spontaneous ignition in storage and production lines: investigation on wood pellets and protein...

FIRE AND MATERIALSFire Mater. 2007; 31:477–494Published online 23 May 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fam.945

Spontaneous ignition in storage and production lines: Investigationon wood pellets and protein powders

Martin Ankjer Pauner∗,† and Henrik Bygbjerg

Danish Institute of Fire and Security Technology, Jernholmen 12, DK-2650 Hvidovre, Denmark

SUMMARY

Three materials were tested in small-scale baskets of cubic dimensions and analyses were performed basedupon the results according to the Frank-Kamenetskii (FK) method and the crossing point (CP) method.Comparison of the FK method and the CP method results was performed additionally. The activationenergy E and the QA value were found. The relationship between critical ambient temperature and thestorage size was determined as well as the relationship between CAT and time to maximum thermalrunaway for the materials. Copyright q 2007 John Wiley & Sons, Ltd.

Received 1 June 2005; Revised 1 November 2006; Accepted 1 November 2006

KEY WORDS: small scale basket test; critical ambient temperature; thermal runaway; activation energy;Frank-Kamenetskii; crossing point method; spontaneous ignition, self-heating; woodpellets, protein powders

SCOPE

The purpose of the investigation was to find the behaviour of different materials with regard toigniting spontaneously and to investigate the usefulness of two general known methods i.e. theFrank-Kamenetskii (FK) method [1–3] and the crossing point (CP) method [4–6]. The underlyingresults are described in six reports issued by the Danish Institute of Fire and Security Technology(DBI) [7–12]. In three reports the results of the small-scale tests were compared to observationsHamlet Protein A/S, a producer of protein powders for the animal food industry, did during anincident in their drying process filter. In three reports the results of small-scale test were carriedout for wood pellets.

∗Correspondence to: Martin Ankjer Pauner, Danish Institute of Fire and Security Technology, Jernholmen 12,DK-2650 Hvidovre, Denmark.

†E-mail: [email protected], www.dbi-net.dk

Copyright q 2007 John Wiley & Sons, Ltd.

478 M. A. PAUNER AND H. BYGBJERG

FRANK-KAMENETSKII THEORY

Spontaneous ignition can occur under different conditions, initiated by chemical, physical orbiological activity inside a stored quantity of organic material. For these reactions or activities todevelop into a condition of self-ignition, they have to be exothermic in nature.

Whatever the source of self-ignition, at least three additional factors control the chain of events:

• The dimensions of the stored material.• The ambient temperature.• The heat conduction through the material.

These three factors interact and can in specific cases lead to unstable self-heating, thermal runawayand self-ignition.

For example, if the heat generation rate of a given reaction inside the material exceeds thecooling rate of the material, the temperature will rise inside the material, leading to an increasedreaction rate. This can eventually lead to thermal runaway and to self-ignition.

The investigations of the properties of the selected protein powders and wood pellets is basedon the FK theory.

FK considered the energy equation for a slab:

�CP�T�t

= ��2T�x2

+ q ′ (1)

where � is the bulk density of the material (kg/m3), CP is the specific heat capacity of the bulkmaterial (J/(kgK)), T is the temperature (K), t is the time (s), � is the thermal conductivity ofthe material (W/(mK)), x is the length (m) and q ′ is the heat generation rate per unit volume(J/(sm3)) and found a stationary solution of the energy equation, where the left-hand side of theequation (the rate of enthalpy change) is negligible, i.e. one gets a time-independent assumptionof the energy equation:

q ′ =−��2T�x2

(2)

The FK theory assumes that the heat generation inside a body follows an Arrhenius model:

q ′ = Q�Ae−E/RT (3)

where Q is the heat of reaction (kJ/g), A is the pre-exponential factor (s−1), E is the apparentactivation energy (J/mol) and R is the universal gas constant (= 8.314 J/mol/K).

From the stationary solution of the heat transfer equation for an infinite slap geometry, FKdeveloped the following expression, where the non-dimensional heat generation rate is found:

� = �QA

�

Er2

RT 20

e−E/RT0 (4)

where � is the dimensionless parameter, r is the characteristic length of the given body (the halfside length for cubes) (m) and T0 is the ambient temperature (K).

Each geometry, cube, sphere or cylinder, has its own critical value denoted with an index ‘C’(when �>�C), at which the material becomes unstable and self-ignites.

