GOSPODARKA SUROWCAMI MINERALNYMI Tom 24 2008 Zeszyt 4/2 ROMAN MAGDA*, TADEUSZ FRANIK* Planning and design of rational parameters of longwall panels in underground hard coal mines Introduction Restructuring of the mining sector in Poland during the period of economic transformations caused the typical model of an underground mine to change. The number of shafts and production horizons have been reduced and the structure of galleries and headings has been simplified. The network of galleries and headings became less intricate as the average production from a single operated working face would increase thanks to the application of more powerful and reliable mining machines and equipment. An increase of the average face production resulted in a decrease in the number of operated longwalls, at the same time the contribution of one face to the total production level would significantly rise. On the other hand, any disturbances of mining activities lead to a relatively significant decrease in the total production of the mine, enhancing the risk involved in maintaining the required production levels. Uncertainty and risk, inherent in the mining sector and further induced by the market economy conditions, have changed the way the panel parameters have been designed and rationalised. Literature on the subject typically recommends modelling of spatial, technical, economic and financial relationships describing the panel locations. In terms of technology and spatial orientation, modelling has become easier whereas the economic and financial aspects are now more difficult to handle. Recent developments of IT technologies have offered new calculation tools which might be widely employed in theoretical considerations and in practical applications: to design the key elements in mines, particularly, panels. A vaster body of data and * Department of Economics and Management in Industry; AGH University of Science and Technology, Kraków, Poland.
108 input information can be easily handled and new computational procedures can be applied which so far have been found too complicated to use. The use of costly equipment in the face operations requires that the management of the company s assets and means of production should be adequate to ensure the required productivity and cost-effectiveness. In order to further improve the work efficiency, it is required that management functions must be developed and perfected. Attention should be given to issues related to uncertainty and risk, associated with the random character of the production processes in underground mines. 1. Analytical method of panel design in the deterministic aspect Even a small reduction of a unit cost of produced coal will always be of key importance, no matter what the economic conditions are. Face production levels have increased significantly in the last ten years, accompanied by intensive restructuring and major technical and technological changes. These activities resulted in increased concentration of production in longwall operations. The average daily output from one face approaches now 4000 ton/day, in individual cases the production levels are several times higher. Reducing the unit cost by 1 PLN/ton for a single face with the average output levels brings the yearly savings of the order of 1 million PLN. In literature on optimisation and modelling of longwall and exploitation panels [1, 2, 8, 9, 10, 11, 12], the optimisation criterion is chosen to be the unit cost of production from a panel. In most cases this cost is related to net output from a panel and the total production during the whole period the panel is operated might be evaluated basing on the net reserves available in the panel. Generally, this cost is associated with mining operations pursued within the panel, covering the development works, mining and liquidation. Accordingly, the following costs are identified, which are connected with: driving maingate and tailgate entries, maintaining maingate and tailgate entries, belt conveyor installation in maingate entry, driving starter entry, transport of longwall face equipment, installation of longwall face equipment, extraction process in the longwall face, reinforcement of maingate and tailgate entries, belt stowing along maingate entry, materials handling to the longwall face, materials handling to roadway faces, removal of longwall face equipment, transport of longwall face equipment removed, liquidation of tailgate and/or maingate entries.
