Wetting-induced ignition in cellulosic materials

Fire Safety Journal 37 (2002) 465–479

Wetting-induced ignition in cellulosic materials

B.F. Graya,*, M.J. Sextona, B. Halliburtonb, C. Macaskilla

aSchool of Mathematics and Statistics, University of Sydney, Sydney 2006, AustraliabSchool of Chemistry, Macquarie University, Sydney 2109, Australia

Received 17 October 2000; received in revised form 16 April 2001; accepted 10 December 2001

Abstract

A mathematical model of the ignition of cellulose is described which includes both the dry

oxidation reaction and also the water-mediated exothermic reaction which is probably

hydrolysis. It also takes account of endothermic evaporation of water inside the porous

material, exothermic condensation of water vapour and transport of water vapour by

diffusion. Appropriate boundary conditions are chosen and the results reported here are

restricted to one spatial dimension, but are time dependent. Experimental data obtained

recently for bagasse (ground extracted sugar cane) are used as input for the model. However, it

is quite likely that the results are of general interest for other cellulose-based materials, many

of which are of considerable commercial importance and many of which are believed to

undergo spontaneous ignition induced by the presence of water or water vapour.

A significant number of experimental observations and conjectures made over a long period

are shown to be predictable and interpretable by use of the model, and good agreement with

experiment occurs where results are available. r 2002 Elsevier Science Ltd. All rights

reserved.

1. Introduction

There have been many instances of combustible materials being ignited bymoisture referred to in the spontaneous combustion literature, mainly involvingcellulose [1–3]. This effect has been attributed to the latent heat of condensation (inthe case of water vapour condensation from a humid atmosphere), heat ofadsorption (wetting) in the case of direct addition of liquid, or indeed both. Theseeffects have been held responsible, without quantitative study, for spontaneous

*Corresponding author. Tel.: +61-02-9449-4156; fax: +61-02-9988-3945.

E-mail address: [email protected] (B.F. Gray).

0379-7112/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 3 7 9 - 7 1 1 2 ( 0 2 ) 0 0 0 0 2 - 4

ignition in coal stacks, grain dust stockpiles, cotton meal stockpiles, cotton bales,linen stacks, dry freshly made chipboard stacks and many other materials. Thegeneral concept, as elaborated in an interesting paper by Back [2], has been that theheat liberated will cause sufficient temperature rise within the material to perturb itover the ‘watershed’ separating subcritical from supercritical behaviour, i.e. it hasbeen conceived as a ‘critical initial value’ [4] problem.As pointed out by Gray and Wake [3] this simple but plausible approach, when

formulated quantitatively, raises many questions, which are not immediatelyobvious. For example, it ignores the fact that the wetted material, although hotteras a result of the perturbation, is now a different material, i.e. its thermal propertieswill all be different. More importantly, the endothermic evaporation of the added

