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By August V. Castelli

Drilling fluids have changed over the years from water and/or water frequently mixed with local clays to scientifically com- pounded materials (mud). This change has occurred due to changes in drilling methods from percussion to rotary: depth maximum from 21 m in the first oil well to more than 9 000 m; and variety in types of well or hole to gas, oil, water, and mineral exploration. Environmental concerns about the composition of the fluid as to heavy metals and oil on the cuttings has recently caused changes in the materials used in the mud. The drilling fluid should perform the following functions (Darley et al., 1980): 1) Carry cuttings from beneath the bit, transport them up the annulus, and permit their separation at the surface. 2) Cool and clean the bit. 3) Reduce friction between the drilling string and the sides of the hole. 4) Maintain the stability of uncased sections of the borehole. 5) Prevent the inflow of fluids-oil, gas, or water-from permeable rocks penetrated. 6) Form a thin, low-permeability filter cake which seals pores and other openings in formations penetrated by the bit. In addition to these, the fluid should: 1) Not injure drilling personnel nor be damaging or offensive to the environment. 2) Not require unusual or expensive methods of completion of the drilled hole. 3) Not interfere with the normal productivity of the fluid- bearing formation. 4) Not corrode or cause excessive wear of drilling equipment. A number of industrial minerals, chemicals, and other materials are used as additives in the drilling fluid to accomplish these functions. Industrial minerals make up the highest percentage of the additives in a drilling fluid. Drilling fluids are classified according to their principal components: water, oil, and gas. If the major component is either water or oil, the component along with the suspension of solids, cuttings and additives is referred to in the trade as a mud. The largest use of some industrial minerals, such as barite and bentonite, is in drilling muds. For other materials, such as gypsum and limestone, drilling usage is only a small percentage of total demand. RAW MATERIALS [Table 1] lists the industrial minerals used in drilling fluids, their form, specifications, and uses. Each raw material will be discussed as to its mineralogy, physical and chemical properties, and the location of major deposits with respect to drilling fluids. Attapulgite Attapulgite is a crystalline hydrated magnesium silicate clay mineral, prized for its viscosity in saline waters. The particles are needle-like rather than the platelets common to most clay minerals. The specific gravity is 2.5 and the Mohs hardness is 1 to 1.5. Attapulgite is one of the materials sometimes referred to as fuller's earth. The major producing areas in the United States are southern Georgia and northwestern Florida. It also is mined in Spain, Senegal, the Republic of South Africa, Turkey, India, and Australia. Barite Barite is crystalline barium sulfate. It has a high specific gravity for a non-metallic mineral, 4.5 when pure, and is used as a weighting agent. Generally, the specific gravity ranges from 4.20 to 4.35. It is relatively soft with a Mohs hardness of 3 to 3.5 and is not very abrasive. Barite is inert, non-toxic, and clean to handle. Common contaminants are quartz, iron minerals, gypsum, and calcium carbonate. If there is considerable gypsum in the barite, it will thicken the mud. The major deposits in the United States are in north central Nevada, near Battle Mountain. The major producing countries, other than the United States, are China, India, Mexico, the former USSR, Turkey, and Morocco. The major deposits in India and Nevada, and some in China, are stratiform, commonly quite pure bodies in bedded sedimentary rocks.

Jan 1, 1994

By Ramon S. Pizarro, W. Joseph Schlitt

Introduction Trying to synthesize innovations occurring in gold processing is not simple. At present, this technology is exploding, brought about by the high price of gold. This price has compelled the mining industry, as a matter of survival, to produce gold. The frantic search for gold deposits continues, from glacial areas to tropical jungles. The search has been fruitful. New exploration techniques have helped to locate deposits. Some are amenable to conventional processing techniques. Others are in unusual settings that challenge the ingenuity of extractive metallurgists. Ore deposits containing traces of invisible gold, refractory mineralization, and impurities and deleterious materials that previously defied treatment are now being profitably processed. Metallurgists have developed various processing methods and equipment for gold ore treatment that reflect differences in ore characteristics, grade, mineralogy, reserves, topography, climate, and location. These processes can be categorized as: • For nonrefractory or readily leachable gold ores - vat leaching, heap leaching, and agitation leaching. • For ores containing free gold - gravity concentration methods, followed by mercury amalgamation, and • For refractory gold ores - flotation, roasting, pressure oxidation, followed by cyanidation leaching. In actual practice, a combination of these processes may be required. This is because gold mineralization, although usually simple, may be associated with other mineral species or with clays that make the ore difficult to treat. Furthermore, after the gold has been solubilized to form a cyanide complex, one of two important processes must be applied to recover the gold. These ore zinc cementation (Merrill-Crow process) and Carbon adsorption, desorption, and electrowinning. New techniques for leaching and recovery are also advancing. These will become the bases for the next generation of gold processing plants. Nonrefractory Gold Ores Nonrefractory ores with readily leachable gold are among the .easiest to treat. Even so, non-refractory ores from epithermal deposits are likely to contain too much clay. When these ores are damp, they may clog the screens and cone crushers. Depending on the type of process, scrubbing the crushed ore is very effective in overcoming clay problems. After dewatering, the slimes enter the cyanidation process and the thickener overflow is stripped of gold values and recycled. Semiautogenous (SAG) mills are also gaining popularity due to lower capital costs and ability to treat wet, sticky ores. If properly sized, the secondary crushing and screening plants, together with a secondary ball mill, can be eliminated. When the ore is of such a low grade that it can not support fine grinding, vat or heap 'teaching may be applicable. These systems are being actively applied in the US and elsewhere. Rapid construction and low capital costs are important features of these plants. Vat leaching is ideally suited for fast leaching ores and small tonnage deposits located in areas with harsh winters or wet tropical climates. For effective vat leaching, the ore is crushed to less than 25 mm (1 in.), agglomerated with lime or cement to control fines, and leached with sodium cyanide solution (upflow or downflow). The degree of size reduction is a tradeoff between increased costs of comminution and improved gold recovery from smaller particles. However, the size of material

