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By Steven J. Page, Andrew B. Cecala, John A. Organiscak

In This Chapter [Drill dust control: wet and dry Enclosed cabs on drills and mobile equipment Haul road dust control] Overburden drilling generates most of the respirable dust that affects workers at surface mines. Both wet and dry methods are available to reduce this drill dust. Overburden removal by mobile excavation equipment such as bulldozers, front-end loaders, and haulage trucks can be dusty, particularly under dry and windy conditions. Tightly enclosed cabs with dust filtration systems can substantially lower the dust exposure of both drill and mobile equipment operators. Haul road dust control can be achieved by water application or chemical application. DRILL DUST CONTROL [Drill dust is controlled with wet or dry systems. Wet systems can be more efficient, but may freeze in the winter. Dry systems require careful maintenance of the drill deck shroud. An improved deck shroud is shown.] Wet Suppression. Wet drilling systems pump water into the bailing air from a water tank mounted on the drill. The water droplets in the bailing air trap dust particles as they travel up the annular space of the drilled hole, thus controlling dust as the air bails the cuttings from the hole [Page 1991]. In wet drilling systems, typical water flow rates are 0.1 to 2.0 gpm depending on the size and type of drill and the moisture level of the overburden. The drill operator controls the flow using a control valve located in the cab. Some drills are equipped with a flow meter to give the opera-tor a visual sign of the flow rate. Raising the water flow will improve dust capture, but too much water causes operational problems. Because of this, the drill operator must exercise care in find-ing the best water flow rate.

Jan 6, 2003

By R Stefansen

Stockyard operations are governed by the interaction between the different disciplines required to successfully schedule and control the supply chain of raw material through the stockyard in combination with the effectivity of the operation of the stockyard equipment. The system demonstrates a proven technology for implementing a centralised operation of full unmanned stockyard equipment, using a high precision absolute positioning system based on a Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) receivers in combination with 3D rangefinders. The system implementation maps the surface profile of the stockyard inventory and allows in combination with proprietary algorithms for full operation of the stockyard machines without on-board operators. The operational impact of delayering the process by moving to a centralised operation is examined, together with the combined effect on the overall safety in the stockyard as a result of a change in reliance on operator skill dependencies. Average performance gains range from 10–20 per cent. The performance of the automation system is related to a consistency and reliability of uniform operation, which has an impact on the life expectancy and the effectiveness of the equipment. The effects of having instantaneous and correct information about the stockyard inventory volume measurement are investigated in relation towards spot price trading in current fast reacting markets.CITATION:Stefansen, R, 2017. Advanced automation for centralised stockyard operations, in Proceedings Iron Ore 2017, pp 105–110 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 24, 2017

By D Nicoli, P Feltoe

The operation of grinding circuits are vital to the success of most mineral processing operations in the provision of effective size reduction whilst maximising throughput. However these same circuits, and especially semi-autogenous grinding (SAG) mills, are highly interactive with product re-circulations and long time delays. This makes the optimal control of these difficult by conventional controllers, such as PID, which generally places a heavy reliance upon operations for control. In order to account for the peculiarities (such as ore type changes) and the abnormal situations that continually beset these circuits, it is necessary to adapt linear control techniques to cater for these situations. The Honeywell Hi-Spec Solutions SmartGrindTM controller is a marriage of multivariable predictive control (MPC) with techniques that provide adaptation of the control to optimise the circuit under all conditions. Optimal control is achieved by incorporating pattern recognition techniques to detect and act on discrete events (eg ore type changes) and adaptation of the MPC to account for known process and equipment non-linearities. AlcoaÆs Wagerup Refinery is the first site worldwide to have this technology applied to the SAG milling circuits and this has resulted in throughput increases in excess of two per cent and significant improvements in circuit operations. This paper describes the implementation of the control to the refineryÆs Mill 3 bauxite grinding circuit and the capacity/operational improvements achieved thereof.