Nomenclature

Constants

E activation energy of dry reaction, 1.08� 105 Jmol�1

Ew activation energy of wet reaction, 6.5� 104 Jmol�1

R universal gas constant, 8.31 Jmol�1K�1

Q exothermicity of dry reaction, 1.7� 107 J kg�1

Z pre-exponential factor of the dry reaction, 2.7� 107m3mol�1 s�1

Qw rb Zw coefficient of the wet reaction, 1.683� 108 Jm3 s�1mol�2

Ze pre-exponential factor of evaporation, 3.41� 104 s�1

Zc pre-exponential factor of condensation, 4.7 s�1

Lv latent heat of vaporization, 42� 103 Jmol�1

k thermal conductivity, 0.5 Jm�1K�1 s�1

DY ; DW diffusivities of water vapour and oxygen resp., 2.5� 10�5m2 s�1

h heat transfer coefficient, 5 Jm�2K�1 s�1

hY ; hW water vapour and oxygen transfer coefficients resp., 5m s�1

mw mass of water, 18� 10�3 kgmol�1

rw density of water, 1� 103 kgm�3

rb density of dry bagasse, 125 kg m�3

cb heat capacity of dry bagasse, 1.4� 103 J kg�1K�1

cw heat capacity of water, 4.19� 103 J kg�1K�1

Ya ambient water vapour concentration, 1.74molm�3

Wa oxygen concentration in air, 8.04molm�3

F moles of O2 consumed per kg of bagasse, 33.33mol kg�1

Variables

p % increase in water contentT temperature, Kt time, sX liquid water, molm�3

Y water vapour, molm�3

W oxygen, molm�3

B.F. Gray et al. / Fire Safety Journal 37 (2002) 465–479466

water will proceed as soon as the perturbation (addition of water) has finished andthis reaction has a significant temperature coefficient and hence stabilizing effect. Itis not at all clear under what conditions the wetted material will becomesupercritical, if any exist at all. Some theoretical work has been carried out on thisproblem by McIntosh et al. [5], where it was shown for an approximate modelwithout spatial variation that a slight change in atmospheric humidity can have amarked effect on the ignition characteristics of a material.Studies on the storage of bagasse (the residue from extracted sugar cane) [6]

showed conclusively that the usual high temperatureFsmall sample basket ignitiontests were not capable of being extrapolated to the practical low temperature-Foccurs in the large size case. In fact, they predicted critical temperatures forthe latter which were of the order of 901C compared with the observed values ofaround 301C. It became clear in that work that below 1001C at least, a water-mediated reaction was taking place. The possibility that this reaction might be ofmicrobial origin was ruled out in follow up work on this project by Dixon [7] whoshowed in carefully controlled experiments that the progress of self-heating in sterileand normal bagasse plies was identical within experimental error. These results havebeen confirmed in our own laboratory-scale calorimetric work to be reportedelsewhere. In the small-scale tests carried out above 1001C rapid drying out of thesample occurred, ruling out the possibility of obtaining information on the wetreaction. The possible effects of a generic water-mediated exothermic reaction andsimultaneous endothermic evaporation in addition to the usual dry high-temperatureoxidation were considered by Gray [8] who showed theoretically that an amazingvariety of behaviour could arise from such systems including oscillatory behaviour,homoclinic bifurcations and up to five steady states for some ranges of parametervalues.This work was generalized by Sisson et al. [9,10] to include spatial variability and

this work led to similar general conclusions of Gray [8] in this more general context.Both studies [8,9] assumed an Arrhenius temperature dependence for the water-

mediated reaction in the absence of more detailed knowledge but more recent studiesof the details of this reaction in the case of bagasse [11,12] have shown this not to bethe case. In fact, the reaction has a fairly sharp cutoff at around 60–701C andquantitative conclusions cannot be drawn without including this feature, although itturns out that the qualitative predictions made in [8,9] still hold.Detailed modelling of the general type carried out by Sisson et al. has now been

performed using the present model and equations, also making direct use of theexperimental data for the bagasse wet reaction [13,14] and the general ignitioncharacteristics of wet bagasse in large stockpiles with critical ambient temperaturesaround 301C have now been obtained satisfactorily using the present model.Here we apply this detailed model, as briefly formulated in the next section, to a

case where a small test pile suffered perturbations such as addition of extraneousliquid water to a partially or wholly dry stockpile, increase in outside relativehumidity (or decrease in outside ambient temperature resulting in condensation), etc.We also show some results where pure temperature perturbations or isothermaladditions of water occur to compare with the general case.

B.F. Gray et al. / Fire Safety Journal 37 (2002) 465–479 467

Although the experimental data used as input to this model are directmeasurements on bagasse, we believe that they will be of generic value for similarsituations for many cellulosic materials such as hay, straw, some grains, woodchippiles, etc.Recent work by Gong et al. [15], which is a continuation and generalization of the

work of Sisson et al. [9,10] addresses the problem of spontaneous ignition in wetlignite. In common with the present paper, they use a multi-variable reaction-diffusion model, but with a quadratic dependence on water concentration and simpleArrhenius dependence on temperature, in contrast with the empirically determinedrate law for bagasse used here that exhibits a local maximum at low temperaturesand linear dependence on liquid water concentration.