Jan 11, 1984

By Charles G. Frush

The function of the mine surveyor is to (a) provide a network of points of accurately known position, covering the entire mine property, (b) obtain the required data for the preparation of useful maps and sections! (c) provide position and directional control for the guidance of the operations, (d) measure the progress of the work, (e) measure the movement of rock masses, and (f) make miscellaneous surveys as needed. Mining properties range from the very small to the extremely large, and from those which involve only surface operations to those involving extensive underground workings. Active mines undergo constant change, necessitating continual updating of the surveys. The differences in the character of the deposits, the scale of mining and the mining methods result in large differences in the surveyor's activities and techniques, but many of the problems involved are common to most mines. The surface work of the mine surveyor is very similar to that, of the plane surveyor in that control points are established by triangulation, trilateration and traversing. Detail is taken by direct measurement, by stadia and by aerial photography. The equipment used, the techniques and the methods of processing the resulting data are likewise very similar. However, the underground work is quite different : A. The lines of sight frequently must be carried through constricted openings, often involving short lines of sight and awkward setups. B. The lighting often is poor, requiring illumination of the backsights and foresights, and the crosshairs. C. The ambient conditions often are difficult, involving falling water, high tem- peratures, poor visibi 'kv and heavy traffic through the area being suneyed. D. The surrounding rock map be unstable, resulting in movement or loss of the surveying stations, as well as hazard to the surveyors. E. The points to be measured often are difficult or impossible to reach. F. Steep vertical sights often are necessary, requiring the use of special equipment. G. Many working levels commonly are involved, requiring the transfer of position and orientation to each with a high level of precision. This section therefore will concentrate on surveying problems peculiar to the mine surveyor, chiefly underground work. 22.1-THE MINE COORDINATE SYSTEM A system of coordinates is essential for all permanent mining operations It is very desirable that all mining operations in a ,given area b~ tied into the same system, as this minimizes problems of boundaries and connections Whenever possible this system should be tied into and made part of the state or regional grid system. It is desirable to orient the coordinate grid on a true-north line and to position the origin of the coordinates so that all of the work will be in the "northeast" quadrant, making the north and east coordinates always positive. This can be done by subtracting suitable constant values from the north and east coordinates of the regional system The residual values are of more convenient magnitude and can be used as the local mine coordinates. If the long axis of the mineralization is not generally north-south or east-west.

Jan 1, 1973

By Robert E. Blackett

To help local governments plan for long-term supplies of sand and gravel for buildings and infrastructure, the Utah Geological Survey is assessing natural aggregate resources (mainly sand and gravel) in the St. George, Utah area. Whereas much of the aggregate in the study area is adequate for road-base construction, high-quality aggregate for Port- land cement concrete is limited due to geology, and also due to land administration and environmental issues. Virgin River alluvial gravels southwest of St. George are generally poor sources of aggregate because they contain clasts of soft sediments and soluble minerals derived from Mesozoic rocks. Elsewhere, widespread secondary calcium carbonate (caliche), as rinds and matrix in gravel, lower the quality of material. Young river-terrace deposits in Fort Pearce Wash, and along the Virgin River above St. George are the primary sources of sand and gravel for the area. Alluvial fans on the east side of the Beaver Dam Mountains, and on the west side of the Hurricane Cliffs are also sources of aggregate. Stream-channel deposits associated with "inverted valleys" north of the towns of St. George and Hurricane, Utah, and older pediment gravels on the west flank of the Beaver Dam Mountains may be future sources of high-quality aggregate. Accelerated urban development during the 1980s and early 1990s has caused St. George and other communities in Washington County to encroach upon sand and gravel pits originally located in rural, undeveloped areas. Urban residents often view nearby sand and gravel operations as undesirable neighbors and pressure elected officials to close the pits. Pit closures effectively eliminate the remaining reserve from the sand and gravel resource base of the area. More- over, resources may also be lost as new homes are built upon undeveloped sand and gravel deposits. The St. George area is particularly susceptible to loss of aggregate resources because high-quality natural aggregate for construction is already in short supply. Moreover, most of the land in the study area is administered by the U.S. Bureau of Land Management and subject to various land-use restrictions. Much of this public land cannot be developed for mineral materials, such as sand and gravel, because of federal regulations protecting rare plants and animals, archaeological sites, and important watershed areas. Of particular concern to resource development are areas designated as Areas of Critical Environmental Concern, Wilderness Areas, and Wilderness Study Areas. Protection for Endangered Species is a critical element in all planning efforts. Those species present in the St. George area or in areas near- by include: the desert tortoise, southwestern willow flycatcher, Virgin River chub, and dwarf bearclaw poppy. As the St. George area is depleted and/or deprived of sand and gravel resources through extraction and urbanization respectively, construction costs will rise unless conservation measures are instituted. To avoid the loss of aggregate resources, the UGS is pursuing a program of data gathering and field surveying of surficial deposits to determine tonnage and quality of the remaining sand and gravel resources. The resource information from this program will help land planners, developers, and government officials make informed decisions concerning urban development throughout the region.

Jan 1, 2001

By Tim Neil, O&apos

The coming years should see moderate growth in the US coal industry. That growth may come at the expense of the oil and natural gas industries. Conoco pegs coal growth at 2% a year, until the year 2000. During that same period, Conoco projects only 0.5% annual oil growth and "a flat or negative trendline" for natural gas. This is compounded by the fact that coal has a delivered cost per Btu that is only half as much as it is for natural gas and only a third as much as it is for oil. So said Ralph Bailey to many of the 2600 attending the opening session of the American Mining Congress Coal Convention, May 12-15, in Pittsburgh, PA. Bailey is chairman of the AMC. He is also chairman of Conoco. While coal's projected growth is not spectacular, "it is in fact almost an assured growth," Bailey said. Weak oil and gas prices will likely prevent faster growth for US coal. Most of coal's increased demand will come from the electric utility industry and expanded steam coal exports. Conoco's study projects that domestic coal demand will be strengthened in the 1990s. By then, the present surge of nuclear power plant constuction will be over. And there will be a lack of acceptably priced, large-scale generation alternatives for utilities. "It is not likely that any electric utility is going to be ordering new nuclear reactors," Bailey said. "And as oil and gas supplies become scarcer and more costly, it is only logical that coal is going to fill the gap." At the same time, Bailey believes the US coal industry must find ways to lower its costs. He said cost excesses can be found in "regulatory overkill, labor, and simply bad habits" hidden by years of high inflation. "Those costs have now been laid bare, because we are going through a pe¬riod of disinflation. We have to put our house in order, particularly if we are going to compete in world markets." Bailey also touched on coal research. "The industry certainly accepts the fact that we must find a way to burn coal as cleanly as possible. A lot of work in that regard is going on. I expect there will be some significant break-throughs." Bailey said the coal industry is being squeezed this year. Last year, coal customers accumulated inventories in anticipation of a major coal strike that never materialized. Now, many utility customers are working down these inventories. So they are not taking deliveries on their coal contracts. But coal use is up in 1985, compared with 1984, Bailey said. So increased coal use, along with supply drawdown, should strengthen the coal market before the year is out, he said. After Bailey's presentation, some 100 speakers addressed policy and technical topics at 15 sessions during the four-day meeting. It was the first time since 1977 that the AMC Coal Convention has been held in Pittsburgh. And this year's attendance was up 40% from the last AMC Coal Convention held two years ago in St. Louis, MO. This year's registrants included 228 companies, 225 manufacturers, and 106 associated members. The only negative was the David Lawrence Convention Center. It was less than ideal. By turns, meeting rooms were too small, too cramped, or too far from one another. The session on longwall mining was so crowded that the doors were propped open so conference delegates could peer in. A concurrent manufacturers' forum session needed 50 more chairs to accommodate those wanting to attend. However, on to summaries of some of the presentations. Coal transportation and export Since Congress approved the 1980 Staggers Rail Act, railroad rates for hauling coal have not been excessive. In fact, rail rates for coal have increased less than 0.5% a year, in real terms, since 1980. Moreover, the market oriented principles written into Staggers are contributing to the improved financial and operational health of the nation's railroads. But no railroad is earning excessive profits. That is the gist of a coal transportation study being completed by the US Department of Energy. William Vaughan is DOE's assistant secretary for fossil energy. He affirmed the thrust of the upcoming report. Vaughan did allow that Interstate Commerce Commission (ICC) regulations on rate reasonableness could permit the railroads to exploit their monopoly power on captive shippers. Luncheon comments later made by Don Hodel confirmed Vaughan's comments on railroad rate justification. Hodel is Secretary of the

