A numerical model to simulate smouldering fires in bulk
materials and dust deposits
Ulrich Krause*, Martin Schmidt, Christian Lohrer
Federal Institute for Materials Research and Testing (BAM), Division II.2 ‘Reactive Substances and Systems’, D-12205 Berlin, Germany
Received 26 January 2005; received in revised form 24 March 2005; accepted 24 March 2005
Abstract
A numerical model is presented which consists of a set of partial differential equations for the transport of heat and mass fractions of eight
chemical species to describe the onset of self-ignition and the propagation of smouldering fires in deposits of bulk materials or dust accumulations.
The chemical reaction sub-model includes solid fuel decomposition and the combustion of char, carbon monoxide and hydrogen.
The model has been validated against lab-scale self-ignition and smouldering propagation experiments and then applied to predictions of
fire scenarios in a lignite coal silo. Predicted reaction temperatures of 550 K and propagation velocities of the smouldering front of about
6 mm/h are in good agreement with experimental values derived from lab-scale experiments.
q 2005 Elsevier Ltd. All rights reserved.
Keywords: Self-ignition; Combustible dust; Bulk materials; Smouldering fires; Numerical modelling
1. Introduction
Fires in solid bulk materials like dusts, grains or granules
may often occur due to a preceding self-ignition process.
Here self-ignition of materials means the onset of
exothermic chemical reactions and a subsequent tempera-
ture rise within a combustible material, without the action of
an additional ignition source.
Some solid substances, e.g. ammonium nitrate or some
peroxides may experience exothermic effects without being
combusted, namely by self-decomposition. Self-decompo-
sition, in general, may be treated using the same or very
similar experimental and theoretical tools as self-ignition.
However, the present paper concentrates on the latter case.
Self-ignition occurs when the thermal equilibrium
between the two counteracting effects of heat release due
to oxidation and heat loss to the surroundings is disturbed. If
the rate of heat production exceeds the heat loss, a
temperature rise within the accumulation of material will
0950-4230/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jlp.2005.03.005
* Corresponding author. Tel.: C49 308 104 4442; fax: C49 308 104
1227.
E-mail address: [email protected] (U. Krause).
consequently take place and initialise a further acceleration
of the reaction. This positive feedback loop finally ends in a
‘self-ignition’.
It is out of the scope of the present paper to summarize
the vast literature on the assessment of self-ignition hazards
by experimental methods and by the so-called thermal
explosion theory. Standard references are, e.g. the book by
Bowes (1984) and the related chapter in the book by
Babrauskas (2003, chap. 9).
The present paper concentrates on the application of a
numerical model addressing the problem of self-ignition
and fire propagation on a technical scale. These models are
based on a set of partial differential equations describing the
distributions of temperature and species concentrations and
their evolution with time in solid bulk materials, dust heaps
and layers, waste dumps, coal heaps, etc. undergoing self-
ignition.
Twenty years ago Ohlemiller (1985) provided a com-
prehensive summary of models existing at this time (most of
them being non-dimensional ones), the relevant presump-
tions and simplifications contained therein and compared
them to what he called a benchmark model (which was a
multi-dimensional one). He concluded that the models
reviewed were not able to reflect smouldering fire
propagation in a realistic manner and that a general model
comprising heat and mass transfer through the fuel bed
Journal of Loss Prevention in the Process Industries 19 (2006) 218–226
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Nomenclature
a (m2/s) thermal diffusivity
c (J kgK1 KK1) specific heat capacity
C (kg/m3) mass concentration
D (m2/s) diffusion coefficient
E (J/mol) apparent activation energy
HR (J/kg) heat of reaction
j (kg mK2 sK1) mass flux
k0 (sK1) pre-exponential factor
M (g/mol) molecular weight
_q (J sK1 mK2) heat flux
R (J molK1 KK1) universal gas constant
Sci (kg mK3 sK1 production/consumption rate of species i
ST (J mK3 sK1) heat production rate
t (s) time
T (K) temperature
a (J mK2 sK1 KK1) heat transfer coefficient
b (m/s) mass transfer coefficient
r (kg/m3) bulk density
n stoichiometric coefficient
Subscripts
a ambient
f fuel
i species i
s surface
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226 219
combined with detailed chemical kinetics on a particle scale
was still too complex.
