Linear Programming to Solve Coal Blending Problem

17th International Mining Congress and Exhibition of Turkey- IMCET 2001,  © 2001, ISBN 975-395-417-4 Optimum Blending of Coal by Linear Programming for the Power Plant at Seyitomer Coal Mine K. Erarslan, H. Aykul, H. Akcakoca & N. Cetin Dumlup? nar University, Department of Mining Engineering, 43100, Kutahya, Turkey ABSTRACT: In this study, a linear programming model is developed to determine the optimum coal blend in terms of quality and quantity. Coal with various features is mined from different panels of Seyitomer Lignite Coal District and fed to a nearby power plant.The quality of the coal is extremely variable through the horizontal and vertical directions, which entails the precise planning of coal blending during the mining and stockpiling stages. Otherwise, a large penalty has to be paid to the power plant. In this study, the objective is to match the calorific values required by the power plant. The quality features and production capacities of coal from different panels are determined and are used in quality constraints. The power plant requires coal in two groups, which are of different qualities and quantities.Therefore, two linear programming models complementing each other are developed in order to determine the blending conditions that satisfy the needs of the plant. The models are introduced and solved m the LINDO package program. Reasonable solutions are obtained and optimal amounts of blending are handled. The model also allows the evaluation of coal panels of low quality. 1 INTRODUCTION' Linear Programming (LP) is one of the most widely used methods of operation research for decision problems.This method is a reasonable and reliable procedure for determining the optimum distribution of resources, optimal production, minimum cost, maximum profit, etc. , which comprise the objectives (Ozturk, 1997). In this method, decision parameters to make the objective optimal are linear or assumed to be linear (Taha, 1992, Hillier and Liebermann, 1995). The general form of the problem is formed by objective function and subjected constraints; (1) (2) where; Z= objective of the model Cj = coefficient of/* decision variable (1=1,2 Xj = / * decision variable N) oefficient of decision variable (i=l,2,.. ,m) b, = limited resource for iJ* constraint LP approximation is widely used in mining as well as in other industrial fields. Open pit limits, production scheduling, material flow in processing plants, blending, equipment selection, method selection, transportation, etc. , are its main applications (Chanda and Wilke, 1992, Dijilani and Dowd, 1994, Huang, 1993, Mann and Wilke, 1992, Meyer, 1969, Smith and You, 1995). However, investment, planning, or selection, in other words any actions requiring decision, can be optimized.Especially in open pit mines and underground mines feeding coal to power plants, the quality and quantity of coal is crucial because the burner blocks of power plants are designed according to specific features of co al. Inability to match coal quality and quantity to these specific features results in either penalty costs for the coal enterprise or a decrease in the power plant's efficiency. In addition, inconsistent coal features lead to wear in the power plant's burning units and all integrated components.In this respect, coal-producing enterprises try to match their coal features to power plants' specifications by blending and homogenizing coal extracted from different panels and levels. Satisfying the requirements of the plant is achieved by selective 719 = mining and/or blending. In this study, a relevant case is considered. Seyitomer coal enterprise in Kutahya, Turkey has problems of quality and quantity in supplying the nearby power plant. A well-planned and organized blending procedure and, accordingly, production plan is necessary.In this paper, the problem, is modeled in terms of linear programming and reasonable solutions are obtained. 2 SEYITOMER COAL ENTERPRISE AND ITS PROBLEM Seyi tomer Lignite Enterprise (SLE) is located 20 km. northwest of Kutahya city center. The basin is characterized as Late Miocene-early Pliocene. The lignite seams in Seyitomer basin consist of two horizontal levels (0-7 ° S), referred to as A and B seams, according to their depths. The seams are separated from each other by waste interbedded formations whose thickness vary from 10 to 50 m.These two seams may exhibit variation according to their occurrence in three sub-regions (Seyitomer, Aslanl? , Ayval? ), where the geological coal formation has been determined by drill holes. The thickness of the A seam, located at the top level of the basin, varies in the range of 5-25 m. {Sofrelec, 1967). The thickness of B seam varies in the range of 2-30 m. In the basin, these two seams are rarely observed together. The seam defined as A Is deposited only in the Seyitomer region and the coal occurrences in the Aslanl? nd Ayval? regions. The B seam consists of 3 different sublevels, referred to, from Uie top to the base of the seam, as B[, B2, Bj Their calorific values decrease towards to the seam base as the interbedded layers get thicker. The