Jan 7, 1985

By Ted D. Maki, Joseph B. Taylor

INTRODUCTION FMC's Paradise Peak mine, located 13 Ian (8 miles) south of Gabbs, Nevada, became opera¬tional in April of 1986 (Figure 1). It was designed and built by Davy McKee, who was instrumental in equipment design and selection. It is the 7th largest gold deposit in the United States with defined reserves of 10.9 mt (12 million st) containing 34 million gms (1.1 million tr oz) of recoverable gold and 933 million gms (30 million tr oz) of recoverable silver. The mine extracts ore by the open-pit method, taking advantage of a 1.5:1 stripping ratio. The mill operates at a 3600 mt/day (4000 st/d) capacity. Crushing is done in three stages to achieve an ore size of minus 0.635 cm (0.25 inches). Grinding further reduces the ore to 85% minus 100 mesh. The ground ore is treated with cyanide in agitated leach tanks and then washed in the counter-current decantation (OCD) thickeners. Zinc is added to the clarified, deaerated pregnant solution to precipitate the precious metals. The precipitate is acid digested to eliminate excess zinc, filtered and retorted to drive off contained mercury. The retorted precipitate is then fluxed, melted and poured through cascade molds. Dore bars are cleaned for shipment and the slag is sent to an in-house slag treatment system. ELECTROSTATIC SEPARATION The dry electrostatic slag treatment system at Paradise Peak is the first installation of its kind. Electrostatic separation has been widely used in mineral processing since the early 1950's. A brief discussion of the theory behind the process is helpful to those not familiar to electrostatic separation. Charging and sepa¬rating slags, dry minerals or other materials by ion bombardment is the most common form of electrostatic separation. Millions of tonnes of minerals are processed each year by this method. In an ion bombardment separation, granular material is fed onto a grounded metal cylinder (or roll) and charged by a corona-producing electrode placed above the roll's surface (Figure 2). While both conductors and non¬conductors become charged, only the conductor is able to lose its charge. The charged non¬conductor, as it rests on the roll's surface, "sees" an oppositely charged image of itself in the metal surface. It is attracted to the image charge, becomes electrostatically pinned to, and moves with the roll's surface. The conductive particle also sees an image and is attracted to it. But upon touching the roll's surface, it discharges rapidly to the grounded surface and is thrown free from the roll's surface with a projectile motion. In the case of precious metal slags, the con¬ductive particles would be metallic prills of dore metal; and the nonconductive particles would be the slag, free of metal. Middling grains, generally, are in the form of a metallic prill encased in or incompletely liberated from slag. LABORATORY TESTING A number of precious metal slag samples have been tested in the laboratory. It has been found that the composition of slags vary widely from one refinery operation to another. Typical laboratory procedure is to crush and size the slag followed by two-stage lab-scale electro¬static separation. The conductor fractions from the first and second pass are then combined as a prill concentrate; middlings fraction and clean slag tailings from the second pass are held separate. Selected results from laboratory testing are shown in Table 1. It is important to note in Table 1 that the assays represent overall silver and gold, not metallic values. From experience, the laboratory results are typically lower in grade and recovery than the industrial installations. This is largely due to the hydroscopic nature of precious metal slags coupled with the high local humidity in Carpco's Jacksonville, Florida, location. Relative humidity in Jacksonville can range form 60-95%, while most mining locations in the

Jan 1, 1987

By Niels Jonassen

INTRODUCTION The occurrence of the radioactive element radium, [2gg~a], often in trace amounts, in the crust of the earth gives rise to a flux of the daughter product radon, ['ii~n], across the earth-air interface. This so-called exhalation process has been studied by many investigators [KO 45, Kra 64, Pe 66, Wi 741] over several decades. In the earlier investigations the exhalation process was studied in a purely geophysical context, but over the last 20 years it has been realized, that under certain conditions the exhalation may be intense enough to also have radiological implications. This is for example the case where relatively radium-rich wastes or by-products, like uranium mill tailings and phospho-gypsum, are stored in larger quantities. In order to be able to predict the radiological impact on the environnent it is necessary to know the rate of exhalation of radon from the surface of the exhaling material. Usually the determination of these exhalation rates has been done by measurements in situ directly upon the accumulated material [~le 74, Ha 791. Although such field measurements have the obvious merit of dealing directly with the full scale problem, the results are often lacking in generality, making predictions for other situations difficult or even impossible. The present paper describes some results of an investigation where it is attempted from laboratory measurements on samples of limited size to obtain material parameters, which are suited for extrapolating and predicting the radiational behaviour of larger accumulations of the material. THEORY Let us consider a sample of a radon exhaling material enclosed in a container with a dead space volume, Vd, and initially containing radon free air. If the total exhalation rate (number of atoms per unit time) is c, the radon concentration (number of atoms per unit volume) N will initially grow with the time t according to the equation [ ] where [R] is the decay constant of radon. As the concentration (or activity) in the container grows, the net exhalation rate will slow down because of back diffusion, and, furthermore, radon atoms may be removed from the container, not only by radioactive decay, but also by diffusion leakage [JO 81 ]. If, however,only the initial. part of the activity growth curve is considered, the total exhalation rate, c, is given by [c = r•Vd(2) where r is the initial activity growth rate in the container. Let the container be cylindrical with an inner cross-section S and filled to a height L with a radon exhaling material with the specific mass p, the porosity E, the radon pore production rate f and the diffusion length i. When the container is left open,i.e. the radon exhalation takes place into a virtually radon free room, the radon area exhalation rate, E, can be written [Jo 80] E = Ef?t tanh L.R (3) assuming the exhalation only takes place in one direction, towards the surface of the material. It appears that for values of L > 2•ithe area exhalation rate becomes E a = Efi (4) independently of the sample dimensions and the total exhalation rate c is then c = E •S (5) For L ;~ 0.5•i, tanh P _ k and equation (3) may be written E ~ EfL (6) then c = EfL•S = p•m= Em •m (7) where m is the mass of the sample and Em = P (8) is the mass exhalation rate. It thus appears that the radon exhalation rate from a given amount of material may often be conveniently expressed by c = E •Sfor L z 2•I (5) a orc = Em •mfor L0.5•i (7) where S is the total exhaling area and m the total exhaling mass, E and E the area and mass exhalation rates respectively defined by equations (4) and (8).]

