Fuel 188 (2017) 500–510
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Full Length Article
Numerical investigation on the self-ignition behaviour of coal dust accumulations: The roles of oxygen, diluent gas and dust volume Dejian Wu a,⇑, Frederik Norman b, Martin Schmidt c, Maarten Vanierschot a, Filip Verplaetsen b, Jan Berghmans a, Eric Van den Bulck a a b c
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium Adinex NV, Brouwerijstraat 5/3, B 2200 Noorderwijk, Belgium Division 2.2 ‘‘Reactive Substances and Systems”, BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, D-12205 Berlin, Germany
h i g h l i g h t s Both self-ignition temperature and ignition delay time of coal dusts clearly decrease with increasing oxygen mole fraction. The inhibiting effect of carbon dioxide is comparatively small on self-ignition and oxygen consumption increases dramatically after ignition. The model is valid to predict the transient temperature and concentration profiles of coal dusts until ignition. Heating value and kinetic parameters have a comparatively pronounced effect on self-ignition.
a r t i c l e
i n f o
Article history: Received 21 April 2016 Received in revised form 15 September 2016 Accepted 11 October 2016
Keywords: Ignition temperature Ignition delay time O2/CO2 ambient Hot oven Numerical simulation
a b s t r a c t Self-ignition of coal dust deposits poses a higher risk of fires in oxygen-enriched oxy-fuel combustion systems. In this work, we develop a numerical method, using the commercial software COMSOL Multiphysics, to investigate self-ignition behaviour of coal dust accumulations with a main emphasis on the roles of oxygen, diluent gas and dust volume. A one-step 2nd-order reaction kinetic model considering both coal density and oxygen density is used to estimate reaction rate using the kinetic parameters from previously conducted hot-oven tests. This model is validated to predict the transient temperature and concentration profiles of South African coal dusts until ignition. The computed self-ignition temperatures of dust volumes show a good agreement with experimental results. In addition, it is found that the inhibiting effect of carbon dioxide is comparatively small and oxygen consumption increases dramatically after ignition. Parameter analysis shows that the heating value and kinetic parameters have a comparatively pronounced effect on self-ignition temperature. The model provides a satisfactory explanation for the dependence of self-ignition behaviour on gas atmospheres, thus helping to further understand the fire risk of self-ignition in oxy-fuel combustion systems. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Oxy-fuel combustion is one of the most promising technologies to reduce carbon dioxide (CO2) and pollutant emissions. The concept replaces air with pure oxygen (O2) or a mixture of O2 and recycled flue gas (mainly CO2) and generates high-concentration CO2 gas products for carbon storage [1,2]. However, the increasing fire risk in the solid-phase self-ignition [3] and the gas-phase explosion [4] for an O2-enhanced combustion environment is still a technological challenge and has not been studied well yet. Dust accumulation often occurs in coal mills and power plants. Once exposed to ⇑ Corresponding author. E-mail address:
[email protected] (D. Wu). http://dx.doi.org/10.1016/j.fuel.2016.10.063 0016-2361/Ó 2016 Elsevier Ltd. All rights reserved.
an oxidizing atmosphere and a mild heat source, this accumulated dust may self-heat to initiate smouldering combustion [5–7]. The fire and explosion risks may vary in the CO2-abundant ambient and further increase in the oxygen-enriched oxy-fuel combustion system. The self-ignition process refers to a physicochemical process of thermal runaway, which depends on the characteristics of combustible bulk materials and packing conditions (particle size, density, volume-to surface ratio, porosity, thermal conductivity, heat capacity etc.), as well as the ambient conditions (temperature, oxygen content, ventilation, etc.) [5,8–10]. Numerical simulations are promising approaches and have been developed to gain insight into the self-ignition behaviour of bench-scale coal dusts [11–13] and metal dusts [14], coal stockpiles [15–19], and underground
D. Wu et al. / Fuel 188 (2017) 500–510
501
Nomenclature A c d d ~ ik D Dik Ea hm ht DHc j K Le M m n p Q r R Rr t T V X Y SIT
pre-exponential factor, m3/kg s specific heat, J/kg K diameter of a single dust, m diffusional driving force Fick diffusivity, m2/s Maxwell-Stefan diffusivity, m2/s apparent activation energy, kJ/mol mass transfer coefficient, m/s heat transfer coefficient, W/m2 K heat of reaction by per kg coal, kJ/kg mass flux, kg/m2 s constant Lewis number molar mass, kg/mol number of the gas species order for Lewis number pressure, Pa volumetric heat release rate, W/m3 rate of reaction, kg/m3 s ideal gas constant, J/mol K radius of baskets, m time, s temperature, K molar diffusion volume, m3/mol mole fraction mass fraction self-ignition temperature