Copyright q 2007 John Wiley & Sons, Ltd. Fire Mater. 2007; 31:477–494DOI: 10.1002/fam

SPONTANEOUS IGNITION IN STORAGE AND PRODUCTION LINES 479

�C states the critical condition in relation to the heat balance of a reaction in a combustiblematerial with a given geometry. �C is often called the Damkohler number [3].

When � exceeds �C, the rate of the exothermal reaction exceeds the rate of heat loss inside thematerial, leading to an inevitable self-ignition.

�C is derived for a number of simple geometries, with different thermal boundary conditions.�C is independent of the properties of the actual reaction of the combustible material [13].

The model is based on a number of assumptions:

• The material is homogeneous and isotropic with regard to chemical and thermal properties.• That only one exothermal reaction governs heat generation.• The activation energy is so high that the condition E/R · T � 1 is true.• Heat transfer through the body is by conduction alone.• The Biot number, which is defined as hr/� (where h is the effective surface heat-transfercoefficient), is sufficiently high that the surface of the body is equal to the ambient temperature.

The assumed boundary conditions for the FK method, with its significant cooling of the surfaceby convection and by radiation, have a high Biot number. A low Biot number (Biot→ 0) signifiesalmost no heat transport from the surface compared to heat conduction in the sample, while a highBiot number (Biot→ ∞) signifies the opposite. The critical value of �, �C for cube when (Biotnumber→ ∞) is 2.52. �C decreases when the Biot number decreases.

Estimates of the Biot number require knowledge of the thermal conductivity of the materialsover a wide range of temperatures as well as the possibility of calculating convective heat transferfrom the sample.

Furthermore, mathematical models of geometries such as hollow cylinders of infinite length,cones and rectangular boxes have been modelled [14–16]. No-references have been found thatempirically verify these general models.

The FK method used is based on Equation (4) for determining �, which can be rewritten as

ln(�C) + 2 ln

(T0r

)= P − E

RT0(5)

where

P = ln

(E

R�QA

�

)

Results from small-scale tests can be plotted with ln(�C)+2 ln(T0/r) on the y-axis against 1/T0 onthe x-axis, with P as the intersection node on the y-axis and −E/R as the gradient on the graph.

Based on the straight regression line for the plotted nodes, critical ambient temperature (CAT)can be estimated for larger sample dimensions or other sample dimensions like cones or pyramidsby rearranging Equation (5):

r =√

�CRT 20 �

EQA�eE/RT0 (6)



CROSSING-POINT (CP) METHOD

The CP method has mainly been used as an easy experimental way to determine E and QA andnot in itself as a self-ignition predicting tool. Though, the CP method can implicitly find CAT fora given size.

Instead of the steady-state solution by the FK method, the CP method looks at the non-steadysolution of the energy equation (1). The assumption is that if two temperatures are measured ina symmetric object, like a cube; one in the centre and one off-centre, then, when they becomeidentical, by definition, no heat is being transferred between the two locations within the cube[4–6, 17–19]. When there are no space-wise temperature gradients the conduction term is zeroand the leftover is obtained from the one-dimensional heat transfer equation:

�CPdT

dt

∣∣∣∣P

= �QAe−E/RTP (7)

where subscript P denotes the condition at the centre of the sample.The above equation is only valid when a symmetrical geometry has a flat temperature profile.

Performing several tests at different oven temperatures make it possible to obtain pairs of datapoints of crossing point temperatures in the centre (TP) versus the temperature gradients dT/dt

ln

(dT

dt

∣∣∣∣P

)= ln

(QA

CP

)− E

RTP(8)

When plotting 1/TP and ln(dTP/dt) from the above relation a straight line is obtained very similarto the straight line in the FK theory. The slope is the same as in the FK theory—E/R, while they-axis interception is ln(QA/CP).The benefit of the CP method is that it is independent of the basket size [4], as no size appears

in Equation (8).To use the CP method for predicting purposes a conversion back to the FK method is done by

using the obtained QA and E value according to FK theory in Equation (6) [3, 19]:

r =√

�C�T 20 CP R

QAE�eE/RT (9)

Knowledge, however, of CP and � of the material tested has to be known in order to make a goodprediction of CAT for a given size. Furthermore, the �C number has to be introduced.

A weak point is that a crossing point between the centre temperature and an off-centre temper-ature assumes that the temperature profile inside the material is flat, but that is not necessarily thecase. Thereby a significant error may be introduced in the calculation.