Jan 1, 2000

By Don Peel

Mineral aggregate, the most widely used mineral resource globally, has attracted little academic or public interest. Of all mining developments, the aggregate resource is seldom factored into resource management decisions. This lack of recognition to the strategic aggregate resource has significant economic, environmental, and social implications. Impact to the economics, the environment, and the community coincide with the key elements of the United Nations concept of ?sustainable development?. To build on the concept, the mining sector contracted the International Institute for Environment and Development to assess how mining activity contributes to sustainability. As a result, a useful assessment process was developed by the Mining, Minerals and Sustainable Development (MMSD) Task Group entitled ?Seven Questions to Sustainability: How to Assess the Contribution of Mining and Mineral Activities.? In Alberta, recent opposition to mineral resource development by community residents offers an opportunity to employ the MMSD?s assessment procedure. The public opposition to the mining activity was addressed through a stakeholder planning process initiated by the municipal council of Sturgeon County, Alberta. As a result the Calahoo/Villeneuve Area Structure Plan (CASP) was formulated and adopted. To measure the effectiveness of the CASP planning process in terms of sustainability, this paper applies the MMSD?s Seven Question assessment to the Calahoo/Villeneuve Area Structure Plan.

May 1, 2004

By E. Martinez

The effect of ultrasonic energy transmitted through a liquid on chrysotile asbestos was investigated. Ultrasonic energy was effective in fiberization of chrysotile crudes as well as standard grades of milled asbestos fibers. Treated samples of several grades of milled fibers had increased wet bulk volumes and decreased settling and filtration rates compared to untreated fibers. Ultrasonics may be a method for fiberization of chrysotile without decreasing length or use of chemical additives that alter surface properties. Cavitation of the liquid on the surface of fiber bundles is believed to be the cause of the fiberization. It was found that ultrasonic energy greatly increased the rate of precipitation of latex on asbestos. When chrysotile asbestos fibers require additional opening or fiberization, the usual method employed is some type of high speed impact or grinding to open the fibers and produce a larger surface area. These methods always cause some degradation in length due to breaking of fibers. In addition, the efficiency of mechanical methods decreases as the diameter of fiber bundles decreases. Chemical methods have been proposed and it is claimed that fiberization down to individual fibers of 200-300 A diam is possible with some wetting agents. However, large amounts of reagent are required, approximately EDWARD MARTINEZ is with Central Research Laboratories, American Smelting and Refining Co., South Plain-field, N.J. TP 63H226. Manuscript, Aug. 12, 1963. Discussion of this paper, submitted in duplicate prior to Mar. 15, 1964, will appear in SME Transactions, September 1964, and AIME Transactions, 1964, vol. 229. 50 pct of the weight of fiber treated, and some of the wetting agent remains on the surface of the chrysotile and cannot be removed by any solvent which does not destroy the asbestos.' This investigation was directed at determining whether ultrasonic energy transmitted through a liquid would be effective in fiberizing chrysotile asbestos. Samples of asbestos crudes and commercially milled fibers were treated; settling and filtration rates of treated and untreated milled fibers were obtained. EQUIPMENT A Westinghouse Corp. ultrasonic cleaning system WEHH was used in this investigation. See Table I for a breakdown of this ultrasonic unit. RESULTS AND DISCUSSION Fiberization of Chrysotile Crudes: Samples of chrysotile crudes were pulled apart with tweezers so that coarse bundles of fiber approximately 1/16 in. in diam were obtained. The bundles were put into a bottle with 200 ml of methanol and the mixture placed into the ultrasonic tank for 30 min at a power output of 1200 w. The test was repeated using water instead of methanol. During the irradiation it was noted that the surfaces of the bundles were being fiberized. The liquid eventually became cloudy with dispersed solids. Fig. 1 is an electron micrograph of the fibers, some reduced to unit dimensions, and a fine material released by the ultrasonic energy. The platy particles in Fig. 1 were identified by electron diffraction and differential thermal analysis as brucite, Mg(OH)2, which must have been intergrown in the chrysotile crudes. Electron micrographs of bulk specimens of chrysotile have shown a fine material filling the interstices between tubular fibers.2,3 Electron diffraction patterns of the fine material collected after ultrasonic treatment indicate that it is amorphous. After decanting the solution, bundles of chrysotile remained somewhat decreased in diameter. Continuing the ultrasonic irradiation of the remaining material resulted in additional fiberization. The opening of the fibers occurred in both methanol and water. Cavitation of the liquid by the ultrasonic energy is undoubtedly responsible for the fiberization. When sound waves are transmitted through a liquid at a

