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Determination of Critical Conditions of Spontaneous Combustion of Coal in Longwall Gob Areas / Wyznaczanie Warunków Krytycznych Samozapalania Węgla W Zrobach Ścian

Determination of Critical Conditions of Spontaneous Combustion of Coal in Longwall Gob Areas /... Arch. Min. Sci., Vol. 60 (2015), No 3, p. 761­776 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.1515/amsc-2015-0050 JANUSZ CYGANKIEWICZ* DETERMINATION OF CRITICAL CONDITIONS OF SPONTANEOUS COMBUSTION OF COAL IN LONGWALL GOB AREAS WYZNACZANIE WARUNKÓW KRYTYCZNYCH SAMOZAPALANIA WGLA W ZROBACH CIAN Decades of experience in the fight against endogenous fire hazard in coal mines indicate a major influence of certain conditions in a given area of the mine on the possibility of fire occurrence, such as: susceptibility of coals to spontaneous combustion, oxygen content in the air incoming to the self-heating coal, conditions of heat exchange between the self-heating coal mass and the environment This paper presents a numerical method for determining the critical conditions of spontaneous combustion of coal in longwall gob areas, i.e. conditions under which spontaneous combustion may occur. It has been assumed that crushed coal in the gob has a shape of a flat layer adjacent from the roof and floor side to the rocks. Our considerations have been limited to coals containing small amount of moisture. A simple model of oxidation kinetics on the coal surface expressed by the Arrhenius equation has been adopted. This model assumes that oxidation rate is independent of the amount of oxygen absorbed by coal. The rate of reaction depends only on temperature, with the parameters of the equation changing after the coal has reached the critical temperature. The article presents also a mathematical model of spontaneous heating of the coal layer in the gob area. It describes the heat balance in the coal as well as the oxygen and heat balance in the flowing gases. The model consists of a system of differential equations which are solved using numerical techniques. The developed computer program enables to perform the relevant calculations. In this paper, on the example of coal from a seam 405, we present the method for determining the following critical parameters of the layer of crushed coal: thickness of the layer, oxygen content in a stream of gases flowing through the layer and thermal conductivity of surrounding rocks. Keywords: spontaneous combustion, coal, mathematical model, numerical solutions, critical conditions of spontaneous combustion CENTRAL MINING INSTITUTE, PLAC GWARKÓW 1, 40-166 KATOWICE, POLAND Wieloletnie dowiazenie w zakresie zwalczania zagroenia poarem endogenicznym w kopalniach wskazuj na zasadniczy wplyw na moliwo zaistnienia poaru niektórych warunków panujcych w danym miejscu kopalni, takich jak: - sklonno wgla do samozapalania - zawarto tlenu w powietrzu doplywajcym do zagrzewajcego si wgla. W pracy przedstawiono numeryczn metod wyznaczania warunków krytycznych samozapalania wgla w zrobach cian, czyli takich po spelnieniu których moe doj do samozapalenia. Przyjto, e znajdujcy si w zrobach rozkruszony wgiel ma ksztalt plaskiej warstwy, ssiadujcej od stropu i spgu ze skalami. Rozwaania ograniczono do wgli charakteryzujcych si nisk zawartoci wilgoci. Przyjto prosty model kinetyki utleniania na powierzchni wgla wyraony równaniem Arrheniusa. Model ten zaklada niezaleno szybkoci utleniania od iloci tlenu pochlonitego przez wgiel. Szybko reakcji zaley jedynie od temperatury , przy czym wystpujce w równaniu parametry zmieniaj si po osigniciu przez wgiel temperatury krytycznej. W artykule przedstawiono matematyczny model samozagrzewania warstwy wgla w zrobach opisujcy bilans ciepla w wglu oraz bilans tlenu i bilans ciepla w przeplywajcych gazach. Tworzce model uklady równa róniczkowych czstkowych rozwizywane s metodami numerycznymi. Opracowany program komputerowy umoliwia wykonywanie stosownych oblicze. W pracy, na przykladzie wgla z pokladu 405 , przedstawiono sposób wyznaczania warunków krytycznych warstwy rozkruszonego wgla: gruboci warstwy, zawartoci tlenu w przeplywajcych przez warstw gazach oraz przewodnoci cieplnej otaczajcych skal. Slowa kluczowe: samozapalanie, wgiel, model matematyczny, rozwizania numeryczne, warunki krytyczne samozapalania Nomenclature: A C Co c Dr H L n R T(x,y,t) Ta Tcr U(x,y,t) x, z f ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ external surface of coal, m2 volume fraction of oxygen in gases, volume fraction of oxygen in gases incoming to the coal layer, specific heat, J/kg×K diffusion coefficient of oxygen, m2/s thermal diffusivity coefficient , m2/s thickness of the layer of coal or rocks, m length of the layer of coal, m order of reaction, reaction rate constant, 1/s temperature of coal, K temperature of activation, K critical temperature, K temperature of gases, K geometric coordinates, m coefficient of heat transfer, W/(m2×K) coefficient of oxygen absorption on the coal surface, coefficient of thermal conductivity, W/m×K gas flow rate, m/s density, kg/m3 Subscripts: 1 ­ rocks in the floor, 2 ­ rocks in the roof, b t l r cr do in p po w s ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ upper boundary, lower boundary, left side right side critical temperature value a range of temperatures below or equal to critical value, initial value, air, a range of temperatures above critical value, coal, rocks. Introduction Spontaneous combustion of coal remains a serious problem for underground coal mines as it causes huge material losses and can put working mining crews in danger. There are known cases of methane ignition resulting