Influence of inert additives on small-scale closed vessel explosions of propane-air mixtures

Fire Safety Journal 111 (2020) 102939

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Influence of inert additives on small-scale closed vessel explosions of propane-air mixtures Venera Giurcan a, Maria Mitu a, *, Codina Movileanu a, Domnina Razus a, Dumitru Oancea b a b

Ilie Murgulescu” Institute of Physical Chemistry, Romanian Academy, 202 Spl. Independentei, 060021, Bucharest, Romania Department of Physical Chemistry, University of Bucharest, 4-12 Regina Elisabeta Blvd., 030018, Bucharest, Romania

A R T I C L E I N F O

A B S T R A C T

Keywords: Combustion Propane Inert additive Small-scale closed vessel Propagation Safety

The propagation of deflagrations in a quiescent stoichiometric propane-air gaseous mixture diluted by 10 vol% of additive (Ar, N2 or CO2) is experimentally studied in a small spherical vessel at various initial pressures (0.5–2.0 bar) and temperatures (298–423 K). The pressure evolution during centrally ignited explosions is characterised by the maximum explosion pressure pmax, the time to peak pressure and the maximum rate of pressure rise (dp/ dt)max. As expected, dilution leads to a decrease in peak explosion pressures and maximum rates of pressure rise, along with an increase in explosion times. Among the examined additives, CO2 has the most significant inerting effect, followed by N2 and Ar. At constant temperature and mixture composition, the peak explosion pressures are linear functions of the total initial pressure. Both the slopes and intercepts of linear correlation pmax ¼ f(p0) are influenced by the amount of inert additive. The slopes depend on the heat of combustion of propane-air-inert mixtures corrected for the endothermic processes in the flame, whereas the intercepts are relevant for the amount of heat transferred to the explosion vessel before the end of combustion. Linear correlations are found for the (dp/dt)max versus initial pressure for all examined diluents.

1. Introduction Flammable mixtures of fuel gases or vapours with air are often formed in industry, especially during the venting of storage tanks or flaring of waste gases. The risk of their accidental ignition, which may lead to destructive explosions, is usually high. Most explosions in closed vessels take place as deflagrations, characterised by increase factors of pressure within 5.0–9.0 and subsonic speeds of flame propagation [1–4]. In special conditions (obstructed tubes or other turbulence-generating configurations), deflagrations may develop into detonations (super­ sonic speeds of propagation) of higher destructive power [3,5]. The assessment of explosion risks in various conditions and the design of equipment and industrial plants where flammable mixtures might be formed requires the knowledge of characteristic parameters of explosions in enclosures. The key parameters of closed vessel explosions running as deflagrations are the maximum (peak) explosion pressure, pmax, the time necessary to reach the maximum explosion pressure, θmax, the maximum rate of pressure rise, (dp/dt)max, and, sometimes, the severity factor (explosion index), KG [2–4]. In addition to these pa­ rameters, the flame speed and the laminar burning velocity are impor­ tant propagation properties that describe the speed of flame propagation

in respect either to the explosion vessel or to the unburned gas behind the flame front [1–3]. The propagation parameters are influenced by the initial composition, pressure and temperature of the fuel-air mixture (factors that determine the amount of released heat and the rate of heat release), the volume and the shape of the enclosure, the size, energy and position of the ignition source and the pre-existing or combustion-created turbulence [1–4]. A comprehensive study of the process should therefore examine the influence of these factors on ex­ plosion evolution. A widely studied fuel is propane, pure or mixed with other light al­ kanes, such as liquefied petroleum gas (LPG). Propane is a by-product of natural gas processing and of some refinery processes. It is commonly used for domestic heating, cooking and as fuel for automotive engines, replacing gasoline, since its use reduces CO2 emissions and other air pollutants, like carbon monoxide and nitrogen oxide. Propane is considered as a fuel of moderate risk, due to several characteristic properties, including the maximum experimental safe gap, the quench­ ing distance and the ignition energy of its mixtures with air [2,6]. However, its storage, transfer, transportation and handling are subject to safety limitations (restrictions and recommendations) because un­ wanted explosions can occur in contact with various energy sources.

* Corresponding author. E-mail address: [email protected] (M. Mitu). https://doi.org/10.1016/j.firesaf.2019.102939 Received 26 June 2019; Received in revised form 13 December 2019; Accepted 16 December 2019 Available online 18 December 2019 0379-7112/© 2019 Elsevier Ltd. All rights reserved.