Nevertheless, different attempts were made to compute
temperature and concentration fields and their evolution
with time in real-scale fire scenarios. In these models it was
assumed that the solid fuel is an isotropic solid body and
variations in its structure (pore size distribution, inhom-
ogeneity) were neglected.
A comparatively simple model based on the one-
dimensional Fourier’s equation of heat conduction in
connection with an Arrhenius-type heat release term was
used by Hensel, Krause, John, and Machnow (1994) to
reproduce successfully hot storage experiments for cork dust
and dust of a German black coal. Earlier, Liang and Tanaka
(1987) and Winters and Cliffe (1985) published one-
dimensional finite element calculations on the self-ignition
of coal. The latter reproduced basket experiments by
Leuschke (1983) on German black coal dust and were able
to mirror the effect that the point in the dust deposit where
self-ignition occurs first moves closer to the surface of the
deposit, the higher the oven temperature is (the deposit being
exposed to a temperature above the critical one).
Among the more recent models, that of Krishnaswamy,
Agarwal, and Gunn (1996) contains a coupled solution of
the temperature field equation with the velocity field, the
concentration field of oxygen and the pressure field. While
the latter ones are considered to be invariant with time, the
temperature field is transient. The model was applied to the
storage of coal stockpiles and the result was the temperature
evolution with time for different conditions of the steady-
state flow, pressure and oxygen concentration fields.
Hull, Lanthier, and Agarwal (1997) used a very similar
approach to investigate the role of oxygen diffusion on self-
ignition of coal stockpiles: time-dependent temperature
field, steady-state oxygen concentration field. The main
conclusion of Hull et al. was that compaction of the bulk
deposit of coal impedes the diffusion of oxygen to the active
sites of particles and thus leads to a higher level of safety.
Another interesting problem connected to self-ignition of
material was highlighted by Griffiths and Kordylewski (1992).
It may occur in practice that material heated-up in a previous
process step is stored at relatively large amounts in an
environment, e.g. at room temperature. The question is then,
whether the material cools down (due to the ‘cold’ storage
temperature) or ignites due to the high initial temperature.
One of the findings of Griffiths and Kordylewski was that
the critical initial temperature only weakly depends on the
ambient temperature at which the material is stored.
Schmidt (2001) and Schmidt and Krause (2000)
proposed a model which consists of separate transport
equations for five chemical species (solid fuel, oxygen, solid
product, gaseous product, nitrogen) which are solved
simultaneously together with the temperature field equation.
Akgun and Essenhigh (2001) presented a two-dimen-
sional time-dependent model considering mass conserva-
tion for oxygen and moisture and energy conservation for
the gas phase and the solid phase. Convective heat and gas
transport were considered by applying Darcy’s law. The
model was applied to coal stockpiles and the dependence of
the temperature evolution with time on the slope of the
stockpile was investigated.
The influence of moisture on the self-ignition of milk
powder was also investigated by Chen (1998) and Chon and
Chen (1999). These models contain conservation equations for
energy and mass fractions of liquid water and water vapour.
Rostami, Murthy, and Hajaligol (2004) reported compu-
tations on the propagation of a smouldering front driven by
convection in a cigarette by using a commercial CFD code.
In addition to the reacting species, the role of moisture was
also considered.
The purpose of the model presented here is to allow for
the computation of real-scale fire scenarios in bulk
materials, coal stockpiles, waste dumps or dust heaps or
layers. The model is based on conservation of energy and
the conservation of mass of eight chemical species. A four-
step reaction mechanism is assumed to model
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226220
the conversion of fuel. The model is validated against lab-
scale self-ignition and smouldering propagation exper-
iments and is applied to large-scale fire scenarios.
The computational examples presented are all in
axisymmetric geometries and therefore two-dimensional,
however, the computer code used allows three-dimensional
calculations as well.
2. A multi-dimensional time-dependent bulk materials
fire model
Promoted by the rapid development of computer
resources, the numerical solution of coupled heat and
mass transfer problems has more and more become a matter
of interest in recent years. In general, numerical simulations
of these phenomena offer the following advantages:
†
There are no limitations for geometry. Three-dimen-sional geometries can be treated as well as ‘sandwich’
materials, i.e. those consisting of different layers each
exhibiting its own material properties.