from spontaneous combustion of coal, which in turn caused human losses. Spontaneous combustion of coal is a result of exothermic oxidation reaction. The process of self-ignition occurs when the flux of heat produced by the reaction exceeds the heat flux absorbed by the environment. This excess of heat raises the temperature of coal. That in turn accelerates the oxidation reaction, leading to a rapid temperature increase and finally to self-ignition of coal. The more limited exchange of heat with environment (i.e. conditions closer to the adiabatic ones) the higher probability of spontaneous combustion. Apart from the conditions of heat exchange with the environment, a huge impact on the possibility of self ignition occurrence has a content of oxygen in gases flowing through the crushed coal as well as the natural susceptibility of coal to oxidation. A description of the phenomena leading to spontaneous combustion of coal is related to the theory of thermal explosion. Its creator, N.N. Semenov, introduced a concept of critical conditions. This theory was further developed by D.A. Frank-Kamieniecki, who in turn put forward a concept of a critical parameter. This theory constituted the starting point for numerous research studies, among others W. Kordylewski, Z. Krajewski (1980); W. Kordylewski, Z. Krajewski (1981); W. Kordylewski (1985). In the recent years, however, Frank-Kamieniecki theory has been subjected to criticism. Along with the development of electronic computing technology, numerical modeling became possible, and thus it became possible to determine the conditions of spontaneous combustion of coal. There is quite an extensive literature concerning a mathematical description of spontaneous heating and self ignition of coal. Previous works: Branny M. et al. (1995, 1997); Krishnaswamy S.K. et al. (1996); Rosema A. et al. (2001); Schmal D. et al. (1985); Schmidt M. et al. (2003); Smith M.A., Glasser D. (2005) were of a cognitive nature and intended to explain the mechanism of spontaneous combustion. In the recent years there have been reported a few works aimed at solving the specific practical issues. In the work of Yuan L., Smith A.C. (2008), the authors attempt to describe spontaneous combustion of coal in longwall gob areas. The work of Taraba B. et al. (2014) presents a description of the process of spontaneous heating of a coal stockpile. 1. Geometric model of a coal deposit A flat layer of crushed coal with a thickness of Hw adjacent from one side to the rock layer with a thickness of H1 and from the other side to the rock layer with a thickness of H2, through which oxygen-containing gases flow at the rate f is taken into consideration. It is assumed that the flow through the layer is pumped, fixed in time and with a constant velocity profile in the cross-section of the layer. This flow is caused by the difference of aerodynamic potentials. Fig. 1 A fragment of a gob area with crushed coal A mathematical model which specifies temperature field T(x,y,t) within the coal deposit, temperature U(x,y,t) and concentration C(x,y,t) of oxygen in flowing gases is taken into consideration. It takes account of coal oxidation, mass transport and diffusion processes as well as adsorption and heat exchange on the surface of the coal deposit. The following notations are introduced: z1 H1 , z 2 H1 Hw, Z H1 Hw H2 (see Fig. 1) 2. Kinetic model of oxidation and model of heat sources A detailed description of oxidation and chemisorption processes is not a subject of this article. The heat produced by oxidation and chemisorption is expressed as: Er mqr T RC (1) where: qr -- heat of oxidation reaction, m -- porosity coefficient of crushed coal, RC -- stream of absorbed oxygen. The rate of oxygen absorption depends on the temperature T and the oxygen concentration C. Based on the experimental research studies a kinetics model of coal oxidation has been built: RC T , C Rdo C ndo e R po C n po Tdo / T T po / T , T , T Tcr , Tcr , (2) A method for determining the critical temperature is described in the works (Cygankiewicz, 2000). Heat exchange between coal and a stream of flowing gases is described by the following relation: E A (U T ) (3) The heat Er evolves directly within the coal, whereas the heat E is absorbed by the flowing gases. In total, the heat released in the air is expressed as: RU = ­E The heat evolved within the coal can be written as: RT = Er + E (5) (4) 3. Energy balance in the layer of coal Energy balance in the self-heating layer of coal can be described by the following equations: c1 T t ws (1 m) c2 T t x 2 T x T x 0, z T 0, T z RT , x x x L, 0 L, z 2 z z1 , , Z. (6) Equation (6) should be considered together with initial, boundary and compatibility conditions. Initial conditions: t = 0: T ( x, z, 0) T1in , T ( x, z, 0) Twin , T ( x, z, 0) T2in ; x x x L, 0 L, z 2 z1 , 2 , , (7) Boundary conditions on the left x = 0 and right x = L side of the considered domain: x T (0, z , t ) x x x T (0, z , t ) T ( L, z , t ) x x T ( L, z , t ) 0, Tl (t )) 0, 0, for z 2 , Z; 1 , l (t )(T (0, z , t ) (8) r (t )(T ( L, z , t ) Tr (t )) T (0, z , t ) T ( L, z , t ) 0, Boundary conditions at the lower z = 0 and upper z = Z boundary of the considered domain: T ( x, 0, t ) T ( x, Z , t ) b (t )(T ( x, 0, t ) t (t )(T ( x, Z , t ) Tb (t )) 0, Tt (t )) 0, (9) Compatibility conditions at the coal-rock phase boundary z = z1 and z = : T ( x, z1 0, t ) T ( x, z1 0, t ), T ( x, z 2 0, t ) T ( x, z 2 0, t ), T ( x, z1 0, t ) T ( x, z 2 0, t ) T ( x, z1 0, t ), T ( x, z 2 0, t ), (10) The following functions are introduced: DT ( x, z , t ) , c1 1 ( x, z , t ) , w c ws 2 2 c2 0 z1 z 0 z1 z z1 , , Z, z1 , , Z, (12) (11) H ( x, z , t ) 0, 0.5RT , cw X ) w (c ws 0, Taking into account the relations (11 and 12), equation (6) can be written as: T t 1 T 1 T DT DT 2H , B x x B x L, 0 , z (13) z1 , 2 The following notations are introduced: d l1 0, d r1 0, d l (t ) d r (t ) dl 2 dr2 0, 0, l (t ), r (t ), el1 1, er1 1, el ( z, t ) er ( z , t ) el 2 1, er 2 1, (0, z , t ), ( L, z , t ), f l1 0, f r1 0, f l (t ) f r (t ) fl 2 fr2 0, 0 l (t ) Tl (t ), r (t ) Tr (t ), (14) d b (t ) d t (t ) b (t ), (t ), t eb et 1, 2, f b (t ) f t (t ) b (t )Tb (t ), (t )Tt (t ) t (15) Using (14), boundary conditions (8) can be written as follows: d l1T (0, z , t ) el1 d r1T ( L, z , t ) er1 x x T (0, z , t ) T ( L, z , t ) x x T (0, z , t ) T ( L, z , t ) f l1 , f r1 , f l (t ), f r (t ), fl2 , fr2 , 1 , d l (t )T (0, z , t ) el ( z , t ) d r (t )T ( L, z , t ) er ( z , t ) d l 2T (0, z , t ) el 2 d r 2 T ( L, z , t ) e r 2 x x , (16) T (0, z , t ) T ( L, z , t ) for z 2 Using (15), boundary conditions (9) can be written as: d b (t )T ( x, 0, t ) eb z T ( x, 0, t ) z f b (t ), f t (t ), (17) d t (t )T ( x, Z , t ) et ( x, t ) T ( x, Z , t ) 4. Oxygen balance in a stream of flowing gases Concentration of oxygen in a stream of gases is described by the following balance equation: C t C x RC , (18) Equation (18) should be considered together with initial and boundary conditions. Initial conditions t = 0: C ( x, z, 0) Boundary conditions: C (0, z , t ) Cin , (19) C0 (t ), x x C ( L, z , t ) 0, 0, ; C ( x, z1 , t ) C ( x, z 2 , t ) 1C ( x, z1 , t ) 2 C ( x, z 2 , t ) (20) x L 0, A function is introduced: G ( x, z , t ) 0.5RC , (21) Taking into account (21), equation (18) can be written as follows: C t C x 2G, (22) The following notations are introduced: pl pr pb pt 1, 0, 1, 2, sl sr sb st 0, 1, , , g l (t ) gr gb gt 0, 0, 0 C0 (t ), (23) Using (23), boundary conditions (20) can be written as: pl C (0, z, t ) sl p r C ( L, z , t ) s r pb C ( x, z1 , t ) sb p t C ( x, z 2 , t ) s t C (0, z, t ) x C ( L, z , t ) g l (t ), gr , g b (t ), g t (t ), , ; (24) C ( x, z1 , t ) C ( x, z 2 , t ) 5. Energy balance in the air stream Energy balance in the air stream is described by the balance equation: p c ps U t U x RU , (25) Equation (25) should be considered together with initial and boundary conditions. Initial conditions t = 0: U ( x, z , 0) U in , Boundary conditions: (26) U (0, z, t ) U 0 (t ), A function is introduced: (27) RU p c ps (28) Taking into account (28), equation (25) can be written as follows: t U x U F, x 2 (29) 6. Discretization The following increments are introduced: x, z, t along Ox, Oz, Ot axes, respectively, and the domain of continuous variables is replaced with the finite set of nodes. The number of nodes is determined along each axis as well as the position of the coal-rock phase boundary ­ J1, J2. Tf / , I L/ , J1 z1 / , J2 / , J Z/ (30) where: Tf -- final time, [] -- denotes the integer part of a number. The coordinates of the nodes xi, zj, tn are placed within the following introduced sets: xi zj tn x i, z 0 i j n 0 I, J, N j, 0 (31) t n, The values of the dependent and independent variables in the nodes xi, zj, tn correspond with the indices i, j, n. For convenience, they can be either subscripts or superscripts. 7. Calculation example The critical conditions are being defined for spontaneous combustion of the coal layer in a seam 405. Coal from this seam contains small amount of moisture. Below are presented geometric parameters of the layer used for calculations, determined by the laboratory studies of the coal and rocks properties. · Time and geometric parameters Time Tf = 100, 200, 300, 400, 1000 h Length of the layer Lw = 6 m Thickness of the layer of coal Hw = 0.5, 0.6, 0.7 m Thickness of the layer of rocks H1 = 1.0 m Thickness of the layer of rocks H2 = 1.0 m · Physical parameters of coal and rocks Porosity coefficient of crushed coal Specific heat of air Specific heat of coal Density of coal Coefficient of thermal conductivity of coal m = 0.45 Cps = 1005.6 J/kgK Cws = 1280.0 J/kgK ws = 815 kg/m3 = 0.3 W/mK Specific heat of rocks in the roof Specific heat of rocks in the floor Density of rocks in the roof Density of rocks in the floor Coefficient of thermal conductivity of rocks in the floor Coefficient of thermal conductivity of rocks in the floor Coefficient of oxygen diffusion in air · Initial parameters Initial temperature of coal Initial temperature of rocks in the roof Initial temperature of rocks in the floor Initial temperature of air Initial concentration of O2 Gas flowrate · Parameters of oxidation kinetics Heat of reaction Reaction rate constant Reaction rate constant Activation temperature Activation temperature Order of reaction Order of reaction Critical temperature Heat transfer coefficient c1 c2 1 2 = 2000 J/kgK = 2000 J/kgK = 2000 kg/m3 = 2000 kg/m3 = 1.0,1.2,1.4,1.5,1.6,1.8,2.0 W/mK = 1.0,1.2,1.4,1.5,1.6,1.8,2.0 W/mK = 1.0­5 m2/s Twin T1in T2in Uin Cin fin qr Rdo Rpo Tdo Tpo ndo npo Tcr l,r,t = 300 K = 300 K = 300 K = 300 K = 0.0 = 0.0006 m/s = 7.6 106 J/m3 = 0.12 1/s = 1875 1/s = 1490 K = 4980 K = 1.6 = 1.6 = 360 K = 0 W/m2K Calculation results The results of performed calculations are presented in Fig. 2-7. Fig. 2 shows temperature distribution in the heated coal and surrounding rocks. Calculations were carried out for the coal layer with the following thicknesses: Hw = 0,5; 0,6 and 0,7 m. The calculation times were 100, 200, 300 and 400 hours. To simplify calculations, the thermal conductivity of rocks in the roof was assumed to be equal to that in the floor and amounted to 1,0 W/mK. As shown in Fig. 2, spontaneous combustion proceeded at its maximum and minimum