Jan 1, 1963

By M. A. Trevits, J. E. Urosek, A. C. Smith, M. P. Valoski

The National Institute for Occupational Safety and Health (NIOSH), in partnership with the Mine Safety and Health Administration (MSHA), is conducting research to test, evaluate, improve or modify coal mine fire-fighting strategies and methodologies through large-scale tests. Since wood is the second most abundant fuel available during a coal mine fire, it was decided that series of large-scale wood crib fire tests were needed to measure the products of combustion and to observe the capability of commonly available direct application fire suppression equipment, namely, fire extinguishers, water and gas-enhanced foam. This paper discusses the wood crib fire tests, provides insight into the products of combustion and describes observations made during the application of the fire suppression agents.

By P. Kluge

Mining engineers frequently encounter complex design problems for which the critical components of the design are difficult to quantify or compare. Teams of people typically work on these designs and human perceptions and judgments play a strong role. To assist with this process, the analytical hierarchical process (AHP) as a decisionmaking tool is described in this paper. Although the technique is used in many other disciplines, it is currently not widely used in mining engineering in South Africa. To use the AHP process, the problem should be treated as a hierarchy that defines the goal, the alternatives to reach it, and the criteria for evaluation of these alternatives. Pair wise comparisons are conducted on the criteria of the hierarchy to establish priorities. The value of the technique is that it is simple to test for consistency amongst the pair wise comparisons to ensure that the answer obtained is better than that provided by a random selection. To illustrate the technique, the use of a backfill support system in a platinum mining project was investigated. Ten design parameters, which will be impacted by the use of backfill, were identified and weighted according to their relative importance. The result of the AHP evaluation was that the use of a backfill support system should be preferred to a conventional support system at the mine.

Jan 1, 2011

Separation of Nickel and Cobalt from Manganese, Magnesium and Calcium by Synergistic Solvent Extraction - From Batch Tests to Pilot Plant Operation The synergistic solvent extraction system consisting of Versatic 10/LIX63/TBP was used for the separation and purification of nickel and cobalt from synthetic laterite leach solution after iron removal. Very encouraging results were obtained for separating nickel and cobalt from manganese, magnesium and calcium. In batch tests, the organic composition of the synergistic system was optimised and very large synergistic shifts for nickel and cobalt were observed. The ?pH50(Mn-Co) and ?pH50(Mn-Ni) values were as large as 1.65 and 2.40, respectively. The extraction and stripping kinetics of nickel and cobalt was fast. Semi continuous extraction tests were conducted with a pH profile of 5.5/6.1/6.5 in three stages at 40¦C. The nickel and cobalt extractions reached 99.9 per cent with only 5 mg/L Ni and <1 mg/L Co left in the raffinate. With two stages of scrubbing, only 2 mg/L Mn and less than 1 mg/L Mg and Ca were left in the scrubbed organic solution. With two stripping stages, the stripping efficiencies of Ni and Co reached over 95 per cent. A fully continuous pilot plant operation was conducted successfully for 280 hours. With an O/A ratio of about 2 and a pH profile of 5.5/5.8/6.0/6.3 for the four stages EX1/EX2/Ex3/EX4, both nickel and cobalt were almost completely extracted. Using a pH profile of 5.4/5.0 for SC1/SC2, the manganese scrubbing efficiency was over 96 per cent. Using three strip stages, over 98 per cent Ni and 99 per cent Co were stripped with only 64 mg/L Ni in the stripped organic solution. The nickel concentration in the loaded strip liquor reached 83 g/L, resulting in a ?Ni of over 28 g/L. The chemical stability of the system was also assessed over 12 weeks under proposed industrial operating conditions. Operation exclusively under strip conditions at 50¦C and 40¦C resulted in LIX63 oxime half lives of 1.1 and 2.1 years, respectively. Operation exclusively under extract conditions at 50¦C and 40¦C resulted in oxime half lives of 0.26 and 0.82 years, respectively. Losses of Versatic 10 were less than four per cent.