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Fire Safety Journal 111 (2020) 102939

Studies on propane-air deflagrations in enclosures have examined the influence of initial composition and pressure, and volume and aspect ratio of the explosion vessel on propagation parameters, like the peak explosion pressures and the maximum rates of pressure rise. Previous experiments were mostly carried out in symmetrical vessels (spheres or cylinders with a low aspect ratio, close to 1) with various volumes (20 L–25.5 m3) but also in elongated vessels, totally closed or vented [7–18], at various initial pressures and ambient initial temperatures. The addition of inert components to fuel-air mixtures within the flammability range results in important variations in all propagation properties, including decreases in flame temperature, pressure rise, maximum rate of pressure rise and burning velocity, and longer induc­ tion periods and explosion times. Due to this influence, the additives can be used for explosion mitigation in industrial processes, as long as their concentration is lower than the minimum inert concentration necessary for suppressing the explosion. Most frequently, nitrogen, carbon dioxide, argon and water (vapor or mist) are used as industrial mitigation agents [2,3,19–23], but other gases (halogenated alkanes and even exhaust gases) can be used for this purpose also [3,15,24]. “Inerting” additives, like N2 or Ar, influence flame propagation through their physical properties (thermal diffusivity and heat capacity) and concentration, responsible for the dilution effect (the diminution of available heat able to sustain the explosion). A special situation appears when CO2 is used for explosion mitigation; through its ability to dissociate within the flame front, CO2 changes the physical properties of the mixture and consumes a part of evolved heat in combustion. In this manner, the inerting effect of CO2 addition on fuel-air explosions is significantly higher than that of Ar, He and N2. Propane combustion with air or other oxidisers in the presence of additives was examined mostly in respect to their laminar burning ve­ locity [25–27], a valuable property for the validation of detailed com­ bustion mechanisms and for computational fluid dynamics modelling of flame propagation in various enclosures. Other studies, with the aim of determining the limiting oxygen concentration and the minimum amount of inert gas necessary to bring propane-air mixtures outside their flammability range, were made using lean or rich propane-air-inert mixtures near their flammability limits [24,28–32]. Only a few experi­ mental data are available on pressure evolution during propane-air ex­ plosions in closed vessels in the presence of inert additives. Pursell [20] reported explosion pressures and maximum rates of pressure rise of propane-air mixtures diluted with various amounts of CO2 (5–20 vol%) obtained in experiments at ambient initial conditions in a standard 20 L spherical vessel. Azatyan [24] studied the explosion inhibition of a rich propane-air mixture ([C3H8] ¼ 7 vol%) by CF3H and reported pressure-time records obtained in a cylindrical vessel with L/D ¼ 2 (V ¼ 3.14 L) at ambient initial conditions. This work presents data from an experimental study on stoichio­ metric propane-air deflagrations in the presence of a constant amount (10 vol%) of additive (Ar, N2 or CO2) at various total initial pressures (0.5–2.0 bar) and temperatures (298–423 K). The peak explosion pres­ sures, the times to peak pressure and the maximum rates of pressure rise are measured from pressure-time records of explosions occurring in a small spherical vessel with central ignition. These data are completed by adiabatic explosion pressures, flame temperatures of isochoric com­ bustion of propane-air-additive systems and adiabatic explosion indices, examined versus experimental results. Our results complete the scarce literature data in respect to flame propagation properties in propane-airinert mixtures, especially at initial pressures and temperatures different from ambient. Even though this study is conducted using a small-scale closed vessel, the results are considered useful for recommendations on propane-air explosion mitigation at various initial pressures and temperatures. Adequate safety protective measures can be formulated only on the basis of systematic studies concerning the characteristic indices of deflagra­ tions taking place in enclosures.

