- Email: [email protected]
Modelling of the effect of size on flocculent dust explosions
Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Modelling of the effect of size on flocculent dust explosions Paola Russo a, *, Paul R. Amyotte b, Faisal I. Khan c, Almerinda Di Benedetto d a
Dipartimento di Ingegneria Chimica Materiali Ambiente, Università di Roma “La Sapienza”, Roma, Italy Process Engineering & Applied Science, Dalhousie University, Halifax, NS, Canada c Process Engineering, Memorial University, St. John’s, NL, Canada d Dipartimento di Ingegneria Chimica, Università di Napoli Federico II, Napoli, Italy b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 December 2012 Received in revised form 6 July 2013 Accepted 21 July 2013
The effect of size on the severity of explosions involving flocculent materials has been simulated by means of a model previously developed for spherical particles and here extended to the cylindrical geometry of flock. The model consists of the identification of the regime (internal and external heating, pyrolysis/devolatilization reaction, and volatiles combustion) controlling the explosion by the evaluation of dimensionless numbers (Bi, Da, Th and Pc) and then of the estimation of the deflagration index as a function of flocculent size. The model has been validated by means of explosion data of polyamide 6.6 (nylon) at varying diameter and length. The comparison between model and experimental data show a fairly good agreement. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Flocculent Nylon fibre Dust explosion Modelling Deflagration index
1. Introduction Airborne nylon fibres ignited by static electricity were to blame in a 1995 explosion at the Malden Mills facility in Methuen, MA. The incident injured 37 people (with devastating, disfiguring injuries) and destroyed the facility (CSB, 2006). In 2001, a severe incident in Biella (Italy) has also been recorded. In this case a huge explosion occurred in a textile industry involving flock coming from the wool processing operation. The explosion resulted in three casualties, the injury of five, as well as considerable damage to the whole factory. Details on the accident, including the layout of the plant and the sequence of events, are reported by Piccinini (2008) and Salatino, Di Benedetto, Chirone, Salzano, and Sanchirico (2012) In the same year an explosion occurred in a nylon flock manufacturing plant located in the north of Italy (Marmo, 2010). The explosion took place inside a dryer and propagated to the connected suction plant. The explosion occurred when the plant was switched on after a long shutdown due to a process fault. Three workers were injured. These accidents show the very low degree of consciousness of the risk of explosions due to fibres; they are usually considered
* Corresponding author. Tel.: þ39 0644585565; fax: þ39 0644585451. E-mail addresses: [email protected], [email protected] (P. Russo). 0950-4230/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jlp.2013.07.012
unlikely to occur and frequently neglected in industrial risk assessments. Although explosion accidents involving fibrous materials still occur, literature studies on the explosivity of artificial or natural fibres are quite limited. Marmo and Cavallero (2008) reported minimum ignition energy data of nylon fibres; von Pidoll (2001, 2002) addressed the issue of ignition of flocculent textiles. Cavallero (2006) has demonstrated the explosive potential of flock fibres, which have significant Pmax and KSt values that generally fall into the class St1. Amyotte, Domaratzki, Lindsay, and MacDonald (2011) reported explosibility data for different sizes of fibrous materials (wood and polyethylene) alone and also with admixed flammable gas. Salatino et al. (2012) performed purposely designed experimental tests to support the key role of dust segregation, formation and ignition of the flammable cloud on the explosion of wool flock. To our knowledge, modelling studies on fibre explosion are not present in the literature. This work aims at filling this gap by developing a model for flocculent materials that includes the effect of size on the explosion deflagration index. In a previous paper (Di Benedetto & Russo, 2007) we developed a model for the evaluation of the most conservative values of thermo-kinetic parameters attained during a dust explosion: maximum overpressure (Pmax), deflagration index (KSt), and burning velocity (Sl). Then the model was used to determine the minimum ignition temperature of dusteair mixtures (Di Benedetto,
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
Di Sarli, & Russo, 2010). The evaluation of such parameters was done by assuming a dust particle size lower than a critical value; in such a hypothesis the pyrolysis/devolatilization step is very fast, leading to gas combustion controlling the dust explosion. For dust particle size larger than the critical value, other phenomena such as devolatilization and particle heating can control the explosion process. Under these conditions, the explosion severity is significantly reduced. The model was then improved to include the effect of dust size on the explosion deflagration index (Di Benedetto, Russo, Amyotte, & Marchand, 2010) assuming a one-dimensional, spherically symmetric system. Depending on the dimensionless number characterizing devolatilization and volatiles combustion kinetics, and internal and external particle heating, different regimes