Sep 13, 2010

By M. Perolo, A. Contini, E. Ramelli, G. Borgonovo, L. Locatelli

This paper presents the ground settlement monitoring system used during the construction of two tunnels bored by two EPB TBMs, beneath the existing and active railway embankment in Bologna (Italy). The tunnels run close to large buildings and beneath bridges and other infrastructure. Data are collected from remote total stations and from electro levels installed directly on the railway tracks. The automated monitoring system acquires and analyses data then sounds an alarm in the event that there is a problem. Alarms are sent out in case of excessive tilt or settlement. Data is provided through a dedicated web application for multiple-party access, to gather, manage and store monitoring data.

Jan 1, 2007

By U. Sachse

This paper explores a systematic approach for mining decision-makers to use when faced with choosing which method to use for a specific rockpass length. The different excavation methods available in the broad South African mining industry are compared against a number of critical parameters, as applied to rockpasses of varying length. This approach is not meant as a definitive, prescriptive planning tool, but rather as a proposed approach to enable designers and planners to choose the best system to excavate their specific rockpasses

Jan 1, 2005

The paper deals with the results of dynamic tests carried out on a range of surface support liners consisting of combinations of mesh (various types), shotcrete, and wire rope lacing. The testing was carried out over the period 1993 to 1998. The dynamic testing method made use of drop weight impact loading of test samples which attempted to simulate realistic in situ conditions, and the range of loading imposed was equivalent to small to severe rockburst conditions. The results of the testing provide quantitative data, in the form of input energy, which is relevant for support design and for the choice of support types appropriate for situations in which significant mine-induced seismicity occurs or is expected to occur. In addition to the wire mesh and shotcrete liner systems tested, estimates of energy capacity are made for other, untested, systems.

Jan 1, 2001

By H. Moosberg-Bustnes

In cement-based products, such as concrete and mortars, a balance between the particle sizes of the components must be kept in order to obtain the required material properties, such as workability and strength. Sometimes the aggregates lack the necessary amount of fines, hence fine particles, i.e., filler materials, have to be added. Large quantities of filler material are needed in the production of modern concrete types; one principle of self-compacting concrete (SCC) is, for instance, the use of large amounts of fillers to reduce the friction between the coarser aggregates. Use of by-products such as slag, dust or sludge from the metallurgical industries as filler materials in concrete may help to conserve natural resources and at the same time be an economically positive option. However, to be able to successfully use the available materials they must be suitable for the planned purpose, i.e., they must be compatible with cement. In this paper three different experimental studies of steel-slags will be discussed. The aim of the studies has been to investigate if it is possible to improve the steel-slags properties, by selective screening, fine wet grinding or remelting, so that the steel-slags can be used as mineral-addition/filler material in concrete. Keywords: concrete, filler, steel-slag, modification

Jan 1, 2004

By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961

By P. Toscano

The objective of this investigation was to determine how the losses of nickel, copper and cobalt in fayalite slags could be controlled for nickel mattes with iron contents below 5 wt%. Laboratory-converting and slag-cleaning experiments were carried out at 1250°C. Several variables were investigated during and after converting to help minimize the amount of nickel and cobalt that reports to the slag. The variables used were oxygen concentration in the blast, coke breeze addition and nitrogen injection stirring. In all the experiments, slag and matte co-existed. Coke additions during converting have little effect on the losses of nickel, copper and cobalt. In fact, coke additions retard the converting process by consuming some of the oxygen injected. On the other hand, coke additions and nitrogen injection applied after converting was completed resulted in decreased slag losses.

