Application of Factorial Analysis to the Study of Vented Dust Explosions in Large Biomass Storage Silos

Abstract

Dust explosions are a major concern in many industrial facilities and particularly in storage areas of biomass materials. Although venting standards (EN 14491 and NFPA 68) provide satisfactory safety levels for most industrial applications, they present some limitations and there exist situations that they do not contemplate. Vented dust explosions in a 4500 m³ silo for the storage of wood pellets were simulated by computational fluid dynamics. Maximum overpressures were registered and compared. The influence of several parameters including initial turbulence level, dust concentration, ignition location, and vent area was studied. A factorial analysis was carried out to determine the importance of each of the four parameters, along with possible interactions between them. The results showed great variations in the overpressures between the different scenarios simulated. Vent area, ignition location, and dust concentration showed similar effects on the overpressure (around 25%), while initial turbulence had half this effect (13%). One interaction effect out of the eleven possible interactions was identified as relevant for this specific industrial scenario: the combination of the ignition location and the initial turbulence, with an additional effect of 5% on the overpressure. The factorial analysis applied in this study could be of interest to the risk assessment of industrial facilities.

1. Introduction

Dust explosions represent a main concern in the industries that handle, process, or store combustible materials that produce fine particles [1]. If these particles are suspended in air due to the movement of the bulk material during transport or conditioning operations (sieving, milling, etc.) [2] or due to the dust lifting from layers and deposits [3] caused by an airflow, pressure wave or vibrations, a rapid combustion process can be triggered by an ignition source with enough energy. This results in the propagation of a flame through the dust/air mixture and the generation of heat and gaseous products, which can produce important overpressures when the explosion occurs within a confined space [4].

This phenomenon has been reported in different types of industrial facilities and equipment, such as dust-collecting systems, dryers, conveyors, and silos. Among them, storage silos for bulk materials represent one of the most common equipment types involved in dust explosion accidents [5].

Hot surfaces and hot lumps of material, mechanical sparks, electric sparks and electrostatic discharges, lightning, and welding and cutting operations are well-known potential ignition sources [6]. In addition, fires –both open flame fires and smoldering fires– can ignite a dust explosion [6]; these fires can be the result of a self-heating process undergone by the bulk material [7] and the emission of flammable volatiles [8]. Similarly, flames by dust explosions could produce subsequent fires in surrounding facilities, buildings, and vegetation if not addressed properly.

Dust explosions represent a significant percentage of the major accidents in the biomass and bioenergy sector [9]. Safety concerns in biomass storage facilities deserve further attention [10]. Particularly, large storage silos for wood pellets are common in biomass power plants, co-firing installations, harbor storage areas, and pellet-manufacturing industries. Therefore, these storage facilities are exposed to explosion risks that should be assessed, managed, and mitigated [11].

Mitigation of dust explosions involves several measures [4] but venting is one of the most popular. Pressure relief or venting consists of allowing explosion gases to escape from the equipment to be protected in order to limit the overpressures generated by the explosion to a level that the equipment can withstand [12]. Venting safeguards the equipment and prevents its bursting, which would eject wall fragments, burning material, hot ashes, and unburned material; this late situation should be avoided to reduce fatalities and prevent subsequent fires and a possible domino effect in the industrial facility [13]. Therefore, venting reduces the potential damage caused by explosions but neither prevents nor extinguishes an explosion.

Standards for dust explosion venting (EN 14491 [14] and NFPA 68 [15]) are based both on theoretical considerations and empirical data. These data were mainly obtained from experimental programs conducted during the 60’s–90’s decades of the 20th century. These standards provide the total vent area required to achieve proper protection of vessels in the event of an internal dust explosion. Both methods are conservative and lead to satisfactory safety levels for most industrial applications since they were developed assuming a homogeneous turbulent dust cloud filling the vessel to be protected [16,17].

The formulae proposed in both standards [14,15], for the simplest scenario, consider a number of parameters related to the dust (the K_St constant in bar∙m∙s⁻¹ and the maximum explosion overpressure P_max in bar, both determined through laboratory experiments [18,19]), the vessel to be protected (the volume V in m³, the length-to-diameter ratio L/D, and the maximum explosion pressure in bar that the vessel can withstand, also named reduced overpressure P_red), and the venting devices (the static activation pressure of the venting devices P_stat in bar, the venting efficiency or inertia, and the presence or not of a duct).