METHOD

Basket tests are conducted in isothermal test condition in various steel mesh cube baskets of sidelength 50, 100, 150, 200 and 300 mm. The test procedure was as follows:

• The basket was packed with the material until the bulk density was equal to the establishedbulk density of the material.



Figure 1. Hollander mesh.

2r½ r

T½

TcTOven

½ r½ r

Figure 2. Position of thermocouples.

• The basket was placed in the centre of the cold oven. The basket was placed on steel 4supporters to enable airflow around the basket on all sides.

• Position the thermocouples.• Start the oven on the set temperature.• All tests conducted were used for both FK and CP analysis, as long as there was a measured

crossing point temperature.• For every new test, fresh material was used.• The number of tests conducted for each cube dimension varied from 2 to 5. In general, if an

accurate CAT value (<± 1K) was found for a material at a given cube dimension no furthertesting on that dimension was performed.

THE OVEN

A computer-controlled forced ventilated oven was used in all tests.Oven: Blue M.Model: CW-6680-FY-MP550.Manufactured by Lunaire International, PA, U.S.A.The internal volume of the oven is approximately 120 l. The oven is equipped with a 25× 25cm

window for monitoring tests. The oven temperature can be controlled up to approximately 700◦C



T TC Space

Temp.Temp.

SpaceTCTOven

Figure 3. Left diagram shows temperature profile and crossing points of TOven and TC and the rightdiagram shows temperature profile and crossing points of T1/2 and TC.

Table I. Critical ambient temperature (CAT) from experimentsaccording to the Frank-Kamenetskii theory.

CAT (K)

Cube (mm) HP100 HP500 6 mm wood pellets

50 438.5 ± 0.6 423∗ 464.8 ± 0.6100 422.6 ± 0.5 393∗ 439.6 ± 0.6150 412.4 ± 0.5 353∗ 427.7 ± 0.5200 403.3 ± 0.5 333∗ 414.4 ± 0.5300 — — 402.0 ± 0.9

—, not tested.∗Value shows only the lowest found ambient temperature whereself-ignition occurs. Value is not actual CAT value.

with a set point precision of 0.01◦C in the range of 0–280◦C. The temperature can be controlledby up to 300 temperature points.

TEST CONTAINERS

Test containers were specially fabricated for the project. They were as follows: five cubic steelcontainers made of Hollander mesh with side lengths of: 50, 100, 150, 200 and 300 mm. In testsituations the open top side of the cube is covered with a lid of the same mesh material as the cubeitself. The mesh was manufactured by Croft Engineering Services, Warrington, U.K. The ratio ofwarp and weft wires in the mesh is 24/100 per inch. According to the manufacturer the mesh hasa theoretical porosity of 49% and rated 80 micron nominal (micron size that will pass through themesh in this case is 112–125 �m absolute) see Figure 1.



0 50 100 150 200 250 300 350 400 450 500200

300

400

500

600

700

800

900

1000

Time [hours]

Tem

per

atu

re [

K]

T½ of 200 mm cube

TC of 200 mm cube

TOven 333K

Figure 4. Temperature versus time for the HP500 sample.

TEMPERATURE MEASUREMENTS

A J-type thermocouple with a 3-mm thick mantle was used for monitoring the oven temperature.For other temperature measurements, K-type thermocouple with a 1-mm mantle was used. Thethermocouples were reused in every test.

POSITIONS OF THERMAL COUPLES

An oven temperature (TOven), a centre temperature (TC) and a temperature measurement (T1/2)positioned at a distance of a quarter of the side length to the edge in all three dimensions weremonitored and recorded in every test. See Figure 2. The TC and T1/2 were inserted from thetop side through holes in the lid and stayed in position by the friction between the hole andthe thermocouple wire. Although this may not sound as a robust solution it worked in all testsbut one.

MEASURED PARAMETERS

CP temperatures and temperature gradients were measured when TC crosses TOven or when TCcrosses T1/2 (the two different CP methods are described by Jones [6] (the ‘HR Method’) and byChen [4], respectively). See principle drawing in Figure 3.



2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

x 10-3

16

16.5

17

17.5

18

18.5

19

19.5

20

20.5

21

1/CAT [1/K]

ln(2

.52)

+2*l

n(C

AT

/r)

[2ln

(K/m

)]

Self ignition data of HP500slope of data y=-4800*1/CAT+31.5Self ignition data of HP100slope of data y=-14900*1/CAT+54.368Self ignition data of 6 mm wood pelletsslope of data y=-11459*1/CAT+45.172

Figure 5. Frank-Kamenetskii (FK) analysis of the three materials. (CAT= critical ambienttemperature, r = half side length of cube).