Jan 1, 2004

By W. de Beer

We present aspects of one of several ongoing case studies used in the development of prediction techniques for major seismic instabilities. The current investigation centres on accelerated coseismic deformation described by the kinematics of failure and on softening, as well as the characterization of areas of interest by measures of the seismic response at such sites.

Jan 1, 1998

By Donald Leroux, Colin Hardie

"New or improved mathematical models of mineral processing machines are published almost on a monthly basis. Often, these models can be calibrated from bench-scale test results and programmed using spreadsheet software to simulate different designs and operating conditions in open-circuit configuration. However, since mineral processing plants frequently operate comminution, separation and/or extraction machines in closed-circuit configurations, open-circuit simulations often have limited applicability.The simulation of closed-circuit configurations necessitates the programming of an iterative loop to bring the circuit to equilibrium. This can be done by using spreadsheet software but often requires advanced programming skills. As an alternative, LIMN® software, which simplifies the programming of closed-circuit configurations within spreadsheets can be used. This software was specifically designed to turn a Microsoft EXCEL® spreadsheet into a closed-circuit modeling and simulation platform with minimal programming.During the past few years, the Mineral Processing Group at the Noranda Technology Centre, has used this software for numerous projects which include the simulation of multi-stage cyclone circuits, closed-circuit regrinding and locked-cycle flotation tests. Using these projects as examples, the flexibility and the easy to use nature of the LIMN® software is demonstrated.INTRODUCTIONMineral processing engineers routinely have to make predictions regarding comminution and separation processes. Predicting the appropriate dimensions of equipment and the process response to changes in operating mode are probably the most common situations that they face. In all cases these predictions are expected to be rapid and accurate.Predictions made by engineers are frequently based on mathematical models. Many first principles, empirical, semi-empirical, steady state and dynamic models of mineral processes can be found in the literature. In fact, new or improved mineral processing models are continuously being proposed and in spite of this variety, process engineers often have to either develop their own or tailor existing models to suit their particular needs."

Jan 1, 2003

By Marco Lombard, Paulus Kapolo, Christopher J. Greet

"The conversion of a concentrator from one grinding media type to another is a major undertaking in terms of both financial and technical risk. So, a strategy of completing sufficient laboratory and field tests to mitigate this risk, and give the operation confidence that advancing to plant trial will give a high probability for success.The objectives of this paper are twofold: to provide the reader with a strategy for mitigating risk prior to undertaking a plant trial; and to provide a statistical basis for analysing plant trial data. That is, when employing an electrochemically inert grinding media in the primary grinding circuit it is possible to change the pulp chemistry of the system and improve the metallurgical response of the ore.This paper tracks the changes in pulp chemistry and metallurgical performance of Rosh Pinah Zinc Corporation’s silver/lead/zinc concentrator as the primary ball mill was converted from forged steel grinding media to high chrome grinding media. The changed in metallurgical performance are correlated to the shift in pulp chemistry.INTRODUCTIONTheoryBruckard et al (2011) recently published an article describe the effect of the grinding environment on the flotation of copper sulphides. While this paper confined its discussion to copper sulphides the arguments presented apply equally to other sulphide mineral systems. Broadly, these studies indicate that most sulphide minerals are more noble than the grinding media used during comminution. Therefore, the sulphide minerals are cathodic with respect to the forged steel grinding media, and the following reactions apply:Cathode (sulphide mineral): ½O2 + H2O + 2e- ? 2OH- (1)Anode (grinding media): Fe ? Fe2+ + 2e- (2)A galvanic couple between the grinding media and the sulphide mineral(s) exists, which increases the corrosion rate of the forged steel media. The corrosion products of the grinding media, iron oxy-hydroxide species, invariably precipitate on to the surfaces of the sulphide minerals thereby affecting their floatability (Johnson, 2002).The application of more electrochemically inert grinding media to “real” ore systems at an industrial level to improve metallurgical performance has not gained universal acceptance. The aim of this paper is to provide a protocol for conducting laboratory and plant test work that clearly demonstrate that metallurgical benefits are not only possible, but measureable, by way of example. In this case, the work conducted at Rosh Pinah Zinc Corporation in Namibia is described."

