystallization is certainly different from that in coarsening, the occurrence of the same orientation relationship in the two processes would be difficult to explain on the basis of oriented nucleation. other advantages of the oriented growth theory are its capability of accounting for the often observed sharpening of the texture in coarsening, and its suitability for explaining the role in the formation of the ''cube texture,, of the most important variables, such as the degree of rolling, the penultimate grain size, and the time and temperature of the last anneal: No similarly consistent explanation of all these effects has ever been offered in terms of oriented nucleation. An important problem in connection with the oriented growth theory is the following: In the ce-c entered system there are four [111] axes and

Jan 1, 1952

By Bernard K. Asdell

Georgia, a state seldom considered to be an important mineral producer, has one surprising feature-it is the nation's largest producer of kaolin. Kaolin is a highly important raw material in the paper, rubber, ceramic whiteware, paint and chemical industries. In 1965, more than 2.7 million tons of kaolin were produced in this state, a 150,000-ton increase over the preceding year, and production continues to climb. Strictly defined, the term "kaolin" applies to a group of hydrous aluminum silicates in which kaolinite is the predominant mineral. Kaolinite is inherently white, non-abrasive, chemically inert, and of a very fine particle size, ranging from sub-micron to 40-microns equivalent spherical diameter. An electron-micrograph of kaolinite is shown in Fig. 1. The particles finer than about 2 microns are thin, elongated plates, hexagonal in outline. The larger particles, coarser than 2 microns, are predominantly vermicular in outline with a foliated structure. Table I shows a typical chemical analysis of commercial, wet-processed kaolin compared to pure kaolinite.

Jan 11, 1967

By R. A. Cunningham, A. S. Murray

If a dense fluid such as mud or water is used for circulation, the formation drilled is influenced by a hydrostatic pressure. This pressure depends on hole depth arid drilling fluid density. Laboratory tests indicute that drilling rates in many forri~ations are decreased with increased pressure,—in some cases as much as 90 per cent. A comparison between laboratory and field tests indicates that drilling fluid head affects drilling rates in the field approximately the, same as in the laboratory. Drillirrg rates of many formations are increased by reducing drilling fluid head. INTRODUCTION For many years it has been noted that field and laboratory drilling rate tests did not agree even when the formations tested were the same. For instance, tests of some shales by the Hughes Tool Co. laboratory indicated drilling rates approximately 20 to 30 ft/hour, whereas in the ground this shale would drill only 3 to 5 ft/hour. A possible reason for this discrepancy is the effect of the high pressure which the drilling fluid exerts against the formation at the bottom of the hole. Consider a small element of rock (Fig. II that is to be removed by a rock bit. If the hole is filled with mud or water. the upper surface of the rock element is subjected to a pressure which depends on hole depth and fluid density. The mass of earth around this rock element presses against the circumferential surface and the lower surface. Because of the probability of shearing stresses between the rock element and the surrounding rock, this element is not under true hydrostatic stress. However, as a first approximation for test purposes the rock element was assumed to he under hydrostatic stress. The effect of hydrostatic pressure on some physical properties of rock has been studied.1,2,3 These tests show that the "differential" compres-sive stress:': necessary to cause rup- ture in rock cylinders is greater when tested under high hydrostatic pressure than when tested under atmospheric conditions. These tests were made with pressures greater than 20,000 psi which is in excess of those normally encountered in oil well drilling. Similar tests were made by the Bureau of Reclamation' using pressures equivalent to those encountered in oil well drilling. Again the "differential" compressive stress necessary to produce failure increased with increasing hydrostatic pressure. These tests indicated that drilling rates would probably decrease. Correlation between these tests and drilling tests was not practical. The purpose of this work is to study the effect of mud column pressure on drilling rate, assuming that the material drilled is in a state of hydrostatic strcss. This problem was initially investigated in the laboratory using variable bit loads and confining pressure;. Confirmation of laboratory results was obtained in the field from a series of carefully controlled drilling tests. Because of the necessity of testing many different types of formations. only results from representative formations will be presented here.