However, venting protection remains a complex issue due to frequent technical and economic difficulties [20]. The above standards calculate such large vent areas in some cases–particularly in low-strength vessels of large volume, such as large steel silos–that they are difficult to implement in practice [21]. Moreover, they do not consider other process or design variables different than those listed above but that could also have an important effect on the venting process. In this sense, it is remarkable that Middha et al. [22] demonstrated by means of numerical simulations that the layout of the vent panels influences the explosion overpressure due to the interaction of flame jets between vent zones and the subsequent reduction in venting efficiency. In addition, standards have a specific range of applications [20]; Coffey and Price [11], for instance, studied a silo with a volume of 101,000 m³, which falls outside of the scope of the standards. Tascón and Aguado [23] also analyzed cases not contemplated by standards conducting both simulations and experimental explosions in a 5 m³ vessel; they demonstrated the influence of the activation pressure of the vent panels and of the relation V^2/3/A (cross-sectional area of a cube with equivalent volume divided by the vent area) on the explosion overpressure. Other aspects that have recently been discussed due to the significant uncertainties still present include the role of turbulence [24], the influence of the length-to-diameter ratio of the vessel [25,26], and the relief through vent ducts [27].

Therefore, it is clear that there is ample room for improvement in the methodologies employed in explosion relief design. There are various factors, design choices, and real industrial scenarios that cannot be properly assessed using the current venting standards, which only consider some specific situations covered by the experiments they are based on. In this sense, numerical simulations are a powerful tool and allow practitioners and researchers to analyze a wider range of possible initial scenarios. Computational fluid dynamics (CFD) codes have already been successfully applied to dust explosions, including aspects like the turbulent concentration field [28,29], the dust lifting phenomenon [3], interconnected vessels [30,31], the investigation of real accidents [32], and the protection of industrial equipment against dust explosions [11,33,34,35]; other types of explosions have also been studied by means of CFD simulations [36,37].

The objective of this study was to perform numerical simulations of vented dust explosions in a biomass storage silo in order to analyze the effects of variations in the initial scenario and the influence of the parameters involved. The importance of each parameter and the interactions between them were also studied.

2. Materials and Methods

2.1. CFD Code

The FLACS-CFD v22.1r2 software from Gexcon, equipped with the specific FLACS-DustEx solver, was utilized for conducting the dust explosion simulations [38].

This software is a finite volume code that solves the conservation equations on a 3-D Cartesian grid. Turbulence is solved by using a Reynolds-averaged Navier-Strokes k–ε model, and the SIMPLE pressure correction algorithm is applied [39]. FLACS-CFD models curved surfaces and subgrid obstacles using a distributed porosity approach, where volume and area porosities (or fractions) are calculated on the cells of the mesh and included in the conservation equations, ranging from 0.0 (100% solid cell) to 1.0 (100% fluid cell) [40]. A detailed description of the governing equations of the code has already been reported and can be found in [41].

The combustion model implemented in the code determines the reaction rate from reactants to products and the propagation of the reaction zone, i.e., the flame. The approach adopted in FLACS-DustEx to calculate the burning velocity of the dust/air mixture in turbulent conditions (S_T) consists of applying Equation (1) using the laminar burning velocity (S_L) values estimated from experimental data measured in the 20-L vessel [18] for several concentrations. The estimates of the laminar burning velocity can be augmented C_L times, being C_L a correction factor introduced to account for the uncertainties behind the calculations. In addition, the experimental explosions in the 20-L vessel also provide the mass fraction of fuel converted to products (λ) for various dust concentrations, which is calculated from the explosion overpressure recorded in the 20-L vessel considering the fuel that must react with air to produce that pressure, prior correction to account both for the igniters and for the cooling effects of vessel walls. Finally, the S_L and λ data for different concentrations are stored in a text file that is used as input for the combustion model. A complete description of the derivation of S_L and λ from the experimental data was reported by Skjold [42,43].