can be established giving rise to different trends of the deflagration index. The model was validated by means of experimental values of the deflagration index for polyethylene at various dust particle sizes. Finally, we showed that the model is able to give a good prediction of deflagration index also of hybrid mixtures (Amyotte et al., 2010; Russo, Sanchirico, & Di Benedetto, 2012) of which explosivity parameters were previously determined (Di Benedetto, GarciaAgreda, Russo, & Sanchirico, 2012; Garcia-Agreda, Di Benedetto, Russo, Salzano, & Sanchirico, 2011; Sanchirico, Di Benedetto, Garcia-Agreda, & Russo, 2011). In the present paper we extend our previous model to flocculent materials of cylindrical geometry. The model aims at predicting the deflagration index relevant to explosion of flocculent material at different dust sizes. By varying the equivalent diameter of the flocculent material, different characteristic times of phenomena occurring during explosion, and hence different dimensionless numbers and different regimes, were obtained. On the basis of the regime controlling the explosion, the deflagration index of the flock was calculated. Finally, the model results were compared with experimental data of the deflagration index from nylon (polyamide 6.6) explosion tests carried out by Iarossi et al. (2012). Thus, the work has relevance to the inherently safer design principle of moderation in terms of avoidance of finely-sized particles (Amyotte, Pegg, & Khan, 2009). 2. Model description During a dust explosion, different physical and chemical processes occur: external and internal particle heating, pyrolysis/ devolatilization reaction, and volatiles combustion. The model analyzes the explosion phenomena by introducing characteristic numbers (Biot number, Bi; Damkohler number, Da; thermal Thiele number, Th; ratio of characteristic reaction times, Pc) that for a given dust define the regime controlling the explosion as a function of the characteristic size of particles. The characteristic size is the dust diameter (d) in the case of spherical particles. The methodology used for the evaluation of the regime controlling the explosion is reported in Section 2.1. Details on the model are given in our previous paper (Di Benedetto, Russo, et al., 2010). According to our previous model, we may compute the deflagration index (KSt) at diameter d with the following equation: KSt ðdÞ ¼ KSt $cðdÞ
(1)
where K st is the asymptotic value of the deflagration index calculated by assuming that the controlling step is the volatiles explosion at dust diameter approaching to zero (d z 0) (Di Benedetto & Russo, 2007); c(d) is a function of the dust size and its value depends on the regime controlling the dust explosion (Di Benedetto, Russo, et al., 2010).
1635
In order to compute KSt as a function of the dust size, we need to determine the regime controlling the dust explosion and then the value of c(d) (Section 2.1) and the value of the asymptotic K St (Section 2.2). In this work we calculated a characteristic size of the flock, Deq as follows:
Deq ¼ 2
sffiffiffiffiffiffiffi df L
(2)
p
where df is the diameter and L is the length of flock. The equivalent diameter, Deq, is the diameter of a sphere having the cross-sectional area equal to that of the fibre (cylinder). Then, the procedure described above can be applied to determine the deflagration index of flocculent materials as a function of the equivalent diameter. 2.1. Determination of the controlling regime For the devolatilization process, according to Di Blasi (1999), the controlling mechanism depends on: the Biot number, Bi, that is a measure of the internal heat conduction time with respect to the external heat transfer time; the Damkohler number, Da, which compares the characteristic times of external heat transfer with the characteristic pyrolysis reaction time; and the thermal Thiele number, Th, comparing the characteristic time associated with internal heat transfer with the characteristic time of pyrolysis chemical reaction (Di Benedetto, Russo, et al., 2010). On the basis of the values of these dimensionless numbers, the following regimes can be observed: Regime I (Bi « 1 and Da » 1): when conversion occurs under external heat transfer control; Regime II (Bi « 1 and Da « 1) or Regime III (Bi » 1 and Th « 1): when conversion occurs under the control of the pyrolysis chemical reaction; Regime IV (Bi » 1 and Th » 1): when conversion occurs under the control of internal heat transfer. Once the regime of the devolatilization process is identified, the step controlling the overall dust explosion phenomenon can be determined by comparing the characteristic time of the devolatilization controlling step with that relevant to the gas combustion (tcomb). To this aim, we define a dimensionless number (Pc) given by the ratio of characteristic time of the pyrolysis/devolatilization reaction to that of volatiles combustion:
Pc ¼
tpyro rSl ¼ tcomb rp dF
(3)
where dF is the flame thickness (typically 1 mm), Sl is the laminar burning velocity (assumed in the range 0.2e0.35 m/s) and rp (kg/ m3 s)is the pyrolysis reaction rate. Table 1 Dimensions of nylon fibres used in explosion tests by Iarossi et al. (2012). dtexa
df (mm)
L (mm)
Deq (mm)
1.7 3.3 3.3 3.3 3.3 3.3
13.7 19.0 19.0 19.0 19.0 19.0
500 300 500 750 900 1000
93.4 85.2 110 135 148 156
a dtex or decitex is a unit of measure for the linear mass density of fibres and is defined as the mass in grams per 10,000 m.