2. The mathematical formulation

Consider a one-dimensional pile of thickness w; where the spatial coordinate x isdefined as x½�w=2;w=2�: This is the simplest case that demonstrates the relevantbehaviour and the one with which a comparison can be made with the experimentalresults of Halliburton [11].The model equations in dimensional form describing the time evolution of

temperature T ; liquid and vapour concentrations X and Y and oxygen concentra-tions W are as follows:

ðrbcbþmwXcwÞqT

qt¼QrbZW expð�E=RTÞ þQwrbZwXW expð�Ew=RTÞ f ðTÞ

þ Lv ZcY � ZeX expð�Lv=RTÞ� �

þ kr2T ; ð1Þ

qY

qt¼ ZeX expð�Lv=RTÞ � ZcY þ DYr2Y ; ð2Þ

qX

qt¼ �ZeX expð�Lv=RTÞ þ ZcY ; ð3Þ

qW

qt¼ � FrbZW expð�E=RTÞ � FrbZwXW expð�Ew=RT Þf ðTÞ

þ Dwr2W : ð4Þ

See the nomenclature section for the list of constants. Two reactions, an oxidationreaction and a moisture-dependent reaction, are represented by the first two terms inthe energy equation (1) and also in the equation describing the mass balance for theoxygen concentration W : The function f ðTÞ in the wet reaction terms is defined as

f ðTÞ ¼ ftanh½0:6ð58� T þ 273Þ� þ 1g=2:

This form is an empirical fit to the experimental data obtained in [11], and reflects thepresence of a maximum in the wet heat release curve that occurs between 501C and601C (e.g. see Fig. 8).


Due to the presence of liquid water, the effects of condensation and evaporationmust be included, and these appear in the energy equation as the third and fourthterms, respectively, as well as in the mass balance equations for liquid waterconcentration X and water vapour concentration Y :We allow for the dependence ofthe total heat capacity of the bagasse pile on liquid water concentration X in theterm appearing on the left-hand side of the energy equation. Heat conduction andwater vapour and oxygen diffusion appear as the last terms in their respectiveequations, whereas diffusion of liquid water is assumed to be insignificant.The boundary conditions for this model are as follows:

kqT

qx7hðT � TaÞ ¼ 0 on x ¼ 7w=2; ð5Þ

DY

qY

qx7hY ðY � YaÞ ¼ 0 on x ¼ 7w=2; ð6Þ

DW

qW

qx7hW ðW � WaÞ ¼ 0 on x ¼ 7w=2; ð7Þ

where the ambient water vapour concentration is defined as Ya ¼1:74molm�3� (Relative humidity). The constants h; hY and hW are the transfercoefficients for heat, vapour and oxygen, respectively, and k, DY and DW are thethermal conductivity and vapour and oxygen diffusivity in the bagasse.To solve the system of PDEs with its associated boundary conditions, we will

implement the method of lines where the spatial derivatives are discretizedtransforming the PDEs into a system of ODEs. Due to the nature of these typesof combustion problems, the availability of ODE integrators which can account forstiffness and multiple time scales makes the method of lines an efficient and accuratemethod of solution. We solve for the interior values Tj ; Yj ; Xj and Wj at the spatialpoints xj ¼ jDx; j ¼ 2yn � 1 using a second order spatial discretization for the heatconduction and vapour and oxygen diffusion terms, as well as the boundaryconditions. That is r2T ¼ ðTj�122Tj þ Tjþ1Þ=ðDxÞ2 where Dx ¼ w=ðn � 1Þ; andsimilarly for r2Y and r2W : The boundary values for temperature T are found by

TB ¼ ð4TB�1 � TB�2 þ 2DxhTa=kÞ=ð3þ 2Dxh=kÞ;

where TB is the boundary point and TB�1; TB�2 are the interior points. The boundaryvalues for Y andW are found in the same manner but with appropriate heat transferand diffusion coefficients.The steady-state solution to the system of PDEs is found by setting the time

derivatives to zero. This implies that the steady-state liquid water level is

Xss ¼Zc

ZeexpðLv=RTssÞYa;

which is dependent on the ambient water vapour concentration Ya and the steady-state temperature Tss:To conduct the heat of wetting experiments, the model equations are integrated to

their steady-state values, then a liquid water concentration change DX is added witha corresponding temperature perturbation DT : Call this time tw: Note that the value


of X ð0; t ¼ twÞ depends on the relative humidity, as well as Tss which is spatiallydependent and varies according to other parameters in the model.The temperature perturbation DT is defined as