Jan 1, 2013

By Max F. Lee, Warren A. Peck

The applicability of the Q-system [Barton et al. 1974] to Australian underground metal mines is discussed with reference to two common design issues: ground support for horizontal mine development, and assessing the stability of bored raises. Installed ground support in mine development is com-pared to empirical estimates using the Q-system and associated support capacity calculations. Data are graphically presented from 59 specially selected sites at 15 contributing mines. The actual performance of large-diameter raise-bored shafts is also compared to empirical stability assessments using a modified version of Q (Qr, after McCracken and Stacey [1989]). Lower-bound Qr values are plotted against raise diameter for 47 selected sites at 23 mines in Australia and Papua New Guinea. The influence on Q and Qr of some geotechnical aspects of the Australian landscape, the dynamic nature of mines (compared to civil construction), and occupational health and safety regulations are discussed. Stability and support assessments that are based just on Q or Qr are not always conclusive. It is often necessary to consider other rock mass parameters, the regulatory environment, and risk issues. These results are interim; further data collection and analysis are required with regard to comparing actual performance versus empirical assessments.

Jan 5, 2007

By S. Rajeswari, D. Gopi

"Pitting corrosion inhibition of 304 stainless steel (SS) in groundwater with a ternary inhibitor mixture (phosphonic acid + bivalent cation + various surfactants) was studied with different environmental variables such as temperature, pH, dissolved oxygen and chloride ions. Critical pitting potential and corrosion potential were calculated for these test media using electrochemical techniques. Under the tested condition, the localized corrosion resistance of 304 SS was determined and the results are discussed. IntroductionPitting corrosion of metals and alloys is a major cause of failure in chemical processing desalination plants, scrubber for flue gas desulphurization (FGD) plants, water storage tanks and pipelines, petroleum refineries, etc.Heat exchangers and condensers in inland thermal and nuclear powerplants utilize groundwater as a coolant, but materials of construction are generally prone to localized corrosion.Localized corrosion attack can be initiated when the passive film on the metal is disrupted. The presence of certain aggressive anions such as chlorides (Cl-) can migrate to the actively corroding area and stabilize pitting corrosion. Attention has been focussed on improving the resistance of stainless steel against localizedcorrosion in aqueous environments.One of the most accepted methods of avoiding corrosion is by the addition of chemicals (inhibitors). Over the past two decades, some phosphonic acids have been explored due to their good corrosion inhibition efficiency and low toxicity (Fang et al., 1993; Karman et al., 1998; Rajendran et al., 1998; Gopi and Rajeswari, 2000a). Bivalent cations like Zn2+ are often applied as additives to inhibit the metal dissolution (Sekine and Hirakawa, 1986; Aruna Bahadur, 1998)."

Jan 1, 2003

By S. Sarac

In this study, graphical and mathematical methods used to determine operating points in single or multiple fan ventilation systems are summarized. The problem is mathematically formulized for parallel connected fans in which analytical solutions are not possible. For n number of parallel connected fans, a non-linear equation system that consists of n number of non-linear equation sis derived. The Newton-Raphson method, which is a numerical analysis method, is adapted to solve this non-linear equation system and the solution steps are given as an algorithm. A computer program based on this algorithm is written and its applicability is proved.

Jan 1, 2000