1636
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638 Table 2 Kinetic parameters of nylon pyrolysis. Kinetic parameter
Value
k (s1) E (J/mol)
7.51$104 94,000
In consideration of the particle size, different regimes can occur; when the particle diameter is lower than a critical value (characteristic for any dust), the heating and pyrolysis/devolatilization steps are very fast (Pc, Da$Pc and Th$Pc << 1) and then gas combustion is controlling the explosion. Conversely, in order to define the different regimes of dust pyrolysis, the previous characteristic numbers (Bi, Da or Th) have to be evaluated. The evaluation of the devolatilization/pyrolysis reaction rate (rp) was performed by using literature experimental data (Leichtnam, Shwartz, & Gadiou, 2000). The data concern the pyrolysis of polyamide 6.6 carried out in a horizontal quartz reactor, with the temperature at 1273 K, and the residence time of the evolved species in the hot zone of the reactor at 0.79 s. We fitted the experimental results of volatiles composition by assuming the equation:
E rp ¼ rVk exp RT
(4)
where V is the total volatiles fraction produced and leaving the particle and r is the density of volatiles. The kinetic parameter values we obtained are given in Table 2. 2.2. Calculation of K St The deflagration index (K St) relevant to the case of explosion controlled by the combustion of volatiles (Di Benedetto & Russo, 2007) is calculated by using the formula:
KSt ¼
dP dt
V 1=3
(5)
max
where the maximum pressure rise, dP/dt)max, is calculated according to the formula proposed by Dahoe and de Goey (2003):
dP dt
max
g1 1 3ðPmax Po Þ Po Pmax P 2=3 P g 1 ¼ Sl Rvessel Po P Pmax Po (6)
where Pmax is the maximum pressure reached in a closed vessel which has been calculated by using the equilibrium module of the CHEMKIN code. Sl is the laminar burning velocity which is calculated by means of the CHEMKIN module which simulates laminar flame propagation, implemented with the GRI-.Mech3.4, a detailed reaction mechanism used for simulation of homogeneous combustion of the volatiles. Rvessel is the radius of the reference spherical vessel (20 l) and Po is the initial pressure (assumed equal to 1 bar). Table 3 Composition of volatiles produced from pyrolysis of nylon. Gas component
% vol
CH4 CO CO2 HCN NH3
72.3 9.3 7.3 7.3 3.8
Fig. 1. Experimental values of KSt and Pmax by Iarossi et al. (2012).
We used as the composition of volatiles produced by the pyrolysis of nylon the concentration values measured by Leichtnam et al. (2000). The analysis of the volatile products is reported in Table 3. 3. Results 3.1. Equivalent diameter In Fig. 1, experimental data of explosion parameters (Pmax, KSt) measured for polyamide 6.6 (nylon) fibres by Iarossi et al. (2012) are reported as a function of equivalent diameter Deq as previously defined (Eq (2)). The data refer to fibres of different size in diameter and in length. The dimensions of the tested fibres and the corresponding calculated Deq values are reported in Table 1. The increase of both diameter and length of the fibres results in larger values of Deq and, correspondingly, in lower values of maximum pressure and deflagration index. This happens up to Deq z 130 mm, while for larger equivalent diameters Pmax and KSt reach an almost constant value. 3.2. Evaluation of the explosion regime In Tables 2 and 4 the kinetic and physical parameters used for calculation of dimensionless numbers of nylon fibres are reported, respectively. The results of calculation give a dimensionless number Pc >> 1 (Pc ¼ 6540e11450 for Sl ¼ 0.2e0.35 m/s) which means that the characteristic time of combustion of volatiles is lower than that of pyrolysis/devolatilization reaction; hence, the pyrolysis is always the controlling mechanism of the explosion. For the determination of the regime controlling the pyrolysis reaction, the dimensionless numbers (Bi, Da, Th) are calculated as a function of the equivalent diameter of the flocculent material under study. Fig. 2 reports the results. It is found that in the range of equivalent diameter investigated the Bi number is close to 1 (which means that the characteristic time of internal and external heat exchange are comparable) while Table 4 Physical parameters of nylon. Parameter 3
r (kg/m ) cp (J/kg K) l (W/m K)
Value 1140 1700 0.25
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
1637
Fig. 2. Dimensionless characteristic numbers as a function of the equivalent diameter.
both Da and Th number are significantly lower than 1, thus suggesting that the explosion is controlled by the pyrolysis chemical reaction (Regime II and III). Having defined the controlling regime for the different equivalent diameters, the c parameter of Equation (1) is calculated as a function of Deq for the different regimes; the results are reported in Fig. 3. 3.3. Evaluation of KSt as a function of size For the evaluation of KSt (Eq. (1)), the asymptotic deflagration index, K St, computed assuming the explosion of the volatiles is the controlling step of the explosion process (particle size / 0), is required. The computed deflagration index, K St, has a maximum value equal to 70 bar m/s, with respect to the maximum experimental value of 50 bar m/s. This difference confirms that the controlling step of the nylon explosions is not the combustion of volatiles, and that both heat transport and pyrolysis reaction play a role. We then calculated the KSt values from the computed asymptotic maximum value (K St ¼ 70 bar m/s) and the values of c for the different regimes reported in Fig. 3.
Fig. 4. Deflagration index KSt as a function of the equivalent diameter: comparison between model and experiments (Iarossi et al., 2012).
The KSt values, as obtained for each regime as a function of equivalent diameter, are shown in Fig. 4. Fig. 4 also includes experimental KSt data (B), which show the transition from Regime III to Regime II in correspondence of Deq equal to 130 mm. This means that by increasing the equivalent diameter the internal heat exchange (Regime III) becomes negligible with respect to external heat exchange (Regime II), but the pyrolysis chemical reaction is always the controlling mechanism. This behaviour is probable due to the increase of thermal conductivity as the Deq, and especially the length of fibre, increases. Indeed, higher length of fibres corresponds to more oriented polymers: the oriented molecular chains in the crystallites are essentially lined up along the direction of orientation thus offering very little thermal resistance along this direction (Choy, Ong, & Chen, 1981). Hence, the improved thermal conductivity determines faster heat exchange by conduction (internal) with respect to those by convection and radiation (external). From comparison, it is observed that the model gives a good prediction of the experimental deflagration index at different fibre size and in the corresponding different regimes. Since the model has been here validated only for low values of df/L ratio (0.02e0.06), future work will evaluate the limiting df/L ratio for model validity. 4. Conclusions A model for flocculent materials that includes the effect of size on the explosion deflagration index has been proposed in the current work. Our previous model developed for spherical particles is extended to flocculent materials by introducing an equivalent diameter. On the basis of this parameter, dimensionless numbers characterizing devolatilization and volatile combustion kinetics, and internal and external particle heating, have been identified. Distinct regimes have also been identified to indicate different trends of the deflagration index. Experimental values of the deflagration index for nylon at various diameters and lengths have been compared with the model values; successful agreement was obtained. References
Fig. 3. c parameter as a function of the equivalent diameter as calculated by the model.