DT ¼5p

1þ X ð0; twÞ;

where p is the percentage increase in water content.For the calculations reported in later Section 3 we use the mixed boundary

conditions, and for the remaining results, we have Dirchlet boundary conditions,i.e. T ¼ Ta¼ 301C; Y ¼ Ya=(1.74molm

�3)� (Relative humidity) and W ¼ Wa ¼8:04molm�3.

3. The bagasse data and simulation

In experimental work which will be described in detail elsewhere [11,12] a verylarge ‘infinite slab’ of bagasse was constructed measuring approximately 8m�8m� 1.2m standing in a vertical position. It was instrumented with a large numberof thermocouples and moisture sensors enabling the continuous measurement andrecording of temperature, humidity and total moisture profiles as functions of timeand space. The dimensions of the slab ensured that to a very high degree ofapproximation the behaviour was one-dimensional, i.e. the only significant spatialvariation was across the shortest dimension (1.2m) of the slab.The material, straight from the mill, contained 50% moisture (on a wet weight

basis) and was at a temperature of approximately 501C. Initially, the temperaturerose quite quickly (not visible in Fig. 1) to a maximum peak then dropped to a quasi-

Fig. 1. Observed temperature traces in 1.2m� 8.0m� 8.0m bagasse slab across a section.


steady value which remained almost constant for many months. This behaviour isshown in Fig. 1.The relatively rapid drop in temperature to slightly above ambient (which was in

the region of 301C for most of the test) occurring after some months represents an‘extinction bifurcation’ caused by a drop in wet reaction rate due to water loss bydiffusion and evaporation.The small temperature rise occurring after approximately 400 days coincides with

a heavy wetting by a sizeable rainstorm. The large temperature rise back to theoriginal ‘quasi-steady’ state occurring after approximately 450 days was due toextreme wetting by a tropical storm which increased the water content sufficiently tocause transition back to the thermally active state of the slab of material. Thistemperature rise represents a reversal of the ‘extinction bifurcation’ which arose dueto gradual drying out of the pile in the first instance. The fact that the ‘active state’persisted for a much shorter period probably indicates that the water content wasless than the original.If these qualitative interpretations are correct it should be possible to simulate

them using the model elaborated in the previous section.This has been done with good agreement with the observed results.Fig. 2 shows the temperature history at the centre of the slab (where the

temperature is a maximum) as calculated by the model with a constant ambienttemperature of 301C and an initial water content of 50% and an initial temperaturefor the bagasse of 551C which was assumed to be spatially uniform as was the caseexperimentally.The system was left to evolve for 500 days by which stage the system had reached a

quasi-steady state with centre temperature of 371C and water content (at the centre)

0 200 400 600 800 100035

40

45

50

55

60

Time (days)

Cen

tre

tem

pera

ture

(o C

)

Fig. 2. Centre temperature of a bagasse slab. At 500 days, a percentage of the initial liquid water level is

added: 10% (dashed) and 70% (solid).


of 23% w/w. At this time a perturbation of 10% of the initial value of water wasadded uniformly to the system, with no direct temperature perturbation. The reasonfor the latter is that the heat of wetting of cellulose is a differential quantity whichdeclines towards zero for initial amounts of water approaching 20% [2]. There is asmall temperature rise of a few degrees gradually declining back to the stable steadystate. This bears a strong resemblance to the observed perturbation shown in Fig. 1after 410 days.In Fig. 2 we also show the effect of a much larger (but still isothermal)

perturbation of the system by the addition of 70% of the initial value of wateruniformly distributed throughout the system, again after around 500 days. In thiscase the system jumps back to the original quasi-steady state in which it had been forthe first 200 days or so (before the extinction bifurcation due to drying out).Subsequently, the drying out process repeats itself and the extinction bifurcation