Jan 1, 1981

By A. Adu-Acheampong

A geotechnical study was conducted to identify the cause(s) of stope instability at the Ashanti Mine (Obuasi, Ghana). As part of the investigation, laboratory testing of rock was performed and the rock mass was classified according to the Q-System (Barton et al., 1974).Numerical analyses were performed using the computer program FLAC (Itasca, 2001). The observed failure zone around the stopes was simulated using both Mohr-Coulomb and Hoek-Brown (Sheorey,1997) models. Yielding along peripheral graphite bands and tensile failure were clearly identified to be the major contributors to stope instability.

Jan 1, 2003

By N. Piret, B. Shoukry, S. Buntenbach

Traditional or artisanal goldmining, also known as small scale goldmining, has a strong and probably a negative environmental impact. The processing methods applied are very frequently a source of severe pollution due to the emissions of mercury by the extraction of gold by means of amalgamation as well as the emissions of cyanide through cyanide leaching of gold bearing ores. The emissions find their way into the environment and contaminate soils, sediments, water and atmosphere. Abnormal concentrations of mercury and cyanides in waterways are known to occur year after year destroying irreplaceable regions of the world. Mercury and cyanide compounds are highly toxic and may directly create permanent damage to the whole ecosystem. Existing methods for recycling of mercury and for decontamination of mercury and cyanide contaminated tailings are not customary applied in small scale mining and are ineffective as well. Based on investigations of traditional and small size goldmining, this paper presents: -processing methods of gold and discarded tailings under consideration of environmental protection; -figures on actual situation; -recommendations for equipment; -some decontamination methods for mercury and residual cyanide. Mineral Processing methods in traditional gold mining Gold is usually existing in its ores as the metal alloyed with metallic silver and perhaps copper. The element may occur in the form of: -native gold -inclusions also of microns or submicroscopic size metal sulfides (auriferous) such as pyrite, pyrrhotite, stibnite, arsenopyrite and galena -combined as telluride or sulphotelluride. The separation process selected depends on whether the gold can be freed from its unfavorable associations (e.g. gangue) at a sufficiently coarse grain-size, or whether it is carried in a heavy sulfide which can be freed similarly. The usual practice is to concentrate the goldbearing mineral at a relatively coarse grain-size and to regrind the ore if necessary. The gold content is concentrated by secondary or tertiary gravital methods or is extracted by chemical methods (amalgamation, cyanidation etc.) Gold, even when of fine grain-size, settle readily due to its high specific gravity from pulps in which the main gangue mineral is quartz or silicates. Amalgamation is the process of separating gold and silver from their associated minerals by binding (entrapping) them into a mixture with mercury. The cyanide process is applied to separate gold or gold-bearing compounds by dissolution from the finely ground ore (CIP, CIL, RIP), or as heap leaching. The dissolved gold is separated from the solids and the metal-rich or pregnant solution is then treated to recover its gold. Gold is also recovered by flotation methods. This process is widely used in treating base metal ores and in separating various sulfide components of ores, as well as in removing the barren gangue. The gold usually associates with a specific product in a sequence of flotation operations and is recovered subsequently in the smelting of the sulfide concentrates and refining of the metallic products, or by cyanidation of the roasted concentrates. Froth-flotation can be applied to separate gold and sulfide minerals from a finely ground pulp. The Amalgamation Process Amalgamation is the main method for the recovery of gold in traditional mining and is applied for the extraction of gold from placers as well as primary ores. The mineral technology used depends on the nature of ore deposits. In winning gold from solid ore, the matrix of minerals and rocks must be crushed and ground to sufficient fineness to liberate the gold. The liberated gold could be treated similar as free gold from placers. Gold is mainly separated from the valueless gangue (barren rock) by utilizing the difference between the density of the impure native metal (density about 16-19) and the gangue (density about 2.5). In simple operations the material is carried by a stream of water down a sluice generally equipped with small transverse barriers (riffles) against which the gold collects. The riffled sluice is the principal device used by artisanal gold miners. Nowadays, spirals as well as centrifuges, such as Knelson separator or Falcon separator, are occasionally applied for gold recovery. Gold may also be recovered from the pulp, by passing it over corduroycovered tables that catch the heavier particles - a method maybe as ancient as gold mining itself. In history, sheep skins were used to catch gold particles in this manner. Furtheron, gravity separation of gold is practiced on jigs, hydraulic traps, shaking tables and

Jan 1, 1995

By S. E. Pérez-Fontes

An experimental study on the oxidation of chalcopyrite (CuFeS2), pyrite (FeS2), covellite (CuS) and chalcocite (Cu2S) particles was conducted by means of differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) techniques. The oxygen concentration in the process gas was set to 40% and 70% (by volume) and a heating rate of 40°C/min was used. Response variables included the temperature of incipient reaction, the total exothermic heat of reaction, particle mass, morphology and mineralogy of the reacted particles. Based on the experimental data and phase stability calculations, reaction mechanisms were proposed to represent the behavior of the particles during oxidation. The reaction mechanisms were verified by X-ray diffraction (XRD) analyses of the oxidized particles and by thermochemical and mass balance calculations to reproduce the DSC and TGA data. Overall kinetic models were developed to represent the evolution of the exothermic heat of reaction as a function of time.

Jan 1, 2007

By A. S. Murphy, E. V. Manlapig, C. Green, J. W. Parkinson

Historically in Australia and the United States many coal mines deposited raw wash plant fines into large slurry impoundments. At the time the technology and market economics did not exist to make it viable to recover coal from these tailings. Today better technology exist to dredge and clean the tailings and there are circumstances where government regulations and market forces have come together to make coal recovery from these old tailings impoundments economically viable. This paper discusses the processes and equipment being used in tailings impoundment reclamation operations in Australia and the United States, and discusses the economic forces driving these operations.