Table II. Found E and QA values by the Frank-Kamenetskii method.

Material Apparent activation energy E (kJ/mol) QA (W/kg)

HP100 124 4.4 E15∗HP500 ∼ 40 ∼ 1.6 E6∗∗6 mm wood pellets 93 1.0 E12∗∗∗

∗Found �= 0.10 W/(mK), �= 630 kg/m3, CP = 1.0 kJ/(kgK).∗∗Found �= 0.08 W/(mK), �= 500 kg/m3, CP = 1.0 kJ/(kgK).∗∗∗Found �= 0.17 W/(mK), �= 603 kg/m3, CP = 2.2 kJ/(kgK).

The resulting CAT for each basket size was calculated in this way: CAT=CATc/2+ nCATc/2,where CATc is the lowest CAT measured and nCATc is the highest ambient temperature measuredwhere self-ignition did not occur.

Time to maximum thermal runaway (TMTR) is defined as when the maximum temperaturegradient of TC occurs.



10-1 100 101 102 103

280

300

320

340

360

380

400

420

440

460

Storage size, side length [log(m)]

CA

T [

K]

Ignition Data of HP500Best fit HP500Ignition Data of HP100Best fit HP100Ignition Data of 6 mm wood pelletBest fit 6 mm wood pellet

Figure 6. Critical curves for storage size for the three materials (CAT= critical ambient temperature).

SAMPLES

Three materials were tested: two different protein powders were provided by Hamlet Protein A/Sand 1 type of wood pellets by SABI Pellets AB provided by the University of Lund. The HP100:a protein powder with a fat content of 2.5% [20] and with grain size: 99% <63 �m. The bulkdensity was determined to be 633 kg/m3, while the moisture content was determined as 10.2% ofthe dry weight. The energy of HP100 is set to 3066 kcal/kg which is about 12.9 MJ/kg.

The HP500: a protein powder, not yet commercialized by Hamlet Protein A/S but underdevelopment, has a fat content of approximately 22% and with coarser grain size: 30%<200 �m.The bulk density was 501 kg/m3, while the moisture content was determined to 5.0% of the dryweight.

The 6 mm wood pellets: cylindrical-shaped wood pieces with a diameter of 6 mm and with abulk density of 603kg/m3 and moisture content was determined to be 8.1% of the dry weight. Thepellets have a guaranteed combustion energy that amounts to approximately 4.9 kWh/kg whichis 17.6 MJ/kg.

FRANK-KAMENETSKII RESULTS

Table I shows the main results of the about 40 conducted baskets tests. For the low-fat proteinpowder HP100 and for the 6mm, wood pellets, a CAT value for each baskets size could be found



10-1 100 101 102 103 104

280

300

320

340

360

380

400

420

440

460

480

T [

K]

Time to maximum thermal runaway [log(days)]

Ignition Data of HP500Best fit HP500Ignition Data of HP100Best fit HP100Ignition Data of 6 mm wood pelletsBest fit 6 mm wood pellets

50 mm cube 100 mm cube

150 mm cube 200 mm cube

300 mm cube

Figure 7. Time to maximum thermal runaway (TMTR) at performed oven temperature levels.

within a narrow interval of approximately ±0.6 K. It is a different case with HP500. For HP500,CAT could not established within the time budget of the project for the main reason that timeto ignition for this product is considerably longer than for the two other products. The reasonto this is probably due to protective anti-oxidants [21, 22] in HP500 which prolong the time toself-ignition until a certain point where all anti-oxidants are depleted and oxidation processes ofthe fat can commence. In Figure 4 an example of this phenomenon is shown by the long phase ofmore than 300 h of steady-state condition where not even a slight self-heating is present. Anotherimportant feature of HP500 is that self-ignition is ambiguous and very difficult to differentiatefrom self-heating. Therefore, the values in Table I of HP500 are not real CAT values, but onlysingle ambient temperature values, where self-ignition occurs.

With the values of Table I, a FK-plot is shown in Figure 5. It is assumed for all cubes that �Cis 2.52—that is the theoretical value of a cube found by FK [1] (when the Biot number→ ∞).No correction of the �C has been attempted for varying Biot numbers of the individual cubes. Asmentioned before it is only for HP100 and the 6 mm wood pellets that a rigid analysis can beperformed. The graph of HP500 can only, based on the ignition data, be considered indicative.