occurs again, as before. These perturbation computer experiments are a rather goodrepresentation of the observed behaviour, particularly when Fig. 3 is taken intoaccount.Fig. 3 shows the time-dependent behaviour of the liquid water concentration at

the centre of the slab, where in fact it displays a spatial minimum (bothexperimentally and theoretically). Since the water sampling at the centre of thepile required the taking of core samples, this was only done at a small number oftimes, but was done for a number of positions across the pile. This showed aminimum at the centre each time but did not provide enough data for a full historyplot.The above observations show the transition from an almost inactive stable quasi-

steady state (with only a few degrees of self-heating above ambient) to a more

Fig. 3. Central liquid water percentage of a bagasse slab. At 500 days, a percentage of the initial liquid

water is added: 10% (dashed), 70% (solid).


reactive, intermediate quasi-steady state showing rather more reaction and self-heating of about 30–351 above ambient temperature. The upward transition occursas a result of the isothermal addition of water and the downward transition(extinction of the intermediate steady state) as a result of the gradual drying out andconsequent quenching of the water mediated reaction.The water loss occurs directly as a result of evaporation, diffusion of water vapour

towards the pile edges, followed by loss to the atmosphere. Throughout thesimulations the relative humidity was maintained at a constant 70%, very similar tothe experimental conditions in Mackay, North Queensland, where the experimentalwork was carried out.In Fig. 4 we show the effect of isothermal addition of liquid water to a pile under

conditions where transition to the ignited state can occur, i.e. thermal runaway. Inthis case the intermediate state with self-heating of 351 (commonly observed inbagasse piles) is by-passed and the low activity state is converted directly to ignition.In this case we started with a relative humidity of only 5% and a higher ambient

temperature of 451C. The pile had a width of 3.75m and settled into a steady statewith 81 self heating. The addition of 33.3% liquid water isothermally resulted in onlya transient response, but the addition of 77.8% liquid water isothermally resulted inignition. This is a conservative estimate of this effect as at the low percentage ofliquid water present at the time of the perturbation a significant heat of wettingwould also be present. Such effects will be discussed more fully in a later section.Although the conditions of the experimental pile were such that it did not ignite,

we believe that our ability to provide a reasonable simulation of what did happenlends weight to our simulation of direct ignition of a pile under different (and notunreasonable) conditions.

0 200 400 600 800 100045

50

55

60

65

70

Time (days)

Cen

tre

tem

pera

ture

(o C

)

Fig. 4. Effect of addition of liquid water for a bagasse slab of 3.75m and ambient temperature 451C:

33.3% (dashed) and 77.8% (solid).


4. Ignition by humidity change

Back [2] has commented on the possibility of ignition by condensation of watervapour resulting from a relatively rapid increase in relative humidity. He commentsspecifically on bales of cotton coming from a dry climate igniting when stored in ahumid harbour climate. He also refers to the spontaneous ignition of freshlyproduced (hence warm and dry) insulating board as well as freshly made cardboardand particle board.An increase in humidity can result in energy release by virtue of both the latent

heat of condensation and any heat of wetting or absorption. However, in the presentmodel it can also increase the rate of heat release by the water-mediated reaction.The mechanism by which this occurs is basically that evaporation of liquid water isslowed by the increased vapour pressure of water vapour with a resultant increase inwater content.We have calculated a series of steady-state curves of centre temperature versus slab

width at various external humidities ranging from 0% to 100%, all at an ambienttemperature of 300C. These are shown in Fig. 5.This diagram has many interesting features. Firstly, we note that for any given

relative humidity there is a maximum pile width above which no low-temperaturestable state exists, i.e. ignition will occur.This maximum possible width is represented by the turning point on each of the

curves. The lower branches of the curves are stable (solid lines) and the upperbranches unstable (dashed lines). The unstable steady states, crudely speaking act as‘watersheds’ separating ignition from non-ignition for pile temperature. Thus forexample, a 5m wide pile, for any humidity, will ignite if it is built of material hotter

0 2 4 6 8 10

30

40

50

60

70

80

90

100

Width (m)

Cen

tre

tem

pera

ture

(o C

)