Jan 1, 2001

By Mark Board

INTRODUCTION As the world's supply of near-surface metalliferous ore bodies is depleted, more emphasis must be placed upon mechanized bulk systems of underground mining. In particular, block caving is becoming increasingly important as a method of mining low to moderate grade deposits at depths of somewhat less than 1219 m (4000 ft). 00 ft). The block caving method requires that the ore body be completely undercut, thereby removing its means of support and inducing failure which progresses from the undercut to the ground surface. As the span of the under- cut increases and the weight of the overlying crushed ore body becomes greater, large stresses are induced on slusher and haulage drifts. Stability of these drifts is critical in block caving operations and often proves to be an extremely difficult task (Kendorski, 1976; McWilliams, 1975). Slusher drift maintenance can be costly, often exceeding that of the original support costs. This chapter analyzes the ground support problems of an Arizona block caving mine. The mine presently uses monolithic concrete liners as a support method. Failure of the liners occurs as the undercut approaches, thus initiating a maintenance problem which will continue until the ore body is depleted in that block or panel. To examine this problem, a simple analysis of the stresses induced by the advancing undercut was per- formed. Utilizing a design method developed by Dixon ( 1973, 1974), the calculated stresses were used to deter- mine the minimum thickness required for varying section shapes of unreinforced concrete liners. It is found that the thicknesses required for stable linings are not economic. Recently developed empirical methods of support de- sign are utilized (Barton, 1974; Bieniawski, 1973) and compared to the analytical method. A final discussion of alternative methods of support is given with recommendations for the use of passive or "yielding" support methods. LAKESHORE MINE (GENERAL GEOLOGY) The Lakeshore copper property is located in Pinal County, AZ, approximately 45 km (28 miles) south of Casa Grande. The Lakeshore deposit is a porphyry cop- per similar to others in Arizona. The ore body consists of disseminated chalcopyrite and fracture fillings in quartz monzonite porphyry (QMP), Cretaceous volcanic (KVS), Precambrian diabase, and Mescal limestone. The ore body has been divided into three distinct zones of mineralization which have been termed (South, 1972) the oxide zone, the sulfide zone, and the tactite zone. The oxide zone occurs in the upper portions of the ore body and consists primarily of leached and oxidized quartz monzonite porphyry and Cretaceous sedimentary and volcanic rocks. The sulfide zone underlies the oxide zone and includes all quartz monzonite porphyry and Cretaceous rocks which have not been oxidized. The thickness of the sulfide zone is variable and ranges from about 61 to 122 m (200 to 400 ft). The tactite zone occurs in a series of Paleozoic metasediments consisting of tactite, quartzite, diabase, hornfels, and dikes of quartz monzonite porphyry. The tactite zone is highly variable in thickness and underlies the Cretaceous volcanic and sediments throughout the mine. Together, the tactite and sulfide zones are known as the thick or tall sulfides. The greatest support stability problems occur in mining of the tactite zone and are therefore the subject of the remainder of this chapter. MINING METHOD The Lakeshore mine is a block caving mine utilizing a panel caving method. The present mine consists of two

Jan 1, 1982

By Richard L. Breithaupt

INTRODUCTION A shuttle car is a self-propelled rubber-tired haul¬age vehicle designed specifically for underground min¬ing, primarily in coal mines (see Figs. 1 and 2). The drive mechanism is located on the sides of the vehicle, and the load is carried in the center. A chain-and-flight conveyor distributes the load when the car is being loaded by a loading machine or continuous miner and also discharges the load onto a conveyor belt or into a mine car. As the name implies, the shuttle car shuttles back and forth between the working face and the un¬loading point and is not required to turn around. Shuttle cars have served as primary haulage in this country since 1940 and still perform this function in most coal mines today. TYPES OF SHUTTLE CARS Shuttle cars may be battery-powered, diesel-powered, or cable-reel electric powered. Battery-powered cars were used between 1940 and 1950, but are almost out of existence today because of their limited power. Diesel cars have been used in coal mines, but are used mostly in noncoal mines where rules and regulations are not as stringent. Also, objections by organized labor have limited the use of diesel-powered shuttle cars in coal mines. Today, the largest number of shuttle cars are cable-reel cars. Electric power is fed through a cable stored on a cable reel that may have a capacity from 152 to 244 m (500 to 800 ft), depending upon the size of the cable and the cable reel (see Table 1). This, of course, limits the travel of a shuttle car. However, time studies have shown that for the most efficient haulage cycle, the length of haulage should not exceed 91 m (300 ft). As haulage distance increases, the waiting time for the loader or miner becomes longer, and haul¬age efficiency suffers. Cable-reel cars are manufactured in standard hand and opposite standard hand models. A standard car has the operator's control on the left front side and the opposite standard car has the opera¬tor's controls on the right front. Generally a loader or miner operates with two shuttle cars, one of each type. This allows the trailing cable to lie on either side of the entry and prevents the cables from fouling each other. Shuttle cars are designed to operate with either dc or ac power. Cars using dc power are designed for 250-v supply and ac cars are designed for either 440, 550, or 950 v, three-phase voltage. Most coal mines that are relatively level can use dc cars where dynamic brak¬ing is not required. For mines having steep grades (in excess of 15%) ac cars are used because ac traction motors have inherent dynamic braking and are safer when tramming downgrade. A recent innovation in shuttle car design in the last five years has been the introduction of an ac/dc car. This design utilizes ac input power through the cable, and the power is rectified on the car to 250-v do for traction motors. The pump motor and conveyor motor are powered by ac voltage. The main advantage of this design is efficiency-a much smaller cable may be used and the smooth operating characteristics of the dc traction motor is obtained. This prevents shock loading on the traction drive train, which is an undesirable feature of ac traction motors. SHUTTLE CAR FEATURES Elevating Discharge Today, all shuttle cars are equipped with an elevating front conveyor that allows the shuttle car to discharge into a mine car or belt feeder without the use of ramps. Hydraulic Power System Today, all shuttle cars are equipped with an hy¬draulic power system. An hydraulic pump is driven by an electric motor which provides hydraulic power for steering, elevating the front conveyor, and powering the