S_T = 15.1 S_L^0.784 u′_rms^0.412 l_I ^0.196,

(1)

where u′_rms is the root-mean-square of the turbulent velocity fluctuations and l_I is the turbulence length scale.

2.2. Scenario

The simulated industrial equipment comprised a wood pellet storage silo with a capacity of 4500 m³. The silo had a cylindrical body with inner dimensions of 20 m in diameter and 13 m in height, plus a conical roof that added 8 m in height. The computational domain occupied a floor area of 48 × 48 m² and 52 m in height (volume = 119,808 m³). The domain was discretized into a uniform grid composed of cubic cells measuring 1 m in size. To adapt the conical roof to the orthogonal grid used by FLACS-CFD, the roof was transformed into a series of toroids with decreasing diameter (see Figure 1). Three monitoring points (MP) were positioned along the vertical z-axis of the silo at heights of 2.25 m (MP-1), 13.25 m (MP-2), and 20.25 m (MP-3) from the silo bottom. However, to avoid alignment with grid lines, a small deviation of −0.25 m was introduced in both the x- and y-axes.

For the simulations it was assumed that the silo was empty of bulk material, i.e., the entire volume was filled with either air or dust/air mixture. The initial pressure was set at 100 kPa, and the initial temperature was 20 °C. The initial dust cloud used in these simulations had a pyramidal shape and occupied the entire height of the silo, from the top of the roof down to the bottom (see Figure 1). This cloud had a volume of 980 m³, representing only a fraction of the silo’s internal volume (21.8%).

This approach tried to replicate a realistic scenario during the initial phase of the filling process: the material (wood pellets) would fall from a conveyor situated above the silo generating a dust cloud that would follow the trajectory of the pellets and widen at the silo bottom. A uniform dust concentration was considered in all the volume of the cloud. Wood dust was used in all the simulations (P_max = 7.9 bar for 500 g/m³ and K_St = 131 bar∙m/s for 1000 g/m³, determined following standardized procedures [18,19]).

Pressure relief panels were included in the roof, each one measuring 1 × 1 m², inertialess, and with an activation pressure of 0.1 bar (gauge pressure). The panels were uniformly distributed around the larger toroid of the roof in all simulations. Some simulations were performed employing 56 panels (see Figure 2) and others using 28.

2.3. Factorial Design

The study aimed to discover the effect of different possible initial conditions on the reduced explosion overpressures reached inside the silo (P_red,sim) during a vented dust explosion. From the whole set of parameters that could modify the explosion development, 4 factors with 2 levels each were chosen. The factors involved in this study were vent area, ignition location, initial turbulence, and dust concentration.

2.3.1. Vent Area

Vent area refers to the total surface area provided by the venting devices installed in the roof in order to protect the silo from explosion overpressures. This factor reflects the vent area that would open during an explosion. The two levels considered in the simulations were 56 m² and 28 m².

2.3.2. Ignition Location

Ignition location refers to the specific point within the dust cloud where the ignition was initiated by an energy source. The ignition energy was set to 1 kJ.

The two levels were the following:

• Top: ignition in the upper third of the cloud height (at 19.75 m above the silo bottom);
• Bottom: ignition in the lower third of the cloud height (at 1.25 m above the silo bottom).

Both locations were positioned along the vertical z-axis of the silo but with a small deviation of −0.25 m in the x- and y-axes to avoid contact with the walls of the grid cells.

2.3.3. Initial Turbulence

FLACS-CFD utilizes three parameters to characterize the turbulence level in the initial fluid flow before the explosion: characteristic velocity, relative turbulence intensity, and turbulence length scale.

The two levels were as follows:

• Low: the three parameters had lower values, resulting in weak initial turbulence.
• High: this corresponded to a more severe turbulent flow.

The specific values for the two initial condition sets are shown in

Table 1. Turbulence initial conditions.