109 The unit cost being taken to be the criterion for the decision-making in matters relating to optimisation of panel or panel field parameters, the modelling procedure might be briefly outlined. The input data are categorised into four groups, as in the example: 1. Geological and mining data (for example: seam thickness, volumetric density, size of headings and galleries, spacing of the double timber). 2. Technical and organisational data (for example: number of shifts, capacity, power ratings and efficiency of machines and equipment). 3. Panel geometry and the mining method (for example: length and range of the working face, pillar dimensions, direction and sequence of longwall operations). 4. Economic and financial data (for example: unit costs, wages, materials, repairs, maintenance, depreciation). In the case of longwall systems widely employed in the coal mining sector in Poland, exploitation panels are divided into longwalls with the working faces. Mining operations are pursued in particular panels and considered as mobile systems associated with mass production processes involving the mining and haulage of the mined output. Mining operations require that the gates and galleries must be first driven and duly equipped (the tail gate and the neck). The equipment has to be provided to the longwall region, followed by start-up and then proper mining activities are continued until the whole deposit to be mined is exhausted. When the longwall mining operations are over, the longwall equipment has to be dissembled and tail gates removed. The length of roadways and the period of time they are operated in particular panels depends on the direction of face advance. Figure 1 shows the typical longwall operation techniques: longwall advance from the gate roadway to the panel, where maingate and tailgate entries are drifted separately for each panel and removed after the mining operations are completed (Fig. 1A), longwall advance from the gate roadway to the panel, where maingate plays a role of tailgate while the neighbouring panel is mined (Fig. 1B), longwall advance in alternating directions: from and towards the panel (Fig. 1C), longwall advance from the panel towards the gate (Fig. 1D). The time structure of the panel operations comprises elementary time sections, taking into account the relationships between particular mining activities. The analysis of time sequence of particular mining operations reveals the following stages: time required to drift maingate and tailgate entries, time required to complete the starter entry, time required to install the mining equipment, time required to longwall extraction, time required to remove the face equipment. Analytical methods of modelling and optimisation of longwall and exploitation panels consist in deriving the formulas governing and time and spatial relationships between major determinants of particular costs, face advance, net production from a longwall and net coal
110 reserves in the panel. In many cases quantities associated with cost estimates are taken on the basis of computed data recorded by the mining companies. Such estimates can be more or less accurate, depending on the accessibility of source data and the vastness of the data body. Introduction of departmental cost accounts, identification of cost centres and introduction of controlling allows a more accurate analytical model to be created that governs the mining operations in the panel. Such model might become a useful tool for optimisation of panel parameters. Comparing the geological and mining data as well as technical and technological data enables us to create optimisation models of the deposit sections to be mined, using the computer simulation tools and commercially available computer software packages, such as STATISTICA or MS PROJECT. Fig. 1. The typical scheme of location of longwalls in exploitation panel Rys. 1. Typowy schemat rozmieszczenia przodków œcianowych w polu wydobywczym
111 2. Design of panel parameters in the stochastic approach Enhanced concentration of mining production from single working faces and, in consequence, reduction in the number of operated faces at the given level, creates a specific situation in terms of uncertainty and involved risk. In underground mining all factors and circumstances that might impact on the mining processes cannot be fully recognised. When operations are ceased at one working face, for various reasons (for instance due to uncertainty as to geological and mining conditions) that might lead to the output reduction by one third or even in some cases by one half of the total production from the mine. It might be extremely difficult to catch up later and keeping to the schedules might prove impossible, hence the potential sales contracts might be lost. As the level of concentration of production from a single face increases, the issues associated with risk and uncertainty in longwall operations now become of key importance. The concepts of uncertainty and risk are often confused or used jointly, or one is sometimes used to replace the other. There is an extensive literature on the subject of risk and uncertainty, with reference to mining as well [3, 4, 5, 6, 13]. In the present study uncertainty is treated as an aspect of reality being a consequence of a great number, complexity and variability of subjects, their mutual relationships, their surroundings and limited control that humans have over reality. In this case we refer to the uncertainty of nature, which is objective, external and having its source in processes that cannot accurately predicted and controlled. Risk, on the other hand, is associated with the decision-making processes which might or might not be taken even when uncertainty levels are identical, as the decision- -makers might prove more or less willing to make risky decisions. Risk in economic activities is associated with the two main factors: 1) risk associated with uncertainty of the nature, 2) risk associated with the investor s attitude to taking risk. Another frequently applied measure of risk is variance of the given criterion in the decision-making process (though its interpretation presents a certain difficulty) or the standard deviation of this criterion, i.e. the square root of variance (easier to interpret in practical applications). Both variance and standard deviation take nonnegative values and the smaller the variance, the smaller standard deviation and hence the risk associated with the decision-making becomes smaller. Investments in the mining sector are associated with particular types of risk, categorised into four groups [5]: 1) geological risk, associated with the size, quality and availability of coal deposits, 2) technological risk associated with the specificity of mining operations and natural hazards, 3) economic and financial risk associated with production costs, uncertainty of demand, competition on the market, price fluctuations, changing interest rates, exchange rates and inflation rates, 4) political risk associated with the changes of legal regulations, taxes and environmental laws.
