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Modelling of spontaneous combustion of coal with moisture content included
Modelling coal with Ahmet
Arisoy
of spontaneous combustion moisture content included and Fehmi
of
Akgiin
faculty of Mechanical Engineering, Technical University of istanbul, Istanbul, Turkey (Received 17 September 1992; revised 18 January 1993)
80191
Giimii+suyu,
A mathematical model for spontaneous combustion of coal has been developed that takes into consideration the moisture content of coal. The one-dimensional non-steady-state model consists of conservation equations for oxygen, water vapour, inherent moisture of the coal, and energy for both gaseous and solid phases. A first-order Arrhenius reaction rate for oxidation under pore diffusion and chemically controlled reaction regimes is considered. The rate of evaporation or condensation is also considered as a function of particle size, isothermal temperature of coal particles, energy of water-coal bonding and water content of coal and gas streams. The equations of the model have been solved numerically by a finite-difference technique, and the influences of gas velocity, particle size and inherent moisture content on the process of spontaneous heating have been examined parametrically. (Keywords: coal storage; moisture content; particle size)
Spontaneous heating of coal is a major problem creating difficulties in mining, storage and transportation, in terms of safety and economics. The problem arises when the amount of heat produced by this process is more than that dissipated by heat transfer to the surroundings. Factors that affect significantly the spontaneous heating of a coal pile are coal rank, temperature, moisture content, particle size, air flow rate and the porosity of the coal pile. Several mathematical models’-8 have been developed to predict the conditions under which coal in a pile could undergo spontaneous combustion and to determine the influences of factors contributing to the spontaneous heating. Nordon’s model’ is quite complete, consisting of the equations for oxygen, water vapour and energy conservation and including particular transport terms for convection, diffusion or conduction. However, the influence of moisture is not incorporated in the solutions. Nordon’s unsteady-state model has been extended with An example of a different model some modifications’-‘. is that of Brooks et al.‘jg’, who developed hierarchically a steady-state model to analyse the thermal stability conditions of coal bed and classified it as safe, conditionally safe or unsafe. There are only a few models in which the influence of moisture on the process is incorporated. The analyses are mainly based on the process of external evaporation (or condensation) through the control volume4s. There have been many experimental studiesgPi3 of moisture effects on the process, but mostly under the extreme conditions of mutual interaction of coal and gas (air, O,, N,, etc.) occurring in practice only in special cases (e.g. saturated gas-dry coal, saturated gas-moist coal, dry gas-dry coal, dry gas-moist coal). In fact, it is not yet well understood how the moisture affects the tendency of coal to self-heating and what is the mechanism of 001~2361/94/02/0281~6 0 1994 Butterworth-Heinemann
Ltd.
adsorption and desorption. However, most investigators conclude that moisture content is one of the most important factors affecting the self-heating of coal. Any changes in the form of equilibrium relation arising from the difference between the humidity level of the surrounding air and the moisture content of the coal result in further temperature changes, depending on the dynamic and equilibrium moisture characteristics. Dry air flowing over relatively moist coal removes moisture from the coal and results in a decrease in its temperature. This means that evaporation should effect some cooling and retard or suppress self-heating. Moist air interacting with relatively dry coal causes a temperature increase, owing to adsorption of water from the atmosphere, which is exothermic (heats of wetting and condensation). In addition to these physical effects on the process, moisture acts as a catalytic agent in the formation of peroxy complexes, for which moisture is essential. This reaction also contributes to the spontaneous heating. For any general treatment of moisture effects on the process, it is thus necessary to consider both the inherent moisture of the coal and the humidity of the air, and also their mutual interaction. In the present study, the evaporation (or condensation) on the particle surface is expressed by the process of diffusion of water vapour from the surface to the gas stream. The modified receding-interface approach of this. It is Cheong et a1.14 can be used to accomplish assumed that the process of evaporation starts from the external surface of the particle and the evaporation surface recedes gradually to the centre of the particle, resulting in an increase in the resistance to mass transfer. This may be applicable only to coals which are more likely to hold moisture owing to their more open texture, such as Turkish coals, whose average inherent moisture is very high.
Fuel 1994
Volume
73 Number
2
281
Modeling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
All previous mathematical models for spontaneous combustion were developed by considering either chemically controlled oxidation or diffusion controlled oxidation, with the assumption of non-porous coal particles, except for the model of Akgiin and Artsoy5, in which chemically and pore diffusion controlled combustion was modelled and the effect of particle size on the process was also analysed by comparing three types of combustion regimes. The aim of the present study has been to extend the previous model with moisture content included. MODEL FOR SPONTANEOUS
COMBUSTION
The complete model involves considerable interaction among the physciochemical properties of coal, heat transfer, oxidant, water vapour and moisture content, the manner in which the coal is stored, and the external environment that interacts with the coal. The present model considers partly the complex interaction of these factors and is based on the following approaches and assumptions. 1. If the
2.
3.
4.
5.
6. 7.
8.
coal has enough moisture (in the range 0.5-8 wt% for maximum rate of overall oxidation), exothermic reactions will exist, owing to the catalytic effect of moisture in the formation of peroxy complexes. The heat due to these reactions is assumed to be added to the heat of reaction. It is assumed that multilayer adsorbed and capillary condensed water are dominant as regards inherent moisture. Thus the major effects of moisture on the process arise from evaporation and condensation. The water vapour within the solid is assumed to be saturated with respect to the local coal temperature, and an activation energy, termed the energy of water-coal bonding, is defined as the difference between the heat of evaporation of water from the coal surface and from a free water surface. In addition, the release of moisture from coal results in an increase in oxidation surface, owing to the opening-up of active centres. This effect, which may contribute to the spontaneous heating, has been neglected. The dependence on particle size of the reaction rate of oxygen is described by considering chemically and pore diffusion controlled reaction regimes. The reaction rate of oxygen, which is described by the Arrhenius equation, is assumed to be first-order with respect to the oxygen mass concentration. Convective heat transfer occurs between the gas and the external surface of the particle. Thermal expansion of the heated gas in the bed is neglected. Only forced convection of air is considered. One-dimensional constant-velocity plug flow of air is assumed. The coal pile is homogeneous and isotropic, with uniform spherical coal particles. The coal density remains constant during the process of evaporation and condensation.