Amyotte, P., Domaratzki, R., Lindsay, M., & MacDonald, D. (2011). Moderation of explosion likelihood and consequences of non-traditional dusts. In Hazards XXII Liverpool, UK, 11e14 April 2011. North West, UK: IChemE. Amyotte, P., Lindsay, M., Domaratzki, R., Marchand, N., Di Benedetto, A., & Russo, P. (2010). Prevention and mitigation of dust and hybrid mixture explosions. Process Safety Progress, 29(1), 17e21.
1638
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
Amyotte, P. R., Pegg, M. J., & Khan, F. I. (2009). Application of inherent safety principles to dust explosion prevention and mitigation. Process Safety and Environmental Protection, 87, 35e39. Cavallero, D. (2006). Studi sperimentali su polveri esplodibili causa di eventi incidentali nell’industria di processo. PhD thesis. Politecnico di Torino. Choy, C. L., Ong, E. L., & Chen, F. C. (1981). Thermal diffusivity and conductivity of crystalline polymers. Journal of Applied Polymer Science, 26(7), 2325e2335. CSB. (2006). Combustible dust hazard study. Report No. 2006-H-1. Washington, DC: U.S. Chemical Safety and Hazard Investigation Board. Dahoe, A. E., & de Goey, L. P. H. (2003). On the determination of the laminar burning velocity from closed vessel gas explosions. Journal of Loss Prevention in the Process Industries, 16(6), 457e478. Di Benedetto, A., Di Sarli, V., & Russo, P. (2010). On the determination of the minimum ignition temperature for dust/air mixtures. Chemical Engineering Transactions, 19, 189e194. Di Benedetto, A., Garcia-Agreda, A., Russo, P., & Sanchirico, R. (2012). Combined effect of ignition energy and initial turbulence on the explosion behavior of lean gas/ dusteair mixtures. Industrial & Engineering Chemistry Research, 51, 7663e7670. Di Benedetto, A., & Russo, P. (2007). Thermo-kinetic modelling of dust explosions. Journal of Loss Prevention in the Process Industries, 20, 303e309. Di Benedetto, A., Russo, P., Amyotte, P., & Marchand, N. (2010). Modelling the effect of particle size on dust explosions. Chemical Engineering Science, 65, 772e779. Di Blasi, C. (1999). Transition between regimes in the degradation of thermoplastic polymers. Polymer Degradation and Stability, 64, 359e367. Garcia-Agreda, A., Di Benedetto, A., Russo, P., Salzano, E., & Sanchirico, R. (2011). Dust/gas mixtures explosion regimes. Powder Technology, 205(1e3), 81e86.
Iarossi, I., Amyotte, P. R., Khan, F. I., Marmo, L., Dastidar, A. G., & Eckhoff, R. K. (2012). Explosibility of polyamide and polyester fibers. In IX ISHPMIE, international symposium on hazards, prevention, and mitigation of industrial explosions, 22e27 July 2012, Cracow, Poland. Leichtnam, J. N., Shwartz, D., & Gadiou, R. (2000). The behaviour of fuel-nitrogen during fast pyrolysis of polyamide at high temperature. Journal of Analytical and Applied Pyrolysis, 55, 255e268. Marmo, L. (2010). Case study of a nylon fibre explosion: an example of explosion risk in a textile plant. Journal of Loss Prevention in the Process Industries, 23, 106e111. Marmo, L., & Cavallero, D. (2008). Minimum ignition energy of nylon fibres. Journal of Loss Prevention in the Process Industries, 21, 449e465. Piccinini, N. (2008). Dust explosion in a wool factory: origin, dynamics and consequences. Fire Safety Journal, 43, 189e204. von Pidoll, U. (2001). The ignition of clouds of sprays, powders and fibers by flames and electric sparks. Journal of Loss Prevention in the Process Industries, 14, 103e109. von Pidoll, U. (2002). Avoidance of the ignition of textile fiber/air mixtures during the electrostatic flocking process. IEEE Transactions on Industry Applications, 38, 401e405. Russo, P., Sanchirico, R., & Di Benedetto, A. (2012). Theoretical evaluation of the explosion regimes of hybrid mixtures. Chemical Engineering Transactions, 26, 51e56. Salatino, P., Di Benedetto, A., Chirone, R., Salzano, E., & Sanchirico, R. (2012). Analysis of an explosion in a wool-processing plant. Industrial & Engineering Chemistry Research. http://dx.doi.org/10.1021/ie2023614. Sanchirico, R., Di Benedetto, A., Garcia-Agreda, A., & Russo, P. (2011). Study of the severity of hybrid mixture explosions and comparison to pure dusteair and vapoureair explosions. Journal of Loss Prevention in the Process Industries, 24, 648e655.
