COMBUSTION AND FLAME 92:475-480 (1993)
BRIEF COMMUNICATION An Analysis of the Ignition of Coal Dust Clouds Dong-ke Zhang and Terry F. Wall Department of Chemical Engineering, The Universityof Newcastle, NSW, 2308, Australia
A C D
c cl d g i p rad v
preexponential factor specific heat cloud density, initial mass of coal per unit cloud volume E activation energy AH heat of reaction h mass transfer coefficient between cloud and ambient Lra d radiative heat loss M mass N number of particles in the cloud Q rate of heat generation or loss R universal gas constant Rcl cloud radius rp particle radius S surface area of a cloud Sp surface area of a particle T temperature t time V* volatile matter content of particles Yo oxygen mass fraction in the cloud Y~ ambient oxygen mass fraction
Greek Symbols a al a2
pg ~Pl ~02
exponential heat transfer coefficient between particle and cloud gas heat transfer coefficient between cloud and ambient gas density oxygen requirement for complete oxidation of unit carbon oxygen requirement for complete oxidation of unit volatile matter
Copyright © 1993 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.
carbon reaction cloud devolatilization cloud gas ignition point particle radiation volatile matter combustion ambient surrounding the cloud
INTRODUCTION The ignition or explosion of coal dust clouds is of interest in the fields of fire safety, and the combustion of pulverized fuel, as well as being a fundamental issue in combustion science. Ignition of coal particles is the result of a complex interaction among different mechanisms including particle heating, devolatilization, heterogeneous oxidation, and gas-phase oxidation and transport phenomena [1, 2]. Both theoretical and experimental studies on single particles have been well developed, with considerable experimental precision and validation of the predictions [1-3]. However, experiments have shown that the ignition temperatures could be reduced by as much as 300°C due to the concentration (cooperative influence) effect associated with particle clouds [1, 3-5]. While we have observed [2, 5] that the ignition temperature decreases with increasing particle size using a drop-tube technique involving the injection of a small mass (~ 2-5 mg) of coal particles, Gururajan  has reported that this effect is not clear (for the same fuel) in continuous ignition experiments involving a higher 0010-2180/93/$6.00
476 loading of coal. The theoretical analysis of coal dust cloud ignition is limited at present to the case of heterogeneous ignition on the surface of the particles [1, 2, 7-9], which does not allow for this effect [1-6]. This brief communication extends the energy equations of Krishna and Berlad  to include coal volatile matter (VM) release and the homogeneous ignition of VM in the gas phase of the cloud. The effects of particle size on the ignition temperature and ambient oxygen concentration on ignition mechanisms, predicted by this extension, are then examined.
D. Z H A N G AND T. F. WALL MODEL FORMULATION For a single particle and the gas inside the cloud volume, two energy conservation equations may be written, respectively, as dr,
MpCp dt = Qp - a,Sp(Tp - Tg) - Lra O - Q d (1) and dTg MgCg dt = Qo - NalSp(Tg - Tp)
- azS(Tg - To). STATEMENT OF THE PROBLEM
The following conditions are considered: 1. Spherical coal particles of mono-size (rp) are uniformly dispersed in a gas containing oxygen (mass fraction, Y0) to form a spherical dust cloud of radius Roy The cloud has uniform properties across the cloud. This cloud is located in an ambient gas of temperature T~o.The system is in a steady state at the point of ignition. 2. The particles undergo devolatilization and surface heterogeneous oxidation (if there is enough oxygen on the particle surface). The volatile matter released reacts with oxygen instantaneously (i.e. at an infinite rate). Hence, the devolatilization rate controls the volatile combustion and thus the heat release. 3. Surface oxidation is included in the particle energy balance, and volatile matter (VM) combustion in the cloud gas balance. Particle-gas heat transfer is considered. The cloud also loses heat to the ambient gas surrounding the cloud. The heat of devolatilization is neglected, as it is small compared with the heat of surface oxidation and VM combustion. 4. The induction time is sufficiently short so that the consumption of fuel or oxidant can be neglected in this period. 5. Convective heat transfer is represented by Nusselt's Number type coefficients. Radiative transfer and natural convection are not considered. This approximation will hold for small clouds. 6. All physical properties are constant.
With the above conditions, Eqs. 1 and 2 reduce to =
- r e)
and Q~, = UotxSp(Tg - Tp) + a2S(Tg - T=).