Jan 1, 1956

By Sir John Cadnan

The production from the Maidan-i-Naftun area for the year ending March, 1928, was 5,340,000 tons (40,210,200 bbl.), an increase of nearly 13 per cent. over the production for the year ending in March, 1927. The production by years since the opening of the field in 1912 is given in the following table: [1 ton = 7.53 bbl.] Year Ended MaRch Tons Year Ended March Tons 1912 (7 months)............. 43,084 1920....................... 1,354,631 1913........................ 80,800 1921....................... 1,767,070 1914........................ 273,635 1922....................... 2,310,098 1915........................ 375,977 1923....................... 2,913,908 1916........................ 449,394 1924....................... 3,583,000 1917........................ 644,074 1925....................... 4,221,000 1918........................ 897,402 1926....................... 4,470,000 1919....................... 1,081,919 1927....................... 4,735,000 1928....................... 5,340,000 The actual production represents only a small proportion of the potential production. The Masjid-i-Suleiman Field The present producing unit, the Masjid-I-Suleiman, is an anticline some 20 miles in length by 4 miles in width, including three domes as so far proved. The producing horizon is a very open, dolomitic limestone, which, while showing much variation in texture and porosity, is so connected that the lowering of pressure in one section of the field quickly affects the whole area. The topography of the field is broken, with differences of well elevations of as much as 1100 ft. The depths to the limestone vary from about 800 to about 5000 ft. The closed-in pressure of the oil wells varies from zero to 50 lb. per sq. in. and that of the gas wells is about 450 Ib. Although the static oil level may be several hundred feet below ground level, in oil wells of high elevation, all the wells flow continuously or intermittently after they are once started—the majority continuously. The gas is very high in hydrogen sulfide in gas-oil wells of low pressure.

Jan 1, 1929

By Richard M. Foose

FIVE miles southwest of Mt. Holly Springs, Cumberland County, Pennsylvania, the Philadelphia Clay Co. has been mining and milling a white clay since 1896; for use in white cement, as a filler in rubber, pigment and paper, in the manufacture of insecticides, and for other minor purposes. Until late in 1942, when the mine was abandoned because of labor shortage, combined underground mining and surface stripping produced approximately 30,000 tons of clay a year, of which 10,000 tons were refined in the mill. GEOLOGY Lower Cambrian Antietam quartzite and the Montalto quartzite, stratigraphically older, trend N.55°E. and make a sharp 1600-ft. anticlinal ridge of the South Mountains. The Tomstown dolomite overlies the Antietam quartzite on the southeast flank of the anticline, which is displaced near its crest by a steeply dipping oblique fault. Erosion of the less resistant Tomstown formation has resulted in a narrow valley at an elevation of 700 ft. Directly on top of the Antietam quartzite and at the base of the Tomstown formation is a zone of sandy white clay, lenticular along the strike of the formations, ranging in thickness from 10 to 300 ft. within a mile. All of the formations dip steeply to the southeast, from 65° to vertical. The clay crops out at an elevation of about 1000 feet. ORIGIN AND CHARACTER The uppermost part of the Antietam formation is sericitic and schistose at many places, and at all these places weathering is in an advanced stage. The clay is the residual product of weathering of this sericitic quartzite or sandy schist. The crude clay has the physical aspect of a sandy kaolin, but there are large areas in the clay formation that are low in free silica, and commonly the 30 ft. adjacent to the Antietam quartzite is notably free of silica. The overlying Tomstown dolomite has been weathered almost completely to a mixed yellow and brown clay, which carries a zone of nodular and chunky limonite and manganese ore, 4 to 12 ft. thick, about l00 ft. from the contact with the white clay. In mining, this zone is an important "marker," indicating where the white clay may be expected in an advancing tunnel. The contact of the white clay formation with the yellow and brown clay of the Tomstown formation is relatively sharp, although the line of contact is irregular and therefore responsible for the lenticular character of the white clay formation. Following is an analysis of the refined clay containing less than one per cent of moisture when dried at 212°F.: Si02, 67.05 per cent; A1203, 22.27; Fe203, 0.40; CaO, 0.00; Ti02, 1.05; MgO, 0.52; Na20, 0.04; K20, 0.88; ignition loss, 7.65; total, 99.86.