Contents lists available at ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Modelling of the effect of size on flocculent dust explosions Paola Russo a, *, Paul R. Amyotte b, Faisal I. Khan c, Almerinda Di Benedetto d a
Dipartimento di Ingegneria Chimica Materiali Ambiente, Università di Roma “La Sapienza”, Roma, Italy Process Engineering & Applied Science, Dalhousie University, Halifax, NS, Canada c Process Engineering, Memorial University, St. John’s, NL, Canada d Dipartimento di Ingegneria Chimica, Università di Napoli Federico II, Napoli, Italy b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 December 2012 Received in revised form 6 July 2013 Accepted 21 July 2013
The effect of size on the severity of explosions involving flocculent materials has been simulated by means of a model previously developed for spherical particles and here extended to the cylindrical geometry of flock. The model consists of the identification of the regime (internal and external heating, pyrolysis/devolatilization reaction, and volatiles combustion) controlling the explosion by the evaluation of dimensionless numbers (Bi, Da, Th and Pc) and then of the estimation of the deflagration index as a function of flocculent size. The model has been validated by means of explosion data of polyamide 6.6 (nylon) at varying diameter and length. The comparison between model and experimental data show a fairly good agreement. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Flocculent Nylon fibre Dust explosion Modelling Deflagration index
1. Introduction Airborne nylon fibres ignited by static electricity were to blame in a 1995 explosion at the Malden Mills facility in Methuen, MA. The incident injured 37 people (with devastating, disfiguring injuries) and destroyed the facility (CSB, 2006). In 2001, a severe incident in Biella (Italy) has also been recorded. In this case a huge explosion occurred in a textile industry involving flock coming from the wool processing operation. The explosion resulted in three casualties, the injury of five, as well as considerable damage to the whole factory. Details on the accident, including the layout of the plant and the sequence of events, are reported by Piccinini (2008) and Salatino, Di Benedetto, Chirone, Salzano, and Sanchirico (2012) In the same year an explosion occurred in a nylon flock manufacturing plant located in the north of Italy (Marmo, 2010). The explosion took place inside a dryer and propagated to the connected suction plant. The explosion occurred when the plant was switched on after a long shutdown due to a process fault. Three workers were injured. These accidents show the very low degree of consciousness of the risk of explosions due to fibres; they are usually considered
* Corresponding author. Tel.: þ39 0644585565; fax: þ39 0644585451. E-mail addresses: [email protected], [email protected] (P. Russo). 0950-4230/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jlp.2013.07.012
unlikely to occur and frequently neglected in industrial risk assessments. Although explosion accidents involving fibrous materials still occur, literature studies on the explosivity of artificial or natural fibres are quite limited. Marmo and Cavallero (2008) reported minimum ignition energy data of nylon fibres; von Pidoll (2001, 2002) addressed the issue of ignition of flocculent textiles. Cavallero (2006) has demonstrated the explosive potential of flock fibres, which have significant Pmax and KSt values that generally fall into the class St1. Amyotte, Domaratzki, Lindsay, and MacDonald (2011) reported explosibility data for different sizes of fibrous materials (wood and polyethylene) alone and also with admixed flammable gas. Salatino et al. (2012) performed purposely designed experimental tests to support the key role of dust segregation, formation and ignition of the flammable cloud on the explosion of wool flock. To our knowledge, modelling studies on fibre explosion are not present in the literature. This work aims at filling this gap by developing a model for flocculent materials that includes the effect of size on the explosion deflagration index. In a previous paper (Di Benedetto & Russo, 2007) we developed a model for the evaluation of the most conservative values of thermo-kinetic parameters attained during a dust explosion: maximum overpressure (Pmax), deflagration index (KSt), and burning velocity (Sl). Then the model was used to determine the minimum ignition temperature of dusteair mixtures (Di Benedetto,
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
Di Sarli, & Russo, 2010). The evaluation of such parameters was done by assuming a dust particle size lower than a critical value; in such a hypothesis the pyrolysis/devolatilization step is very fast, leading to gas combustion controlling the dust explosion. For dust particle size larger than the critical value, other phenomena such as devolatilization and particle heating can control the explosion process. Under these conditions, the explosion severity is significantly reduced. The model was then improved to include the effect of dust size on the explosion deflagration index (Di Benedetto, Russo, Amyotte, & Marchand, 2010) assuming a one-dimensional, spherically symmetric system. Depending on the dimensionless number characterizing devolatilization and volatiles combustion kinetics, and internal and external particle heating, different regimes can be established giving rise to different trends of the deflagration index. The model was validated by means of experimental values of the deflagration index for polyethylene at various dust particle sizes. Finally, we showed that the model is able to give a good prediction of deflagration index also of hybrid mixtures (Amyotte et al., 2010; Russo, Sanchirico, & Di Benedetto, 2012) of which explosivity parameters were previously determined (Di Benedetto, GarciaAgreda, Russo, & Sanchirico, 2012; Garcia-Agreda, Di Benedetto, Russo, Salzano, & Sanchirico, 2011; Sanchirico, Di Benedetto, Garcia-Agreda, & Russo, 2011). In the present paper we extend our previous model to flocculent materials of cylindrical geometry. The model aims at predicting the deflagration index relevant to explosion of flocculent material at different dust sizes. By varying the equivalent diameter of the flocculent material, different characteristic times of phenomena occurring during explosion, and hence different dimensionless numbers and different regimes, were obtained. On the basis of the regime controlling the explosion, the deflagration index of the flock was calculated. Finally, the model results were compared with experimental data of the deflagration index from nylon (polyamide 6.6) explosion tests carried out by Iarossi et al. (2012). Thus, the work has relevance to the inherently safer design principle of moderation in terms of avoidance of finely-sized particles (Amyotte, Pegg, & Khan, 2009). 2. Model description During a dust explosion, different physical and chemical processes occur: external and internal particle heating, pyrolysis/ devolatilization reaction, and volatiles combustion. The model analyzes the explosion phenomena by introducing characteristic numbers (Biot number, Bi; Damkohler number, Da; thermal Thiele number, Th; ratio of characteristic reaction times, Pc) that for a given dust define the regime controlling the explosion as a function of the characteristic size of particles. The characteristic size is the dust diameter (d) in the case of spherical particles. The methodology used for the evaluation of the regime controlling the explosion is reported in Section 2.1. Details on the model are given in our previous paper (Di Benedetto, Russo, et al., 2010). According to our previous model, we may compute the deflagration index (KSt) at diameter d with the following equation: KSt ðdÞ ¼ KSt $cðdÞ
(1)
where K st is the asymptotic value of the deflagration index calculated by assuming that the controlling step is the volatiles explosion at dust diameter approaching to zero (d z 0) (Di Benedetto & Russo, 2007); c(d) is a function of the dust size and its value depends on the regime controlling the dust explosion (Di Benedetto, Russo, et al., 2010).