†
Any kind of boundary conditions (Dirichlet, vonNeumann, Newtonian cooling) can be considered. In
addition, the boundary conditions may vary in space and
time.
†
The dependence of the temperature evolution with timecan be treated such that the entire process of heating,
self-ignition, runaway and burnout can be followed
continuously.
†
Information is obtained on local distributions of thechemical species of interest and their evolution with
time.
†
Kinetic and diffusion-controlled reaction regimes may beconsidered.
The input that has to be provided to the model covers
†
material properties like thermal conductivity, specificheat capacity, porosity or bulk density, diffusion
coefficients and the calorific value,
†
data on chemical kinetics like the apparent activationenergies and the pre-exponential factors in the Arrhenius
equations (see below) representing the different reaction
steps under consideration.
†
stoichiometric data including the elemental compositionof the fuel and the solid product and the composition of
the gaseous reaction products,
†
boundary and initial conditions,†
geometry data.The material properties all have to be measured for the
specific bulk material in question if they cannot be taken from
literature. The kinetic data can be derived from methods of
thermal analysis like differential scanning calorimetry or
from standard hot storage tests (basket tests). As described by
Malow and Krause (2004), comparable results are obtained
as long as the exothermicity observed in both apparatus is
based on the same chemical conversion.
In many cases, the chemical structure of the fuel will be
unknown, e.g. in the case of coal, waste or biomass. The
structure of the solid reaction product, e.g. char, is usually
unknown as well. To derive stoichiometric data an
elemental analysis may be performed to obtain the mass
fractions of those elements contained in the fuel being most
important for the chemical conversion, e.g. C, H, N, S and
O, see Schmidt (2001).
Furthermore, the composition of gaseous reaction
products has to be known which, however, depends mainly
on the reaction temperature and the availability of oxygen.
A reasonable approach to obtain modelling input on the gas
composition during different stages of the fire (smouldering,
glowing fire, flame) is to apply the method of Fourier
Transform Infrared Spectroscopy (FTIR) at different reac-
tion temperatures during the fuel conversion, see Warnecke
(2004).
Boundary and initial conditions as well as the geometry
data depend on the specific scenario applied to the model.
The main simplifications underlying the present model
are:
†
heat and mass are transferred throughout the accumu-lation of bulk material only by conduction and diffusion,
respectively (this does not exclude convection at the
outer surface of the deposit),
†
the accumulation of bulk material is considered to be ahomogeneous and isotropic body (locally uniform
thermal transport coefficients),
†
the influences of moisture and particle size distributionare not considered,
†
the thermal conductivity and the diffusion coefficients donot vary with temperature or species concentrations. The
porosity is implicitly contained in the bulk density.
These simplifications were made to keep the computational
efforts in the current state of the model development low. They
are not restrictions of the model in principle, but can all be
dropped during the further development of the model.
Hence, the balance equations are written
vT
vtZ a!div grad T CST (1)
for the heat transfer and
vCi
vtZ Di !div grad Ci CSci (2)
for the transportation of a chemical species i.
T in Eq. (1) is the temperature, a the thermal diffusivity, t
the time and ST the heat source term. Ci in Eq. (2) is the mass
concentration of a species i, Di is the binary diffusion
coefficient of species i into the mixture and Sci is the rate of
production or consumption of species i.
Table 1
Mass fractions of C, H, N, and O in a German lignite coal (waf)
Element C H N O S
Mass fraction (%) 57.3 5.5 0.2 34.0 3.0
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226 221
In the model, it was supposed that the fuel is converted
undergoing the following reaction steps: decomposition of
the fuel to char, carbon monoxide, carbon dioxide and
hydrogen (Eq. (3)), char combustion (Eq. (4)), oxidation of
carbon monoxide (Eq. (5)) and oxidation of hydrogen
(Eq. (6)). A fictitious ‘fuel molecule’ was assumed based on
an elemental analysis of the mass fractions of C, H, N and O
contained in the virgin fuel. Table 1 shows the elemental
composition of a typical German lignite coal (water and ash
free), on which Eq. (3) is based on.