Jan 1, 1944

By L. R. Nelson

Cyprus Pima is a medium-sized open-pit copper mine located 35 km (22 miles) south of Tucson, AZ. The ore body was discovered using geophysical prospecting methods in 1953 and was originally worked as a small underground mine followed by small open-pit operations. As mining equipment grew larger and the economic ore grade dropped, the operation grew in size, through four expansions, to the present 50 500 tpd (56 500 stpd) milling rate. The remaining stripping ratio is about 2.5 to 1. Mining equipment includes 11 electric shovels ranging in size from 6 to 15 m3 (8 to 20 cu yd) and 42 diesel-electric haulage trucks ranging in size from 89 to 223 t (100 to 250 st). Mine planning is performed at Cyprus Pima to serve several functions. The most important is to plan ahead, one year at a time, to predict the ore grade and stripping requirements on a month-by-month schedule. This yearly plan is necessary for budget preparation and is revised once each quarter to incorporate variations in actual production experienced during the preceding quarter.

Jan 1, 1979

By Edward Salisbury Dana

THE remarkable advance in the Science of Mineralogy, during the years that have elapsed since this Text-Book was first issued in 1877, has made it necessary, in the preparation of a new edition, to rewrite the whole as well as to add much new matter and many new illustrations. The work being designed chiefly to meet the wants of class or private instruction, this object has at once determined the choice of topics discussed, the order and fullness of treatment and the method of presentation. In the chapter on. Crystallography, the different types of crystal forms are described under the now accepted thirty-two groups classed according to their symmetry. The names given to these groups are based, so far as possible, upon the characteristic form of each, and are intended also to suggest the terms formerly applied in accordance with the principles of hemihedrism. The order adopted is that which alone seems suited to the demands of the elementary student, the special and mathematically simple groups of the isometric system being described first. Especial prominence is given to the "normal group" under the successive systems, that is, to the group which is relatively of most common occurrence and which shows the highest degree of symmetry. The methods of Miller are followed as regards the indices of the different forms and the mathematical calculations. In the chapters on Physical and Chemical Mineralogy, the plan of the former edition is retained of presenting somewhat fully the elementary prin¬ciples of the science upon which the mineral characters depend; this is par¬ticularly true in the department of Optics. The effort has been made to give the student the means of becoming practically familiar with all the modern methods of investigation now commonly applied. Especial attention is, therefore, given to the optical properties of crystals as revealed by the micro¬scope. Further, frequent references are introduced to important papers on the different subjects discussed, in order to direct the student's attention to the original literature. The Descriptive part of the volume is essentially an abridgment of the Sixth Edition of Dana's System of Mineralogy, prepared by the author (1892). To this work (and future Appendices) the student is, therefore, referred for fuller descriptions of the crystallographic and optical properties of species, for analyses, lists of localities, etc.; also for the authorities for data here quoted. In certain directions, however, the work has been expanded when the interests

Jan 1, 1922

By Todd L. Hollingsworth, Jeremy K. Hobbs

In 2001, the Radomiro Tomic Mine located near Calamq Chile, added a tertiary crushing facility. An 84" wide mobile tripper is used to fill their tertiary crushing storage facility. This paper is a we study to demonstrate the drive and control systems in use on the tripper. Of special note is the design concept used to allow the system to operate multiple motors in both demand and regenerative modes through a single VFD. Also noted is the use of touch screen local controls, handheld radio controls, starting/stopping/ braking philosophies, safety device interfaces, and the local to remote control interface.