1635
In order to compute KSt as a function of the dust size, we need to determine the regime controlling the dust explosion and then the value of c(d) (Section 2.1) and the value of the asymptotic K St (Section 2.2). In this work we calculated a characteristic size of the flock, Deq as follows:
Deq ¼ 2
sffiffiffiffiffiffiffi df L
(2)
p
where df is the diameter and L is the length of flock. The equivalent diameter, Deq, is the diameter of a sphere having the cross-sectional area equal to that of the fibre (cylinder). Then, the procedure described above can be applied to determine the deflagration index of flocculent materials as a function of the equivalent diameter. 2.1. Determination of the controlling regime For the devolatilization process, according to Di Blasi (1999), the controlling mechanism depends on: the Biot number, Bi, that is a measure of the internal heat conduction time with respect to the external heat transfer time; the Damkohler number, Da, which compares the characteristic times of external heat transfer with the characteristic pyrolysis reaction time; and the thermal Thiele number, Th, comparing the characteristic time associated with internal heat transfer with the characteristic time of pyrolysis chemical reaction (Di Benedetto, Russo, et al., 2010). On the basis of the values of these dimensionless numbers, the following regimes can be observed: Regime I (Bi « 1 and Da » 1): when conversion occurs under external heat transfer control; Regime II (Bi « 1 and Da « 1) or Regime III (Bi » 1 and Th « 1): when conversion occurs under the control of the pyrolysis chemical reaction; Regime IV (Bi » 1 and Th » 1): when conversion occurs under the control of internal heat transfer. Once the regime of the devolatilization process is identified, the step controlling the overall dust explosion phenomenon can be determined by comparing the characteristic time of the devolatilization controlling step with that relevant to the gas combustion (tcomb). To this aim, we define a dimensionless number (Pc) given by the ratio of characteristic time of the pyrolysis/devolatilization reaction to that of volatiles combustion:
Pc ¼
tpyro rSl ¼ tcomb rp dF
(3)
where dF is the flame thickness (typically 1 mm), Sl is the laminar burning velocity (assumed in the range 0.2e0.35 m/s) and rp (kg/ m3 s)is the pyrolysis reaction rate. Table 1 Dimensions of nylon fibres used in explosion tests by Iarossi et al. (2012). dtexa
df (mm)
L (mm)
Deq (mm)
1.7 3.3 3.3 3.3 3.3 3.3
13.7 19.0 19.0 19.0 19.0 19.0
500 300 500 750 900 1000
93.4 85.2 110 135 148 156
a dtex or decitex is a unit of measure for the linear mass density of fibres and is defined as the mass in grams per 10,000 m.