With the above assumptions, the model consists of six governing equations with appropriate boundary conditions. The equations of oxygen, vapour and energy conservation for both the gaseous and solid phases are coupled equations including particular terms of the accumulation, the flux terms of convection and diffusion
282
Fuel 1994
Volume
73 Number
2
or conduction, source terms with respect to oxidation and evaporation (or condensation) and also heat exchange between the solid and gas phases. These equations are given below; for the boundary conditions and symbols, see Appendix A and Nomenclature respectively. Oxygen mass conservation in the gas phase:
Oxygen mass balance in the coal particle:
-$~~2.~r2)=p,.Aexp( -&)
(2)
Moisture conservation in the gas phase:
(l-u)~+~~=Dl,(l-o)~+ur, Moisture conservation
(3)
in the coal particle:
aw -Ps,t=cv
(4)
Energy conservation for the solid phase:
aK
UP& -
at
= &xS
+ aah(T,-
TJ-crAH,r,
+ ~sAH,p,,l,=.Aexp
(5)
Energy conservation for the gas phase:
=&(I-u)$- ;ah(T,-
T,)
Determination of effectiveness factor for oxidation
In general, reaction of a porous coal particle with oxygen may be divided into three regimes depending on the mechanism that controls the rate of combustion’5,‘6. In a previous mode15, a compariscl,t was made between them at low temperatures. The reaction regime considered in this study is chemically and pore diffusion controlled combustion. In this regime, oxygen may reach the centre of the particle, but an oxygen concentration gradient within the particle occurs with an increase in temperature. Thus the dependence on particle size of the overall oxidation rate is described by defining an effectiveness factor, the ratio of the actual to the maximum volumetric oxidation rate: s=-
3
D2,(~pz01ar),=,
R (Pi,), =,J exp( - E/&T,)
(7)
Determination of evaporation/condensation rate
The modelling of the rate of evaporation (or condensation) of moisture for a coal particle is a complicated process and involves consideration of the physical and
Modelling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
chemical aspects of moisture such as equilibrium moisture and kinetic parameters. It can be influenced by a large number of factors, including temperature, particle size, particle structure related to hygroscopicity, moisture content of the particle and relative humidity of ambient gas. It is thus necessary to identify the dominant types of water-coal linkage. It is concluded that there are three major groups: chemically bonded water; water adsorbed by physiochemical forces; and free water held by physicomechanical forces*,’ 7. The rate of evaporation of adsorbed water can be expressed in terms of the diffusion of sorbed water driven by the gradient between the vapour density in the bulk gas stream and the vapour density above the coal surface, which depends on moisture content, temperature and energy of watercoal bonding. The rate of evaporation of free water is mainly related to the capillary effect of the pores and the gradient of vapour density between the saturated liquid above the evaporation surface and the gas phase. To simplify the solution, it is assumed that gradual removal of adsorbed and free water from coal may occur simultaneously by vapour diffusion commencing from the external surface of the particle and then through the pores. If the capillary effect is neglected, the evaporation surface remains uniform and only its radius decreases as the process proceeds. Thus the rate of evaporation at any moment also depends on the particle size and the radius and rate of movement of the evaporation surface. In this case, the evaporation rate will be controlled by moisture diffusion within the solid material. The evaporation (or condensation) rate for a coal particle at the radius of the evaporation surface can then be expressed by assuming a moving surface: rw= --
3S2 R3
wp,-
dS
(8)
dt
where S is the radius of the evaporation surface at any moment. The rate of movement of the evaporation surface can be obtained by a water balance at the surface of evaporation, as apzw
4nS2p~W$=4nS2D2,--
ar r=S
Rearranging, the moving rate of the evaporation becomes dS -_= dt
D2w
aP2w
p,W
ar
surface
reduced to R2k(p,,-pws) dS -- D2w - psW S(D,,SkRS+
&
(14)
kR2)
The water vapour density on the evaporation surface which is in equilibrium with the initial vapour of the gas phase depends on the moisture content, temperature and energy of water-coal bonding, and is given by Evseev and Voroshilov* as
( >
pws=pfexp--
Q
(15)
RgTs
RESULTS AND DISCUSSION The model equations, written in the form of fully implicit finite-difference procedure’*, have been solved numerically by the Newton-Raphson iterative technique. The results are presented in Figures 1-7 as profiles of temperature rise of coal, oxygen mass concentration in the gas phase, moisture content of coal, and maximum temperature rise in the bed as a function of position and time. These profiles were used to compare the effects of certain factors under the bed conditions given in Appendix B. The main purpose of the calculations was to evaluate the role of moisture in spontaneous heating for different particle sizes and gas velocities. A full parametric investigation was therefore not undertaken here. The reader is referred to a previous paper5 for the temperature and particle size effects on the combustion regimes at low temperature with moisture content neglected. In the calculations it was assumed that the initial temperature of air was the same as the initial temperature of the coal, chosen as 298 K. The temperature rise given in the figures is based on this reference value. Figure I shows the temperature rise and oxygen mass concentration in the gaseous phase at 30,60,90 and 120 days as a function of position in the coal bed under the standard conditions. The maximum temperature appears at - 1.7 m from the air entry after 40 days and its position moves towards the inflow side, owing to shortage of oxygen for heat production in the bed. Extension of the maximum-temperature region towards the downstream face is mainly caused by heat liberation due to condensation and also by convective heat transport. As the temperature starts to rise, the oxygen concentration 0.24