rate, respectively, in the thickest (0,7 m) and in the thinnest layer (0,5 m). Fig. 3 demonstrates distributions of oxygen content in gases flowing through the examined deposit of crushed coal. They correspond to the temperature distributions shown in Fig. 2. Fig. 4 presents the results of studies on the impact of a thickness of the coal layer from a seam 405 Hw deposited in the gob area on the predicted course of spontaneous combustion development. The latter is shown as a dependence of the maximum temperature of coal within the deposit on time. The values of a coal layer thickness Hw used in calculations were as follows: 0,3; 0,4; 0,5; 0,6 and 0,7 m, the oxygen volume fraction in the stream of incoming air was 0,2 and the coefficient of thermal conductivity of rocks in the roof and floor was = 1,0 W/mK. As it can be seen from Fig 4., the thicker layer of coal (i.e. the closer the conditions to the adiabatic Fig. 2 Temperature distribution in the crushed coal deposit with thicknesses of Hw = 0,5; 0,6 and 0,7 m and in surrounding rocks during spontaneous heating, after 100, 200, 300 and 400 hours from its beginning Fig. 3 Oxygen concentration distribution in gases flowing through the crushed coal deposit with thicknesses of Hw = 0,5; 0,6 and 0,7 m during spontaneous heating, after 100, 200, 300 and 400 hours from its beginning ones), the more rapid process of spontaneous heating. There exists a certain critical thickness of the coal layer, below which spontaneous combustion will not occur. Fig. 5 shows the impact of oxygen content in the air incoming to the coal layer on the development of spontaneous combustion process. The higher is the concentration of oxygen the faster development of this process. As with a thickness of the coal layer, there is a critical value of oxygen concentration, below which spontaneous combustion will not occur. Fig. 6 shows the influence of thermal conductivity of rocks on the course of spontaneous heating of the coal layer with a thickness Hw = 0,6 m from a seam 405. The assumed volume fraction of oxygen in the air incoming to the coal deposit was 0,2. As can be noticed from Fig. 6, an increase in thermal conductivity of rocks slows down the process of self-heating. For simplicity of calculation, the thermal conductivity of rocks in the roof 1 was assumed to be equal to the thermal conductivity of rocks in the floor 2. It is, of course, possible to perform calculations for the case when 1 2. Fig. 7 contains summarized values of critical conditions of spontaneous combustion of coal from a seam 405 in longwall gob areas. The values of a coal layer thickness Hw were plotted on the X axis against the values of thermal conductivity coefficient of surrounding rocks on the Y axis. For particular values of oxygen concentration in the stream of incoming air the curves of critical parameters were determined. For example, a coal layer thickness Hw = 1,0 m, oxygen concentration C = 0,1 and thermal conductivity of rocks = 1,14 W/mK constitute the critical conditions of spontaneous combustion of coal in the seam. Fig. 4 Impact of a thickness Hw of the coal layer remaining in the gob on the predicted course of spontaneous heating of the coal layer (Hw = 0,3, 0,4, 0,5, 0,6, 0,7 m) 1 = 2 = 1,0 W/mK Fig. 5 Impact of oxygen volume fraction in a stream of incoming air on the predicted course of spontaneous heating of the coal layer (Hw = 1,0 m , 1 = 2 = 1,5 W/mK , Co = 0,08; 0,10; 0,12; 0,14; 0,16; 0,18; 0,20) Fig. 6 Impact of the thermal conductivity coefficient l on the predicted course of spontaneous heating of the coal layer (Hw = 0,6m, 1 = 2 = 1,0; 1,2; 1,4; 1,6; 1,8; 2,0 W/mK) Fig. 7 The critical conditions of spontaneous combustion of coal in the gob area in seam 405 8. Summary The method presented in this paper for determining the critical conditions of spontaneous combustion of the flat layer of crushed coal can be useful in the mining practice to evaluate the risk of endogenous fire occurrence in longwall gob areas. This risk may be posed by the coal entering a gob from located closely over the roof the non-balance seam of remained thin coal bed, or by the coal which got to a gob in consequence of geological disturbances. However, one should not forget about the simplifying assumptions adopted in this work. They limit the application range of the presented method to coal seams with a low content of moisture, for which the process of evaporation can be ignored in the calculations. Other assumptions made in this work include that the rate of coal oxidation is fixed in time and that the aspect of oxygen transport in coal particles with a diameter greater than 2 mm is disregarded. The advantage of the presented method lies in its simplicity and relatively few and easily determined parameters of coal and surrounding rocks present in the mathematical model. One can therefore expect that this method will find application in engineering calculations. However, its verification on the basis of mining examinations is required. It is also worthwhile to undertake further studies on the development of more complex mathematical models of spontaneous combustion which would take into account the variability of coal oxidation rate, evaporation of moisture and its influence on spontaneous combustion, as well as oxygen diffusion within coal particles. Acknowledgments Content of this paper is the result of work carried out as part of I2mine project ("Innovative Technologies and Concepts for the Intelligent Deep Mine of the Future") funded by the 7th Framework Program of the European Commission under Grant No. 280855. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Mining Sciences de Gruyter