1636
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638 Table 2 Kinetic parameters of nylon pyrolysis. Kinetic parameter
Value
k (s1) E (J/mol)
7.51$104 94,000
In consideration of the particle size, different regimes can occur; when the particle diameter is lower than a critical value (characteristic for any dust), the heating and pyrolysis/devolatilization steps are very fast (Pc, Da$Pc and Th$Pc << 1) and then gas combustion is controlling the explosion. Conversely, in order to define the different regimes of dust pyrolysis, the previous characteristic numbers (Bi, Da or Th) have to be evaluated. The evaluation of the devolatilization/pyrolysis reaction rate (rp) was performed by using literature experimental data (Leichtnam, Shwartz, & Gadiou, 2000). The data concern the pyrolysis of polyamide 6.6 carried out in a horizontal quartz reactor, with the temperature at 1273 K, and the residence time of the evolved species in the hot zone of the reactor at 0.79 s. We fitted the experimental results of volatiles composition by assuming the equation:
E rp ¼ rVk exp RT
(4)
where V is the total volatiles fraction produced and leaving the particle and r is the density of volatiles. The kinetic parameter values we obtained are given in Table 2. 2.2. Calculation of K St The deflagration index (K St) relevant to the case of explosion controlled by the combustion of volatiles (Di Benedetto & Russo, 2007) is calculated by using the formula:
KSt ¼
dP dt
V 1=3
(5)
max
where the maximum pressure rise, dP/dt)max, is calculated according to the formula proposed by Dahoe and de Goey (2003):
dP dt
max
g1 1 3ðPmax Po Þ Po Pmax P 2=3 P g 1 ¼ Sl Rvessel Po P Pmax Po (6)
where Pmax is the maximum pressure reached in a closed vessel which has been calculated by using the equilibrium module of the CHEMKIN code. Sl is the laminar burning velocity which is calculated by means of the CHEMKIN module which simulates laminar flame propagation, implemented with the GRI-.Mech3.4, a detailed reaction mechanism used for simulation of homogeneous combustion of the volatiles. Rvessel is the radius of the reference spherical vessel (20 l) and Po is the initial pressure (assumed equal to 1 bar). Table 3 Composition of volatiles produced from pyrolysis of nylon. Gas component
% vol
CH4 CO CO2 HCN NH3
72.3 9.3 7.3 7.3 3.8
Fig. 1. Experimental values of KSt and Pmax by Iarossi et al. (2012).
We used as the composition of volatiles produced by the pyrolysis of nylon the concentration values measured by Leichtnam et al. (2000). The analysis of the volatile products is reported in Table 3. 3. Results 3.1. Equivalent diameter In Fig. 1, experimental data of explosion parameters (Pmax, KSt) measured for polyamide 6.6 (nylon) fibres by Iarossi et al. (2012) are reported as a function of equivalent diameter Deq as previously defined (Eq (2)). The data refer to fibres of different size in diameter and in length. The dimensions of the tested fibres and the corresponding calculated Deq values are reported in Table 1. The increase of both diameter and length of the fibres results in larger values of Deq and, correspondingly, in lower values of maximum pressure and deflagration index. This happens up to Deq z 130 mm, while for larger equivalent diameters Pmax and KSt reach an almost constant value. 3.2. Evaluation of the explosion regime In Tables 2 and 4 the kinetic and physical parameters used for calculation of dimensionless numbers of nylon fibres are reported, respectively. The results of calculation give a dimensionless number Pc >> 1 (Pc ¼ 6540e11450 for Sl ¼ 0.2e0.35 m/s) which means that the characteristic time of combustion of volatiles is lower than that of pyrolysis/devolatilization reaction; hence, the pyrolysis is always the controlling mechanism of the explosion. For the determination of the regime controlling the pyrolysis reaction, the dimensionless numbers (Bi, Da, Th) are calculated as a function of the equivalent diameter of the flocculent material under study. Fig. 2 reports the results. It is found that in the range of equivalent diameter investigated the Bi number is close to 1 (which means that the characteristic time of internal and external heat exchange are comparable) while Table 4 Physical parameters of nylon. Parameter 3
r (kg/m ) cp (J/kg K) l (W/m K)
Value 1140 1700 0.25
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
1637
Fig. 2. Dimensionless characteristic numbers as a function of the equivalent diameter.
both Da and Th number are significantly lower than 1, thus suggesting that the explosion is controlled by the pyrolysis chemical reaction (Regime II and III). Having defined the controlling regime for the different equivalent diameters, the c parameter of Equation (1) is calculated as a function of Deq for the different regimes; the results are reported in Fig. 3. 3.3. Evaluation of KSt as a function of size For the evaluation of KSt (Eq. (1)), the asymptotic deflagration index, K St, computed assuming the explosion of the volatiles is the controlling step of the explosion process (particle size / 0), is required. The computed deflagration index, K St, has a maximum value equal to 70 bar m/s, with respect to the maximum experimental value of 50 bar m/s. This difference confirms that the controlling step of the nylon explosions is not the combustion of volatiles, and that both heat transport and pyrolysis reaction play a role. We then calculated the KSt values from the computed asymptotic maximum value (K St ¼ 70 bar m/s) and the values of c for the different regimes reported in Fig. 3.
Fig. 4. Deflagration index KSt as a function of the equivalent diameter: comparison between model and experiments (Iarossi et al., 2012).
The KSt values, as obtained for each regime as a function of equivalent diameter, are shown in Fig. 4. Fig. 4 also includes experimental KSt data (B), which show the transition from Regime III to Regime II in correspondence of Deq equal to 130 mm. This means that by increasing the equivalent diameter the internal heat exchange (Regime III) becomes negligible with respect to external heat exchange (Regime II), but the pyrolysis chemical reaction is always the controlling mechanism. This behaviour is probable due to the increase of thermal conductivity as the Deq, and especially the length of fibre, increases. Indeed, higher length of fibres corresponds to more oriented polymers: the oriented molecular chains in the crystallites are essentially lined up along the direction of orientation thus offering very little thermal resistance along this direction (Choy, Ong, & Chen, 1981). Hence, the improved thermal conductivity determines faster heat exchange by conduction (internal) with respect to those by convection and radiation (external). From comparison, it is observed that the model gives a good prediction of the experimental deflagration index at different fibre size and in the corresponding different regimes. Since the model has been here validated only for low values of df/L ratio (0.02e0.06), future work will evaluate the limiting df/L ratio for model validity. 4. Conclusions A model for flocculent materials that includes the effect of size on the explosion deflagration index has been proposed in the current work. Our previous model developed for spherical particles is extended to flocculent materials by introducing an equivalent diameter. On the basis of this parameter, dimensionless numbers characterizing devolatilization and volatile combustion kinetics, and internal and external particle heating, have been identified. Distinct regimes have also been identified to indicate different trends of the deflagration index. Experimental values of the deflagration index for nylon at various diameters and lengths have been compared with the model values; successful agreement was obtained. References
Fig. 3. c parameter as a function of the equivalent diameter as calculated by the model.