Table II shows the derived results from the slopes of Figure 5. The QA values of HP100 andHP500 are found by the following assumptions; the specific heat capacity C is 1 kJ/(kgK) (usedin the CP method), and the heat conductivity � is function of the bulk density � with the followingrelation � = 1.6× 10−4� [23], although this relation was developed for non-granular cellulosicand lignocellulosic materials for bulk densities between 300 and 1100 kg/m3. The values of



2.25 2.3 2.35 2.4 2.45 2.5 2.55

x 10-3

-8.5

-8

-7.5

-7

-6.5

-6

-5.5

-5

-4.5

-4

Tem

per

atu

re g

row

th [

ln(K

/s)]

1/Tp [1/K]

CP data of Tc and T½Slope CP data of Tc and T½ (y=-13168*x+25.017)

CP data of Tc and TOven

Slope CP data of Tc and TOven

(y=-12884*x+24.540)

Figure 8. Crossing point (CP) results of HP100 (TP = temperature of TC at CP).

� = 0.17 W/(mK) and C= 2.2 kJ/(kgK) for the 6 mm wood pellets are taken from test resultsconducted at 23◦C and performed at the Swedish National Testing and Research Institute [24].

Figure 6 depicts, based on the FK analysis, the CAT at a given storage size of cubic dimensions.The curves are extrapolated to larger dimensions. The shaded area in Figure 6 depicts extrapolationsthat are more than one decade larger to the nearest data point. This area is therefore in general termsuncertain and should not be used as a criterion for engineering purposes. Not only is it unreliableto use these data due to the gross error at high extrapolations, but also because the knowledge ofother biological and bacterial reaction is unknown at these low-temperature levels. The predictionof CAT of a 1m3 size cube would be according to the analysis approx. 370K or just below 100◦Cfor both HP100 and the 6 mm wood pellets, where the curves intersect. As mentioned before foruncertain analysis of HP500, a CAT at normal room temperature would seemingly self-ignite acubic body of HP500 at a size of mere 125 dm3.

TMTR is another parameter that can be extracted from isothermal basket test data. Time to self-ignition can be difficult to determine experimentally because flames and smouldering combustionare hard to detect. Instead, TMTR can easily be found from the temperature curves given inFigure 4 and is assumed equal to time to self-ignition. TMTR is extracted by finding the steepesttangent to the temperature curve of the centre temperature. Figure 7 shows, if thermal runawayoccurs in tests, TMTR at different tested oven temperature levels for the three materials. Best fitsare found for the three data set point and extrapolated to lower temperature regions. TMTR datafrom HP100 and the 6mm wood pellets were extracted from tests where samples are self-ignited.



2.1 2.2 2.3 2.4 2.5

x 10-3

-7.5

-7

-6.5

-6

-

-5

-4.5

-4

-3.5

-3

Tem

per

atu

re g

row

th [

ln(K

/s)]

1/Tp [1/K]

CP data of Tc and T½

Slope CP data of Tc and T½

(y=-9153.6*x+15.496)

CP data of Tc and Toven

Slope CP data of Tc and TOven

(y=-9393.7*x+16.208)

5.5

Figure 9. Crossing point (CP) results of 6 mm wood pellets (TP = temperature of TC at CP).

TMTR data of HP500 were extracted both from tests with self-ignition, but also from samples thatshowed a distinctive self-heating, but at the end never self-ignited.

Although HP500 has a certain amount of protection from possible anti-oxidants it can be seenthat the TMTR is significantly lower at a given ambient temperature—in fact TMTR seems tooccur about one time decade faster for HP500 than for the two other materials. The shaded area inFigure 7 is, like in Figure 6, extrapolations that are more than one decade higher than the nearestdata point.