100% 70%

50% 20% 10% 5%

0%

Fig. 5. Steady-state bifurcation diagrams with ambient temperature of 301C for various relative

humidities.


than 751C but a 2m wide pile would cool down if constructed of material at thistemperature.A 6m pile, if constructed of material cooler than 551C would cool down to near

ambient temperature in external relative humidity of 0%, 5% and 10%. However,for relative humidity of 20% and higher there would be no stable low-temperaturesteady state for this pile and ignition would occur. Similarly, if a pile were to beconstructed in a very low humidity environment it would exist in a stable conditionon the lower branch of the curve but an increase of relative humidity at constanttemperature to anything greater than 20% would result in ignition.The dashed curve linking the turning points of the bifurcation curves for 0%, 5%,

10% and 20% is a continuous development from the completely dry bifurcationpoint at nearly 9m width. In this case there is only the dry oxidation reaction takingplace and producing heat. We can think of the wet reaction being a perturbation ofthis up to 20% relative humidity. However, the dashed curve linking the turningpoints on the curves for relative humidities 20%, 50%, 70% and 100% is notcontinuously linked to the former as shown by the discontinuous curves in Fig. 6.For the higher relative humidities the ignition point (the turning point on the

curve) represents a qualitatively different phenomenon from dry ignition. The stablesteady state which ceases to exist at the bifurcation is the ‘active state’ referred to inan earlier section. It is represented by the flattened part of the curves in Fig. 5 forrelative humidities 50–100%. The centre temperature in this case is about 601C, i.e.of the order of 30 degrees above ambient temperature. These figures are notparticularly sensitive to input parameters such as density, conductivity, diffusivity,etc. and thus have a generic significance. It can safely be said that for cellulosicmaterials exhibiting a heat release curve similar to that measured for bagasse,ignition by a ‘dry’ mechanism will be related to a stable subcritical state showing

4 5 6 7 8 9 10 11 1235

40

45

50

55

60

65

Width (m)

Cen

tre

tem

pera

ture

(o C

)

Fig. 6. Turning points of steady-state bifurcation curves shown in Fig. 5.


only a few degrees of self-heating. On the other hand, ignition by a ‘wet’ mechanismis related to stable subcritical behaviour showing the order of 30–351 self-heating.This has been known for a long time in the sugar industry, but not properlyunderstood or quantified in this way. The ‘rule of thumb’ in North Queensland haslong been ‘‘If it gets above 701C it is going to ignite!’’ Ambient temperatures of 30–351C year round are common so self-heating of 301 has been recognized empiricallyas stable non-ignition behaviour, in accord with our calculations.The simplest interpretation of humidity-induced ignition is to observe that (in

Fig. 5) the bifurcation curve moves to the left as humidity increases and when theturning point passes to a value smaller than the actual width of the pile no stablesteady state exists and ignition occurs. The physical mechanisms of condensation,wetting, etc. are built into the bifurcation diagram in the calculation of the positionand nature (stable or unstable) of the steady states occurring, and most importantlywhen they bifurcate and consequently cease to exist.

5. Ignition by direct wetting

We can also use this model to study the effects of addition of liquid water directlyto the pile, in contrast to condensation from the vapour phase as in the previoussection. As an example we will take an ambient temperature of 301C, relativehumidities of 20%, 70% and 100%. We consider a pile with an initial temperature of301C and integrate the differential equations until a stable steady state is reached(obviously, we have to choose the other parameters so that one does exist before theperturbation). Since we are adding liquid water in this case the latent heat is notrelevant but any heat of wetting is. Back [2] gives a graphical dependence of thisquantity on water content for cotton. His figures show for that case that the heat ofwetting drops off quite rapidly with initial water content. We have followed thisempirical approach and assumed the relationship