coal seams [20–24]. Several numerical models coupling heat and mass transfer equations have been developed to study the process of self-ignition of porous coal beds. However, all above models adopted 1st-order reaction kinetic models either on fuel-basis [11–14] or on oxygen-basis [15–18,21,22], might not well reflect the effect of oxygen and diluent gas on the ignition behaviour of dust layers in oxy-fuel combustion conditions. On the one hand, the corresponding fuel-basis kinetic parameters were typically estimated either by the Frank-Kamenetzkii (F-K) model with basket heating methods [11,12,20] or by thermogravimetric analysis and differential scanning calorimetry (TGA-DSC) [25,26]. On the other hand, the oxygen-basis kinetic model might be more accurate to reflect the effect of oxygen mole fraction on the reaction rate. However, the technical challenge is that neither an effective method is available for kinetic parameters estimation, nor the accurate heating value of oxygen consumption (kJ/mol O2) for a specific solid fuel. Previous work in our laboratory experimentally investigated the fire risk posed by self-ignition of coal dust accumulations in various O2/CO2 atmospheres [3]. In this paper, we develop a twodimensional numerical model to investigate the self-ignition behaviour of South African (SA) coal dust accumulations and predict the transient temperature and concentration fields during the selfignition process. A one-step 2nd-order reaction kinetic model considering both coal and oxygen density is adopted to describe the thermal and oxidation rate. The numerical results are compared to previous experimental results [3]. The influences of the thermal and kinetic parameters are also analysed. 2. Mathematical model As prescribed by the experimental investigation [3], the selfignition temperature (SIT) and the ignition delay time (ti) of the coal dust were determined using a 64-L oven and five equidistant cylindrical mesh wire baskets with volumes of 25, 50, 100, 400, and
Greek symbols thermal diffusivity, m2/s bulk porosity stoichiometric coefficient k heat conductivity, W/m K q density, kg/m3
a e m
Superscripts and Subscripts 0 initial a ambient of oven ac active component of coal b bulk of basket c coal dust cb centre of basket ct calculation termination e effective g gas i ignition i gas species j gas species k gas species max maximum SI self-ignition wall wall of basket
1600 mL. Both the oven and coal dust sample were flushed by air or the premixed O2/CO2 gas prior to each experiment. When the test started, the rate of inlet ambient gas was set to 2 L/min which was monitored by a Rotameter. Once the oven was stabilized at the target temperature, the basket with a pre-flushed coal dust sample was placed in the oven for each test. More details can be found in the work of Wu et al. [3]. Considering the fact that the gas flow is comparatively low and the particle size is extremely fine, it is justified to ignore the effect of convection over diffusion in the coal dust accumulations domain. Furthermore, the cylindrical basket is axisymmetric, thus we solve the two-dimensional axis-symmetrical time-dependent conservation equations for the bulk material. The domain for the computation is shown in Fig. 1. The model geometry consists of three open boundaries (bottom, top and right sides) and the axisymmetric axis or vertical centreline r = 0 (left side). The radius of the dust accumulation domain is Rr and the height is 2Rr. For simplicity, the following assumptions are made: Only the diffusional effect is considered in the domain as this is the dominant transport mechanism; The drying process in the simulations is not considered due to the small moisture content of the coal; Effects of gas conditions on the heat and mass transfer coefficients, as well as on the stoichiometric coefficients are neglected; Properties such as bulk porosity, thermal conductivity and specific heat capacity of both coal dusts and gas mixtures are independent of time and temperature; A one-step global oxidation reaction formulation is considered as shown in Eq. (1). 2.1. Chemical kinetics Because coal has non-uniform a physical structure and a complex composition, the self-ignition process involves many
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For the diluent gas N2 or CO2 from the initial binary gas atmospheres, the reaction rate is zero. 2.2. Governing equations On the basis of the assumptions that only diffusion is considered, the conservation equations describing the mechanisms of heat and mass transport in the dust accumulation are the following [11–13,15–18]:
@T ¼ r ðke rTÞ þ Q ð1 eb Þqc cc þ eb qg cg @t
ð5Þ
is the conservation of energy, where qg is the density of the mixture gas, cc and cg are the specific heat capacities of coal and the gas mixture respectively, and ke denotes the effective thermal conductivity for the porous coal dust which can be expressed as
ke ¼ ð1 eb Þkc þ eb kg :
ð6Þ
For the immobile solid coal, the mass conservation can be formulated as Fig. 1. 2D axisymmetric geometry of dust accumulation in an equidistant cylindrical basket.