Amyotte, P., Domaratzki, R., Lindsay, M., & MacDonald, D. (2011). Moderation of explosion likelihood and consequences of non-traditional dusts. In Hazards XXII Liverpool, UK, 11e14 April 2011. North West, UK: IChemE. Amyotte, P., Lindsay, M., Domaratzki, R., Marchand, N., Di Benedetto, A., & Russo, P. (2010). Prevention and mitigation of dust and hybrid mixture explosions. Process Safety Progress, 29(1), 17e21.
1638
P. Russo et al. / Journal of Loss Prevention in the Process Industries 26 (2013) 1634e1638
Amyotte, P. R., Pegg, M. J., & Khan, F. I. (2009). Application of inherent safety principles to dust explosion prevention and mitigation. Process Safety and Environmental Protection, 87, 35e39. Cavallero, D. (2006). Studi sperimentali su polveri esplodibili causa di eventi incidentali nell’industria di processo. PhD thesis. Politecnico di Torino. Choy, C. L., Ong, E. L., & Chen, F. C. (1981). Thermal diffusivity and conductivity of crystalline polymers. Journal of Applied Polymer Science, 26(7), 2325e2335. CSB. (2006). Combustible dust hazard study. Report No. 2006-H-1. Washington, DC: U.S. Chemical Safety and Hazard Investigation Board. Dahoe, A. E., & de Goey, L. P. H. (2003). On the determination of the laminar burning velocity from closed vessel gas explosions. Journal of Loss Prevention in the Process Industries, 16(6), 457e478. Di Benedetto, A., Di Sarli, V., & Russo, P. (2010). On the determination of the minimum ignition temperature for dust/air mixtures. Chemical Engineering Transactions, 19, 189e194. Di Benedetto, A., Garcia-Agreda, A., Russo, P., & Sanchirico, R. (2012). Combined effect of ignition energy and initial turbulence on the explosion behavior of lean gas/ dusteair mixtures. Industrial & Engineering Chemistry Research, 51, 7663e7670. Di Benedetto, A., & Russo, P. (2007). Thermo-kinetic modelling of dust explosions. Journal of Loss Prevention in the Process Industries, 20, 303e309. Di Benedetto, A., Russo, P., Amyotte, P., & Marchand, N. (2010). Modelling the effect of particle size on dust explosions. Chemical Engineering Science, 65, 772e779. Di Blasi, C. (1999). Transition between regimes in the degradation of thermoplastic polymers. Polymer Degradation and Stability, 64, 359e367. Garcia-Agreda, A., Di Benedetto, A., Russo, P., Salzano, E., & Sanchirico, R. (2011). Dust/gas mixtures explosion regimes. Powder Technology, 205(1e3), 81e86.
Iarossi, I., Amyotte, P. R., Khan, F. I., Marmo, L., Dastidar, A. G., & Eckhoff, R. K. (2012). Explosibility of polyamide and polyester fibers. In IX ISHPMIE, international symposium on hazards, prevention, and mitigation of industrial explosions, 22e27 July 2012, Cracow, Poland. Leichtnam, J. N., Shwartz, D., & Gadiou, R. (2000). The behaviour of fuel-nitrogen during fast pyrolysis of polyamide at high temperature. Journal of Analytical and Applied Pyrolysis, 55, 255e268. Marmo, L. (2010). Case study of a nylon fibre explosion: an example of explosion risk in a textile plant. Journal of Loss Prevention in the Process Industries, 23, 106e111. Marmo, L., & Cavallero, D. (2008). Minimum ignition energy of nylon fibres. Journal of Loss Prevention in the Process Industries, 21, 449e465. Piccinini, N. (2008). Dust explosion in a wool factory: origin, dynamics and consequences. Fire Safety Journal, 43, 189e204. von Pidoll, U. (2001). The ignition of clouds of sprays, powders and fibers by flames and electric sparks. Journal of Loss Prevention in the Process Industries, 14, 103e109. von Pidoll, U. (2002). Avoidance of the ignition of textile fiber/air mixtures during the electrostatic flocking process. IEEE Transactions on Industry Applications, 38, 401e405. Russo, P., Sanchirico, R., & Di Benedetto, A. (2012). Theoretical evaluation of the explosion regimes of hybrid mixtures. Chemical Engineering Transactions, 26, 51e56. Salatino, P., Di Benedetto, A., Chirone, R., Salzano, E., & Sanchirico, R. (2012). Analysis of an explosion in a wool-processing plant. Industrial & Engineering Chemistry Research. http://dx.doi.org/10.1021/ie2023614. Sanchirico, R., Di Benedetto, A., Garcia-Agreda, A., & Russo, P. (2011). Study of the severity of hybrid mixture explosions and comparison to pure dusteair and vapoureair explosions. Journal of Loss Prevention in the Process Industries, 24, 648e655.