2. Experimental The experimental setup consists of the following main parts: a vac­ uum and gas-feed line, a combustion vessel, an ignition controller, a data acquisition system connected with a pressure transducer and an ion­ isation probe. A schematic of the experimental setup is given in Fig. 1. A vacuum and gas-feed line, tight at pressures between 0.5 mbar and 4.5 bar, connect the combustion vessels with the gas cylinders containing fuel and air, with a metallic cylinder for mixture storage and a vacuum pump. The measurements on spherical expanding flames of propane-airinert mixtures were performed in a closed spherical vessel (V ¼ 0.52 L), which can withstand an internal pressure of 40 bar under static conditions. The vessel was equipped with several ports for the gas feed and evacuation valve, the ionisation probe (tip mounted 3 mm away from the side wall), ignition electrodes and a pressure transducer. The combustion vessel was electrically heated and its temperature was adjusted (�1 � C) using an AEM 1RT96 controller and monitored by a Ktype thermocouple. Ignition was made with inductive-capacitive sparks produced between stainless steel electrodes (1 mm diameter, round tips) by a standard auto induction coil. A spark gap of constant width (3 mm) was located in the geometrical centre of the vessel. Spark energies were adjusted to a minimum value, between 1 and 5 mJ, in order to avoid the turbulence produced by an excessive energy input at initiation. The pressure evolution during explosions was measured by a piezo­ electric pressure transducer (Kistler 601A) connected to a charge amplifier (Kistler 5001SN). The signals from the ionisation probe amplifier and from the charge amplifier were acquired using an acqui­ sition data system TestLab™ Tektronix 2505 (acquisition card type AA1), usually at 104 signals per second. The studied mixtures are the stoichiometric propane-air diluted with 10% inert gas (N2, Ar or CO2) (concentration expressed in respect to [C3H8] þ [air] þ [additive]) at variable initial pressures p0 ¼ 0.5–2.0 bar and temperatures T0 ¼ 298–433 K. The used reagents were propane (99.99%), argon (99.99%), nitrogen (99.99%) and carbon dioxide (99.5%) from SIAD Italy, which were used without further purification. The fuel-air mixtures were prepared by a partial pressure method in steel cylinders, at 4 bar total pressure. Before each test, the combustion vessel was evacuated down to 0.5 mbar. The explosive mixture was admitted and allowed 15 min to become quiescent and thermally equilibrated. For each initial condition of explosive mixtures, three experiments were performed. For a few systems (e.g. propane-air-argon at ambient initial conditions), several sets of seven experiments were conducted in identical conditions. The standard error in the measured explosion pressures was �5%. Other details concerning the explosion vessel and the experimental set-up were previously given [15–17]. 3. Data evaluation and computing procedure The rates of pressure rise were computed by numerical derivation using the Savitzky-Golay method, based on least squares quartic poly­ nomial fitting across a moving window within the data. This method has

Fig. 1. Schematic diagram of the test equipment. 2

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Fire Safety Journal 111 (2020) 102939

the advantage of producing a smoothed first derivative without filtering the data. In all cases, we used a 10% smoothing level, since higher values of this level (e.g. 20%) lead to a reduction of the noise accompanied by the signal distortion. More details are given in previous studies [16,17]. The adiabatic explosion pressures and the flame temperatures were calculated with the 0-D COSILAB package. This program is based on a general algorithm designed to compute the equilibrium composition of products for any fuel-oxidiser gaseous mixture using the thermodynamic criterion of chemical equilibrium: the minimum of free Gibbs energy at constant temperature and pressure or the minimum of free Helmholtz energy at constant temperature and volume. A total of 53 compounds were considered as combustion products [33]. The kinetic modelling of propane-air-additive was made by means of the 1-D COSILAB package, developed by Rogg and Peters [33]. In the present case, premixed adiabatic laminar free flames were examined. The runs used the GRI 3.0 mechanism, based on 53 chemical species that participate in 325 elementary reactions. The input data were taken from thermodynamic and molecular databases of Sandia National Labora­ tories, USA, according to the international standard (format for CHEMKIN). The kinetic modelling delivered the laminar burning ve­ locities and the profiles of temperature, species mass fractions and volumetric rate of heat release in the flame front.

mixtures at various initial temperatures are shown in Fig. 3(b). At constant initial temperature and composition, the peak explosion pressures follow a linear correlation against the initial pressure, ac­ cording to Eq. (1): pmax ¼ a þ b⋅p0

4. Results and discussion 4.1. Peak explosion pressures A representative set of pressure-time records obtained during cen­ trally ignited explosions in the spherical vessel is given in Fig. 2, where data for the stoichiometric propane-air and propane-air diluted with 10% inert gas (Ar, N2 or CO2) mixtures at p0 ¼ 1 bar and T0 ¼ 298 K are given. According to these data and from observing the peak explosion pressures and the explosion times, CO2 is the most efficient inerting additive, followed by N2 and Ar. Such a variation was observed for all examined initial pressures and temperatures. For the studied systems, the dependence of pmax, the maximum ex­ plosion pressure (peak explosion pressure) on p0, the initial pressure, was examined. Illustrative results obtained at 298 K, referring to propane-air and propane-air-additive mixtures, are given in Fig. 3(a). The peak explosion pressures of C3H8-air-diluent mixtures change as CO2 < N2 < Ar as a result of the additive’s ability to change the thermal properties of flammable mixtures by changing their heat capacity and thermal conductivity, and consequently the flame temperature and heat losses during flame propagation. Other data obtained for C3H8-air-Ar

8

T0 = 298 K p0 = 1 bar (1)

p / bar

6

(2) (3)

4

(4)

2

(1) No additive (2) 10% Ar (3) 10% N2 (4) 10% CO2

0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

(1)

