3.9. Dust Explosion

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3.9. Dust Explosion

Dust explosions, initiated by rapid combustion of flammable particulates, pose serious explosion hazard in process industry. While to basics are reasonably understood, fires and explosions from solid particulates and liquid particulates continue to contribute toward considerable material damage and loss of life (Lemkowitz and Pasman, 2014). Next to vapor cloud and boiling liquid expanding vapor explosions, dust explosions can be attributed to cause for several injuries, fatalities, and significant financial loss (Abbasi and Abbasi, 2007; Eckhoff, 2003). Given the right conditions, most unoxidized material can burn. While there does not seem to be any unanimous opinion (Abbasi and Abbasi, 2007; Mannan and Lees, 2005; NFPA 68 Guide for Venting of Deflagrations, 2002) on classifying dust particles based on maximum particle size, ranging from less than 420 μm (NFPA 68 Guide for Venting of Deflagrations, 2002) to less than 1000 μm (Palmer, 1973; Mannan and Lees, 2005), severity of dust explosion has been proven as a function of its particle size and distribution (Di Benedetto et al., 2010; Huang et al., 2009; Pritchard, 2004). At the other end it is reported that the maximum explosion pressure does not increase below 50 μm (Eckhoff, 2003). As explained (Pritchard, 2004), the reasoning behind limiting particle size can be explained through understanding of reaction mechanism leading to dust explosion phenomena. In the homogeneous gas phase, the event is initiated by pyrolysis or devolatization, followed by gas phase mixing and combustion. The slowest among devolatization, mixing, and combustion as determined by their time constants will be the rate-determining step in the whole phenomena and thus affecting the maximum explosion pressure. With diminishing particle size, as the surface area is increased resulting in increased devolatisation rate, if it does not remain the rate-determining step of the overall phenomena, the effect of particle size on maximum pressure will cease to exist below a certain particle size.

Modeling dust explosion involves estimation of properties related to the chemical of interest, calculation of sensitivity of the explosion to the flow properties and heat transfer of the dust cloud (Di Benedetto and Russo, 2007). In general, the severity of dust explosion can be quantified by the following parameters (Lemkowitz and Pasman, 2014) as illustrated in the following table:

Severity Parameters	Description
Tendency toward detonation	Increases with increased reactivity and decreasing particle size
Maximum explosion pressure or P_max	Largely defined by the maximum explosion temperature. The maximum explosion overpressure, P_max, is the difference between the pressure at the time of ignition and that at the highest pressure attained in the dynamic pressure curve during a dust explosion.
Maximum rate of pressure rise or ${(\frac{d P}{d t})}_{max}$ ${(\frac{d P}{d t})}_{max}$	Generally measured from initial condition.
Maximum volume normalized rate of pressure rise or K_st	Value of maximum rate of pressure rise, normalized to a volume of 1-m³ volume sphere.
Flame speed (S_f) or laminar burning velocity (S_u)	Speed of flame relative to stationary observer

Among these, a typical approach to estimate dust explosion severity is to estimate parameters of importance through laboratory scale experiments, such as deflagration index (K_st) and maximum pressure (P_max) in 1-m³ laboratory test vessels. The obvious concern in directly using these results in an industrial setting is the clear omission of taking into account the effect of change in scale, which is significant. The cube-root law attempts to address the scale-up concern through the following equation:

${(\frac{d P}{d t})}_{max} V^{\frac{1}{3}} = K_{st}$ ${(\frac{d P}{d t})}_{max} V^{\frac{1}{3}} = K_{st}$

The assumption, which has been found generally valid, is that P_max will occur at the same time when

{(\frac{d P}{d t})}_{max}

${(\frac{d P}{d t})}_{max}$

happens. Even with the cube-root law, however, the applicability of the model is subjected to the following set of restrictions (Dahoe et al., 1996; Eckhoff, 2003):

• Geometrically similar vessels

• Negligible flame thickness

• Same burning velocity

• Point ignition occurs at the center of the vessels

The effect of flame thickness has been dealt with more precisely in Dahoe et al. (1996), specifically for confined dust explosions in spherical vessels as the article title suggests. The three-zone model developed in this work requires the input of laboratory scale experimental results to be scaled up more accurately to the industrial level. The three-zone model was developed to assess the sensitivity of flame thickness on the pressure development and deflagration index for a confined dust explosion in a spherical vessel. It divided, in each scenario (different flame thickness), in three various phases, from initiation of the dust explosion to fully developed expanding flame zone and finally the flame zone reaching to the vessel wall. Based on this analysis, the modified model by the authors can be represented as

${(\frac{d P}{d t})}_{max} V^{\frac{1}{3}} = K_{st} f (\frac{\partial}{R_{vessel}})$ ${(\frac{d P}{d t})}_{max} V^{\frac{1}{3}} = K_{st} f (\frac{\partial}{R_{vessel}})$

The effect of variation in burning velocity and flame thickness is incorporated into the model through the function

f (\frac{\partial}{R_{vessel}})

$f (\frac{\partial}{R_{vessel}})$

. Details of calculations are provided in the article and are not provided here.

One of the generic approaches in modeling dust explosions at the macroscale level involves TNT equivalency modeling with 7–10% explosion efficiency. Vent sizing procedure for dust explosion range from the Nomograph method, the Swedish method, the Norwegian method, the Radandt scaling law, the K-factor method, and the equivalence coefficient method have been discussed and compared with experimental results in several articles (Eckhoff, 2003; Tascón et al., 2009).

3.9.1. Molecular Modeling of Dust Explosion

In the previous section, we have mentioned the cube-root law, utilized to scale-up laboratory scale results related to severity of dust explosion. The factors that affect the deflagration index (K_st) and maximum pressure (P_max), such as particle size, moisture content, humidity, oxygen availability, shape, concentration, ignition source, and others (Pritchard, 2004), are not explicitly incorporated in the model and are implicitly embedded within the estimated parameter values. The molecular modeling based approach through QSPR, based on experimentally obtained data set, can be implemented as an alternative route for estimating the deflagration index (K_st) and maximum pressure (P_max), for similar chemicals. Such an approach has the potential to obviate or atleast greatly reduce the need for expensive testing (Lemkowitz and Pasman, 2014). Appropriately done, this also translates into having the ability estimate dust explosion characteristics in a consistent manner, independent of influences of experimental methods and equipments, a major caveat in gaining insights from experimental data sets. Gao et al. (2013) demonstrated sensitivity of explosion to various testing procedures. Application of QSPR has been proven to be successful in process safety studies (Saraf et al., 2003, 2004; Katritzky et al., 2007; Pan et al., 2011) from estimating reactivity hazards, flash points, and flammability limits among others. In a similar manner, studies have been performed to characterize dust explosibility through QSPR.

3.9.2. Practical Considerations

The generic concerns for development of QSPR model from experimental data are also applicable here. In addition, for estimation of K_st and P_max, the QSPR models developed based on a representative particle size, for estimation of K_st and P_max parameters, are good approaches for assessing the level of hazard at a screening level when experimental data are not available. More importantly, as pointed out (Reyes et al., 2011), care should be taken if estimated values are close to category demarcation values (K_st = 200 and 300). In such a scenario, experimental data should be sought after or a conservative approach should be taken.

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Table of Contents for 3.9. Dust Explosion

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3.9. Dust Explosion

3.9.1. Molecular Modeling of Dust Explosion

3.9.2. Practical Considerations

Table of Contents for
3.9. Dust Explosion