These two equations describe the steady-state situation. Two ignition modes could occur depending on the cloud condition and the ambient temperature: one is heterogeneous ignition on the particles surface, the other homogeneous ignition of VM in the cloud gas. Therefore, we may establish two criteria for the two ignition modes. For heterogeneous ignition, if Qp is an Arrhenius-type rate with an exponential dependence on Tp, Eq. 3 would give the familiar Semenov-type distribution of singular points (steady state). Following the methods set out by Krishna and Berlad , eliminating T= from Eqs. 3 and 4 the critical condition for heterogeneous ignition is obtained as alSpazS QP = UOqSp + ot2 c(Tpo
- No~lSp + ot2S Qv
l + m
NotlS p + ot2S OTp
DUST CLOUD IGNITION
For homogeneous ignition, according to the second assumption, Qo depends only on the particle devolatilization rate, and hence the particle temperature. It is further assumed that the particle devolatilization rate expression is of Arrhenius-type with an exponential dependence on Tp. Then, from Eq. 4, the critical conditions for homogeneous ignition are
Qo = a2S(Tg - T~) - N Q p
OQp = ot2S - N - -
Q~ + NQp a2S Qp alSp
Tg = Tp
Case 1. Heterogeneous Ignition When Q~ << Qp, heterogeneous ignition dominates. This mechanism will be more important when the volatile matter content V*, or cloud density is low. Two conditions are considered:
Case la: NotlSp/ot2S >> 1, Eqs. 6 and 9 reduce to
The simultaneous solution of Eqs. 5 and 6 or Eqs. 7 and 8 will give the values of T~ for autoignition of the cloud:
Toni = Tg
strongly coupled nonlinear equations is unlikely at present. However, some general results can be obtained for limiting cases.
= Or2 NSp 3/-''''~ t S1/2 ]
× EcAc PgYoAHc
Zcc,i = Tp ,i
where Eqs. 9a and 9b are for homogeneous ignition and heterogeneous ignition, respectively. These equations require specification of Qp and Qv:
Case lb: NotlSp/oteS << 1, Eqs. 6 and 9 reduce to
Qp = SpA HcAc PgYo exp -
Qo = AHoNAdMpV* exp -
Then, from Eqs. 10 and 11, the relative dependence of Tp and Tg is given by
aiR E~Ac PgYoAHc
AHcAcpgYo(Ec)E exp - ~ eq
c RTp2 . (13)
Equations 5-13 describe the cloud ignition problem. Complete analytical solution of these
= Tp,i[1 -
Equations 14-17 are those of Krishna and Berlad . The most convenient forms have been given by Essenhigh et al.  that is, for the case of a dense cloud: T.a-2 c¢,i
where a is an approximation arising from the power series expansion of exp(-Ec/RTp). For
D. ZHANG AND T. F. WALL
pulverized coal combustion, a - - E c / R T p (ranging from 5 to 20) . Equation 18, in which D is the cloud particle density, proportional t o NSp3/2/S 3/2, indicates that the ignition temperature for a dense cloud decreases as the particle becomes smaller, or as the cloud density or the cloud size increase. For the case of a dilute cloud, Eqs. 16 and 17 reduce to
Noting that T ~ ia - 2
Tp = Tg, Eqs. 20 and 21 simplify to
From Eq. 22, for homogeneous ignition of VM in the cloud, the ignition temperature only depends on the cloud size and density. It decreases with an increase in cloud size or density, but does not vary with particle size. DISCUSSION
which is the result obtained for single particles at constant oxygen concentration , As already confirmed by many investigators, Eq. 19 indicates that, for single particles undergoing heterogeneous ignition, the ignition temperature decreases with particle size.
Case 2. Homogeneous Ignition
Qp << 02, homogeneous ignition of VM in cloud gas phase predominates. This may occur when the volatile matter content V*, or the cloud density is high, or oxygen concentration in the cloud, Yo, is low (Qp small). From Eqs. 8-10, When
TP2 exp -
_ NMp ( AH~AaV*E d )
(),constant, (constant) Rcl2D
T~i= T p (1 -
The result for heterogeneous ignition of a dilute cloud is that for a single particle (Eq. 19) and predicts the experimental trends found by many investigators . The result for homogeneous ignition (Eq. 22) suggests that particle size is not important. However, the analysis assumes a steady state and will not apply to experiments when the heating time for particles is limited (e.g., the steady-state assumption fails). Here, fine particles with shorter heating times, must be expected to ignite preferentially. The definition of cloud radius (R d) is also not always apparent. In an experiment where a pulse of coal is dropped into a hot furnace [2, 5, 10, 11], this cloud dimension will be related to that occupied by the injected pulse. For an autoignition experiment  the radius will be that of a local region that is heated by a spark or wall. In other words, the radius is not necessarily that of the furnace, but corresponds to the volume of the local ignition, from which propagation occurs. In a given experiment, however, the cloud dimension may be sufficiently constant (although unknown) so that the trend with the other variables (in Eqs. 18 and 22) can be examined experimentally. The analysis related to homogeneous ignition also assumes that sufficient oxygen is available to burn the volatile matter released. At high cloud concentration this may not be so and no cloud concentration effect (as predicted by Eq. 22) would be expected. It appears that this steady-state analytical technique can be used to determine the ignition conditions for coal dust clouds. Equation 22 is partly supported by the experimental results of Hertzberg . He reported that for