Determination of Critical Conditions of Spontaneous Combustion of Coal in Longwall Gob Areas / Wyznaczanie Warunków Krytycznych Samozapalania Węgla W Zrobach Ścian

Archives of Mining Sciences , Volume 60 (3) – Sep 1, 2015

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Abstract

Arch. Min. Sci., Vol. 60 (2015), No 3, p. 761­776 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.1515/amsc-2015-0050 JANUSZ CYGANKIEWICZ* DETERMINATION OF CRITICAL CONDITIONS OF SPONTANEOUS COMBUSTION OF COAL IN LONGWALL GOB AREAS WYZNACZANIE WARUNKÓW KRYTYCZNYCH SAMOZAPALANIA WGLA W ZROBACH CIAN Decades of experience in the fight against endogenous fire hazard in coal mines indicate a major influence of certain conditions in a given area of the mine on the possibility of fire occurrence, such as: susceptibility of coals to spontaneous combustion, oxygen content in the air incoming to the self-heating coal, conditions of heat exchange between the self-heating coal mass and the environment This paper presents a numerical method for determining the critical conditions of spontaneous combustion of coal in longwall gob areas, i.e. conditions under which spontaneous combustion may occur. It has been assumed that crushed coal in the gob has a shape of a flat layer adjacent from the roof and floor side to the rocks. Our considerations have been limited to coals containing small amount of moisture. A simple model of oxidation kinetics on the coal surface expressed by the Arrhenius equation has been adopted. This model assumes that oxidation rate is independent of the amount of oxygen absorbed by coal. The rate of reaction depends only on temperature, with the parameters of the equation changing after the coal has reached the critical temperature. The article presents also a mathematical model of spontaneous heating of the coal layer in the gob area. It describes the heat balance in the coal as well as the oxygen and heat balance in the flowing gases. The model consists of a system of differential equations which are solved using numerical techniques. The developed computer program enables to perform the relevant calculations. In this paper, on the example of coal from a seam 405, we present the method for determining the following critical parameters of the layer of crushed coal: thickness of the layer, oxygen content in a stream of gases flowing through the layer and thermal conductivity of surrounding rocks. Keywords: spontaneous combustion, coal, mathematical model, numerical solutions, critical conditions of spontaneous combustion CENTRAL MINING INSTITUTE, PLAC GWARKÓW 1, 40-166 KATOWICE, POLAND Wieloletnie dowiazenie w zakresie zwalczania zagroenia poarem endogenicznym w kopalniach wskazuj na zasadniczy wplyw na moliwo zaistnienia poaru niektórych warunków panujcych w danym miejscu kopalni, takich jak: - sklonno wgla do samozapalania - zawarto tlenu w powietrzu doplywajcym do zagrzewajcego si wgla. W pracy przedstawiono numeryczn metod wyznaczania warunków krytycznych samozapalania wgla w zrobach cian, czyli takich po spelnieniu których moe doj do samozapalenia. Przyjto, e znajdujcy si w zrobach rozkruszony wgiel ma ksztalt plaskiej warstwy, ssiadujcej od stropu i spgu ze skalami. Rozwaania ograniczono do wgli charakteryzujcych si nisk zawartoci wilgoci. Przyjto prosty model kinetyki utleniania na powierzchni wgla wyraony równaniem Arrheniusa. Model ten zaklada niezaleno szybkoci utleniania od iloci tlenu pochlonitego przez wgiel. Szybko reakcji zaley jedynie od temperatury , przy czym wystpujce w równaniu parametry zmieniaj si po osigniciu przez wgiel temperatury krytycznej. W artykule przedstawiono matematyczny model samozagrzewania warstwy wgla w zrobach opisujcy bilans ciepla w wglu oraz bilans tlenu i bilans ciepla w przeplywajcych gazach. Tworzce model uklady równa róniczkowych czstkowych rozwizywane s metodami numerycznymi. Opracowany program komputerowy umoliwia wykonywanie stosownych oblicze. W pracy, na przykladzie wgla z pokladu 405 , przedstawiono sposób wyznaczania warunków krytycznych warstwy rozkruszonego wgla: gruboci warstwy, zawartoci tlenu w przeplywajcych przez warstw gazach oraz przewodnoci cieplnej otaczajcych skal. Slowa kluczowe: samozapalanie, wgiel, model matematyczny, rozwizania numeryczne, warunki krytyczne samozapalania Nomenclature: A C Co c Dr H L n R T(x,y,t) Ta Tcr U(x,y,t) x, z f ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ external surface of coal, m2 volume fraction of oxygen in gases, volume fraction of oxygen in gases incoming to the coal layer, specific heat, J/kg×K diffusion coefficient of oxygen, m2/s thermal diffusivity coefficient , m2/s thickness of the layer of coal or rocks, m length of the layer of coal, m order of reaction, reaction rate constant, 1/s temperature of coal, K temperature of activation, K critical temperature, K temperature of gases, K geometric coordinates, m coefficient of heat transfer, W/(m2×K) coefficient of oxygen absorption on the coal surface, coefficient of thermal conductivity, W/m×K gas flow rate, m/s density, kg/m3 Subscripts: 1 ­ rocks in the floor, 2 ­ rocks in the roof, b t l r cr do in p po w s ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ upper boundary, lower boundary, left side right side critical temperature value a range of temperatures below or equal to critical value, initial value, air, a range of temperatures above critical value, coal, rocks. Introduction Spontaneous combustion of coal remains a serious problem for underground coal mines as it causes huge material losses and can put working mining crews in danger. There are known cases of methane ignition resulting from spontaneous