(10)
r=S
With the assumption of a linear gradient for the water vapour density between the external surface of the particle and the evaporation surface, the rate of vapour transfer can be expressed as apzw
- 41~~0~~ ~
ar
=constant
for S
R
(11)
By integrating with the boundary conditions at
r=S:
p2w=pws
at
r=R:
ap,, D,,--ar
(12) 0
=k(Plw-Pzwlr=lJ
(13)
r=R
the rate of movement
of the evaporation
surface is
2
4
Distance
from
6 air entry
8
10
(m)
Figure 1
Calculated temperature rise and oxygen mass fraction in a moist coal bed at different times
Fuel 1994
Volume
73 Number 2
profiles
283
Modeling
of spontaneous
combustion
of coal: A. Arisoy and F. Akgiin
rapidly decreases in the bed. Thus most of the downstream region becomes starved of oxygen. The influences of coal moisture and gas flow velocity on the maximum temperature rise are shown in Figure 2. Comparison of the curves of dry and moist coal shows immediately that the moisture content of the coal has a great impact on spontaneous heating. Calculations show that the rate of temperature rise is higher at higher velocity for dry coal. This is also valid at temperatures up to 330K for moist coal, but then the rate of temperature rise decreases owing to the increased evaporation rate at higher velocities. There are no differences between the heating rates of dry and moist coal up to 3 lCL315 K, because evaporation is very slow initially; it gradually becomes effective as the temperature increases. For a moist coal bed, the maximum temperature levels off at N 360 K, as illustrated in Figure 2 by curve a, and this level depends on the local evaporation and oxidation rates. As can be seen from curves a, b and c, a higher gas velocity results in a lower temperature level because of the higher evaporation rate. These temperature levels confirm that the evaporation process retards the temperature rise until coal water is removed at a certain point. However, it is expected that the coal will ignite after the coal becomes dry at this point. The influence of gas velocity on the temperature rise profile along the bed is shown in Figure 3. The decrease in the maximum temperature is due to the higher evaporation rate. As the gas velocity increases, the
0.141
0
0 y 5 ts _
8
10
(m)
Drofiles for different times at a eas
0.1
5 C 0.08 0 u ;
0.06
z ‘= E 0.04 1 o 0.02 0
2
4 Distance
Figure
m 60 2
entry
0.12
Moist coal - : Dry cod
1 t ’ .I I
air
0.14
-:
c’b,‘e
z
6 from
Figure 4 Calculated coal moisture veiocity of 0.5 x 10-5ms-’
0
‘;
;
4 Distance
0 80
2
velocity
5
8 from
Calculated coal moisture of 1.0x 10-5ms-’
air
entry
8 (m)
profiles for different
times at a gas
m
!!
40
-
0
30
60 Time
Figure 2 Influence of gas velocity moist and dry coal beds
90
120
(days) on maximum
temperature
rise in
SOV(m/o) : 0.6 Id5 - - : 1.0 ld
-
: 2.0
2
4 Diotanoo
6 from
air
ontry
8
lo-
5
10
(m)
Figure3 Calculated temperature rise profiles for different gas velocities in a moist coal bed after 120 days
284
Fuel 1994
Volume
73 Number
2
maximum temperature also tends to move downstream because of higher convective heat transport. Therefore the distance to the point of maximum temperature rise is proportional to the velocity of the gas. The change in coal moisture content due to evaporation and condensation is shown in Figures 4 and 5 at gas velocities of 0.5 x lo- ’ and 1.0 x lo- ’ m s- 1 respectively, The coal moisture profiles are plotted against bed size at 30, 60, 90 and 120 days. The coal is dried by evaporation in the region of maximum temperature, and the condensation process begins from the point where the temperature gradient becomes negative in the bed. Normally the evaporation rate is higher at higher velocities, but this higher evaporation rate retards the self-heating much more, and this results in a lower constant temperature level as shown in Figure 2. Although evaporation occurs over a wide region, a lower temperature level locally results in less evaporation (compare Figure 4 with Figure 5). Oxidation and drying rates are also functions of particle size. The influences of particle size on the temperature rise and change in coal moisture content are shown in Figures 6 and 7 respectively. As is well known, oxidation and evaporation rates increase with decreasing particle size because of the lower diffusional resistance and greater external surface area. With increasing particle size, the decreases in these rates result respectively in a lower temperature rise as a result of the lower oxidation
Modelling of spontaneous combustion of coal: A. Arisoy and F. Akgiin -_
temperature rise and moves the maximum-temperature point downstream.