heterogeneous reactions which can be generally classified into evaporation, pyrolysis and oxidation [7]. For the self-ignition process, these dominant oxidation reactions can occur on both the external surface of coal particles and the internal surface of coal pores as shown in Fig. 1. Similarly to Ref. [27], a one-step global oxidation reaction is used to characterise the self-ignition process of the coal in the dry basis at low temperatures. The average stoichiometric coefficient for the coal with moisture content can be determined according to the elemental and proximate analyses [13]. Therefore, South African (SA) coal combustion can be simply described as
C56:3 H42:6 O7:3 þ 1:5H2 O þ Ash þmO2 O2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} CoalH2 O
! mCO2 CO2 þ mCO CO þ mH2 O H2 OðgÞ þ mCH4 CH4 þAsh; |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
ð1Þ
Gas products
where m is the chemical stoichiometric coefficient and C56:3 H42:6 O7:3 is the chemical formula of the active component on a basis of 1000 g coal. More details have been given by Wu et al. [27]. Generally, the second-order heterogeneous oxidation rate of coal under various oxygen concentration conditions can be formulated by the Arrhenius law as:
Ea r c ¼ ð1 eb ÞqO2 qc Ac exp ; RT
ð2Þ
where eb is the bulk porosity, qO2 and qc are respectively the oxygen density and coal density, Ac and Ea are the apparent exponential factor and the apparent activation energy, respectively. For the coal self-ignition process, the volumetric heat release rate thus can be written as
Q ¼ r c DH c ;
ð3Þ
where DHc is the heat of oxidation per kg coal. Consequently, the reaction rate of oxygen and gas products can be specified as
rj ¼
mj M j r; mc Mac c
ð4Þ
where M is the molar mass. Similarly with Ref. [13], gaseous products can be analysed by Fourier Transform Infrared Spectrometry (FTIR) with the assumption that the stoichiometric coefficients remain constant for the entire combustion process (see Table 3).
ð1 eb Þ
@ qc ¼ r c : @t
ð7Þ
As mentioned above, the gas system mainly contains three components: inert gas (N2/CO2), oxidant (O2) and gas products, where the gas species concentrations are in the same order of magnitude and none of the species can be identified as a solvent. Therefore, the Maxwell-Stefan equations [28] accounting for all interactions of species in a mixture are used in this paper. The gas species transport mass conservation reads as:
@ðqg Y i Þ þ rðji Þ ¼ r i ; @t
ð8Þ
where Y is the mass fraction (0 6 Y i 6 1), the subscript i denotes the gas species including O2, inert gas (N2/CO2) and gas products (only CO2, CO and H2O are considered here since CH4 is neglected due to its small stoichiometric coefficients listed in Table 3), and ji is the mass flux relative to the mass averaged velocity resulting from the diffusion or convection which can be formulated as
ji ¼ sjiðrÞ þ njiðzÞ ¼ qg Y i
m X ~ ik dk ; D
ð9Þ
k¼1
where s and n are the radial and axial vector respectively, jiðrÞ and jiðzÞ are the corresponding scalar mass fluxes on the radial and axial direction respectively (see Fig. 1), subscript k is the gas species and m is the number of the gas species, thus we have m X Yi ¼ 1
ð10Þ
i¼1
~ ik are the multicomponent Fick diffusivities, the thermal diffuand D sivity is neglected and dk is the diffusional driving force acting on species k, which can be expressed as
dk ¼ rX k þ ðX k Y k Þrpa =pa ;
ð11Þ
where X k is the mole fraction (0 6 X k 6 1), pa is the ambient absolute pressure and rpa is neglected. Using the ideal gas law, we have
qg ¼
pa Mg ; RT
ð12Þ
Yi ¼
X i Mi and Mg
ð13Þ
Mg ¼
m X Yi i
Mi
!1 ;
ð14Þ
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where M is the molar mass. For the purpose of computational stability, the inert gas (N2/CO2) is taken as the mass constraint due to its highest percentage in the mixture gas and the mass fraction of the inert gas can be derived by Eq. (10). The symmetric multicomponent Fick diffusivities strongly depend on the gas composition and are related to the multicomponent Maxwell-Stefan diffusivities Dik , given by [29]
X ðadjBi Þjk XiXk j–i ¼ Y i Y k X and ~ Dik Dij ðadjBi Þjk
ð15Þ
j–i
ð16Þ
where j is one of the gas species and ðadjBi Þjk is the jkth component of the adjoint of the matrix Bi . For low-density gas mixtures, Dik (Dik ¼ Dki ) can be replaced with the binary diffusivities for the species pairs, which can be described with an empirical equation [30]:
T 1:75 2
pa ðV i1=3 þ V 1=3 k Þ
1 1 þ Mi Mk
0:5
;
ð17Þ