Jan 1, 2004

By Donald P. Bellum, Lee Nugent

Southwestern Utah is well known for its scenic attractions. The beauties of Bryce Canyon, Zion Canyon and the Grand Canyon are of world renown. Thusly, Cedar City is known, at least by the local Chamber of Commerce, as the Gateway to the Utah Parks. However, of the thousands of tourists flocking to Utah's many points of interest by way of Cedar City, few realize that any mining takes place in the vicinity, in spite of the fact that iron mines have been in continuous operation for 40 years. The Pinto-Iron Springs Mining District is only 15 miles west of Cedar City, and is the largest iron ore producing district in the West. In recent years, the shipments have ranged from 2% to 4 million tons per year making Utah the fifth-ranking state in iron ore production.

Jan 11, 1963

By Harry M. Mikami, Harold A. Heiligman

The term chromite is often used to cover all chrome ores and concentrates which are the designations actually employed by most industrial users and producers. Chromite is, of course, the predominant mineral in chrome ores which are aggregates of chromite and gangue minerals, most commonly magnesian silicates. Most chrome ores now used are petrographically chromitites which is a rock, rather than an individual mineral term. The title of this chapter, following past usage, is meant in the broad sense. Chromite is the only primary commercial source of chromium. This book is intended to deal only with nonmetallic minerals and rocks. Chromite uses are both metallic (ferroalloys) and nonmetallic (refractories and chemicals), but any discussion of mineralogy, geology, and mining is common for all types. A number of the major commercial ores are interchangeable, and their uses are determined by economic considerations. Mineralogy COMPOSITION [Chromite is a term embracing a wide range of chromium-bearing spinel*-group minerals the compositions of which can be expressed as (Mg,Fe2+)0.(Cr,AI,Fe3+ )203.t This can be further generalized to R2+O.R23+03 and the molecular RO: R,03 ratio is generally close to one. The exact composition may be arbitrarily expressed as a solid solution of six end-members, MgAI2O4, MgCr2O4, MgFe2O4 FeCr2O4, FeA12O4, and Fe2+.Fe23+04 with the proportions of each stated or plotted in the six-cornered prism of Johnston and Stevens61 or this scheme may be simplified to comprise only three endmembers making up a composition triangle, Fig 1. [ ] FIG 1-Triaxial composition diagram showing molecular compositions of chromites listed in Table 1. The RO.Fe2O3 corner includes Ti02 norms listed in the table. Note that the high-alumina chromites (1, 2, 3, 9), form a cluster well apart from the high-Cr2O3 chromites. There is a tendency for high-iron chromites to be higher in Fe2O3 + TiO2 but it is not a consistent or systematic relationship. The MgO/RO ratio must also be known to characterize the chromite chemically. Simplest and most convenient method is Thayer's' in which a chromite such as (Mg.65Fe.352+)O.(Cr.40Al.50Fe.103+)203 would be written as (Mge,) Cr eAlo. The molecular pro- portions of ferrous and ferric oxides can be seen at a glance as the divalent and trivalent oxides]

Jan 1, 1960

By Thomas Fraser, David R. Mitchell

THE primary purpose of the loading plant is to transfer the finished product from the preparation machines to the railroad car, truck, or barge in which it is to go to market. Secondary purposes of the loading plant are: to prevent excessive degradation of sizes during loading, to reduce segregation as much as possible, and to prevent excessive quantities of very good or off-grade coal from entering any one car. Nonuniformity of consignments is one of the chief sources of complaints by consumers and coal merchants. A properly designed loading plant will do much to reduce complaints and insure uniformity, not only from shipment to shipment but also in each individual consignment along the length of the car and in cross section. DEGRADATION IN STORAGE, LOADING AND SHIPMENT The object in loading is not only to handle the coal without breakage and segregation, but also to produce a well-trimmed load that will ride to its destination without spillage o~ breakage en route. The small sizes present in a car-of prepared coal as received by the purchaser consist of: missed small sizes not screened out in the preparation plant, breakage during loading, and breakage caused by handling en route. For domestic sizes of anthracite shipped from the Pennsylvania anthracite field to Atlantic coast cities, the dealers' loss because of breakage in loading and shipment amounts to from 2 to 5 per cent and for anthracite shipped to Middle West cities, the loss is 8 to 9 per cent. This difference is in part because dealers in the Middle West rescreen their coal more thoroughly than is usual in the East. One dealer handling Illinois No. 6 coal shipped from southern Illinois mines to Chicago reports an average size loss of 10 per cent when lump coal is unloaded with a fork. This runs as low as 5 per cent for carefully loaded coal and as high as 15 per cent for carelessly loaded coal. An Ohio dealer estimates the degradation in loading and shipment of West Virginia coals consigned to Ohio cities as follows: Pocahontas lump