CROSSING POINT RESULTS

Along with the FK analysis, a CP analysis is made for each product. Figures 8–10 show, for thethree materials, the plotting of the crossing point data of TC and TOven (Figure 3, left drawing) andof the crossing point data of TC and T1/2 (Figure 3, right drawing). The crossing points shouldideally be lying on a straight line, but all three materials show a considerable scatter. The bestresult with least scatter is the CP data of TC and TOven for the 6mm wood pellets, while the scatterof CP data of TC and T1/2 is more severe. Logically this can be explained by the fact that thepositioning error in every test is only critical for TC and T1/2 that both have to be replaced aftereach test, while TOven stays in the same position in every test. Therefore, systematically error mustbe higher for CP data of TC and T1/2. However, this is not true for HP100, where the scatter ismore or less the same between the two CP set-ups. Only a few tests with HP500 were performed



Tem

per

atu

re g

row

th ln

[K/s

]

1/Tp [1/K]

2.3 2.4 2.5 2.6 2.7 2.8 2.9

x 10-3

-11

-10

-9

-8

-7

-6

-5

-4

-3CP data of T

0 and T

Oven

Slope CP of data of T0 and T

Oven (y=-11541·x+22.78)

Figure 10. Crossing point (CP) results of HP500. (TP = temperature of TC at CP).

Table III. Comparison of the main results between the Frank-Kamenetskiimethod and the crossing point method.

Apparent activation energy E (kJ/mol) QA (W/kg)

Material CP method FK method CP method FK method

HP100 107–109 124 4.5–7.3 E13 4.4 E15HP500 96 ∼ 40 7.8 E12 ∼ 1.6 E66 mm wood pellets 76–78 93 1.2–2.4 E10 1.0 E12

with T1/2, therefore, only the CP analysis of TC and TOven is shown in Figure 10. Here, the scatteris tremendous and is very likely caused by the presence of anti-oxidants in HP500.

By using the same parameters of heat capacity C and thermal conductivity � for the materialsas in Table III the following data are found.

Generally, the trend for HP100 and the 6 mm wood pellets shows that the measured activationenergy found with the CP method is about 20% less than when measured with the FK method. Themeasured QA value found with the CP method is about 100 times smaller than when measuredwith the FK method. For HP500, the differences between the two methods are very large. A wayof interpreting the very different results of HP500 is that the CP result depicts the material with



10-1 100 101 102300

320

340

360

380

400

420

440

460

480

500

Storage size, side length [log(m)]

CA

T[K

]

Critical curve for storage size (FK)Data points for storage size (FK)Critical curve for storage size, CP data of T

C and T

½

Critical curve for storage size, CP data of TC and T

Oven

Figure 11. Predictions of critical ambient temperature (CAT) and storage size for 6mm woodpellets. Comparison of Frank-Kamenetskii (FK) and crossing point (CP) results, when CP =

2.2 kJ/(kgK), � = 0.17 W/(mK) and �C is set to 2.52.

only a slight depletion of anti-oxidants whereas the FK result depicts the anti-oxidant depletedstate. The Swedish National Testing and Research Institute [24] found, using the CP method, anE value of 69 kJ/mol and a QA value of 0.08–0.16× 1010 W/kg for the very same 6 mm woodpellets. For comparison Chen et al. [4] found E = 90 ± 3 kJ/mol and QA= 3.19× 1011 W/kgfor untreated sawdust. In another recent paper on wood pellets [25] it was found, by performingmicro-calorimeter tests, that the apparent activation E varied from 60 to 80 kJ/mol.

A comparison of the two methods’ predictions of CAT at a given storage size is shown inFigures 11 and 12 for HP100 and for the 6 mm wood pellets. As already given in Table III thelower E and QA values from the CP data result in an apparently lower CAT values for a givenstorage size compared to the FK found CAT value.

CONCLUSION AND DISCUSSION

When the fire in a filter at Hamlet Protein A/S started, it was caused by a production stop in adrying process. HP100 powder was stacked in a cylindrical filter with a diameter of about 2 m.The thickness of the stack was later estimated to be 30–40cm. The process temperature was foundto have been about 120◦C. These data fit well with experimentally found self-ignition data foundin this investigation. When the �C number is corrected for the geometry of a short cylinder [16]:



10-1 100 101

360

380

400

420

440

460

480

Storage size, side length log(m)

CA

T [

K]

Critical curve for storage size (FK)Data points for storage size (FK)Critical curve for storage size, CP data of T

C and T

½

Critical curve for storage size, CP data of TC and T

Oven

Figure 12. Predictions of critical ambient temperature (CAT) and storage size forHP100. Comparison of Frank-Kamenetskii (FK) and crossing point (CP) results, when

CP = 1 kJ/(kgK), �= 0.17 W/(mK) and �C is set to 2.52.