Jan 1, 1982

By Dale R. Ralston, Roy E. Williams, Gerry V. Winter, George L. Bloomsburg

INTRODUCTION The majority of ground water flow models have been developed for large computer systems. Most of these operate under a batch mode of operation, that is, the data are input with a deck of punched cards. The advent of micro- and minicomputers over the last few years opens the possibility of adapting many of these large flow programs to the smaller computers. In general, this adaptation will require more computer time to run the program, but in many cases if the small computer is in-house, the overall cost may be less than that required for a large computer. There are also a number of peripheral devices that can be used to make the data input much easier. As an example, the use of a digitizer with a finite element or finite difference mesh reduces the data input time considerably; the use of a graphics terminal for display of the mesh immediately after it is developed shows immediately whether there are errors in the location of node points. DEVELOPMENT OF AN INTERACTIVE SYSTEM The finite element program, UNSAT2, has been used over the past several years by the authors for several ground water flow problems (Bloomsburg, 1977; Bloomsburg and Wells, 1978; Zahl and Bloomsburg, 1980). In the past these programs have been run on an IBM 370/ 145 computer under the batch mode of operation. One difficulty that has been encountered has been in determining the length of time step that must be specified for operation of the program. The problem is that if the time steps are too large, the program becomes un- stable and operation ceases. If this happens in the middle of the problem, the only alternative is to reduce the length of time step and repeat the entire run. This problem has been alleviated in other pro- grams by using a subroutine that determines the time step automatically. If the solution becomes unstable, the time step is reduced automatically and that portion of the solution is repeated. With an interactive system this can be done by storing the output pressures and restarting the program with the new output pressures. Under the batch mode of operation, there is an option in UNSAT2 that allows restarting of the program from the last point of solution, but this must be specified when originally starting the program. The interactive computer system that we use currently consists of a PDP 1 1 /23 with hard disk drive, CRT terminal, plotter, graphics terminal, digitizer, and printer. The computer has 256 K bytes of core storage and the hard disk drive will accept a 5.2 M byte disk. To run a large program on a computer such as this, some overlaying must occur; that is, subroutines are stored on disk and put into core storage only when they are actually needed for running the program. UNSAT2 required very few changes to run on this computer but some changes were necessary to take advantage of the interactive capabilities of the system. One of these changes consists of the development of a program called DBUILD to build the data file for running the program. This program calls for each piece of data by prompt statement and gives instructions for using the digitizer. The data are then entered in completely unformated form. The node points must be entered in order and the coordinates are determined automatically by the digitizer. The pressure readings or initial conditions on each node point are entered through the terminal. All element information also is entered through the terminal. After DBUILD is run the mesh may be displayed immediately on the graphics scope whereupon any error in node point

Jan 1, 1986

By Peter V. Avotins

During last year's AIME meeting in New Orleans, Deepak Malhotra and I were discussing some of the topics that would be presented in this Symposium. It seemed appropriate that along with papers on specific reagent and flocculant types, we should address research management aspects of new product development. This development is a long, arduous task that requires a significant technical and fiscal commitment by the chemical company and potential users. A flow chart depicting the research process is shown in Figure 1. The sequence of events are plotted on an undefined time line. Our experience has shown that it takes 3-5 years to complete a typical reagent development project. A new project starts with an idea of how to do something better. The ideas range from relatively simple product modifications to opportunities created by technological change. An example of this is the use of flocculants in tailings operations to close the water recycle loop. The change was brought about by the need to conserve water and comply with environmental statutes. The result was the development and wide-spread use of synthetic polymers to help in solid-liquid separation. More recently the ups and downs of oil prices have led to development of coal water slurries as an alternative to fuel oil. The slurries contain high levels of chemicals (up to 3%) to insure proper stability and burn characteristics. There are technical changes under way right now that may lead to ideas for other new products. One exciting source of new technology is the ability to manipulate genetic material of microbes to select for specific capabilities. This has evolved by leaps and bounds over the past 5 years. Biologically assisted leaching and removal of wastewater impurities are two possible end uses. I'm sure that there are many others. The ideas can originate anywhere and are often half-baked at first, but to lead to new products they must be refined to provide project definition and eventually a research plan. A chemical ,development project cannot be started without approval to commit the company's resources. The internal selling job is often very difficult. The company must see clear financial benefits in order to launch efforts that may not pay off for many years. It is critical to project the total market, profitability, eventual market share, and timing of introduction of the new product. There is much uncertainty in this and the research manager is often skating on thin ice to retain his credibility. Once we obtain support from upper management, the research team is assembled to start the project. The teams generally consist of organic chemists, research metallurgists, and technicians. They have access to analytical scientists and technicians for surface and analytical chemistry. The projects are often augmented by help from university staff and consultants. This is particularly true where there is a need to develop fundamental understanding of the technology in addition to synthesis of chemicals. The project now proceeds along two lines. First, there is an emphasis on understanding the prior art. Extensive literature and patent searches are undertaken to provide research leads and to keep from "reinventing the wheel" and infringing on someone else's patent. The scientists and technologists are qualified to conduct computer-assisted library searches. This process usually uncovers 80-90% of the relevant information. The remainder is very much harder to get and requires the help of professional library search staff with scientific backgrounds. Along with literature searching, the team begins synthesis of new compounds. These are screened by use of techniques such as microflotation or filtration in a Buchner funnel. The scientists are looking for the direction of response as they modify structural features . Inevitably, a large number of candidates reach the next stage, a laboratory bench test. At this point it is possible to set up a research plan and use project management techniques to monitor progress. The bench tests are conducted in larger equipment, usually requiring 100-1000 grams of test substrate. Typical laboratory flotation tests are run in Denver or Wemco cells.