DT ¼5p

1þ X ð0; twÞ

between temperature rise and water content at the time of the perturbation. Thisequation determines the relationship between the two components of theperturbation applied, i.e. the water content increase and the (assumed simultaneous)corresponding temperature increase. For convenience we also assume that these twoperturbations are spatially homogeneous, but the results are not at all sensitive tothis.For the humidity values mentioned above we have integrated the differential

equations to steady state and then applied the perturbation repeatedly until a criticalperturbation was determined, i.e. the smallest one which produced ignition. This hasbeen done for a series of pile sizes (widths) and the results are shown in Fig. 7.The apparent irregularities in these curves arise as a direct result of the shapes of

the bifurcation curves in Fig. 5. In this figure we have plotted temperature rise as ameasure of the perturbation but the relation given above shows that we could


equally well have used amount of water added or some arbitrary combination of thetwo as a suitable norm. The physical interpretation is straightforward, for examplethe 0% humidity case for an 8m pile requires only sufficient water addition to raisethe temperature by around 101. This case is clearly sensitive to water addition as onewould expect. On the other hand, in 70% relative humidity the existence of stablesteady states for piles wider than 3.5m is highly questionable and addition of extrawater is not very significant as evidenced by the very steep curve for this case.Since we are using a model which involves a low-temperature exothermic wet

reaction it is of some interest to examine how much of the effect shown in Fig. 7 isdue to increased reaction rate, due to water concentration and how much of it is dueto the temperature increase associated with the wetting. Accordingly, we haverepeated the computer experiments with perturbations consisting of a temperaturerise only, other conditions being identical with the previous runs. These com-putations show that the non-thermal component of each perturbation is negligible.We can safely conclude that dropping the wet reaction term would give rather similarresults to the above and such ‘wetting-induced ignition’ can occur even in theabsence of the wet reaction.Basically, this is a question of sensitivity of the heat release rate to the two

independent variables, moisture concentration and temperature. The sensitivity withrespect to temperature is much the larger of the two.Fig. 8 shows a number of heat generation curves as functions of reactant

temperature for various (constant) water contents corresponding to equilibrium withvarious values of relative humidity as shown in the figure.Reference to Figs. 5 and 6 reveals the existence of two distinct series of fold

bifurcations over a limited relative humidity range. This is easily interpreted in termsof Fig. 8 from which it can be seen that a necessary condition for such a range is the

0 2 4 6 8 100

20

40

60

80

100

120

Tem

pera

ture

per

turb

atio

n (

C

o

)

Width (m)

RH = 0%

RH = 70%

RH = 0%

RH = 70% RH = 20%

Fig. 7. Water-dependent temperature perturbation for relative humidities 0%, 70% and 100%.


existence of two turning points (local maximum and local minimum) in the heatrelease curve. These disappear below 18% relative humidity.

6. Conclusions

We have formulated and numerically integrated a reaction diffusion modelincluding experimentally measured water-mediated exothermic reaction, dryoxidative exothermic reaction, endothermic water evaporation, exothermic watervapour condensation, water vapour diffusion, heat conduction and appropriateboundary conditions for water vapour and temperature.This model was originally formulated to describe the behaviour of large piles of

bagasse and to provide a means of studying the optimization of water loss from thepile in order to increase its calorific value for electricity production.We have shown that this model is capable of describing a wide variety of effects

involving addition of liquid water, water vapour or both with correspondingtemperature increases arising from condensation and wetting (adsorption).We have shown that addition of liquid water to a pile in a stable steady-state

condition can cause ignition.We have shown that increasing relative humidity outside the pile can cause

ignition of a pile in a stable steady state already attained by exposure to a lowerexternal relative humidity.Although these calculations use input obtained by direct experiment on bagasse,

we believe they may be of generic significance for the possible occurrence ofspontaneous ignition induced by interaction of water or water vapour. This may be

10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Centre temperature ( o C)

Hea

t gen

erat

ion

rate

RH = 100%

RH = 0%

Fig. 8. Dimensionless heat generation rate (dry+wet reaction terms) at equilibrium for relative humidities

0%, 5%, 10%, 20%, 50%, 70% and 100%.


of significance for other commercially important bodies such as cotton bales,woodchip piles, peat stacks, haystacks, chipboard and particle board, brown coal,lignite and other materials.

Acknowledgements

The authors wish to thank the Australian Research Council and the SugarResearch Institute, Mackay, Queensland for the award of a SPIRT collaborativeresearch grant and a graduate scholarship to B.H.

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Wetting-induced ignition in cellulosic materials