�C(D) = 2+ 0.841(D/H)2 = 39.4 for a stacking layer height of 30 cm and a diameter of 2m, theprediction by the FK method finds that CAT for such a geometry is only 112◦C. Therefore, at theactual conditions at Hamlet Protein A/S the stack of HP100 eventually had to self-ignite.

HP100 had a lower CAT in small-scale tests than the 6mm wood pellets had. However, becauseof a higher E value of HP100 the FK method predicts a turnover between the two materialsat a cube size of 80 cm side length. It is difficult to find results on critical conditions for suchspecialized products as HP100 and HP500 (specialized nutrition fodder for piglets). Gorsnkovet al. [26] have, however, using mathematical calculations found critical conditions of variousfood products. For a product designated, ‘mixed fodder for pigs’ [26], an E value was foundto be 93.5 kJ/mol and with the QA value determined to 8.89× 1011 W/kg. In the same paperanother product like the ‘sunflower oilcake’ had an E value of 42 kJ/mol and with the QA valuedetermined to be 1.51× 106 W/kg very similar to the HP 500 results found by the FK method inthis report. The ‘grass powder’ product, also in the paper of Gorsnkov et al. [26], resembles verymuch the values found for HP100 by the FK method.

Wood pellets as fuel in big power plants is a fairly new topic. Not much has been investigatedon wood pellets’ self-ignition behaviour. There have been some major fires in storage silos in bothDenmark and Sweden, which presumably have been caused by self-ignition of the wood pellets. Ifone takes the result of the FK prediction then it seems that the wood pellets are quite a safe product



with regard to self-ignition (critical side length of 30m at 27◦C), whereas the CP method predictsmuch smaller critical side length (7–8 m) at the same temperature. The CP method prediction atlarge storage sizes seems more in line with the actual fire cases.

The conclusions on the above investigations are that the FK method is solid within the range ofdimensions that are tested. The FK method is by far the best method when accessing knowledgeon bio-products in production processes where the operational temperatures are relatively high e.g.drying processes and in storage sizes less than about 2m3 dependant on the largest tested dimensionand for situations where the ambient temperature is no less than 80–90◦C. For larger dimensionsand lower ambient temperatures, the error of using an uncorrected number for �C and the influencemoisture transport make the FK predictions questionable. For products like HP500 a completeanalysis is difficult to achieve, though knowledge of the product’s hazardous characteristics wasfound to a certain degree.

The CP method is a lot less time consuming than the FK method. The CP results on E and QAvalues were in general smaller than those obtained from the FK analysis. This could be explainedby the use of uncorrected �C number in the FK analysis. The quality of the predictions by the CPmethod, at least in this investigation, is influenced by comparably more severe uncertainties thanthe FK method. Even for a perfect CP analysis with crossing points on a straight line, it still wouldbe considerably dependant on knowledge of the material’s heat capacity CP at relevant temperaturelevels. That is the reason why the predictions by the CP method lie so far from the experimentallyfound CAT values, though the prediction of HP100 is quite good. This means eventually that asignificant amount of work on establishing knowledge of CP has to be done in parallel to a CPanalysis in order to predict self-ignition even in small scales.

NOMENCLATURE

A is the pre-exponential factor (s−1)

CP is the specific heat capacity of the bulk material (J/(kgK))

E is the apparent activation energy (J/mol)P is a constant, the interception with the y-axis in the FK plotQ is the heat of reaction (kJ/g)R is the universal gas constant (= 8.314 Jmol−1 K−1)

T is the temperature (K)T0 is the ambient temperature (K)TP is the CP temperature in the centre of the cube (K)TOven is the measured oven temperature (the ambient temperature) (K)TC is the measured centre temperature in the cube (K)T1/2 is the measured temperature positioned at a distance of a quarter of the side

length to the edge in all three dimensions (K)CAT is the critical ambient temperature (K)CATc is the lowest CAT measured experimentally (K)CP is the crossing point of two temperatures (dimensionless)nCATc is the highest ambient temperature measured experimentally where self-ignition

did not occur (K)TMTR is the time to maximum thermal runaway (≈ time to self-ignition) (s)h is the effective surface heat-transfer coefficient (W/(m2 K))



q ′ is the heat generation rate per unit volume (J/(sm3))

r is the characteristic length of the given body (the half side length for cubes) (m)x is the distance (m)� dimensionless parameter (dimensionless)�C is the critical value of a given geometry (dimensionless)� is the thermal conductivity of the bulk material (W/(mK))

� is the bulk density of the material (kg/m3)

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