combustion of coal, which in turn caused human losses. Spontaneous combustion of coal is a result of exothermic oxidation reaction. The process of self-ignition occurs when the flux of heat produced by the reaction exceeds the heat flux absorbed by the environment. This excess of heat raises the temperature of coal. That in turn accelerates the oxidation reaction, leading to a rapid temperature increase and finally to self-ignition of coal. The more limited exchange of heat with environment (i.e. conditions closer to the adiabatic ones) the higher probability of spontaneous combustion. Apart from the conditions of heat exchange with the environment, a huge impact on the possibility of self ignition occurrence has a content of oxygen in gases flowing through the crushed coal as well as the natural susceptibility of coal to oxidation. A description of the phenomena leading to spontaneous combustion of coal is related to the theory of thermal explosion. Its creator, N.N. Semenov, introduced a concept of critical conditions. This theory was further developed by D.A. Frank-Kamieniecki, who in turn put forward a concept of a critical parameter. This theory constituted the starting point for numerous research studies, among others W. Kordylewski, Z. Krajewski (1980); W. Kordylewski, Z. Krajewski (1981); W. Kordylewski (1985). In the recent years, however, Frank-Kamieniecki theory has been subjected to criticism. Along with the development of electronic computing technology, numerical modeling became possible, and thus it became possible to determine the conditions of spontaneous combustion of coal. There is quite an extensive literature concerning a mathematical description of spontaneous heating and self ignition of coal. Previous works: Branny M. et al. (1995, 1997); Krishnaswamy S.K. et al. (1996); Rosema A. et al. (2001); Schmal D. et al. (1985); Schmidt M. et al. (2003); Smith M.A., Glasser D. (2005) were of a cognitive nature and intended to explain the mechanism of spontaneous combustion. In the recent years there have been reported a few works aimed at solving the specific practical issues. In the work of Yuan L., Smith A.C. (2008), the authors attempt to describe spontaneous combustion of coal in longwall gob areas. The work of Taraba B. et al. (2014) presents a description of the process of spontaneous heating of a coal stockpile. 1. Geometric model of a coal deposit A flat layer of crushed coal with a thickness of Hw adjacent from one side to the rock layer with a thickness of H1 and from the other side to the rock layer with a thickness of H2, through which oxygen-containing gases flow at the rate f is taken into consideration. It is assumed that the flow through the layer is pumped, fixed in time and with a constant velocity profile in the cross-section of the layer. This flow is caused by the difference of aerodynamic potentials. Fig. 1 A fragment of a gob area with crushed coal A mathematical model which specifies temperature field T(x,y,t) within the coal deposit, temperature U(x,y,t) and concentration C(x,y,t) of oxygen in flowing gases is taken into consideration. It takes account of coal oxidation, mass transport and diffusion processes as well as adsorption and heat exchange on the surface of the coal deposit. The following notations are introduced: z1 H1 , z 2 H1 Hw, Z H1 Hw H2 (see Fig. 1) 2. Kinetic model of oxidation and model of heat sources A detailed description of oxidation and chemisorption processes is not a subject of this article. The heat produced by oxidation and chemisorption is expressed as: Er mqr T RC (1) where: qr -- heat of oxidation reaction, m -- porosity coefficient of crushed coal, RC -- stream of absorbed oxygen. The rate of oxygen absorption depends on the temperature T and the oxygen concentration C. Based on the experimental research studies a kinetics model of coal oxidation has been built: RC T , C Rdo C ndo e R po C n po Tdo / T T po / T , T , T Tcr , Tcr , (2) A method for determining the critical temperature is described in the works (Cygankiewicz, 2000). Heat exchange between coal and a stream of flowing gases is described by the following relation: E A (U T ) (3) The heat Er evolves directly within the coal, whereas the heat E is absorbed by the flowing gases. In total, the heat released in the air is expressed as: RU = ­E The heat evolved within the coal can be written as: RT = Er + E (5) (4) 3. Energy balance in the layer of coal Energy balance in the self-heating layer of coal can be described by the following equations: c1 T t ws (1 m) c2 T t x 2 T x T x 0, z T 0, T z RT , x x x L, 0 L, z 2 z z1 , , Z. (6) Equation (6) should be considered together with initial, boundary and compatibility conditions. Initial conditions: t = 0: T ( x, z, 0) T1in , T ( x, z, 0) Twin , T ( x, z, 0) T2in ; x x x L, 0 L, z 2 z1 , 2 , , (7) Boundary conditions on the left x = 0 and right x = L side of the considered domain: x T (0, z , t ) x x x T (0, z , t ) T ( L, z , t ) x x T ( L, z , t ) 0, Tl (t )) 0, 0, for z 2 , Z; 1 , l (t )(T (0, z , t ) (8) r (t )(T ( L, z , t ) Tr (t )) T (0, z , t ) T ( L, z , t ) 0, Boundary conditions at the lower z = 0 and upper z = Z boundary of the considered domain: T ( x, 0, t ) T ( x, Z , t ) b (t )(T ( x, 0, t ) t (t )(T ( x, Z , t ) Tb (t )) 0, Tt (t )) 0, (9) Compatibility conditions at the coal-rock phase boundary z = z1 and z = : T ( x, z1 0, t ) T ( x, z1 0, t ), T ( x, z 2 0, t ) T ( x, z 2 0, t ), T ( x, z1 0, t ) T ( x, z 2 0, t ) T ( x, z1 0, t ), T ( x, z 2 0, t ), (10) The following functions are introduced: DT ( x, z , t ) , c1 1 ( x, z , t ) , w c ws 2 2 c2 0 z1 z 0 z1 z z1 , , Z, z1 , , Z, (12) (11) H ( x, z , t ) 0, 0.5RT , cw X ) w (c ws 0, Taking into account the relations (11 and 12), equation (6) can be written as: T t 1 T 1 T DT DT 2H , B x x B x L, 0 , z (13) z1 , 2 The following notations are introduced: d l1 0, d r1 0, d l (t ) d r (t ) dl 2 dr2 0, 0, l (t ), r (t ), el1 1, er1 1, el ( z, t ) er ( z , t ) el 2 1, er 2 1, (0, z , t ), ( L, z , t ), f l1 0, f r1 0, f l (t ) f r (t ) fl 2 fr2 0, 0 l (t ) Tl (t ), r (t ) Tr (t ), (14) d b (t ) d t (t ) b (t ), (t ), t eb et 1, 2, f b (t ) f t (t ) b (t )Tb (t ), (t )Tt (t ) t (15) Using (14), boundary conditions (8) can be written as follows: d l1T (0, z , t ) el1 d r1T ( L, z , t ) er1 x x T (0, z , t ) T ( L, z , t ) x x T (0, z , t ) T ( L, z , t ) f l1 , f r1 , f l (t ), f r (t ), fl2 , fr2 , 1 , d l (t )T (0, z , t ) el ( z , t ) d r (t )T ( L, z , t ) er ( z , t ) d l 2T (0, z , t ) el 2 d r 2 T ( L, z , t ) e r 2 x x , (16) T (0, z , t ) T ( L, z , t ) for z 2 Using (15), boundary conditions (9) can be written as: d b (t )T ( x, 0, t ) eb z T ( x, 0, t ) z f b (t ), f t (t ), (17) d t (t )T ( x, Z , t ) et ( x, t ) T ( x, Z , t ) 4. Oxygen balance in a stream of flowing gases Concentration of oxygen in a stream of gases is described by the following balance equation: C t C x RC , (18) Equation (18) should be considered together with initial and boundary conditions. Initial conditions t = 0: C ( x, z, 0) Boundary conditions: C (0, z , t ) Cin , (19) C0 (t ), x x C ( L, z , t ) 0, 0, ; C ( x, z1 , t ) C ( x, z 2 , t ) 1C ( x, z1 , t ) 2 C ( x, z 2 , t ) (20) x L 0, A function is introduced: G ( x, z , t ) 0.5RC , (21) Taking into account (21), equation (18) can be written as follows: C t C x 2G, (22) The following notations are introduced: pl pr pb pt 1, 0, 1, 2, sl sr sb st 0, 1, , , g l (t ) gr gb gt 0, 0, 0 C0 (t ), (23) Using (23), boundary conditions (20) can be written as: pl C (0, z, t ) sl p r C ( L, z , t ) s r pb C ( x, z1 , t ) sb p t C ( x, z 2 , t ) s t C (0, z, t ) x C ( L, z , t ) g l (t ), gr , g b (t ), g t (t ), , ; (24) C ( x, z1 , t ) C ( x, z 2 , t ) 5. Energy balance in the air stream Energy balance in the air stream is described by the balance equation: p c ps U t U x RU , (25) Equation (25) should be considered together with initial and boundary conditions. Initial conditions t = 0: U ( x, z , 0) U in , Boundary conditions: (26) U (0, z, t ) U 0 (t ), A function is introduced: (27) RU p c ps (28) Taking into account (28), equation (25) can be written as follows: t U x U F, x 2 (29) 6. Discretization The following increments are introduced: x, z, t along Ox, Oz, Ot axes, respectively, and the domain of continuous variables is replaced with the finite set of nodes. The number of nodes is determined along each axis as well as the position of the coal-rock phase boundary ­ J1, J2. Tf / , I L/ , J1 z1 / , J2 / , J Z/ (30) where: Tf -- final time, [] -- denotes the integer part of a number. The coordinates of the nodes xi, zj, tn are placed within the following introduced sets: xi zj tn x i, z 0 i j n 0 I, J, N j, 0 (31) t n, The values of the dependent and independent variables in the nodes xi, zj, tn correspond with the indices i, j, n. For convenience, they can be either subscripts or superscripts. 7. Calculation example The critical conditions are being defined for spontaneous combustion of the coal layer in a seam 405. Coal from this seam contains small amount of moisture. Below are presented geometric parameters of the layer used for calculations, determined by the laboratory studies of the coal and rocks properties. · Time and geometric parameters Time Tf = 100, 200, 300, 400, 1000 h Length of the layer Lw = 6 m Thickness of the layer of coal Hw = 0.5, 0.6, 0.7 m Thickness of the layer of rocks H1 = 1.0 m Thickness of the layer of rocks H2 = 1.0 m · Physical parameters of coal and rocks Porosity coefficient of crushed coal Specific heat of air Specific heat of coal Density of coal Coefficient of thermal conductivity of coal m = 0.45 Cps = 1005.6 J/kgK Cws = 1280.0 J/kgK ws = 815 kg/m3 = 0.3 W/mK Specific heat of rocks in the roof Specific heat of rocks in the floor Density of rocks in the roof Density of rocks in the floor Coefficient of thermal conductivity of rocks in the floor Coefficient of thermal conductivity of rocks in the floor Coefficient of oxygen diffusion in air · Initial parameters Initial temperature of coal Initial temperature of rocks in the roof Initial temperature of rocks in the floor Initial temperature of air Initial concentration of O2 Gas flowrate · Parameters of oxidation kinetics Heat of reaction Reaction rate constant Reaction rate constant Activation temperature Activation temperature Order of reaction Order of reaction Critical temperature Heat transfer coefficient c1 c2 1 2 = 2000 J/kgK = 2000 J/kgK = 2000 kg/m3 = 2000 kg/m3 = 1.0,1.2,1.4,1.5,1.6,1.8,2.0 W/mK = 1.0,1.2,1.4,1.5,1.6,1.8,2.0 W/mK = 1.0­5 m2/s Twin T1in T2in Uin Cin fin qr Rdo Rpo Tdo Tpo ndo npo Tcr l,r,t = 300 K = 300 K = 300 K = 300 K = 0.0 = 0.0006 m/s = 7.6 106 J/m3 = 0.12 1/s = 1875 1/s = 1490 K = 4980 K = 1.6 = 1.6 = 360 K = 0 W/m2K Calculation results The results of performed calculations are presented in Fig. 2-7. Fig. 2 shows temperature distribution in the heated coal and surrounding rocks. Calculations were carried out for the coal layer with the following thicknesses: Hw = 0,5; 0,6 and 0,7 m. The calculation times were 100, 200, 300 and 400 hours. To simplify calculations, the thermal conductivity of rocks in the roof was assumed to be equal to that in the floor and amounted to 1,0 W/mK. As shown in Fig. 2, spontaneous combustion proceeded at its maximum and minimum rate, respectively, in