d (ml
~-:
0.01
~
REFERENCES 1 2 3 4
5
0’
1
0
2
Dlstsnoe
8
6
4
from
sir entry
10
(ml
Figure 6 Calculated temperature rise profiles for different particle sizes in a moist coal bed after 120 days
6 7 8 9 10 11 12 13 14 15 16 17 18
-
: 0.01
NOMENCLATURE
-
: 0.02
A
: 0.03 01-----0
’
1
2
4
Distance Figure 7
Calculated after 120 days
8
6
from
coal moisture
air entry
profiles
10
(ml
for different
Nordon, P. Fuel 1979, 58,456 Edwards, J. C. Paper A83-21, Metallurgical Society of AIME, 1983 Edwards, J. C. US Bureau of Mines, Report of Investigations 9296, 1990 Schmal, D. in ‘Coal Science and Technology 14’ (Ed. C. R. Nelson), Elsevier, Amsterdam, 1989, p. 133 Akgiin, F. and Artsoy, A. in Proc. 1st Int. Conf. on Combustion Technology for a Clean Environment, Portugal, 1991. Vol. 1, Sect. 9.4, p. 27 Brooks, K. and Glasser, D. Fuel 1986, 65, 1035 Brooks, K., Svanas, N. and Glasser, D. Fuel 1988,67, 651 Evseev, V. S. and Voroshilov, S. P. Sov. Min. Sci. 1986,22,140 Bhattacharvva. K. K. Fuel 1972. 51. 214 Bhattacharyya. K. K. Fuel 1971; SO, 367 Hodges, J. D. and Hinsley, F. B. Min. Eng. (London) 1964, 211 Nordon, P. and Bainbridge, N. N. Fuel 1979, 58, 450 Guin, J. A., Curtis, C. W., Sahawnet. B. M. and Thomas, D. C. Ind. Eng. Chem. Process Des. Dec. 1986, 25, 543 Cheong, H. W., Jeffreys, G. V. and Mumford, C. J. AIChE. 1. 1986, 32, 1334 Karsner, G. G. and Perlmutter, D. D. AIChE J. 1981, 27, 920 Beshty, B. S. Combust. Flame 1981, 32, 295 Banerjee, S. C. ‘Spontaneous Combustion of Coal and Mines Fires’, Balkema, Rotterdam, 1985 Patankar, S. V. ‘Numerical Heat Transfer and Fluid Flow’, Hemisphere Publishing Co., New York, 1980
particle
sizes
rate but a higher temperature rise as a result of the smaller retarding effect of water due to the lower evaporation rate. The net effect is a decrease in temperature rise with increasing particle size as shown in Figure 6, although the change in moisture content of the coal becomes smaller as shown in Figure 7. CONCLUSIONS A mathematical model for the spontaneous combustion of stored coal has been developed. The resulting onedimensional unsteady-state model can be used for different purposes, such as predicting the conditions within a certain coal pile under which the coal could spontaneously ignite and determining the influence of certain factors that play an important role in the design of coal piles. Calculations show that the moisture content of coal has a major retarding effect on spontaneous heating. The time needed for the temperature to reach -350K for moist coal is about twice that for dry coal. This temperature is maintained until the coal becomes dry. An increase in gas velocity results in a decrease in the maximum temperature rise because the evaporation rate increases; on the other hand, the temperature rise is proportional to the gas velocity for a dry coal bed. An increase in coal particle size also decreases the maximum
pre-exponential factor (s- ‘) specific heat capacity (J kg- ’ K- ‘) c, d particle diameter (m) diffusion coefficient (m’ s- ‘) D activation energy (J mol- ‘) h” heat transfer coefficient (W me2 K- ‘) AHO heat of reaction of oxygen with coal (J kg- ’ 0,) heat of evaporation of water (J kg- ’ H,O) AH, k mass transfer coefficient (m s-i) L length of coal bed (m) energy of water-coal bonding (J mall ‘) Q r radius (m) evaporation/condensation rate of water vapour rw (kgH,0m-3s-‘) R radius of particle (m) universal gas constant (J mol-’ K- ‘) R, s radius of evaporation surface (m) t time (s) T temperature (K) V gas velocity (m s- ‘) W coal moisture content at time t (kgkg- ‘) W initial moisture content of coal (kg kg- ‘) X distance from air entry (m) ci compaction degree of coal bed (m3 m - 3, effectiveness factor for oxidation (-) ?. thermal conductivity (W m- ’ K- ‘) density (kg m-“) P water vapour density over the free surface of Pf water (kg mP3) water vapour density over the evaporation PWS surface (kg me3) Subscripts g S
W
gas solid water vapour
Fuel 1994 Volume 73 Number 2
285
Modelling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
oxygen ambient conditions in gas phase in solid phase
0
a 1 2
APPENDIX
At
APPENDIX
A
The model provides a mathematical framework for a forthcoming experimental study for which an adiabatic horizontal tunnel has been constructed. The following boundary conditions used in the calculations therefore differ from those of an open pile.