Jan 1, 1986

By W. F. Riggs

INTRODUCTION Flotation equipment is becoming more definitive in design as well as greater in dimension. The last ten years have witnessed the implementation of large flotation cells ranging in size from 28 to 85 cubic meters. However, small plants still operate with cells as small as 3 cubic meters. These changes have increased the operational sensitivity of the flotation system to the chemical reagents used. No scientific study has been undertaken to develop the relationship between the size of equipment and the response of reagents in the flotation system. Hence, this article is an attempt to present several observations from past experience for the purpose of stimulating future research in an area previously ignored and perhaps subsequently not used to advantage. CONVENTIONAL FLOTATION Recent advances in conventional flotation cell design have been made in two areas: a. Flotation cells are becoming larger, and b. Basic design of flotation cells has changed. They can be classified into two types: deep cell and shallow draft cell. Size and design changes of flotation cells have a greater effect on frother performance than on the performance of other chemical reagents. Hence, the discussion in the following sections is restricted to the impact of frothers in the flotation system. Flotation Cell Size The advent of increasing flotation cell size has resulted in the increase of frother consumption. There appears to be a correlation between reduced horsepower (kilowatt) consumption and increased frother consumption per ton of ore processed in the circuit. This is more prevalent when the frother chemistry remains unchanged. Another reason for increased frother consumption is the increased distance between the rotating central shaft and the lip of the cell for larger flotation machines. Increasing this distance results in increased surface area corresponding to the larger cell size. Reduced power input per ton combined with the need for longer, stronger load support of the froth bubble as a result of increasing cell size has resulted in the development of a new series of stronger and more persistent frothers. By the same token, these newer, stronger frothers are difficult to control when applied to the smaller cells. This is true even at lower dosages because the break point between too much frother and not enough frother for optimum metallurgy is normally very narrow. This problem is often exaggerated when operators have established an optimum setting for pulp level and air for the particular frother in use. Generally, the tendency is to operate the flotation cells simply by adjusting frother dosage. The increase in frother strength to accommodate the large cells often results in the realization, after a retrofit, that the existing pump box or sump which is still handling the same volume of concentrate is no longer adequate in size. Flotation Cell Design The two most common flotation cell designs installed during the past ten years are the deep cell and the shallow draft cell. The deep cell provides for complete mixing of air and pulp at the bottom of the cell. The shallow draft cell does all the mixing/pumping in the bottom haft of the cell whereas the mixing of the air is performed further up the shaft and is brought into contact with the pulp midway up the vortex. There are many preferences for one or the other. It is the author's contention that both designs have very valid concepts and must simply be suited to the particular situation as required by the operator. The following comments are subjective observations which should be explored in greater detail. The deep cell mixes both air and pulp together at the bottom of the cell requiring a full depth ascending of the homogenized air to the surface to form the froth layer. This design, in combination with charged air, provides for good concentrate grade control under adverse conditions of selectivity, especially when faced with a fine grind and a slime-laden gangue. A selective frother can be applied without a competitive loss in recovery. One of the conditions for good selectivity in this environment is operating at medium pulp solids concentration in the range of twenty-six to thirty-four per cent (26-34%). When a higher solids concentration is used in combination with a coarse grind, it becomes difficult to maintain the same recovery with a selective frother due to higher pulp viscosity. This condition sometimes results in an unacceptable coalescence of the air bubbles as they ascend the full height of the deep cell. The increased pulp viscosity at higher solids concentration can also retard the flotation kinetics. The combination of decreased surface area of dispersed air and slower kinetics can result in reduced recovery causing coarse particles to continue to drop

Jan 1, 1989

L.R. Bower In regard to the paper by J.B. Gwiazda, it makes a highly technical approach to show that the µ factor used by designers of lemniscate-guided roof supports has never really been confirmed as a maximum and assumes that convergence is vertical. Also, the paper does not appear to take into account deflection of structures, which occurs when the lemniscate and base members are fully loaded to their maximum stress level, nor the front to back line of the support in relation to differential roof to floor movements caused by strata movements under pressure. It is not unusual for differential movements to be slightly diagonal to the line of the support, particularly in faulted areas and on gradient faces. The paper also does not take into account consolidation of fines immediately above and below the support. Generally speaking, any differential movement is from face to waste and under these conditions the µ of 0.3, which appears to be an international standard, has worked in practice. However, if the face end of the support is lower than the waste end, then the µ of 0.3 can be considerably increased, giving rise to the damage mentioned in the paper. The ideal design should aim for a slightly forward bias in the lemniscate guide so that the last increment of setting is toward the face, tending to close any fissures that may have developed during the support advance cycle. The support should also be fitted with positive set valves to ensure that a high setting load density is attained to minimize bed separation. As far as powered supports are concerned, convergence is irresistible and all powered supports converge at their rated yield load. A similar principle can be applied to the differential roof to floor movements to drastically reduce the very high forces that would otherwise be applied to the lemniscate structures and pins and that, in turn, are transferred to the base arrangement and floor loading. Any differential movements are usually catered for by the 0.3 µ factor or deflection of structures in the lemniscate guide arrangement and consolidation of the floor. The floor loading, due to differential movement, is in addition to the support convergence load and requires additional bearing area to avoid possible floor penetration. Some seven years ago, Fletcher Sutcliffe Wild Ltd. (FSW) introduced a lemniscate-guided shield support where the lemniscate linkage is connected to the roof bar through two horizontally converging rams to allow differential movement to take place above a given rated figure. This is a known force and can be guarded against, whereas with rigid connections the forces, as yet, are unconfirmed. By careful design, a horizontal force in excess of 6 MN (60 tons) opposes differential movements for a total ram loading of only 2.5 MN (25 tons), or 1.25 MN (12% tons) each. This principle can considerably reduce the length and weight of the support in comparison with a rigid pin-type structure ; also, the yield load rating can be increased without affecting the lemniscate forces. The graph shows the tensile and compressive forces in a lemniscate linkage of a support with and without hydrostore. These forces react into both the roof beam and base members and, as can be seen from the support height to linkage load graph, a considerable reduction in these reactions is gained by the use of the FSW patented hydrostore system. Floor loading is considerably reduced under maximum µ conditions, and by allowing the roof bar to move with the strata, some degree of improvement to strata control is achieved in line with the assumptions in the paper. In practice, these movements have only been in the region of a few millimeters, which, in turn, reflects on the improvements to strata control by the addition of positive set valves. Supports to this design of both 450- and 280-t (496-and 309-st) rating have been successfully used in the United Kingdom for several years, negotiating many faulted areas without one single reported need for repair or maintenance. This includes supports left unattended during the year-long strike, proving the reliability of the system.