the thickest (0,7 m) and in the thinnest layer (0,5 m). Fig. 3 demonstrates distributions of oxygen content in gases flowing through the examined deposit of crushed coal. They correspond to the temperature distributions shown in Fig. 2. Fig. 4 presents the results of studies on the impact of a thickness of the coal layer from a seam 405 Hw deposited in the gob area on the predicted course of spontaneous combustion development. The latter is shown as a dependence of the maximum temperature of coal within the deposit on time. The values of a coal layer thickness Hw used in calculations were as follows: 0,3; 0,4; 0,5; 0,6 and 0,7 m, the oxygen volume fraction in the stream of incoming air was 0,2 and the coefficient of thermal conductivity of rocks in the roof and floor was = 1,0 W/mK. As it can be seen from Fig 4., the thicker layer of coal (i.e. the closer the conditions to the adiabatic Fig. 2 Temperature distribution in the crushed coal deposit with thicknesses of Hw = 0,5; 0,6 and 0,7 m and in surrounding rocks during spontaneous heating, after 100, 200, 300 and 400 hours from its beginning Fig. 3 Oxygen concentration distribution in gases flowing through the crushed coal deposit with thicknesses of Hw = 0,5; 0,6 and 0,7 m during spontaneous heating, after 100, 200, 300 and 400 hours from its beginning ones), the more rapid process of spontaneous heating. There exists a certain critical thickness of the coal layer, below which spontaneous combustion will not occur. Fig. 5 shows the impact of oxygen content in the air incoming to the coal layer on the development of spontaneous combustion process. The higher is the concentration of oxygen the faster development of this process. As with a thickness of the coal layer, there is a critical value of oxygen concentration, below which spontaneous combustion will not occur. Fig. 6 shows the influence of thermal conductivity of rocks on the course of spontaneous heating of the coal layer with a thickness Hw = 0,6 m from a seam 405. The assumed volume fraction of oxygen in the air incoming to the coal deposit was 0,2. As can be noticed from Fig. 6, an increase in thermal conductivity of rocks slows down the process of self-heating. For simplicity of calculation, the thermal conductivity of rocks in the roof 1 was assumed to be equal to the thermal conductivity of rocks in the floor 2. It is, of course, possible to perform calculations for the case when 1 2. Fig. 7 contains summarized values of critical conditions of spontaneous combustion of coal from a seam 405 in longwall gob areas. The values of a coal layer thickness Hw were plotted on the X axis against the values of thermal conductivity coefficient of surrounding rocks on the Y axis. For particular values of oxygen concentration in the stream of incoming air the curves of critical parameters were determined. For example, a coal layer thickness Hw = 1,0 m, oxygen concentration C = 0,1 and thermal conductivity of rocks = 1,14 W/mK constitute the critical conditions of spontaneous combustion of coal in the seam. Fig. 4 Impact of a thickness Hw of the coal layer remaining in the gob on the predicted course of spontaneous heating of the coal layer (Hw = 0,3, 0,4, 0,5, 0,6, 0,7 m) 1 = 2 = 1,0 W/mK Fig. 5 Impact of oxygen volume fraction in a stream of incoming air on the predicted course of spontaneous heating of the coal layer (Hw = 1,0 m , 1 = 2 = 1,5 W/mK , Co = 0,08; 0,10; 0,12; 0,14; 0,16; 0,18; 0,20) Fig. 6 Impact of the thermal conductivity coefficient l on the predicted course of spontaneous heating of the coal layer (Hw = 0,6m, 1 = 2 = 1,0; 1,2; 1,4; 1,6; 1,8; 2,0 W/mK) Fig. 7 The critical conditions of spontaneous combustion of coal in the gob area in seam 405 8. Summary The method presented in this paper for determining the critical conditions of spontaneous combustion of the flat layer of crushed coal can be useful in the mining practice to evaluate the risk of endogenous fire occurrence in longwall gob areas. This risk may be posed by the coal entering a gob from located closely over the roof the non-balance seam of remained thin coal bed, or by the coal which got to a gob in consequence of geological disturbances. However, one should not forget about the simplifying assumptions adopted in this work. They limit the application range of the presented method to coal seams with a low content of moisture, for which the process of evaporation can be ignored in the calculations. Other assumptions made in this work include that the rate of coal oxidation is fixed in time and that the aspect of oxygen transport in coal particles with a diameter greater than 2 mm is disregarded. The advantage of the presented method lies in its simplicity and relatively few and easily determined parameters of coal and surrounding rocks present in the mathematical model. One can therefore expect that this method will find application in engineering calculations. However, its verification on the basis of mining examinations is required. It is also worthwhile to undertake further studies on the development of more complex mathematical models of spontaneous combustion which would take into account the variability of coal oxidation rate, evaporation of moisture and its influence on spontaneous combustion, as well as oxygen diffusion within coal particles. Acknowledgments Content of this paper is the result of work carried out as part of I2mine project ("Innovative Technologies and Concepts for the Intelligent Deep Mine of the Future") funded by the 7th Framework Program of the European Commission under Grant No. 280855.

Journal

Archives of Mining Sciencesde Gruyter

Published: Sep 1, 2015

References