At x=0:
A,g=h(~,-T,,), 3qg, PlW=
At
286
x=fi
PlO= P%S
(Al)
PkW
T,=O “T8,O aplLO ==O aPlw
. ax
9
ax
r=R:
’
ax-’
Fuel 1994 Volume 73 Number 2
(A2)
k(p,,-p,,)=Dz,,=
ap,,
(A4)
B
Data from the literature for the physical and chemical properties of coal and gas used in the calculations for the standard conditions, and parametric variations (in parentheses): A
=2.933~10~s-~
C,, = lOOOJkgK-’ C,, = lOOOJkg-‘K-l C,,= 1870Jkg-‘K-l d
= 0.01
(0.02; 0.03) m D1, =2.0x 10-5m2s-1 Dzo = 2.3 x 10-8m2 s-l D,,=2.5x10-5mZs-1 D,,=2.25x10-6m2s-1 E = 70OOOJmol-’ h =3Wm-‘K-l
AH, = 9.375 x lo6 J kg- ’ O2 AH,=2.4x106Jkg-‘Hz0 k =2.6x 10-3ms-1 Q = 1746.2Jmol-’ v =0.5x10-5 (1 x 10m5;2x 10-5)ms-1 W = O.lO(O)kgkg-’ =0.7m3mm3 f =0.2Wm-‘K-l Ai =O.O26Wm-‘K-l Ps = 1.16kgmy3 PS = l100kgme3
Arisoy
of spontaneous combustion moisture content included and Fehmi
of
Akgiin
faculty of Mechanical Engineering, Technical University of istanbul, Istanbul, Turkey (Received 17 September 1992; revised 18 January 1993)
80191
Giimii+suyu,
A mathematical model for spontaneous combustion of coal has been developed that takes into consideration the moisture content of coal. The one-dimensional non-steady-state model consists of conservation equations for oxygen, water vapour, inherent moisture of the coal, and energy for both gaseous and solid phases. A first-order Arrhenius reaction rate for oxidation under pore diffusion and chemically controlled reaction regimes is considered. The rate of evaporation or condensation is also considered as a function of particle size, isothermal temperature of coal particles, energy of water-coal bonding and water content of coal and gas streams. The equations of the model have been solved numerically by a finite-difference technique, and the influences of gas velocity, particle size and inherent moisture content on the process of spontaneous heating have been examined parametrically. (Keywords: coal storage; moisture content; particle size)
Spontaneous heating of coal is a major problem creating difficulties in mining, storage and transportation, in terms of safety and economics. The problem arises when the amount of heat produced by this process is more than that dissipated by heat transfer to the surroundings. Factors that affect significantly the spontaneous heating of a coal pile are coal rank, temperature, moisture content, particle size, air flow rate and the porosity of the coal pile. Several mathematical models’-8 have been developed to predict the conditions under which coal in a pile could undergo spontaneous combustion and to determine the influences of factors contributing to the spontaneous heating. Nordon’s model’ is quite complete, consisting of the equations for oxygen, water vapour and energy conservation and including particular transport terms for convection, diffusion or conduction. However, the influence of moisture is not incorporated in the solutions. Nordon’s unsteady-state model has been extended with An example of a different model some modifications’-‘. is that of Brooks et al.‘jg’, who developed hierarchically a steady-state model to analyse the thermal stability conditions of coal bed and classified it as safe, conditionally safe or unsafe. There are only a few models in which the influence of moisture on the process is incorporated. The analyses are mainly based on the process of external evaporation (or condensation) through the control volume4s. There have been many experimental studiesgPi3 of moisture effects on the process, but mostly under the extreme conditions of mutual interaction of coal and gas (air, O,, N,, etc.) occurring in practice only in special cases (e.g. saturated gas-dry coal, saturated gas-moist coal, dry gas-dry coal, dry gas-moist coal). In fact, it is not yet well understood how the moisture affects the tendency of coal to self-heating and what is the mechanism of 001~2361/94/02/0281~6 0 1994 Butterworth-Heinemann
Ltd.
adsorption and desorption. However, most investigators conclude that moisture content is one of the most important factors affecting the self-heating of coal. Any changes in the form of equilibrium relation arising from the difference between the humidity level of the surrounding air and the moisture content of the coal result in further temperature changes, depending on the dynamic and equilibrium moisture characteristics. Dry air flowing over relatively moist coal removes moisture from the coal and results in a decrease in its temperature. This means that evaporation should effect some cooling and retard or suppress self-heating. Moist air interacting with relatively dry coal causes a temperature increase, owing to adsorption of water from the atmosphere, which is exothermic (heats of wetting and condensation). In addition to these physical effects on the process, moisture acts as a catalytic agent in the formation of peroxy complexes, for which moisture is essential. This reaction also contributes to the spontaneous heating. For any general treatment of moisture effects on the process, it is thus necessary to consider both the inherent moisture of the coal and the humidity of the air, and also their mutual interaction. In the present study, the evaporation (or condensation) on the particle surface is expressed by the process of diffusion of water vapour from the surface to the gas stream. The modified receding-interface approach of this. It is Cheong et a1.14 can be used to accomplish assumed that the process of evaporation starts from the external surface of the particle and the evaporation surface recedes gradually to the centre of the particle, resulting in an increase in the resistance to mass transfer. This may be applicable only to coals which are more likely to hold moisture owing to their more open texture, such as Turkish coals, whose average inherent moisture is very high.
Fuel 1994
Volume
73 Number
2
281
Modeling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
All previous mathematical models for spontaneous combustion were developed by considering either chemically controlled oxidation or diffusion controlled oxidation, with the assumption of non-porous coal particles, except for the model of Akgiin and Artsoy5, in which chemically and pore diffusion controlled combustion was modelled and the effect of particle size on the process was also analysed by comparing three types of combustion regimes. The aim of the present study has been to extend the previous model with moisture content included. MODEL FOR SPONTANEOUS
COMBUSTION
The complete model involves considerable interaction among the physciochemical properties of coal, heat transfer, oxidant, water vapour and moisture content, the manner in which the coal is stored, and the external environment that interacts with the coal. The present model considers partly the complex interaction of these factors and is based on the following approaches and assumptions. 1. If the
2.
3.
4.
5.
6. 7.
8.
coal has enough moisture (in the range 0.5-8 wt% for maximum rate of overall oxidation), exothermic reactions will exist, owing to the catalytic effect of moisture in the formation of peroxy complexes. The heat due to these reactions is assumed to be added to the heat of reaction. It is assumed that multilayer adsorbed and capillary condensed water are dominant as regards inherent moisture. Thus the major effects of moisture on the process arise from evaporation and condensation. The water vapour within the solid is assumed to be saturated with respect to the local coal temperature, and an activation energy, termed the energy of water-coal bonding, is defined as the difference between the heat of evaporation of water from the coal surface and from a free water surface. In addition, the release of moisture from coal results in an increase in oxidation surface, owing to the opening-up of active centres. This effect, which may contribute to the spontaneous heating, has been neglected. The dependence on particle size of the reaction rate of oxygen is described by considering chemically and pore diffusion controlled reaction regimes. The reaction rate of oxygen, which is described by the Arrhenius equation, is assumed to be first-order with respect to the oxygen mass concentration. Convective heat transfer occurs between the gas and the external surface of the particle. Thermal expansion of the heated gas in the bed is neglected. Only forced convection of air is considered. One-dimensional constant-velocity plug flow of air is assumed. The coal pile is homogeneous and isotropic, with uniform spherical coal particles. The coal density remains constant during the process of evaporation and condensation.