DUST CLOUD IGNITION some high VM fuels (Pittsburgh coal and polyethylene, Fig. 4 in Ref. 4), the minimum autoignition temperature became independent of particle size, when the particle size was below certain characteristic diameters. For -particles greater than such diameters, the autoignition temperature increased with particle size, probably due to the larger particles requiring a longer heating time for fast devolatilization to occur (intraparticle effect). Hertzberg  also claimed that the particle size may still be a "hidden variable." However, Eq. 22 may offer an explanation of the particle size invariant autoignition, that is, homogeneous ignition is the controlling mechanism. Gururajan  has also reported that, for the same fuels, the ignition temperature decreased with increasing particle size in drop-tube (pulse) ignition experiments, but such a trend is not clear in continuous ignition experiments involving higher cloud densities, The differences may be associated with the different cloud concentrations in the two different experiments. In the light of the above analysis, we have performed both pulse and continuous ignition experiments using various feeding rates of the sample (corresponding to different cloud densities ). The results indicate that the ignition temperature decreases with increasing particle size at low coal feeding rates but becomes invariant at high feeding rates. This observation supports the prediction of Eq. 22. For heterogeneous ignition, as already discussed by Krishna and Berlad  and later by Essenhigh et al. , the two limiting-case (Cases la and lb) results are qualitatively supported by some of the experimental results of Cassel 'and Liebman  on the ignition of metal dust clouds. They reported that the ignition temperatures dropped by 50°-300°C for magnesium particles and magnesium-aluminium particles due to cloud-particle density effect, and the drop in ignition temperatures was greatest for Jthe fine particles. As mentioned above, Eq. 19 has been widely tested. However, quantitative confirmation of Eqs. 18 and 22 requires further experiment. Furthermore, a theoretical problem still remains. We have not developed a criterion for 'the determination of either heterogeneous or homogeneous ignition. This may be partially
479 solved by introducing the mass conservation equation for oxygen species, that is,
NSpAc pgYo exp - -~p +NAeMpV*exp
~°1 - ~
= hSpg(Y~ - Yo),
which is then solved for the oxygen mass fraction in the cloud for heterogeneous oxidation on the particle surface, assuming ~ = q~2 = q~: 1
Yo = Y~ q~NSpA c Pg exp hSpg
exp(_ ) SpA cOgexp
(24) Qualitatively, Eq. 24 suggests that the heterogeneous ignition is likely to occur for a high value of ambient oxygen fraction, while for small values of Y~, Yo approaches zero, and homogeneous ignition controls. This is supported by the recent experimental results of Zhang and colleagues [10, 11], that the effect of volatile matter on ignition is reduced when the oxygen concentration is increased. At low oxygen concentrations, the contribution from volatile matter combustion to ignition is significant and the ignition seems to be in the gas phase (homogeneous). With pure oxygen, the difference in ignition temperatures between that of char and of its parent coal is reduced and the ignition appears to be more heterogeneous in nature. Equation 24 explains these observations. FINAL COMMENTS The proposed relationships between the ignition temperature of a coal dust cloud and system variables offers an explanation of experimental observations in a few limiting cases.
D. Z H A N G A N D T. F. W A L L
T h e two i m p o r t a n t contributions of this w o r k are the predictions of the effect of particle size on ignition t e m p e r a t u r e at various cloud concentrations and the effect of oxygen c o n c e n t r a tion on ignition mechanisms. T h e ignition temp e r a t u r e decreases with increasing particle size at low cloud concentrations, but b e c o m e s invariant at high concentrations. F o r a coal dust cloud, h o m o g e n e o u s ignition is m o r e likely at low a m b i e n t oxygen concentrations, but the h e t e r o g e n e o u s ignition will d o m i n a t e at high a m b i e n t oxygen concentrations. While these conclusions are s u p p o r t e d by s o m e e x p e r i m e n tal data, further experiments are necessary in which the variables are b e t t e r defined.
2. Wall, T. F., Gupta, R. P., Gururajan, V. S., and Zhang, D. K., Fuel 70:1011-1016 (1991). 3. Cassel, H. M., and Liebman, I., Combust. Flame 18:467-475 (1959). 4. Hertzberg, M., Fuel, 70:1115-1123 (1991). 5. Wall, T. F., Gururajan, V. S., Lucas, J. A. Gupta, R. P., Zhang, D. K., Young, B. C., and Smith, I. W., TwentyThird Symposium (International) on Combustion, The
6. 7. 8. 9. 10. 11.
Combustion Institute, Pittsburgh, 1991, pp. 1177-1184. Gururajan, V. S., Ph.D. thesis, The University of Newcastle, NSW 2308, 1989. Krishna, C. R., and Berlad, A. L., Combust. Flame 37:207-210 (1980). Higuera, F. J., and Linan, A., Combust. Flame 75:325-342 (1989). Baek, S. W., Combust. Flame 81:366-377 (1990). Zhang, D. K., Ph.D. thesis, The University of Newcastle, NSW 2308, 1992. Zhang, D. K. Wall, T. F., Harris, D. J., Smith, I. W., Chen, J. Y., and Stanmore, B. R., Fuel, 71:1239-1246 (1992).
1. Essenhigh, R. H., Misra, M. K., and Shaw, D. W., Combust. Flame 77:3-30 (1989).
Received 22 April 1992; revised 29 November 1992