where K is a constant with the value of 3.16e8 Pa m2 =s and V equals the molar diffusion volume of the species. The molar diffusion volumes can be referred from Ref. [31] shown in Table 3. 2.3. Boundary and initial conditions Similarly with literature [11–13], a Neumann condition was used for both the temperature field of porous dusts and the concentration field of gas species. This suggests that a heat flux and a mass flux were defined for the heat transfer and the gas species transport, respectively. The 2D geometry of dust volumes is shown in Fig. 1. The boundary conditions for Eq. (5) are
ke
Y O2 ¼ Y O2 ;0 ; Y N2 ¼ Y N2 ;0 ; Y CO2 ¼ Y CO2 ;0 ; Y GP ¼ 0; T ¼ T 0 ;
ð22Þ
where the initial value of Y O2 ;0 , Y N2 ;0 and Y CO2 ;0 depends on the gas atmospheres, e.g., for air condition Y O2 ;0 ¼ 0:23, Y N2 ;0 ¼ 0:77 and Y CO2 ;0 ¼ 0. 3. Simulation
~ kj D ~ ij ; i – j; ðBi Þkj ¼ D
Dik ¼ K
At t ¼ 0, the entire coal accumulation is unreacted, the temperatures of the coal and gas are constant, as well as the gas composition. Thus we have
@T @T ¼ ht;z¼0 ðT a T wall Þ; ke @z z¼0 @z z¼2Rr @T ¼ ht;z¼2Rr ðT a T wall Þ; ke @r r¼Rr @T ¼ ht;r¼Rr ðT a T wall Þ; ¼ 0 @r r¼0
ð18Þ
For simplicity then, we assume all the boundaries have the same heat transfer coefficient,
ht;z¼0 ¼ ht;z¼2Rr ¼ ht;r¼Rr ¼ ht
ð19Þ
COMSOL Multiphysics software is adopted to solve the partial differential equations in this study. Tables 1–3 summarize the properties of the input parameters in the simulation. Most of the parameters are experimentally determined, while the rest are taken from literature. Similarly with European Standard EN15188 [33], the ignition criterion is defined when the measured sample temperature exceeds the oven temperature by 60 °C as the maximum subcritical temperature is taken as the self-ignition temperature and the ignition delay time (t i ) is defined as the interval of time between reaching the oven temperature and ignition. Once ignition was observed, the resolution between ignition and no ignition cases was fine tuned to within 1 K. A one-step self-ignition model, excluding char and gas-phase reactions, is more likely to suffer from the varying timescales and consequent convergence problems in the simulation because the oxygen consumption rate is controlled by oxygen transport at high temperatures [20]. Wessling et al. [20] used the operatorsplitting approach to overcome the varying timescale problem. Song et al. [22] proposed a simplified model to represent the rate of oxygen consumption controlled by oxygen diffusion for the combustion area. Because the current work is only valid for the self-heating period until ignition, all of the simulations were terminated once the temperature reaches a threshold which is defined as the calculation termination temperature (T ct ) in this paper. For simplicity, we take 210 °C as the T ct for all the simulations in this work based on the experimental SIT results [3], e.g., the maximum experimental SIT (136 °C) was determined from 25 mL SA coal dust volume in 21% O2/79% CO2 atmosphere. Several baskets with volume of 25, 50, 100, 400 and 1600 mL were meshed in our model. An average grid size of 4e4 m was found to produce sufficiently grid independent results of ignition and has been used in all the simulations for the sake of saving calculation time. Considering the same heat and mass transfer boundary conditions are used for the upper and lower boundaries (see Eq. (18)–(20)), only 1/4 symmetry domain of coal dust is modelled for
Similarly, for the boundary conditions of mass species [32], we have
jiðzÞ
z¼0
¼ jiðrÞ
r¼Rr
¼ jiðzÞ
¼ hm ðY i;a Y i Þðqg þ qg;a Þ=2 and jiðrÞ ¼ jiðzÞ r¼0 r¼0 ¼ jiðrÞ ¼ jiðzÞ ¼ jiðrÞ ¼ 0; z¼0
Table 1 Properties of SA coal dust.
z¼2Rr
r¼Rr
z¼2Rr
ð20Þ
where qg and qg;a are the gas mixture densities on the bulk boundary and in the oven ambient respectively, Y i;a is the mass fraction of specie i in the oven ambient and hm is the mass transfer coefficient on the boundary, which can be obtained from the analogy of heat and mass transfer [32],
ht ¼ qg;a cg;a Le1n ; hm
ð21Þ
where Le ¼ ag;a =Dg;a is the Lewis number (the ratio of thermal diffusivity and mass diffusivity at the oven ambient conditions). It is reasonable to assume a value of n ¼ 1=3 for most applications.
Parameters
Description
SA coal dust
Source
DHc kc
Heating value (MJ/kg) Effective thermal conductivity (W/m K) Apparent activation energy (kJ/mol) Apparent pre-exponential factor (m3/kg s) Coal density (kg/m3)
27.37 0.172
Exp. [3]
98.5
[3]
1.82e7
Estimated
1200
[27]
Bulk density (kg/m3) Bulk porosity Specific heat capacity at 25 °C (J/ kg K) Median dust diameter (m) Mole mass of the active component of SA coal (g/mol)
600 0.5 1130
Exp. [27] Exp.