With the above assumptions, the model consists of six governing equations with appropriate boundary conditions. The equations of oxygen, vapour and energy conservation for both the gaseous and solid phases are coupled equations including particular terms of the accumulation, the flux terms of convection and diffusion
282
Fuel 1994
Volume
73 Number
2
or conduction, source terms with respect to oxidation and evaporation (or condensation) and also heat exchange between the solid and gas phases. These equations are given below; for the boundary conditions and symbols, see Appendix A and Nomenclature respectively. Oxygen mass conservation in the gas phase:
Oxygen mass balance in the coal particle:
-$~~2.~r2)=p,.Aexp( -&)
(2)
Moisture conservation in the gas phase:
(l-u)~+~~=Dl,(l-o)~+ur, Moisture conservation
(3)
in the coal particle:
aw -Ps,t=cv
(4)
Energy conservation for the solid phase:
aK
UP& -
at
= &xS
+ aah(T,-
TJ-crAH,r,
+ ~sAH,p,,l,=.Aexp
(5)
Energy conservation for the gas phase:
=&(I-u)$- ;ah(T,-
T,)
Determination of effectiveness factor for oxidation
In general, reaction of a porous coal particle with oxygen may be divided into three regimes depending on the mechanism that controls the rate of combustion’5,‘6. In a previous mode15, a compariscl,t was made between them at low temperatures. The reaction regime considered in this study is chemically and pore diffusion controlled combustion. In this regime, oxygen may reach the centre of the particle, but an oxygen concentration gradient within the particle occurs with an increase in temperature. Thus the dependence on particle size of the overall oxidation rate is described by defining an effectiveness factor, the ratio of the actual to the maximum volumetric oxidation rate: s=-
3
D2,(~pz01ar),=,
R (Pi,), =,J exp( - E/&T,)
(7)
Determination of evaporation/condensation rate
The modelling of the rate of evaporation (or condensation) of moisture for a coal particle is a complicated process and involves consideration of the physical and
Modelling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
chemical aspects of moisture such as equilibrium moisture and kinetic parameters. It can be influenced by a large number of factors, including temperature, particle size, particle structure related to hygroscopicity, moisture content of the particle and relative humidity of ambient gas. It is thus necessary to identify the dominant types of water-coal linkage. It is concluded that there are three major groups: chemically bonded water; water adsorbed by physiochemical forces; and free water held by physicomechanical forces*,’ 7. The rate of evaporation of adsorbed water can be expressed in terms of the diffusion of sorbed water driven by the gradient between the vapour density in the bulk gas stream and the vapour density above the coal surface, which depends on moisture content, temperature and energy of watercoal bonding. The rate of evaporation of free water is mainly related to the capillary effect of the pores and the gradient of vapour density between the saturated liquid above the evaporation surface and the gas phase. To simplify the solution, it is assumed that gradual removal of adsorbed and free water from coal may occur simultaneously by vapour diffusion commencing from the external surface of the particle and then through the pores. If the capillary effect is neglected, the evaporation surface remains uniform and only its radius decreases as the process proceeds. Thus the rate of evaporation at any moment also depends on the particle size and the radius and rate of movement of the evaporation surface. In this case, the evaporation rate will be controlled by moisture diffusion within the solid material. The evaporation (or condensation) rate for a coal particle at the radius of the evaporation surface can then be expressed by assuming a moving surface: rw= --
3S2 R3
wp,-
dS
(8)
dt
where S is the radius of the evaporation surface at any moment. The rate of movement of the evaporation surface can be obtained by a water balance at the surface of evaporation, as apzw
4nS2p~W$=4nS2D2,--
ar r=S
Rearranging, the moving rate of the evaporation becomes dS -_= dt
D2w
aP2w
p,W
ar
surface
reduced to R2k(p,,-pws) dS -- D2w - psW S(D,,SkRS+
&
(14)
kR2)
The water vapour density on the evaporation surface which is in equilibrium with the initial vapour of the gas phase depends on the moisture content, temperature and energy of water-coal bonding, and is given by Evseev and Voroshilov* as
( >
pws=pfexp--
Q
(15)
RgTs
RESULTS AND DISCUSSION The model equations, written in the form of fully implicit finite-difference procedure’*, have been solved numerically by the Newton-Raphson iterative technique. The results are presented in Figures 1-7 as profiles of temperature rise of coal, oxygen mass concentration in the gas phase, moisture content of coal, and maximum temperature rise in the bed as a function of position and time. These profiles were used to compare the effects of certain factors under the bed conditions given in Appendix B. The main purpose of the calculations was to evaluate the role of moisture in spontaneous heating for different particle sizes and gas velocities. A full parametric investigation was therefore not undertaken here. The reader is referred to a previous paper5 for the temperature and particle size effects on the combustion regimes at low temperature with moisture content neglected. In the calculations it was assumed that the initial temperature of air was the same as the initial temperature of the coal, chosen as 298 K. The temperature rise given in the figures is based on this reference value. Figure I shows the temperature rise and oxygen mass concentration in the gaseous phase at 30,60,90 and 120 days as a function of position in the coal bed under the standard conditions. The maximum temperature appears at - 1.7 m from the air entry after 40 days and its position moves towards the inflow side, owing to shortage of oxygen for heat production in the bed. Extension of the maximum-temperature region towards the downstream face is mainly caused by heat liberation due to condensation and also by convective heat transport. As the temperature starts to rise, the oxygen concentration 0.24
