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: ulrich.krause@bam.de (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

www.elsevier.com/locate/jlp

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, von

Neumann, Newtonian cooling) can be considered. In

addition, the boundary conditions may vary in space and

time.

†

The dependence of the temperature evolution with time

can 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 the

chemical species of interest and their evolution with

time.

†

Kinetic and diffusion-controlled reaction regimes may be

considered.

The input that has to be provided to the model covers

†

material properties like thermal conductivity, specific

heat capacity, porosity or bulk density, diffusion

coefficients and the calorific value,

†

data on chemical kinetics like the apparent activation

energies and the pre-exponential factors in the Arrhenius

equations (see below) representing the different reaction

steps under consideration.

†

stoichiometric data including the elemental composition

of 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 a

homogeneous and isotropic body (locally uniform

thermal transport coefficients),

†

the influences of moisture and particle size distribution

are not considered,

†

the thermal conductivity and the diffusion coefficients do

not 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 due

to 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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