Jan 1, 1950

By S. E. Maddigan, B. R. Zimmerman

Most metallurgists are well acquainted with the contributions already made to the study of metals by the use of X-rays. On the one hand, the radiographic method is constantly becoming of increasing importance as a nondestructive testing procedure, while on the other hand the techniques of X-ray diffraction have made important contributions to the fundamental knowledge in studies of phase diagrams, stress conditions, and so forth. A new, and as yet insufficiently appreciated, tool exists in the application of microradiography to alloy structures. This new procedure in many respects bears the same relation to microscopic investigations as does macroradiography to the gross inspection of metal surfaces. However, where macroradiography is used ordinarily to determine the soundness of the metal structure, this new method can be used not only to investigate micro-un-soundness but also to examine the distribution of the constituent elements within the body of the alloy. When combined with the normal procedures of microscopy, this offers a technique of great potential power. It is intended in this paper to present a few examples of copper-base alloys demonstrating the additional knowledge obtained from the microradiographic method. The detection of micro-unsoundness is demonstrated in Fig. I for a sample of cartridge brass as cast. The sample ap- peared quite sound when viewed under the microscope, but in reality was thickly populated with minute voids. This application of the method conforms in every way to conventional large-scale radiography and has been used to facilitate production of metal for vacuum devices.' The true potentialities of the technique are revealed by comparison of Figs, 2a and 2b, which are respectively a photomicrograph and a microradiograph of a cast alloy of 80 per cent Cu, 10 per cent Sn, 10 per cent Pb. The remarkable difference in appearance provides some concept of the additional information this method may yield when used as an auxiliary to microscopic studies. Fig. 2a shows two phases of the copper-tin system plus segregated_ lumps of lead. Fig. 2b, on the other hand, shows with exceptional clarity the actual dendritic growth of the metal crystals during solidification. The practice of microradiography depends upon the laws of absorption of X-rays. This subject has been reviewed thoroughly in recent papers,l,2,3 but for clarity a brief resume will be given here. As is well known, when a beam of X-rays is transmitted through a, layer of homogeneous material, the intensity is reduced according to the relation: where Il is the transmitted intensity, I0 is the incident intensity, µ1 is the linear absorption coefficient of the material, t1 is the thickness of the material.