(10)
r=S
With the assumption of a linear gradient for the water vapour density between the external surface of the particle and the evaporation surface, the rate of vapour transfer can be expressed as apzw
- 41~~0~~ ~
ar
=constant
for S
R
(11)
By integrating with the boundary conditions at
r=S:
p2w=pws
at
r=R:
ap,, D,,--ar
(12) 0
=k(Plw-Pzwlr=lJ
(13)
r=R
the rate of movement
of the evaporation
surface is
2
4
Distance
from
6 air entry
8
10
(m)
Figure 1
Calculated temperature rise and oxygen mass fraction in a moist coal bed at different times
Fuel 1994
Volume
73 Number 2
profiles
283
Modeling
of spontaneous
combustion
of coal: A. Arisoy and F. Akgiin
rapidly decreases in the bed. Thus most of the downstream region becomes starved of oxygen. The influences of coal moisture and gas flow velocity on the maximum temperature rise are shown in Figure 2. Comparison of the curves of dry and moist coal shows immediately that the moisture content of the coal has a great impact on spontaneous heating. Calculations show that the rate of temperature rise is higher at higher velocity for dry coal. This is also valid at temperatures up to 330K for moist coal, but then the rate of temperature rise decreases owing to the increased evaporation rate at higher velocities. There are no differences between the heating rates of dry and moist coal up to 3 lCL315 K, because evaporation is very slow initially; it gradually becomes effective as the temperature increases. For a moist coal bed, the maximum temperature levels off at N 360 K, as illustrated in Figure 2 by curve a, and this level depends on the local evaporation and oxidation rates. As can be seen from curves a, b and c, a higher gas velocity results in a lower temperature level because of the higher evaporation rate. These temperature levels confirm that the evaporation process retards the temperature rise until coal water is removed at a certain point. However, it is expected that the coal will ignite after the coal becomes dry at this point. The influence of gas velocity on the temperature rise profile along the bed is shown in Figure 3. The decrease in the maximum temperature is due to the higher evaporation rate. As the gas velocity increases, the
0.141
0
0 y 5 ts _
8
10
(m)
Drofiles for different times at a eas
0.1
5 C 0.08 0 u ;
0.06
z ‘= E 0.04 1 o 0.02 0
2
4 Distance
Figure
m 60 2
entry
0.12
Moist coal - : Dry cod
1 t ’ .I I
air
0.14
-:
c’b,‘e
z
6 from
Figure 4 Calculated coal moisture veiocity of 0.5 x 10-5ms-’
0
‘;
;
4 Distance
0 80
2
velocity
5
8 from
Calculated coal moisture of 1.0x 10-5ms-’
air
entry
8 (m)
profiles for different
times at a gas
m
!!
40
-
0
30
60 Time
Figure 2 Influence of gas velocity moist and dry coal beds
90
120
(days) on maximum
temperature
rise in
SOV(m/o) : 0.6 Id5 - - : 1.0 ld
-
: 2.0
2
4 Diotanoo
6 from
air
ontry
8
lo-
5
10
(m)
Figure3 Calculated temperature rise profiles for different gas velocities in a moist coal bed after 120 days
284
Fuel 1994
Volume
73 Number
2
maximum temperature also tends to move downstream because of higher convective heat transport. Therefore the distance to the point of maximum temperature rise is proportional to the velocity of the gas. The change in coal moisture content due to evaporation and condensation is shown in Figures 4 and 5 at gas velocities of 0.5 x lo- ’ and 1.0 x lo- ’ m s- 1 respectively, The coal moisture profiles are plotted against bed size at 30, 60, 90 and 120 days. The coal is dried by evaporation in the region of maximum temperature, and the condensation process begins from the point where the temperature gradient becomes negative in the bed. Normally the evaporation rate is higher at higher velocities, but this higher evaporation rate retards the self-heating much more, and this results in a lower constant temperature level as shown in Figure 2. Although evaporation occurs over a wide region, a lower temperature level locally results in less evaporation (compare Figure 4 with Figure 5). Oxidation and drying rates are also functions of particle size. The influences of particle size on the temperature rise and change in coal moisture content are shown in Figures 6 and 7 respectively. As is well known, oxidation and evaporation rates increase with decreasing particle size because of the lower diffusional resistance and greater external surface area. With increasing particle size, the decreases in these rates result respectively in a lower temperature rise as a result of the lower oxidation
Modelling of spontaneous combustion of coal: A. Arisoy and F. Akgiin -_
temperature rise and moves the maximum-temperature point downstream.