Level	Characteristic Velocity (m/s)	Relative Turbulence Intensity	Turbulence Length Scale (m)
Low	0.15	0.80	0.03
High	0.50	1.00	0.10

. In the low-level scenario, the air velocity and relative turbulence intensity are based on experimental measurements carried out by Hauert et al. in a 12 m³ silo when fed mechanically with maize starch [44]. These low-level values have been used in previous simulations [34] and were obtained by considering average numbers for the entire volume and making adjustments to account for the volume increase. Further discussion on these aspects can be found in [34].

2.3.4. Dust Concentration

Dust concentration represents the quantity of combustible dust in the homogeneous dust/air cloud formed into the vessel, expressed in g/m³. The two levels were set at 300 g/m³ and 500 g/m³. The latter was the concentration that generated the maximum overpressure (P_max = 7.9 bar) in the 20-L vessel [18], while the former was based on measurements in an experimental silo [44]. These two values have already been used in previous CFD simulations [34,41].

2.4. Factorial Analysis

A 2^k factorial analysis [45] was applied to determine the influence of the factors on P_red,_sim, as well as to examine potential interactions between the factors.

The levels of each factor were assigned values −1 or +1, as indicated in

Table 2. Levels of the four factors.

	A (Vent Area)	B (Ignition Location)	C (Initial Turbulence)	D (Dust Concentration)
−1	56 m2	Top	Low	300 g/m3
+1	28 m2	Bottom	High	500 g/m3

. These values were used to generate all possible combinations of factors and levels, as shown in

Table 3. Combinations of levels for the 4 factors.

Case	A	B	C	D
01	−1	−1	−1	−1
02	−1	−1	−1	+1
03	−1	−1	+1	−1
04	−1	−1	+1	+1
05	−1	+1	−1	−1
06	−1	+1	−1	+1
07	−1	+1	+1	−1
08	−1	+1	+1	+1
09	+1	−1	−1	−1
10	+1	−1	−1	+1
11	+1	−1	+1	−1
12	+1	−1	+1	+1
13	+1	+1	−1	−1
14	+1	+1	−1	+1
15	+1	+1	+1	−1
16	+1	+1	+1	+1

. In this study, 4 factors with 2 levels resulted in a total of 16 different cases. The factors were denoted with letters A, B, C, and D.

The statistical model for the 2⁴ design included 4 main effects (A, B, C, and D), 6 two-factor interactions (AB, AC, AD, BC, BD, and CD), 4 three-factor interactions (ABC, ABD, ACD, and BCD), and one four-factor interaction (ABCD). The contrast coefficients used in estimating the factorial effects–both the main effects and the interaction effects–were selected following the rules reported by Montgomery [46] for a single replicate of the 2⁴ design.

The factorial analysis required the calculation of the q, Q, and Y values for the 4 main effects and the 11 interactions:

• q: the sum of the products of P_red,_sim and the corresponding contrast coefficient, considering the 16 cases;
• Q: calculated as q divided by the number of cases (16);
• Q²: the square of Q (the total Q² is the sum of all Q² values);
• Y: the percentage of each Q² in relation to the total Q².

3. Results

Table 4. Case-by-case variables and reduced explosion overpressures (P_red,_sim) obtained in the simulations.

Case	Vent Area (m2)	Ignition Location	Initial Turbulence	Dust Concentration (g/m3)	Pred,sim (Bar)	Class
03	56	Top	High	300	0.108	1
01	56	Top	Low	300	0.155	1
05	56	Bottom	Low	300	0.270	1
02	56	Top	Low	500	0.293	1
04	56	Top	High	500	0.321	1
09	28	Top	Low	300	0.344	1
11	28	Top	High	300	0.439	1
13	28	Bottom	Low	300	0.534	2
07	56	Bottom	High	300	0.578	2
06	56	Bottom	Low	500	0.584	2
10	28	Top	Low	500	0.744	2
15	28	Bottom	High	300	1.067	3
14	28	Bottom	Low	500	1.096	3
12	28	Top	High	500	1.146	3
08	56	Bottom	High	500	1.159	3
16	28	Bottom	High	500	1.878	4

shows the maximum values of the explosion-reduced overpressures obtained in the CFD simulations (P_red,_sim). The cases have been ordered from lowest to highest P_red,_sim. According to standards [14,15,18,19], all pressures are expressed in bars throughout the manuscript. Gauge pressure is used in all tables and figures.