1.5e5 833
Exp. Assumed
Ea Ac
qc;0 qb;0 eb ¼ 1 qb;0 =qc;0 cc dc Mac
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Table 2 Properties of the ambient mixture gases at 50 °C and 1 atm [34]. Parameters
Description
cg;a
Specific heat capacity (J/kg K) Thermal diffusivity (m2/s) Thermal conductivity (W/m K)
ag,a kg
Ambient condition Air
21% O2/79% CO2
30% O2/70% CO2
40% O2/60% CO2
50% O2/50% CO2
1013 2.55e5 0.028
878 1.52e5 0.021
882 1.6e5 0.022
887 1.71e5 0.022
892 1.82e5 0.023
Table 3 Summary of the default value of other parameters used in the calculations. Parameters
Description
Data
Source
ht pa T0 V O2 V CO2 V N2 V H2 O V CO
Heat transfer coefficient (W/m2 K) Ambient absolute pressure (kPa) Initial coal temperature (°C) O2 molar diffusion volumes (m3/mol) CO2 molar diffusion volumes (m3/mol) N2 molar diffusion volumes (m3/mol) H2O molar diffusion volumes (m3/mol) CO molar diffusion volumes (m3/mol) Stoichiometric coefficient of coal Stoichiometric coefficient of O2 Stoichiometric coefficient of CO2 Stoichiometric coefficient of CO Stoichiometric coefficient of H2O Stoichiometric coefficient of CH4
11 101 20 1.66e5 2.69e5 1.79e5 1.27e5 1.89e5 1 54.6 40 16 22.1 0.34
[12] Exp. Exp. [31] [31] [31] [31] [31] Exp. Exp. Exp. Exp. Exp. Exp.
mc mO2 mCO2 mCO mH2O mCH4
a 2D-axisymmetrical cylinder basket. The mesh used in the computation domain in the case of 25 mL dust volume is shown in Fig. 2. The time step of simulations is set as 30 s for output of results, which is the same as the frequency of experimental data collecting. Moreover, the calculation termination time or computational duration (tct ) was set to be consistent with the time (t max ) when reaching the maximum temperature (T max ) under the experimental maximum subcritical temperature (SIT) conditions for keeping the better fitting between numerical and experimental temperature evolution (Tcb vs. t) curves. For example, Fig. 3 shows the experimental evolution of the sample central temperature (T cb ) in the case of 400 mL SA coal dust in air under both the minimum supercritical temperature and the maximum subcritical oven temperature, thus we take tmax (i.e., 345 min) as the calculation termination time for 400 mL SA coal. Similarly, the value of t ct for other dust volumes can be determined as: 50 min for 25 mL,
Fig. 2. Mesh used in the numerical modelling in the case of 25 mL dust volume.
76 min for 50 mL, 136 min for 100 mL and 1268 min for 1600 mL SA coal dust, respectively. Further prolonging the calculation termination time was found not to influence SITs significantly, especially with increasing dust volumes. In addition, the effect of gas conditions on t ct is neglected in this work as it has little effect on heat and mass transfer coefficients. 4. Results and discussion 4.1. Self-ignition temperature Table 4 lists the calculated self-ignition temperatures (SITs) for SA coal dust under different sample sizes and ambient conditions. A comparison of experimental and calculated SITs of SA coal at different dust volumes in various gas atmospheres is shown in Fig. 4. Clearly, SITs decrease from around 130 °C to even lower than 100 °C as the sample volume increases from 25 mL to 1600 mL, showing a strong size effect. In comparison with SITs in air, those for the ambient of 21% O2/79% CO2 are found to be only 0–1 °C higher for SA coal dust, agreeing with the experimental findings [3]. It is probably because O2 has a lower diffusivity in CO2 than in N2, which will be analysed in Section 4.3. Such a small increment in SIT indicates a small inhibiting effect of CO2, which was also observed in the work of Qiao et al. [35]. Unlike the results observed by a thermogravimetric (TG) test [26] and a drop-tube furnace (DTF) [36] that the coal ignition process in a mixture of 30% O2/70% CO2 displayed no difference with that in air, the SITs show a pronounced difference between these two ambient conditions. The reason is probably because that the diversity of coal ignition behaviours between O2/CO2 and O2/N2 atmospheres decreases with reducing heating rate [26]. The different heating rates may result from different experimental apparatuses: lower than 1 °C/ min for isothermal hot-oven tests, while the order of magnitude of the heating rate in °C/min is several or tens for TG tests and thousands for DTF tests, respectively. On the other hand, SITs decrease by about 10 °C for all dust volumes as X O2 increases from 21% to 50%. Therefore the enhancement
Fig. 3. Experimental evolution of sample central temperature at the minimum supercritical temperature and the maximum subcritical temperature for 400 mL SA coal dust in air.