d (ml
~-:
0.01
~
REFERENCES 1 2 3 4
5
0’
1
0
2
Dlstsnoe
8
6
4
from
sir entry
10
(ml
Figure 6 Calculated temperature rise profiles for different particle sizes in a moist coal bed after 120 days
6 7 8 9 10 11 12 13 14 15 16 17 18
-
: 0.01
NOMENCLATURE
-
: 0.02
A
: 0.03 01-----0
’
1
2
4
Distance Figure 7
Calculated after 120 days
8
6
from
coal moisture
air entry
profiles
10
(ml
for different
Nordon, P. Fuel 1979, 58,456 Edwards, J. C. Paper A83-21, Metallurgical Society of AIME, 1983 Edwards, J. C. US Bureau of Mines, Report of Investigations 9296, 1990 Schmal, D. in ‘Coal Science and Technology 14’ (Ed. C. R. Nelson), Elsevier, Amsterdam, 1989, p. 133 Akgiin, F. and Artsoy, A. in Proc. 1st Int. Conf. on Combustion Technology for a Clean Environment, Portugal, 1991. Vol. 1, Sect. 9.4, p. 27 Brooks, K. and Glasser, D. Fuel 1986, 65, 1035 Brooks, K., Svanas, N. and Glasser, D. Fuel 1988,67, 651 Evseev, V. S. and Voroshilov, S. P. Sov. Min. Sci. 1986,22,140 Bhattacharvva. K. K. Fuel 1972. 51. 214 Bhattacharyya. K. K. Fuel 1971; SO, 367 Hodges, J. D. and Hinsley, F. B. Min. Eng. (London) 1964, 211 Nordon, P. and Bainbridge, N. N. Fuel 1979, 58, 450 Guin, J. A., Curtis, C. W., Sahawnet. B. M. and Thomas, D. C. Ind. Eng. Chem. Process Des. Dec. 1986, 25, 543 Cheong, H. W., Jeffreys, G. V. and Mumford, C. J. AIChE. 1. 1986, 32, 1334 Karsner, G. G. and Perlmutter, D. D. AIChE J. 1981, 27, 920 Beshty, B. S. Combust. Flame 1981, 32, 295 Banerjee, S. C. ‘Spontaneous Combustion of Coal and Mines Fires’, Balkema, Rotterdam, 1985 Patankar, S. V. ‘Numerical Heat Transfer and Fluid Flow’, Hemisphere Publishing Co., New York, 1980
particle
sizes
rate but a higher temperature rise as a result of the smaller retarding effect of water due to the lower evaporation rate. The net effect is a decrease in temperature rise with increasing particle size as shown in Figure 6, although the change in moisture content of the coal becomes smaller as shown in Figure 7. CONCLUSIONS A mathematical model for the spontaneous combustion of stored coal has been developed. The resulting onedimensional unsteady-state model can be used for different purposes, such as predicting the conditions within a certain coal pile under which the coal could spontaneously ignite and determining the influence of certain factors that play an important role in the design of coal piles. Calculations show that the moisture content of coal has a major retarding effect on spontaneous heating. The time needed for the temperature to reach -350K for moist coal is about twice that for dry coal. This temperature is maintained until the coal becomes dry. An increase in gas velocity results in a decrease in the maximum temperature rise because the evaporation rate increases; on the other hand, the temperature rise is proportional to the gas velocity for a dry coal bed. An increase in coal particle size also decreases the maximum
pre-exponential factor (s- ‘) specific heat capacity (J kg- ’ K- ‘) c, d particle diameter (m) diffusion coefficient (m’ s- ‘) D activation energy (J mol- ‘) h” heat transfer coefficient (W me2 K- ‘) AHO heat of reaction of oxygen with coal (J kg- ’ 0,) heat of evaporation of water (J kg- ’ H,O) AH, k mass transfer coefficient (m s-i) L length of coal bed (m) energy of water-coal bonding (J mall ‘) Q r radius (m) evaporation/condensation rate of water vapour rw (kgH,0m-3s-‘) R radius of particle (m) universal gas constant (J mol-’ K- ‘) R, s radius of evaporation surface (m) t time (s) T temperature (K) V gas velocity (m s- ‘) W coal moisture content at time t (kgkg- ‘) W initial moisture content of coal (kg kg- ‘) X distance from air entry (m) ci compaction degree of coal bed (m3 m - 3, effectiveness factor for oxidation (-) ?. thermal conductivity (W m- ’ K- ‘) density (kg m-“) P water vapour density over the free surface of Pf water (kg mP3) water vapour density over the evaporation PWS surface (kg me3) Subscripts g S
W
gas solid water vapour
Fuel 1994 Volume 73 Number 2
285
Modelling
of spontaneous combustion of coal: A. Arisoy and F. Akgiin
oxygen ambient conditions in gas phase in solid phase
0
a 1 2
APPENDIX
At
APPENDIX
A
The model provides a mathematical framework for a forthcoming experimental study for which an adiabatic horizontal tunnel has been constructed. The following boundary conditions used in the calculations therefore differ from those of an open pile.
At x=0:
A,g=h(~,-T,,), 3qg, PlW=
At
286
x=fi
PlO= P%S
(Al)
PkW
T,=O “T8,O aplLO ==O aPlw
. ax
9
ax
r=R:
’
ax-’
Fuel 1994 Volume 73 Number 2
(A2)
k(p,,-p,,)=Dz,,=
ap,,
(A4)
B
Data from the literature for the physical and chemical properties of coal and gas used in the calculations for the standard conditions, and parametric variations (in parentheses): A
=2.933~10~s-~
C,, = lOOOJkgK-’ C,, = lOOOJkg-‘K-l C,,= 1870Jkg-‘K-l d
= 0.01
(0.02; 0.03) m D1, =2.0x 10-5m2s-1 Dzo = 2.3 x 10-8m2 s-l D,,=2.5x10-5mZs-1 D,,=2.25x10-6m2s-1 E = 70OOOJmol-’ h =3Wm-‘K-l
AH, = 9.375 x lo6 J kg- ’ O2 AH,=2.4x106Jkg-‘Hz0 k =2.6x 10-3ms-1 Q = 1746.2Jmol-’ v =0.5x10-5 (1 x 10m5;2x 10-5)ms-1 W = O.lO(O)kgkg-’ =0.7m3mm3 f =0.2Wm-‘K-l Ai =O.O26Wm-‘K-l Ps = 1.16kgmy3 PS = l100kgme3