112 The first three categories of risk are of major importance for modelling and optimisation of panel parameters: geological, technological and economic and financial risk. In the case of deposits that are heterogeneous in terms of quality and quantity their actual parameters might not be found at all. That group includes coal seams of variable thickness and changing quality parameters (calorific value, ash and sulphur content), which determine the final coal price and in consequence, sales revenues. Technological risk can be partly treated as a derivative of the geological risk, and partly as that associated with the applied mining technologies and methods. In underground mining operations there are several endogenous and exogenous factors that might disturb the production cycle and hence disturb the timely production. The output from the working face is a random variable, its random character is the consequence of uncertainty of geological and mining conditions, particularly the natural hazards and the risk of being unable to stick to the schedules. The panel as the place where costs are generated is associated with the economic and financial risk, mainly due to fluctuating prices of fixed assets, materials and services, interest rates, currency exchange rates and inflation rates. When given costs can be ascribed to specific points and right conclusions are drawn from the budgeting and controlling data, the costs of longwall mining might be more accurately predicted, thus the risk associated with forecasts of particular cost parameters can be reduced, too. The use of the available mathematical and computational tools allows the aspects of uncertainty and risk to be taken into account in modelling and optimisation of panel and panel field parameters. One of such models is that based on the integrative method of mapping and cost-effectiveness analysis of mining processes in an underground coal mine [10]. This model, referred to as deterministic, was applied in the 1990s. It involves functional relationships between the elements of the spatial, engineering and time structure of the mining processes in the coal mine and the stream of costs and financial effects and can be applied to determine the effects of uncertainty and risk on the specified criteria for the investment decisions. That is achieved by dividing the input data into those that are determined and random (independent). For the random data the descriptive statistics and probability distributions are derived on the basis of source data collected n practical applications. The Monte Carlo method permits the simulations to be performed on the analytical model. In each iteration procedure the random variables are drawn accordingly, to fit the probability distribution pattern determined a priori. After a large number of random draws, we get a set of values of the adopted optimisation criterion. Statistical treatment of those values yields the expected value of the investigated criterion and the standard deviation, which is thought to be the measure of risk. The developed mathematical model was further used in Monte Carlo simulations, in accordance with the procedure set out elsewhere [3]. The simulation procedure can be highlighted using the example of two selected random variables: seam thickness (as an example of the random variable associated with geological risk), cyclic factor (a random variable associated with technological processes).
For thus assumed random variables we obtained the probability distributions and descriptive statistics. This paper is limited in scope, so the full table of input data and the result of statistical treatment are omitted here and can be found in [3]. The normal distribution, among those available in the package STATISTICA, is found to give the best fit both for the measurement data and practical results [7]. Simulations of the unit cost involved 500 draws of input data sets, having the random character, in relation to the probability distribution patterns determined a priori. The reverse distribution function was applied and the calculation procedure was repeated 500 times, utilising the model developed for each version of the calculation procedure for the given face length and range. The number of variants included the pairs of assumed face ranges (1000, 1500, 2500, 3000 m) and the face length (200, 225, 250, 275, 300 m). For each variant we obtain 500 results expressing the unit cost and the probability distribution pattern is fitted using the program STATISTICA. In each variant the log-normal distribution appears to give the best fit. Selected example is shown in Figure 2, illustrating how to fit the probability function of a unit costs for the working face range 1500 m and length 275 m. The risk profile, measured by the standard deviation, is best shown revealing the relationship between the expected value of the unit cost and its standard deviation form the fixed face range and variable face length. A selected plot obtained for the face range 1500 m is shown in Figure 3. As the face length increases, the expected value of the unit cost from the panel falls down to the lowest value obtained for face length 300 m, yet the minimal risk, 113 Fig. 2. Probability function of a unit cost for the longwall range 1500 m and length 275 m Rys. 2. Funkcja prawdopodobieñstwa kosztu jednostkowego dla przodka œcianowego 1500 m i d³ugoœæ 275 m
114 Fig. 3. Relationship between the expected value of the unit cost and risk measured by standard deviation Rys. 3. Relacja pomiêdzy spodziewan¹ wartoœci¹ kosztu jednostkowego i ryzykiem mierzonym odchyleniem standardowym expressed by the standard deviation of the unit cost is registered for the face range 275 m. When the face length exceeds 275 m, the risk level tends to increase. This is a simplified example, giving some insight into selected aspects of the issues associated with uncertainty and risk involved in optimisation of longwall panel parameters. Further improvement of the cost management systems in collieries will allow more complex and accurate optimisation models to be developed to take into account various aspects of uncertainty and risk in the design of panel parameters. Conclusions The present-day achievements in data processing enable the creation and development of more accurate mathematical and economic model which might support decision-making processes, at the stage of projecting, design and planning of mining activities. Of particular importance is modelling of mining operations in longwalls and panels where costly technical equipment is concentrated and the personnel have to be highly qualified. Intensive restructuring of the coal mining sector involving the technical and technological aspects as well aims to ensure high concentration of coal production from the working faces. Accordingly, the longwall and panel parameters have to be adjusted to the conditions of highly-concentrated coal production, at the same time ensuring the reliability of production processes.