E.g. for crushed lignite coal, Eqs. (3)–(6) yield
C241H228O46 /213C C18CO2 C10CO C114H2 (3)
C CO2/CO2 (4)
2CO CO2 /2CO2 (5)
2H2 CO2 /2H2O (6)
The oxidation of nitrogen and sulphur has been neglected
in this example.
As obvious from Eqs. (3)–(6), seven different chemical
species are taken into account. For each of these species, an
equation of the type of Eq. (2) has to be incorporated into the
model. To match the effect of inerting an additional
equation of the type of Eq. (2) is included for nitrogen in
the gas phase. For nitrogen, the source term is zero.
Each species considered is converted at its specific rate
during each of the reactions taken into account, e.g. the solid
fuel when decomposed according to Eq. (3) exhibits an
Arrhenius-type reaction rate as given in Eq. (7)
dCf
dtZKCfk0 exp K
E
RT
� �(7)
k0 is the pre-exponential factor and E the apparent
activation energy specific for the reaction given by Eq. (3)
and R is the universal gas constant. The reaction rate is of
first order as it is assumed that the decomposition reaction
depends, besides the temperature, on the concentration of
the fuel only.
For the rates of the species produced in this reaction, the
following equation applies
dCi
dtZ
yi
yf
Mi
Mf
dCf
dt(8)
where the index i refers to the species C, CO, CO2 and
H2, the yi is the stoichiometric coefficient and the Mi is
the molecular weight. Note that the stoichiometric
coefficients are always negative for reactants and positive
for products.
The rate equations with respect to the other reactions are
analogous, however, a dependence of the reaction rate of the
respective fuel (C, CO and H2) on the concentration of
oxygen has been included to reflect the influence of oxygen
diffusion on the reaction rate. Appendix A gives an
overview over the particular reaction rates of the different
species considered in the different reactions.
Appendix B shows the apparent activation energies and
the pre-exponential factors for the reactions according to
Eqs. (3)–(6) as used in the computations described below
together with the remaining input quantities.
The source term in the temperature field equation is
computed as
ST Z1
rc
X4
iZ1
DHR;i
dCi
dt(9)
The initial and boundary conditions have to be selected
according to the case under consideration. In many cases, the
bulk material undergoing self-ignition might have a free
surface across which heat is exchanged with the surrounding.
At such a surface, the heat flux may be calculated from Eq. (10)
_q Z aðTs KTaÞ (10)
with the heat transfer coefficient a, the surface temperature Ts
and the ambient temperature Ta. The mass flux of an individual
species k into the heap of bulk material (or out of it,
respectively) can be calculated using an analogous
equation (11)
ji Z biðCisKCia
Þ (11)
with the mass transfer coefficient bi, the concentration of
species i at the surface Cis and the concentration of species i in
the ambient atmosphere Cia.
If symmetry axes exist within the heap of bulk material,
they can be used as boundaries, too. This reduces the
numerical effort. At a symmetry axis the heat and mass
fluxes are zero.
As initial condition, the local distributions of the
temperature and the concentration of each species k have
to be known.
Thus, the system of equations is mathematically closed.
For solving the system of equations numerically in our case,
the commercial Finite-Element-Code FEMLAB was used.
3. Computational examples
3.1. Self-ignition of lignite coal dust at reduced volume
fractions of oxygen
Inerting is mostly applied to prevent explosions of dusts
or smouldering gases released from dusts or bulk materials
under the action of heat. In some practical applications,
however, dusts or bulk materials are stored in an atmosphere
with reduced volume fraction of oxygen to reduce
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226222
the hazard of a fire. In these cases, it is interesting to know
the maximum permissible volume fraction of oxygen.
Experimental investigations on the self-ignition of dusts
at reduced volume fractions of oxygen in the ambient
atmosphere have been reported by Schmidt, Lohrer, and
Krause (2003). Performing lab-scale hot storage exper-
iments it could be shown that the self-ignition temperatures
increase with decreasing level of oxygen volume fraction.
As a validation example, these experiments have been
simulated using the model presented in Section 2.
Fig. 1 shows a comparison of computed and experimen-
tal self-ignition temperatures (SIT) of lignite coal dust in
dependence on the volume fraction of oxygen in the ambient
air.