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D. Wu et al. / Fuel 188 (2017) 500–510 Table 4 Calculated SIT (°C) for SA coal dust under different dust volumes and ambient conditions. Ambient condition
Air O2/CO2 mixture
Dust volumes
XO2 (%)
XCO2 (%)
XN2 (%)
25 mL
50 mL
100 mL
400 mL
1600 mL
21 21 30 40 50
0 79 70 60 50
79 0 0 0 0
130 131 126 121 119
123 124 119 116 113
116 117 112 109 107
106 106 102 99 97
95 95 91 88 86
4.2. Central temperature evolution curve
Fig. 4. Comparison of the numerical SIT and experimental SIT [3] of SA coal dust volumes.
effect on self-ignition risk by increasing X O2 is much more significant than the inhibiting effect of CO2. Those results have a satisfactory agreement with the former experimental observations [3], which validates that the model is reliable. However, comparatively large deviations between experimental and numerical SITs are found for small dust volumes such as 25, 50 and 100 mL. This is probably caused by the improper kinetic parameters derived by the F-K model based on the assumption of an infinite Biot number [33]. In other words, the F-K model becomes less accurate with decreasing dust volume. Moreover, these deviations increase with increasing X O2 probably caused by the overestimation of the calculation termination time. Note that all the computed SIT values are slightly below the experimental values, which agrees with the findings in the computational work in lower X O2 by Schmidt et al. [11]. These conservative numerical results might result from using the gross heating value of coal (DHc ) for the entire computation process. This is reasonable for safety considerations.
Fig. 5(a) shows an example of the comparison of typical central temperature evolution (Tcb vs. t) curves at the centre of 1600 mL SA coal dust samples in air between the experiments and simulations near the critical ignition temperature conditions. Comparatively, a large deviation is observed between computed and experimental Tcb vs. t curves after around 60 °C is exceeded in the centre of the sample. The relatively higher computed temperatures after this point during the heating process is mainly caused by the neglected latent heat of water content (the drying process or the evaporation of water is a typical endothermic reaction) [37]. In order to verify the effect of water content on the heating process, 100 mL SA coal dust for both dried (in a vacuum oven for 24 h at 50 °C) and raw (2.7% water content by mass) was tested in air at an oven temperature of 108 °C. It shows that there is a slight difference in the beginning but the distinct difference can be seen after around 53 °C as shown in Fig. 5(b).
Fig. 6. Computed ignition delay time of SA coal vs. the oxygen mole fraction ðX O2 Þ at the minimum supercritical temperature on the basis of 21% O2/79% CO2.
Fig. 5. (a) Comparison of the numerical and experimental central temperature evolution in the case of 1600 mL SA coal dust sample in air at supercritical temperatures; (b) the effect of water content on heating process in the case of 100 mL SA coal dust.
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Table 5 Ignition delay time t i (min) of SA coal dust at various dust volumes and gas conditions. Ambient condition
Air O2/CO2 mixture
Dust volume (mL)
XO2 (%)
XCO2 (%)
XN2 (%)
25 (132 °C)
50 (125 °C)
100 (118 °C)
400 (107 °C)
1600 (96 °C)
21 21 30 40 50
0 79 70 60 50
79 0 0 0 0
17.5 21 11 6.5 5
32 36 18 11.5 8
60.5 68 29.5 18.5 15
183 176.5 79 50 34
576 618 213.5 119.5 82.5
Fig. 7. (a) Comparison of the numerical and experimental [3] evolutions of sample central temperature for 400 SA coal dust in air; (b) ignition delay time (ti) vs. Ta for 400 mL SA coal dust in air.
Fig. 8. Predicted contours with time for 400 mL SA coal dust in air at 107 °C: (a) temperature, (b) coal density and (c) O2 mole fraction.
In addition, the experimental errors such as the inaccurate placing position of the central thermocouple and the unstable T a (±1 °C) also contribute to the deviation between the experimental
and the numerical curves. Note that the ambient oven temperature (T a ) nearby the critical ignition temperature becomes greatly sensitive for the temperature evolution, e.g., there are pronounced
D. Wu et al. / Fuel 188 (2017) 500–510
deviations of the numerical Tcb vs. t curves between 96 °C (1 °C above SIT) and 95 °C (SIT) in the case of 1600 mL SA coal dust in air. This is reasonable because the ignition delay time decreases from infinite at SIT (the maximum subcritical temperature). Similarly, slight increases of the hot plate temperature by some perturbation were also found to trigger a thermal runaway in Yuan et al. [14]. Although it is difficult to predict accurate ignition delay times, the computed values derived from the Tcb vs. t curves shown in Fig. 5a can be used to reflect the general trend as well. Fig. 6 summarizes the computed ignition delay times (ti) for SA coal under different dust volumes and ambient conditions at the minimum supercritical temperature on the basis of 21% O2/79% CO2 conditions, and their detailed values are listed in Table 5. For the SA coal dust in air, t i increases from 17.5 min (at 132 °C) to 576 min (at 96 °C) as the dust volume increases from 25 mL to 1600 mL. This trend is converse with the effect of dust volume on the self-ignition temperature (SIT), which suggests that the dust volume has a compensation effect for the fire risk of self-ignition: an increasing dust volume decreases SITs but increases t i . Compared to the one in air (21% O2/79% N2), t i is found to be slightly higher in the ambient of 21% O2/79% CO2 due to the comparatively higher inhibiting effect of CO2, which agrees with the diluent gas effect on the SITs. Moreover, the ignition delay is found to decrease significantly as X O2 increases from 21% to 30%, and then this decreasing trend continues but more gradually with further increasing X O2 to 50% for each dust volume. Consequently, the phenomena observed above for the safety parameters of self-ignition (i.e., self-ignition temperature and ignition delay time) suggest a remarkably higher fire risk of coal dust accumulations in oxygenenriched oxy-fuel combustion systems.