Jan 8, 1986

By Michael A. Linkous, Mark J. Zdunczyk

Silica in the form of sand and sandstone is one of the most common, and at the same time, unique industrial minerals. Found in every rock type of every geologic age and virtually everywhere in the world, silica is used in products that touch just about every aspect of daily life. Imagine a world in the 1990s without computer chips, fiber optics, or glass, and you have just begun to understand how important silica is to the quality of life we enjoy. The elements silicon (Si) and oxygen (0) comprise roughly 60% of the earth's lithosphere to a depth of about 16 km. The crystal structure of silicon dioxide consists of one atom of silicon bonded to four surrounding atoms of oxygen to form a three-dimensional network of SiO, tetrahedra. This network makes up the mineral quartz (Murphy and Henderson, 1983), the most common detrital mineral in most sandstones. Quartz is also a major constituent of many igneous and metamorphic rocks and is widespread as a siliceous cementing agent in various rock types. Although quartz is common, sandstones, quartzites, and pegmatites and the unconsolidated sediments derived from them that have a silica content high enough and pure enough to meet today's market demands for quality and consistency are not common. USES AND SPECIFICATIONS Silica sand that is mined and processed for industrial uses must conform to the chemical and physical specifications set by customers. In the United States almost half of the silica sand produced is used in the manufacture of glass. Other important products include foundry sand, ground silica, blasting sand, and fracturing sand. Glass Sand Silica is the principal glass-forming oxide in a glass batch. Glass manufacturers develop model specifications for each source of silica sand used. These specifications broadly define the limits and ranges for chemical and physical properties of the sand and are used by the manufacturer in calculating the desired batch mix or formula. Some specifications may be critical to a glassmaker and require very stringent limits on the quantity of impurities in the sand. For example, the total iron oxide content of a batch is extremely crucial when making white or flint glasses (Mills, 1983). Iron is present in almost every raw material used in a glass batch and must be carefully controlled in order to obtain a consistent color in the finished product. It is difficult, however, for a raw material supplier to tightly control the chemistry of a naturally occurring material such as silica sand. To a great extent the commercial quality of a sand is determined by its geologic history. Realizing this, glass producers tailor their model specifications to each source of approved material. In general, a glass company is concerned most about the consistency of raw materials on a day-to-day basis. Soda-lime-silica glass was the earliest type of manmade glass (Baker-Can, 1967) and still accounts for most of the glass manufactured for commercial use today (Mills, 1983). It is relatively easy to melt and shape and is less expensive per ton to produce than most other types of glass (Baker-Can, 1967). Soda-lime-silica glass is used in fabricating containers, flat glass products, incandescent and fluorescent lamps, glass fiber, and many other products. Heavy minerals such as ilmenite, leucoxene, kyanite, and zircon are impurities on which strict limits are placed for a glass batch. Because of their refractory nature they either do not melt or only partially melt, which results in stones or feathers in finished glass. Aluminosilicates such as kyanite also contribute unwanted alumina to the batch as they partially melt. Limits are especially rigid for refractory mineral grains coarser than 0.60 to 0.425 mm (30 to 40 mesh). [Tables 1 and 2] present typical specifications for silica sand used in flat glass and container glass products. The percentages shown represent an average of many companies7 specifications.

Jan 1, 1994

By P. H. S. W. Kulatilake

To exploit an underground mine effectively and safely, it is important to have a good understanding of the geotechnical behavior around underground excavations made in the mine. The aim of this study was to investigate the geotechnical behavior around a tunnel excavated in a metal mine in China at the three-dimensional level. Using the information available on lithology, geological structures, in-situ stress measurements, physical and mechanical properties of intact rock, discontinuities and interfaces between different rocks, a three-dimensional numerical model was built by using the 3DEC software to simulate a tunnel excavation under a high in-situ stress condition. Effect of the discontinuity network, possible intact rock and discontinuity parameter variability, representation of rock masses as discontinuum or continuum material and rock support system on the deformation, stress, failure zone and stability around the tunnel was investigated. A very good agreement was obtained between the collected field deformation monitoring results and the results of the conducted numerical stress analyses.

Jan 1, 2012

By J. M. Mutmansky

Introduction Since the Hardy Cross numerical algorithm was applied to the solution of mine ventilation networks, numerous developments have taken place in ventilation network analysis procedures. The Newton-Raphson method, the linear theory method and the second-order approximation method are three of the additional approaches that have been applied. The efficiency of a ventilation network analysis procedure depends not only on the method of solving the system of equations derived from ventilation networks but also on the method of deriving the equations through selection of the meshes. This paper investigates the impacts of three mesh selection methods on the efficiencies of four ventilation network procedures. The minimum-resistance spanning tree method is the most popular procedure for selecting meshes. The shortest-path method was suggested by Epp and Fowler (1970) for improvement of the Newton-Raphson method. The minimum-resistance-path method is suggested here as the third method of selecting meshes. The effects of these three methods on the Hardy Cross method, the Newton-Raphson method, the linear theory method and the second-order approximation method are analyzed in this paper. These network analysis methods have been summarized in the paper by Kim and Mutmansky (1991). Mesh selection methods A procedure for mine ventilation network solution based on mesh equations typically consists of two steps: • the mesh selection step and • the network solution step. The mesh selection step establishes a set of independent equations to solve the network. The resulting equations are nonlinear. One method of solving nonlinear equations is to linearize the equations and iteratively solve these linear equations. The four analysis methods previously discussed in this paper use this approach. The linear equations required for solution can be written in matrix form as: P•dQ = dF (1) where P is the pseudo-resistance matrix, Q is the quantity matrix, and F is the Jacobian matrix (Kim and Mutmansky, 1991). The efficiency of the solution method depends on the characteristics of the P matrix, which in turn depend on the method of selecting meshes. To understand the impacts of the mesh selection methods on the efficiency of the ventilation network analysis procedures, the characteristics of the P matrix must be understood first. The diagonal elements of the P matrix, m in number, are the sums of the pseudo-resistances of the branches contained in the m meshes necessary for solution. The off-diagonal elements are the sums of the pseudo-resistances of the branches shared by two meshes. For example, P12 (first row, second column element of the P matrix) is the sum of the pseudo-resistances of the branches common to mesh 1 and mesh 2. When solving the system of equations expressed in Eq. (1), three of the iterative procedures (the Newton-Raphson, the linear theory and the second-order approximation methods) use the direct factorization method (Burden and Faires, 1985) on the P matrix. When the direct factorization method is used, the computational efficiency is enhanced by larger diagonal elements and a sparser P matrix. Generally, the sparsity of the P matrix is more important than the size of the diagonal elements. There is no known mathematical method of predicting the efficiency of these procedures, but heuristic methods can be used to study the efficiency. The Hardy Cross algorithm applies the Gauss-Seidel method of splitting the P matrix and applies the Newton-Raphson procedure. The efficiency of the Hardy Cross method depends on the spectral radius of the matrix[[D-L]-1U], where D is the diagonal, L is the lower triangle and U is the upper triangle of the P matrix for the Newton-Raphson method (Ortega, 1972). The smaller the value of the spectral radius, the faster the convergence. As with the other three methods, larger diagonal elements and a sparser matrix aid in faster convergence. With the Hardy Cross method, however, the size of the diagonal elements is more important than the sparsity of the matrix. Remembering that each of the diagonal elements of the P matrix is the sum of the pseudo-resistances of the branches in a mesh and that each off-diagonal element is the sum of the pseudo-resistances of the branches shared by two different meshes, the following strategies can be used: • Avoid having branches with larger resistance values shared by multiple meshes. This increases the size of the diagonal elements and reduces the chance of off-diagonal elements being large.

Jan 1, 1993