Jan 1, 1944

By S. E. Maddigan, B. R. Zimmerman

Most metallurgists are well acquainted with the contributions already made to the study of metals by the use of X-rays. On the one hand, the radiographic method is constantly becoming of increasing importance as a nondestructive testing procedure, while on the other hand the techniques of X-ray diffraction have made important contributions to the fundamental knowledge in studies of phase diagrams, stress conditions, and so forth. A new, and as yet insufficiently appreciated, tool exists in the application of microradiography to alloy structures. This new procedure in many respects bears the same relation to microscopic investigations as does macroradiography to the gross inspection of metal surfaces. However, where macroradiography is used ordinarily to determine the soundness of the metal structure, this new method can be used not only to investigate micro-un-soundness but also to examine the distribution of the constituent elements within the body of the alloy. When combined with the normal procedures of microscopy, this offers a technique of great potential power. It is intended in this paper to present a few examples of copper-base alloys demonstrating the additional knowledge obtained from the microradiographic method. The detection of micro-unsoundness is demonstrated in Fig. I for a sample of cartridge brass as cast. The sample ap- peared quite sound when viewed under the microscope, but in reality was thickly populated with minute voids. This application of the method conforms in every way to conventional large-scale radiography and has been used to facilitate production of metal for vacuum devices.' The true potentialities of the technique are revealed by comparison of Figs, 2a and 2b, which are respectively a photomicrograph and a microradiograph of a cast alloy of 80 per cent Cu, 10 per cent Sn, 10 per cent Pb. The remarkable difference in appearance provides some concept of the additional information this method may yield when used as an auxiliary to microscopic studies. Fig. 2a shows two phases of the copper-tin system plus segregated_ lumps of lead. Fig. 2b, on the other hand, shows with exceptional clarity the actual dendritic growth of the metal crystals during solidification. The practice of microradiography depends upon the laws of absorption of X-rays. This subject has been reviewed thoroughly in recent papers,l,2,3 but for clarity a brief resume will be given here. As is well known, when a beam of X-rays is transmitted through a, layer of homogeneous material, the intensity is reduced according to the relation: where Il is the transmitted intensity, I0 is the incident intensity, µ1 is the linear absorption coefficient of the material, t1 is the thickness of the material.

Jan 1, 1944

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,' but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation' and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a'c' and c'b are equal to a'b cos +, and a'b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m'c' and c'b are projected as lengths from point a, rather than from point a'. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

By Camillo Premoli

Namibia is one of Africa's newest nations. A German colony until 1915, it then became a South African protectorate until 1990, when it gained independence after an armed struggle that lasted more than two decades. However, no trace of past bitterness can be found today in the capital, Windhoek, or in the countryside. Namibia is now one of the safest parts of Africa. Namibia's industrial base and infrastructure have been untouched by war. Swapo, the ruling party, has embarked on a successful policy of reconciliation and economic development. The GNP per capita is a surprising $1500 (from the World Bank), one of the highest in Africa. Namibia's population stands at 1.3 million, including about 100,000 whites. Namibia is a very sparsely populated country (1.7 inhabitants per km2). About 70% of the people are farmers. Namibia has a surface area of 824,232 km2 (318,261 sq miles), about the size of France and Germany combined. The semi-arid climate and generally flat morphology make the country well suited to mineral exploration. About 40% of the country presents abundant rock outcrops. The rest is buried under the Kalahari sands. However, this cover in most of the country hardly exceeds 200 m (655 ft), and Australian technology has shown that large mineral deposits (Roxby Downs) can nowadays be found at even greater depths. Mining is Namibia's largest industry. In 1991, it accounted for 22% of the country's GDP, about 70% to 80% of its exports by value and 25% of internally generated government revenues. The Ministry of Mines and Energy (MME) is responsible for formulating and implementing national mineral policies. This agency has recently introduced legislation aimed at encouraging new and long-term investment in the mineral sector. The variety of Namibian mineral resources, both metallic and nonmetallic, is rivaled by few countries worldwide.