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Fig. 7(a) compares the experimental and numerical evolutions of sample central temperature (Tcb) for 400 mL SA coal dust in air at different oven ambient temperatures (Ta), and Fig. 7(b) summarizes the computed ignition delay time (ti) varying with the oven ambient temperature for three 400 mL coal dusts in air. As shown in Fig. 7(a), the numerical ignition occurrence is much earlier than the experimental one at the same supercritical T a in the case of 110 °C and 120 °C. Correspondingly, all the computed t i values derived from Fig. 7(a) are below the experimental values under the same conditions as shown in Fig. 7(b). The numerical ignition delay time is found to sharply decrease from the infinity at SIT as the oven ambient temperature increases, which also agrees well with the experimental observation [3]. Note that with further increasing T a , the ignition location might not initiate from the centre of the dust sample [38], thus the ignition delay time derived from the Tcb vs. t curves cannot be taken as one of the selfignition parameters. 4.3. Temperature and concentration profiles Fig. 8 illustrates the predicted evolutions of temperature, coal density and oxygen mole fraction for the 400 mL SA coal dust in air at 107 °C. As shown in Fig. 8a, dust accumulation in the basket is initially heated by the hot air ambient from the boundaries to the geometric centre at the beginning (t = 30 min). With rising temperature, the dust begins to self-heat due to the exothermic reaction, which leads to local (off-centre) temperatures higher than the oven temperature at 110 min as a positive feedback. This off-centre higher temperature region has also been observed in the experiments [3]. Once the central temperature (Tcb) overtakes the
Fig. 9. Gas product mole fraction profiles with time for 400 mL SA coal dust in air at oven temperature of 107 °C: (a) CO2, (b) CO and (c) H2O (g).
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Fig. 10. The centre point temperature and gas components evolution for 400 mL SA coal dust in air at oven temperature of 107 °C.
boundary temperature, then it tends to be the highest temperature in the basket domain due to the poor heat conduction until ignition when the temperature rise is over 60 °C at 303 min. The temperature rise facilitates the rate of the exothermic reaction, which leads to further temperature increase and the subsequent smouldering combustion controlled by oxygen transport. Correspondingly, coal consumption is extremely small before ignition and the consumption is mainly located at the centre of the basket due to the poor heat conduction as illustrated in Fig. 8b, which is consistent with the temperature evolution. Evidently, the oxygen consumption is considerably low before ignition at low temperatures. However, the oxygen consumption rapidly increases once ignition is triggered: oxygen mole fraction in the centre reduces from 0.19 to 0.16 after 3 min ignition at t = 306 min as shown in Fig. 8c. This rapid drop of oxygen concentration also agrees with the sharp increase of temperature in the centre (increment of 36 °C from 303 min to 306 min) shown in Fig. 8a. This is because the higher temperature rise is caused by the exothermic oxidation reaction. Fig. 9 shows the predicted evolution of the gas products for the 400 mL SA coal dust in air at 107 °C. The mole fraction profiles of gas products present an opposite evolution with oxygen mole fraction, and the value of each species of gas products depends on the stoichiometric coefficient listed in Table 3. It should be noted that the mole fraction or percentage of N2 (inert/diluent gas) is equal to the rest part of the mixture gas excluding O2 and gas products for air combustion, while the mole fraction of CO2 in the mixture gas is the sum of the CO2 (diluent gas) and CO2 in the gas products for O2/CO2 combustion atmospheres. The corresponding temperature and gas components evolution at the central point (ignition location) is shown in Fig. 10. Both the oxygen consumption rate and the gas products release rate are found to be comparatively small before ignition, which is consistent with the finding in Wu et al. [38]. It reveals that the model in this paper coupled with kinetics, heat and mass transfer equations is valid to predict the self-ignition behaviour of coal dusts. Fig. 11 compares the evolution of the central temperature (Tcb) and the Fick diffusivity of O2 at the central point in air (21% O2/79% N2) and in 21% O2/79% CO2 atmosphere in the case of 400 mL SA coal at 107 °C. It shows that T cb in air is slightly higher than it in 21% O2/79% CO2 atmosphere, although the difference between these two conditions is small. Clearly, the Fick diffusivity of O2 is proportional to temperature. In addition, at the comparable temperatures the value of the O2 diffusivity in 21% O2/79% CO2 is always smaller than it in air. This may explain why SITs in 21% O2/79% CO2 were found to be slightly higher than in air.