The comparison shows a satisfying agreement for
oxygen volume fractions higher than 5% with the computed
values being systematically lower than the experimental
ones (hence being on the safe side). The observed increase
of the self-ignition temperatures at lower volume fractions
of oxygen is also reflected in the computations. However,
for the very low oxygen volume fractions (below 5%), the
experimental values exceed the computed ones for about
30–50 K. One reason for these differences lies in the
reaction model being unchanged over the entire span of
oxygen volume fractions while the experiments indicated a
change in the reaction mechanism at lower oxygen
volume fractions, see Schmidt et al. (2003). Another reason
may be the difficulty to differentiate between ‘ignition’ and
‘non-ignition’ at low oxygen fractions. As pointed out by
Schmidt, Malow, Lohrer, and Krause (2002), the lower the
oxygen content, smaller is the peak temperatures reached in
a smouldering fire triggered by self-ignition. A sharp
transition between steady state and runaway within
a narrow range of ambient temperatures, as it is observed
Fig. 1. Self-ignition temperatures of lignite coal dust in dependence on the volum
three different sample volumes in lab scale (cylinders with lengthZdiameter).
at 21% of ambient oxygen volume fraction, does not exist
for low content of oxygen. In the experiments, therefore,
‘ignition’ was identified by three different indications: a
significant rise of the sample temperature above the oven
temperature, a significant loss of mass and a change in
colour of the bulk material. In the computations ‘ignition’
was identified by a steep rise in the conversion rate of the
fuel.
3.2. Propagation of a smouldering fire through a dust
accumulation
As a second example, the propagation of a reaction front
through a dust accumulation is presented. Corresponding
experiments have been reported by Lohrer, Schmidt, and
Krause (2004). Lignite coal dust was filled into a sample
holder with 3.2 l in volume and centrally ignited by a
cylindrical heated coil of 10 mm in diameter and 30 mm in
length. The electrical power of the coil was about 100 W
maintained over a period of 35 min.
After ignition, a smouldering fire developed and propa-
gated through the dust accumulation. Using the model
described in Section 2, the propagation of the reaction front
could be computed. Fig. 2 shows the progress of the reaction
front in terms of the variation of the bulk density.
As observed in the experiments, the fuel is not
combusted completely in the smouldering reaction, but a
solid reaction product is formed which exhibits a bulk
density of about half of that of the original solid fuel. This is
in good agreement with the experimental observations.
An average propagation velocity can be derived from the
radius of the dust sample divided by the time between
the ignition and the arrival of the reaction front at the
surface of the dust accumulation. A comparison between
e fraction of oxygen, comparison of experimental and computed values for
Fig. 2. Distribution of the solid fuel concentration during the propagation of
a smouldering front in a 3.2 l sample of lignite coal.
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226 223
experimental and computed propagation velocities is given
in Table 2.
Both computational examples discussed so far show a
qualitative agreement of the computations with the
experimental findings. The comparatively simple reaction
model leaves space for improvement. Schmidt (2001) could
show that the numerical solution of the system of equations
is very sensitive against changes in the apparent activation
energy and the pre-exponential factor. Hence, the validity of
the computational results depends to a certain extent on the
accuracy of the kinetic data.
Other validation examples of the present model have been
published by Lohrer, Krause, and Steinbach (2004) and
Schmidt (2001). In general, the model is capable of reflecting
self-heating and smouldering fire propagation with sufficient
quality for engineering purposes. Its application to real-scale
problems can give qualitative insight into the evolution of
smouldering fires in large accumulations of material, which
would impossibly be obtained by experiments. However, at
the current state one would go far to derive quantitative
conclusions from the computations. An example for the
application of the model to storage of lignite coal in a silo is
given in Section 3.3.
Table 2
Experimental and computed propagation velocities for smouldering fires of
lignite coal dust ignited by a heated coil
Volume (l) Propagation velocity
(experimental) (mm/h)
Propagation velocity
(computed) (mm/h)
3.2 7.2 8.3
6.4 5.7 5.4
3.3. Smouldering fire propagation in silo filled with crushed
lignite coal
To give an example of a real-scale computation, self-
ignition in a silo filled with crushed lignite coal has been
predicted. The cylindrical part of the silo had a height of
10 m and a diameter of 3 m. The funnel had a height of 3 m
and ended in a discharge opening of 400 mm in diameter.