The maximum values were recorded at MP-3 in all cases except for case 03 at MP-1. Thus, almost all maximum overpressures were obtained near the silo roof. The mean P_red,_sim was 0.670 bar but the standard deviation achieved 0.481, i.e., the pressures varied a lot between cases, presenting a very high coefficient of variation of 72%.

Then, the values of P_red,_sim were grouped by intervals into the following four pressure classes:

• Class 1: P_red,_sim ≤ 0.5 bar;
• Class 2: 0.5 bar < P_red,_sim ≤ 1.0 bar;
• Class 3: 1.0 bar < P_red,_sim ≤ 1.5 bar;
• Class 4: 1.5 bar < P_red,_sim.

Table 4 also shows the Class and the level of each of the four factors. Class 1 and Class 2 accounted for almost 70% of the cases. The remaining 30% corresponded to Class 3 and only case 16 was above 1.5 bar (Class 4).

Figure 3 illustrates some examples of the pressure-time curves, one for each of the four classes defined. The curves showed two pressure peaks: the first one corresponds to the activation of the vent panels and the second one is P_red,_sim. The first peak was less apparent for Class 1 and Class 2 since the pressure was hardly reduced after the vent opening and it rapidly continued rising.

The effect of each factor was studied individually, as well as the 11 possible interaction effects between them.

Table 5. Analysis of the variables.

	A	B	C	D	BC
q	3.780	3.616	2.676	3.726	1.720
Q	0.236	0.226	0.167	0.233	0.108
Q2 (a)	0.056	0.051	0.028	0.054	0.012
Y	26%	24%	13%	25%	5%

^(a) total Q² = 0.217.

provides a summary of the results of this analysis and indicates the most influential effects. As can be seen, vent area, ignition location, and dust concentration had a similar effect on the variation of P_red,_sim, around 25%. In contrast, initial turbulence had half this effect on P_red,_sim. All values of Q were positive, which means that the levels of the factors assigned with +1 helped to increase the value of P_red,_sim, while those assigned with −1 tended to reduce the value of P_red,_sim.

One interaction effect out of the 11 possible interactions was identified as relevant: the combination of the ignition location and the initial turbulence (BC), with an additional interaction effect of 5%. Its Q value was positive, i.e., its effect on P_red,_sim will depend on the two variables following the patterns indicated in

Table 6. Interaction effect for ignition location plus turbulence.

Ignition	Turbulence	Additional Effect on Pred,sim
−1	−1	Increment
−1	+1	Decrement
+1	−1	Decrement
+1	+1	Increment

.

The importance of this interaction effect is evident considering that case 01 did not present the lowest pressure even though all its factors were level-1. The additional interaction effect between ignition and turbulence allowed it to have a higher P_red,_sim than that in case 03.

Finally, results were compared to venting standards [14,15]. Figure 4 illustrates the whole set of simulations, along with the EN 14491 and NFPA curves.

4. Discussion

The trends that can be drawn from the overpressure results are coherent and match the expected behavior [1]: the higher the turbulence or the dust concentration and the smaller the vent area, the higher the explosion overpressure. On the other hand, a comparison between the cases with different ignition locations indicates that bottom ignition produced overpressures 2.5 times higher on average (maximum = 5.35, minimum = 1.47) than those obtained for top ignition; this tendency was already found by Bartknecht in his 20 m³ experimental tests [47]. Interestingly, Bartknecht also reported that the pressures measured in the top area of the vessels were higher than those registered in the lower part [47]; as mentioned above, all simulations except one reached their maximum P_red,_sim in MP-3, which was located near the top of the roof, 20.25 m from the bottom.