Jan 1, 1994

By R. T. Hukki

This paper presents a series of equations for mechanical ball wear, relating parameters of ball size, mill speed, and mill diameter. The fundamental equation, Eq. 12, presented here is introduced to correlate these basic parameters and thus define and clarify the concept of ball wear. This equation is offered as a general rule, which may be modified to apply to individual problems of grinding. BALL wear as observed in grinding installations is the combined result of mechanical wear and corrosion. Corrosion should be a linear function of the ball surface available. Ball corrosion, however, has been studied so little that its effect, although of great importance, cannot be included in the analyses given here. In a separate paper' it is shown that 1 n = 0.7663 np----=— rpm [1] vD P = c, np D kw [2] T=c²(np)n De tph [3] In these equations n — actual mill speed, rpm np = calculated percentage critical speed D = ID of mill in feet P = power required to operate a mill, kw T = capacity of a mill, tph C¹ and c² - appropriate constants in = exponent of numerical value of 1 5 m 1.5 Exponent m is the slope of a straight line on logarithmic paper relating mill speed (on the abscissa) and mill capacity (on the ordinate). It is generally accepted, although not sharply defined, that ball wear in mills running at low (cascading) speeds is a function of the ball surface available. Accordingly, the wear of a single ball may be considered to be a homogeneous, linear function of its surface and of the distance traveled. Thus dw = f¹(d2) . f2(ds) [4] where dw is the wear of a single ball in time dt, d the diameter of the average ball in ball charge, and ds the distance traveled by the ball in time dt. Indicating that ds - a D n dt, the wear of the average ball in time dt becomes dw = f¹(d2) . f2(Dn dt) 1 --- f¹ (d1) f² (D c3 np-----— dt) \/D = c,d² n, D dt The rate of wear of the average ball is given by dw/dt. dw/dt = c, d² np D lb per hr [5] The weight of the ball charge per unit of mill length is a function of D The number of balls of size d in the ball charge is = f³(D2)/f4(d³). The rate of wear of the total ball charge equals the number of balls times rate of wear of the average ball. Thus rate of total ball wear = — . (dw/dt) w. c, . (l/d) . n,, D lb per hr [6] which is the equation of ball wear in low speed mills. In a mill running at a low speed, grinding is the result of rubbing action within the ball mass and between the ball mass and mill liners. When the speed of the mill is gradually increased toward the critical, the impacting effect of freely falling balls becomes increasingly prominent in comparison with the rubbing action. Reduction of ore takes place partly by rubbing, partly by impact. The share of the freely falling balls in the reduction of ore reaches its practical maximum at a speed somewhat less than the critical; at that speed grinding by rubbing has decreased to a low value. It may be reasonable to think that size reduction by freely falling balls should reach its theoretical maximum at the critical speed, if the fall of the balls were not hindered by the shell of the mill beyond the top point; grinding by rubbing would cease at the critical speed. As a first approximation, wear of freely falling balls may be considered to be a homogeneous, linear function of the force at which they strike pieces of rock and other balls at the toe of the ball charge. The force equals mass times acceleration. The mass of a ball is a function of d3 and its acceleration is a function of the peripheral speed of the mill. The wear of a single ball of size d representing the average ball in a ball charge will therefore be w¹ = f3(F) = f (d3) f7 (v). [7] Indicating that v = D n, and n = c³ np 1/vD, Eq. 7 becomes W1 = cn d3 np Do.5 lb per hr. [8] Total wear of the ball charge equals number of balls times the wear of the average ball. Number of

Jan 1, 1955

By M. Van Weyenbergh, G. Van Esbroeck

THE copper mines of the Katanga region in the Belgian Congo lie along the same mineralized belt as those of Northern Rhodesia. There are two distinct types of deposits in that belt, the dolomitic and the quartzitic. In the dolomitic type the metallic minerals are found in a dolomitic limestone country rock. Through oxidation and enrichment,, large deposits of high-grade oxidized copper ores were formed, some of which are being worked by the Union Miniére du Haut Katanga. Such deposits are all in Katanga. The quartzitic deposits are found in Katanga and Northern Rhodesia. Here the primary mineralization occurred in sandstones and quartzites, in horizons stratigraphically lower than the dolomites. These rocks are not favorable to secondary enrichment and the oxidized zone is poorer than the sulphide zone, which alone contains the ore. There are also in Katanga a few ore-bearing veins. One of them is being worked in the Prince Leopold mine at Kipushi. PRINCE LEOPOLD MINE The Kipushi ore body fills a fault vein and invades the wall rocks more or less extensively by metasomatic replacement. The vein strikes north-northeast and south-southwest and dips to the west. The variable dip averages 60ºto a depth of 300 ft., and more uniformly 80º below 400 ft. In the upper section the average width is 200 ft. and below the width is about 150 ft. The length of the ore body is 2300 feet. The eastern side of the vein-the footwall-is dolomitic and contains irregular masses of ore sometimes extending 100 ft. or more from the main

Jan 1, 1939