The total volume of the silo was 78 m3.
Due to the axisymmetry of the silo, a two-dimensional
computation was performed. It was supposed that the silo was
completely filled with the coal. An adaptive finite element
mesh was used for the computations with a comparatively fine
meshing in the funnel and along the symmetry axis and a
comparatively coarse meshing near the outer surface. The
mesh consisted of about 12,000 elements. In this range of
elements, the computations were insensitive to the grid size.
For the computational example, the initial temperature of
the coal was taken to be 25 8C while the ambient
temperature was set to 40 8C. The latter value was selected
to reflect the conditions at a location with a relatively hot
climate (however, day and night cycles of the ambient
temperature were not considered in this example). Fig. 3
depicts the evolution with time of the temperature
distribution within the silo.
The induction period for the self-ignition to occur was
about 240 days in this example. As the transport of oxygen
through the silo walls was supposed to be unlimited in this
example, two hot spots developed. The reason for this may
be explained as follows:
Suppose, the silo would be considered as if consisting of
two independent parts one stacked upon the other. Neglecting
the funnel, the volume of each part would be about 35 m3 and
the volume-to-surface ratio V/S of each would be 0.57 m.
According to the measured self-ignition temperatures of
the lignite coal in question as reported by Krause (2005), an
Fig. 3. Temperature distribution during a smouldering fire in a silo filled
with crushed lignite coal (silo volume 78 m3, crushed lignite coal stored at
an ambient temperature of 40 8C, walls permeable for O2).
Fig. 5. Temperature distribution during a smouldering fire in a silo filled
with crushed lignite coal (silo volume 78 m3, crushed lignite coal stored at
an ambient temperature of 40 8C, only silo top and discharge opening
permeable for O2).
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226224
extrapolation to a V/S of 0.57 leads to a self-ignition
temperature of about 15 8C.
Hence, at an ambient temperature of 40 8C each of the
two sub-volumes is stored under super-critical conditions
and hot spots therefore occur in both of them.
After ignition, a smouldering fire propagated for about
11 days until it reached the wall of the silo. The computed
temperature in the reaction front of about 550 K was within
the range typical for smouldering fire propagation in lignite
coal, see Schmidt (2001). An average propagation velocity
computed was 6.1 mm/h which is in satisfying agreement
with the experimental value given in Table 1.
For the same example, Fig. 4 exhibits the evolution of
time of the concentration of oxygen.
In a next step, the self-ignition and smouldering fire
propagation were modelled under the condition of non-
permeable silo walls. For the combustion only the initial
oxygen contained in the voids between the particles with a
volume fraction of 21% in the gas phase and the oxygen,
which could pass into the silo via the silo, top and the
discharge opening at the funnel bottom were available. The
other conditions were the same as in the previous example.
The temperature distribution at different points of time
under the conditions of limited oxygen supply is shown in
Fig. 5, while Fig. 6 exhibits the related distribution of oxygen.
In contrast to Fig. 3 (unlimited supply ofoxygen), in Fig. 5 only
one hot spot is visible. This hot spot occurs in the upper part of
the silo. In the lower part there is no sufficient oxygen available
tocause a significant temperature rise. Inaddition, self-ignition
occurs 72 days later than for the case of unlimited oxygen.
After ignition, the vertical propagation (into the direction
of the open end) of the temperature front is about twice
much faster than the horizontal, while for the unlimited
oxygen supply the velocity of the temperature front was
about the same in both directions. (Buoyancy was not taken
into account in both cases.)
Fig. 4. Distribution of the volume fraction of oxygen during a smouldering fire
in a silo filled with crushed lignite coal (silo volume 78 m3, crushed lignite coal
stored at an ambient temperature of 40 8C, walls permeable for O2).
The propagation velocity of the smouldering front was
about 4.7 mm/h in the upwards direction which is 77% of
the one computed for unlimited oxygen supply.