The CFD simulations gave huge differences in the reduced explosion overpressure between the different cases considered, all of which represent situations that could happen in reality. As can be seen in Figure 4, some cases were above the venting standards curves, while others were below. It is important to note that the turbulence levels considered here are quite conservative for a large silo with a mechanical filling system. However, pneumatic filling –sometimes used in biomass storage facilities– or extraordinary events, like an external primary explosion entering the silo, could lead to these turbulence levels or even much higher. The importance of turbulence in industrial equipment venting was already highlighted in the pioneering research work by Eckhoff [48]. Moreover, a correction factor of C_L = 2 was used in these simulations to account for the quite coarse grid and to consider a worst-case behavior related to dust combustion and flame propagation; lower pressures are expected if a lower correction factor is used. The role played by C_L, alone and in combination with the cell size, has already been studied in [23]. It is expected that further simulations cover more possible scenarios, including different volumes and length-to-diameter ratios, along with other dust cloud sizes.

Although the FLACS-DustEx code has been extensively validated against different sets of experimental data [23,27,43], it is not possible to compare the simulations presented here with experimental results, since no data are available on dust explosions in such a large volume. This desirable comparison would serve to improve the accuracy of the simulations. For that reason, the numerical results presented here should be considered with caution, particularly the comparison of overpressures and vent areas with venting standards. Different P_red,sim values would be obtained depending on the levels adopted for each factor. The qualitative trends and relations between parameters could be considered more relevant. It is also important to highlight the limitations that still persist in the dust explosion field [49], including the uncertainties over the dust concentration and turbulence fields in large industrial equipment and the interactions between the different variables and physical phenomena involved.

The results from the factorial analysis indicated that the most relevant parameters in the scenario studied were the vent area, ignition location, and dust concentration, whereas the turbulence level had lower importance. However, the levels of these factors to be considered in CFD simulations should be tailored to each specific scenario considering the real industrial facility and the process conditions.

On the other hand, the interaction turbulence/ignition position might have different origins, but no clear explanation was found; here it is pertinent to remark on the multi-peak nature of venting and the complex interactions between the different physical processes that define each pressure peak, still not fully understood [50].

Although limited, the results in Table 4 do indicate several trends that could have implications for the industry. Firstly, the significant role played by the dust concentration. When the concentration was reduced from 500 g/m³ to 300 g/m³, the pressure lowered by 53% on average, i.e., P_red,sim halved. This means that the generation and accumulation of fine particles should be addressed. Though the presence of dust is unavoidable during the handling of bulk materials, the amount matters. Therefore, gentle conveying systems that minimize impacts and rubbing or grinding actions are to be preferred [51]. In addition, installing dust collecting systems throughout the loading and unloading points of the conveying line could decrease the total amount of dust. Additionally, filling systems that reduce product breakage and dust generation in the silo, such as spiral chutes, should be selected. All these measures, which match the principles of inherently safer design [52], can help to mitigate the consequences of a possible explosion accident.

Secondly, the influence of the level of turbulence on P_red,sim. The lower turbulence level varied P_red,sim by −31% on average. Again, the filling system selected for the silo could have an influence here, along with the operational velocity [53].

Thirdly, higher explosion overpressures were obtained when the ignition was located near the bottom of the silo. Controlling where the ignition takes place in the inner volume of the silo is not feasible, but some specific preventing measures can be applied to reduce ignition probability at the base of the silo. To avoid a thermite reaction between a foreign body made of aluminum impacting rusty steel [54], stainless steel could be used to define an impact zone covering the center of the silo floor [11]. Also, all equipment within the silo, including the discharging systems, should be suitable for hazardous areas. Finally, these results have proved that the factorial analysis could be useful, not only for designing lab-scale explosion experiments [55] but also for planning CFD simulations. This methodology could be applied to the assessment of explosion risks in storage facilities, which can integrate CFD simulations [32], and also to the improvement of guidelines and standards on explosion venting.

5. Conclusions

CFD simulations of vented dust explosions in a 4500 m³ silo for wood pellets were carried out. The influence of the initial turbulence level, dust concentration, ignition location, and vent area on the reduced explosion overpressure was analyzed by defining a set of different study cases. A factorial analysis determined the importance of these variables: 25% for the three latter and 13% for the former. In addition, one interaction effect between ignition location and initial turbulence was detected for the explosion scenario considered in this study, with an additional effect of 5%.

This methodology has proved useful to study detailed situations not specifically contemplated by venting standards and to analyze the effects of initial variables. CFD models combined with factorial analysis could help practitioners to assess explosion risks in industrial storage facilities.