115 Underlying most methods used in optimisation of longwalls and panel systems is the deterministic model of the coal production whereby an assumption is made that all input parameters in the optimisation are known beforehand. Actually, some of these parameters are random in character and hence the concept to apply the stochastic model and Monte Carlo simulations of selected parameters. Application of the Monte Carlo method better illustrates the real nature of the coal production process for the purpose of production planning and design and for the risk analysis. The study was financed from State budget 2006 2009 as research project No. 4 T12A 064 30. REFERENCES [1] F r a n i k T., M a g d a R., 1989 Kszta³towanie siê kosztów utrzymania chodników przyœcianowych w polu eksploatacyjnym. Gospodarka Surowcami Mineralnymi z. 4, Kraków. [2] G r y g l i k D., 2001 Metoda modelowania i optymalizacji parametrów pól eksploatacyjnych w kopalni wêgla kamiennego z uwzglêdnieniem niepewnoœci i ryzyka. Praca doktorska, AGH, Kraków. [3] Jajuga K., Jajuga T., 1999 Inwestycje. Instrumenty finansowe. Ryzyko finansowe. In ynieria finansowa. Wydawnictwo Naukowe PWN, Warszawa. [4] K a r b o w n i k A., 1986 Studium wielkoœci wydobycia projektowanej kopalni podziemnej wêgla kamiennego z uwzglêdnieniem niepewnoœci informacji. Zeszyty Naukowe Politechniki Œl¹skiej Górnictwo z. 893, Gliwice. [5] K i c k i J., S a ³ u g a P., 2000 Niektóre aspekty oceny ryzyka w inwestycjach górniczych. Materia³y z konferencji Szko³a Eksploatacji Podziemnej 2000, Kraków. [6] K o w a l i k S., 1996 Podejmowanie decyzji w górnictwie w warunkach niepewnoœci. Zeszyty Naukowe Politechniki Œl¹skiej z. 1332, Gliwice. [7] L u s z n i e w i c z A., S ³ a b y T., 2001 Statystyka z pakietem komputerowym STATISTICATMPL. Wydawnictwo C.H. Beck, Warszawa. [8] M a g d a R., 1985 Optimization of the rate of return of the mine production process. International Journal of Mining Engineering no. 3. [9] M a g d a R., 1994 Mathematical model for estimating the economic effectiveness of production process in coal panels and an example of its practical application. International Journal of Production Economics, 34. [10] M a g d a R., 1994 Application of integrational theory of mine production process modelling to optimization of selected parameters of coal panels. Proceedings of the third international Symposium of Mine Plannig and Equipment Selection. Istanbul, October 1994. [11] M a g d a R., F r a n i k T., D o m a ñ s k i J., 1992 Ocena istotnoœci wp³ywu wybranych czynników techniczno-organizacyjnych na optymalne parametry geometryczne pól œcianowych. Archiwum Górnictwa vol. 37, nr 3 (PAN), Kraków. [12] M a g d a R., F r a n i k T., 1989 Optymalizacja wybranych parametrów pola eksploatacyjnego. Gospodarka Surowcami Mineralnymi z. 3, Kraków. [13] S a ³ u g a P., 2001 Symulacja Monte Carlo w ocenie ekonomicznej eksploatacji z³o a wêgla kamiennego. Materia³y Konferencyjne Szko³y Eksploatacji Podziemnej, Kraków.