upper level coal seams B| and B2, which have a high calorific value and are produced in sorted size and quality (+100 mm), have supplied the market for public heating. The B3 coal, which is of low quality and contains fine coal (-100 mm) from the processing plant, is sold to the power plant.At the enterprise, production is performed by the open pit mining method. The overburden, whose thickness varies from 35 to 60 m. , is loosened by drilling and blasting. The stripping method is the excavator and truck and dragline method. The 1 electrical excavators have a 10-yd bucket volume and the dragline has a 70-yd bucket capacity. Production and transportation are also by excavatortruck and loader-truck meu? ods. It is impossible to process the coal with wet washing techniques.For this reason, only crushing, sieving and sorting can be appl ied to the coals of the region. There are three plants working for the power plant and three plants working for the market in the enterprise. The coal is dispatched to the market or the power plant according to its quality. 720 Recently, in terms of quality and quantity the demands of the plant have not been fulfilled and in order to overcome the problem selective mining has been used. Consequently, there is an increasing tendency to use ripping and bulldozers and loaders (Aykul, 2000). APPLICATION OF LINEAR PROGRAMMING IN SLE 3. 1 Definition of the Problem In Seyitomer Coal Mine, six different coal types produced from different panels and levels are treated. The terms for these coals, their average calorific values and annual quantity to be extracted according to Ideal planning are shown in Table 1. These coals need to be blended in accordance with the specifications required by the power plant's burning units. Seyitomer power plant has four burning units. The operating conditions of these units are shown in Table 2.The annual coal requirement of the power plant is 6,000,000 tons: the first three burning units (Unit 1, Unit 2 and Unit 3), with the same requirements, need 4,500,000 tons, while the last burning unit (Unit 4) requires 1,500,000 tons. Table 1. Determined features of coal types according to ideal planning in SLE Coal Type Calorific Amount Value (ton/year) (kcal/kg) FineCoal(-lOO) (From Plants) 1675 2,000,000 Stock of Kizik 1750 800,000 Stock of Marl 1428 > 250,000 B| Level 2000 < 600,000 B; Level 1800 < 600,000 B, Level 1600 > 1,500,000 Table 2.Operating Conditions of Power Plant Power Plant Base Heat Content Grain Size (mm) Units (Kcal/kg) Unit 1 1750 ± 100 0-200 Unit2 1750+100 0-200 Umt3 1750 ± 100 0-200 Unit 4 1600  ± ! 00 0-200 The blending requirements of the coal are as follows: i. Coal coming from the processing plants (fine coal), and that produced from the stock of Kizik, stock of marl, the B3 level, B2 level and B| level can supply Unit 1, Unit 2 and Unit 3. it. Coal produced from the stock of Kizik, stock of marl and B3 level can supply Unit 4.Two different linear models were developed since there are two design specifications in the power plant. Therefore, first, the amount of coal of the B3 level and stock of K? z? k are determined fo. ‘ Unit 4 with the help of the first linear program, and then the rest of the determined amounts are used in the second linear program developed for Unit 1, Unit 2 and Unit 3. After determining these conditions, the main aim is to obtain coal blends that have the maximum heating calorific value in the range of specifications (Kaya, 2000). . 2 Constitution 0/the Model The objective function for Unit 4 maximizing the first blend's calorific value, which has a maximum limitation by the constraints, is shown in Equation 1 : (3) Subjected to Equations 4 to 11: (4) (5) The restrictions are shown in Equations 13 to 21. 4,500,000 (13) (14) (15) (16) (17) (18) (19) (20) (21) (6) (7) (8) (9) (10) (11) Here, X2 : Amount of coal from stock of K? z? k, t. Xj : Amount of coal from stock of marl, t. Xe : Amount of coal from B3 level, t.The objective function for Unit 1, Unit 2 and Unit 3 maximizing the second blend's calorific value restricted by a subjected constraint is shown in Equation 12. (12) Amount of fine coal from processing plants, t. Amount of coal from stock of K? z? k, t. Amount of coal from B| level, t. Amount of coal from B2 level, t. Amount of coal from B3 level, t. 3. 3 Solutions of Models The LINDO package program is used to solve the models. The optimum quality and quantity results of the final tables for Unit 4 are shown In Table 3 (Kaya, 2000). Table 3 Final results of model for Urul 4 Coal Types Coal Amount Heal Content (ton/year) (kcal/kg) Stock of K? ? k 500. 000* 1750 (X2) Stock of marl (X,) 250,000* 1428 750. 000* 1600 B, Level (X,) 1,500. 000 Blend of Coals 1620 5* h *Optimam values ai 7†² iteration As it may be seen in Table 3, t he blend quality of the coal is found to be 1620 kcal/kg. This value is within the range of the specific design values of Unit 4. The final tables for Unit 1, Unit 2 and Unit 3 are shown in Table 4. 721 Table 4. Final results of model for Unit 4 Coal Amount Heat Content Coal Types (ton/year) (kcal/kg) 2,000,000* 1675 Fine coal (Xi) Stock of K? z? k 300,000* 1750