Another difference becomes obvious when comparing
Figs. 4 and 6. While in Fig. 4 the depletion of oxygen
appears only behind the reaction front, in Fig. 6 nearly the
entire silo is emptied from oxygen, despite the reaction zone
is limited to the upper central part of the silo. This means
that the model is able to reflect the diffusion of oxygen from
the virgin part of the material to the reaction zone.
Despite the fact, that the agreement of the model with the
lab-scale experiments is currently not better than fair, the
computations show plausible patterns of self-ignition and
smouldering fire propagation in real-scale scenarios which
are beyond the possibilities of experimental investigation.
Fig. 6. Distribution of the volume fraction of oxygen during a smouldering
fire in a silo filled with crushed lignite coal (silo volume 78 m3, crushed
lignite coal stored at an ambient temperature of 40 8C, only silo top and
discharge opening permeable for O2).
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226 225
4. Conclusions
The model presented in this paper covers the entire
process of fire initialisation and propagation during the
storage of a bulk material accumulation. This process is
characterised by the following phases:
†
Spe
Fue
C
CO
CO
H2
O2
H2O
N2
temperature equalisation between the stored material and
its surrounding (if initially different),
†
heat accumulation and subsequent temperature rise dueto exothermic reactions within the bulk (or dust) deposit,
†
propagation of a smouldering front.However, the results of the computations largely depend on
the accuracy and quality of the input data, which normally
have to be generated by experiments. Hence, the reliability of
the experimental procedures remains a key matter of interest.
Undoubtedly, advanced computer modelling of self-
ignition and smouldering combustion will more and more
cies Reaction 1 Reaction 2
C241H228O46 /213C
C18CO2 C10CO
C114H2
CCO2/CO2
l dCf
dt
� �1
ZKCfk0;1 exp KE1
RT
� �0
yC;1
yf;1
MC
Mf
dCf
dt
� �1
dCC
dt
� �2
ZKCCk0;2exp K
�
yCO;1
yf;1
MCO
Mf
dCf
dt
� �1
0
2yCO2 ;1
yf;1
MCO2
Mf
dCf
dt
� �1
yCO2 ;2
yC;2
MCO2
MC
dCC
dt
� �2
yH2 ;4
yf;1
MH2
Mf
dCf
dt
� �1
0
0 yO2 ;2
yC;2
MO2
MC
dCC
dt
� �2
0 0
0 0
become a common tool for assessing the risk of spontaneous
fires in solid bulk materials. Current models differ mainly in
the number of chemical components considered which is
linked to the number of transport equations treated. The
model presented here includes seven chemical species, but
an extension is limited only by computer resources. A
further refinement of the model including the transport of
water as liquid and vapour is currently under development,
see Lohrer et al. (2004).
Acknowledgements
The dust fire modelling project was co-sponsored by
BASF AG, Degussa AG and Vattenfall Europe Mining AG.
This is gratefully acknowledged.
Appendix A. Reaction rates
Reaction 3 Reaction 4
2COCO2/2CO2 2H2CO2/2H2O
0 0
E2
RT
�0 0
dCCO
dt
� �3
ZKCCOk0;3 exp KE3
RT
� �0
yCO2 ;3
yCO;3
MCO2
MCO
dCCO
dt
� �3
0
0 dCH2
dt
� �4
ZKCH2k0;4 exp K
E4
RT
� �
yO2 ;3
yC;3
MO2
MC
dCC
dt
� �3
yO2 ;4
yH2 ;4
MO2
MH2
dCH2
dt
� �4
0 yH2O;4
yH2 ;4
MH2O
MH2
dCH2
dt
� �4
0 0
U. Krause et al. / Journal of Loss Prevention in the Process Industries 19 (2006) 218–226226
Appendix B. Input data for crushed lignite coal
r a Di DHR,f DHR,C DHR,CO DHR,H2
560 kg/m3 1.34!10K7 m2/s 2!10K5 m2/s 2.2035!107 J/kg 2.7!107 J/kg 1.004!107 J/kg 1.588!107 J/kg
k0,1 k0,2 k0,3 k0,4 E1/R E2/R E3/R E4/R
2.357!106 2.44!105 3.981!1014a 3.311!1013a 12 682 8 157 20 600a 23 200a
a Data from Gorner (1991), all other data determined experimentally by the present authors.
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