116 PLANOWANIE I PROJEKT RACJONALNYCH PARAMETRÓW P YT PRZODKA ŒCIANOWEGO W PODZIEMNYCH KOPALNIACH WÊGLA KAMIENNEGO S³owa kluczowe Wydobycie wêgla kamiennego, optymalizacja przodka œcianowego i pól wydobycia, zarz¹dzanie ryzykiem, symulacja, metoda Monte Carlo Streszczenie Usprawnienie procesów zarz¹dzania w firmach górniczych jest g³ównym czynnikiem zwiêkszenia ich efektywnoœci. Dzia³ania restrukturyzacyjne w sektorze górnictwa wêglowego zmieni³y strukturê zarz¹dzania i systemy organizacyjne w kopalniach i firmach górniczych. Zidentyfikowano stanowiska kosztów i odpowiedzialnoœci, rachunkowoœæ kosztów wydzia³owych, wprowadzono systemy bud etowania i kontroli, które otworzy³y nowe perspektywy dla opracowania modeli i metod matematycznych dla optymalizacji dzia³alnoœci kopalni. Pole wybierania jest postrzegane jako kosztowny element przestrzennej struktury dzia³añ górniczych, poniewa obejmuje ono zarówno produkcjê górnicz¹, jak i prace rozwojowe. Grupa s¹siednich pól wybierania u ytkowanych przez to samo urz¹dzenie mo na okreœliæ jako grupê pól wybierania. Zarówno przodek œcianowy, jak i pola wybierania s¹ punktami generowania kosztów. Uwzglêdniaj¹c zastosowanie wydzia³owej rachunkowoœci kosztów, koszty mo na identyfikowaæ i uwzglêdniaæ w punktach, gdzie s¹ one generowane. Daje to nowy potencja³ badaniom, szczególnie w badaniach analitycznych, tworzeniu modeli symulacji i procedurach obliczania opartych na najlepszych technikach komputerowych i dostêpnych pakietach modelowania numerycznego. Badanie to podaje skrócony zarys pewnego pola w ramach metodologii projektowania racjonalnych parametrów pól wybierania przodka œcianowego, pocz¹wszy od metody analitycznej w podejœciu deterministycznym, a po metodê wspomagan¹ przez modelowanie stochastyczne. Zastosowanie metody Monte Carlo umo liwia tak¹ procedurê symulacji, która przy ka dej iteracji zmiennych losowych prowadzi je w taki sposób, aby odpowiada³y one rozk³adowi prawdopodobieñstwa okreœlonemu a priori. Po pewnej liczbie ci¹gów losowych otrzymujemy zestaw wartoœci przyjêtego kryterium optymalizacji. Statystyczne podejœcie do tych wartoœci daje spodziewan¹ wartoœæ badanego kryterium i odchylenie standardowe, które jest uwa ane za najlepsz¹ ocenê ryzyka. PLANNING AND DESIGN OF RATIONAL PARAMETERS OF LONGWALL PANELS IN UNDERGROUND HARD COAL MINES Key words Hard coal mining, longwall and exploitation panels optimization, risk management, simulation, Monte Carlo method Abstract Improvement of the management processes in mining companies is the major factor to improve their efficiency. Restructuring actions in the coal mining sector have changed the management structure and organisational systems in the mines and mining companies. Cost and responsibility centres have been identified, the departmental cost accounting, budgeting and controlling systems have been introduced, which opened new perspectives for development of mathematical models and methods to optimise the mine operations. A panel is perceived as a costly element of the spatial structure of mining activities, as it involves both the mining production and development works. A group of neighbouring panels operated by the same equipment unit might be defined as a panel field. Both longwall and exploitation panels are the points where costs are generated. Owing to the application of the departmental cost accounting, costs can be identified and accounted at points where they are generated. This offers new potential for research, particularly in analytical studies, creation of simulation models
117 and calculation procedures supported by state-of-the-art computer techniques and the available numerical modelling packages. This study briefly outlines a certain field within the framework of methodology of designing rational parameters of longwall panels, starting from the analytical method in the deterministic approach, right through to the method supported by stochastic modelling. Application of the Monte Carlo method permits a simulation procedure such that during each iteration the random variables are drawn in such a manner as to fit the probability distribution pattern determined a priori. After a large number of random draws, we get a set of values of the adopted optimisation criterion. Statistical treatment of those values yields the expected value of the investigated criterion and the standard deviation, which is thought to be the best measure of risk.