Fig. 11. The central point temperature and Fick diffusivity of O2 evolution for 400 mL SA coal dust at oven temperature of 107 °C in air and in 21% O2/79% CO2.
Fig. 12. Dependence of SIT on thermal parameters.
4.4. Parameter analysis An extensive sensitivity analysis, including thermal properties and kinetic parameters, is conducted based on the validated model. Fig. 12 describes the impact of variations of the thermal parameters on the SIT of 400 mL SA coal dust by factors ranging from 30% to 30%. Results show that the SIT increases with increasing specific heat, heat conductivity and heat transfer coefficient, but the dependence of SIT on these parameters is not regarded as significant. In contrast, the increase of the heating value of coal (DHc) significantly decreases the SIT, suggesting a relatively pronounced influence on SIT. This is because increasing DHc accelerates the reaction rate and directly promotes the heat release rate. Therefore, the heating value of coal plays a comparatively important role during the self-ignition process. Fig. 13 demonstrates the effect of kinetic parameters on the calculated value of the self-ignition temperature for SA coal dust in air with various dust volumes: (a) pre-exponential factor and (b) apparent activation energy. It shows that kinetic parameters have a considerably stronger influence on the calculated SIT compared to thermal parameters shown in Fig. 12. Particularly, the dependence of the SIT on Ea is much more sensitive since Ea is in the exponential term of Eq. (2). Although for various dust volumes, the modification of kinetic parameters shows a consistent and stable influence on SIT. In addition, increasing the pre-exponential factor (Ac) decreases SITs, while the apparent activation energy plays an
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Fig. 13. Dependence of SIT on: (a) pre-exponential factor; (b) apparent activation energy.
opposite role on SIT. This suggests a compensation effect between Ac and Ea on the self-ignition behaviour as observed in the experimental work [3]. 5. Conclusions In this work, a comprehensive 2-D model considering both coal density and oxygen density is implemented in COMSOL Multiphysics to study the self-ignition behaviour of SA coal dust in oxy-fuel combustion atmospheres. The standardized hot-oven test under both air and O2/CO2 gas mixture conditions with O2 mole fraction from 21% to 50% is simulated, and the transient temperature and concentration profiles are studied. Results show that the fire risk of self-ignition increases in the oxy-fuel combustion system: both the calculated self-ignition temperature and the calculated ignition delay time decrease with increasing mole fraction of oxygen. In addition, parameter analysis shows that the effect of heating value and kinetic parameters on self-ignition is comparatively pronounced using the validated model. These results indicate that the model provides a satisfactory explanation for the dependence on gas conditions of self-ignition behaviour. It is the first time to develop a physics-based self-ignition model of coal dust volumes in O2-enriched oxy-fuel atmospheres, thus this insight is of high value to improve our understanding of the roles of oxygen, diluent gas and dust volume. Acknowledgements The authors gratefully acknowledge the financial contribution from the European FP7 project RELCOM. D. Wu thanks for the financial support from China Scholarship Council. References [1] Toftegaard MB, Brix J, Jensen PA, Glarborg P, Jensen AD. Oxy-fuel combustion of solid fuels. Prog Energy Combust Sci 2010;36:581–625. [2] Chen L, Yong SZ, Ghoniem AF. Oxy-fuel combustion of pulverized coal: characterization, fundamentals stabilization and CFD modelling. Prog Energy Combust Sci 2012;38:156–214. [3] Wu D, Huang X, Norman F, Verplaetsen F, Berghmans J, Van den Bulck E. Experimental investigation on the self-ignition behaviour of coal dust accumulations in oxy-fuel combustion system. Fuel 2015;160:245–54. [4] Wu D, Norman F, Verplaetsen F, Van den Bulck E. Experimental study on the minimum ignition temperature of coal dust clouds in oxy-fuel combustion atmospheres. J Hazard Mater 2016;307:274–80. [5] Bowes PC. Self-heating: evaluating and controlling the hazards. London: Elsevier; 1984. [6] Carras JN, Young BC. Self-heating of coal and related materials - models, application and test methods. Prog Energy Combust Sci 1994;20:1–15. [7] Wang H, Dlugogorski BZ, Kennedy EM. Coal oxidation at low temperatures: oxygen consumption, oxidation products, reaction mechanism and kinetic modelling. Prog Energy Combust Sci 2003;29:487–513. [8] Babrauskas V. Ignition handbook. Washington: Fire Science Publishers; 2003.
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