The slope, intercept and coefficients of determination of these cor­ relations are partly given in Table 1. Data referring to propane-air-inert stoichiometric mixtures at initial temperatures higher than ambient are given in the Appendix, as Table A.1. Such correlations were already found for explosions of propane-air and other flammable mixtures in closed vessels of various dimensions and shapes [2,8,13–16,18,34,35] and are used to determine the peak explosion pressure at any initial pressure, close to the range of studied initial pressures, only when combustion propagates as a deflagration. In Fig. 3(a), the data obtained for the explosion of the stoichiometric C3H8-air mixture are plotted together with data referring to C3H8-airinert mixtures, to show the decrease of peak explosion pressures when additives are present in the flammable C3H8-air mixture. Considering the decrease of the fuel content after dilution from 4.02 to 3.62 vol%, a fair comparison of inerting effects should be made between the lean propane-air mixture ([C3H8] ¼ 3.62 vol%), and the stoichiometric C3H8air-inert mixtures already examined. In such a manner, the “test” mixture should be the stoichiometric propane-air mixture, diluted with 10% excess air. Data from Table 1 reveal that data characteristic for this “test” mixture are very close to those characteristic for the C3H8-air-N2 mixture, within the experimental errors; therefore, there is no need to use this mixture for further comparison. Literature reports few experi­ mental measurements on explosion pressures reached in the closed vessel combustion of propane-air-inert mixtures. Pursell et al. reported pmax ¼ 6.0 bar for a rich propane-air mixture ([C3H8] ¼ 5.0 vol%; equivalence ratio φ ¼ 1.25) diluted with 10 vol% CO2 in experiments at ambient initial conditions, using a 20 L sphere with central ignition [20]. The authors examined this rich propane-air mixture diluted with increasing CO2 amounts and reported its complete inerting at [CO2] ¼ 20 vol%. Azatyan et al. reported the explosion pressures of another rich propane-air mixture ([C3H8] ¼ 7.0 vol%; equivalence ratio φ ¼ 1.59) in the presence of various amounts of CF3H from measurements in an elongated cylinder (L/D ¼ 2.0) with volume V ¼ 3.14 L [24]. The in­ crease of inhibitor concentration within 7–10 vol% determines the progressive decrease of explosion pressures and rates of pressure rise and the increase of explosion times. The computed adiabatic explosion pressures show the same trend of variation when examined against the initial pressure, i.e., a linear variation, within the range of examined initial pressures. In each initial condition, the adiabatic explosion pressures are higher compared to experimental explosion pressures as a consequence of heat losses occurring in a closed vessel. Typical results of adiabatic explosion pressures compared with experimental ones, referring to propane-airinert mixtures in various initial conditions, are shown in Fig. 4, where the pressure ratio πmax ¼ pmax/p0 is plotted against the initial pressure. Similar variations are observed for the adiabatic flame temperatures versus the initial pressure, as shown by Fig. 5. The influence of initial temperature on peak explosion pressures is observed from the data in Figs. 3(b) and 4(b), where the increase of initial temperature results in the decrease of peak explosion pressures for all examined additives. This variation is better seen in Fig. 6, where the explosion pressures measured in experiments at ambient initial pressure are given. Such a variation was found for both experimental and calculated (adiabatic) explosion pressures of other gaseous flam­ mable mixtures: methane-air (Pekalski et al. [36], measurements made in a standardised 20 L sphere); synthetic biogas (CH4–CO2 mixture)-air (Dupont and Accorsi [37], experiments made in a 20 L sphere); LPG-air (Huzayyin et al. [13], experiments in a 2.56 L cylinder); n-hexane-air (Zhang [38], experiments in a 11.9 L cylinder). The observed decrease of peak pressures in preheated flammable

0.08

t/s Fig. 2. Pressure-time diagrams for explosions of the stoichiometric propane-air mixture diluted with 10 vol% inert (Ar, N2, CO2) at p0 ¼ 1 bar and T0 ¼ 298 K. 3

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Fire Safety Journal 111 (2020) 102939

20

16 14

14

12 10 8

12 10 8

6

6

4

4

2 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2

2.0

C3H8-air-10% Ar

T0 = 298 K T0 = 333 K T0 = 363 K T0 = 393 K T0 = 423 K

16

pmax / bar

pmax / bar

18

No additive 10% Ar 10% N2 10% CO2

18

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

p0 / bar

p0 / bar

(a)

(b)

Fig. 3. Initial pressure influence on experimental maximum explosion pressures: (a) propane-air-inert mixtures at T0 ¼ 298 K; (b) propane-air-argon mixtures at various initial temperatures.

where α and β are empirical coefficients. A set of results (slopes and intercepts of πmax versus reciprocal tem­ perature) for N2-diluted propane-air mixtures is given in Table 2 using data at various initial pressures. Similar results found for propane-air and propane-air diluted with Ar or CO2 are given in Table A2 of the Appendix. The influence of initial pressure and temperature on the maximum explosion pressures can be understood by examining an equation derived from the heat balance of constant volume combustion in a gaseous fuel-air mixture, as described in previous studies [16,40–42]: � � r l Δc U ’ γ 1 pmax ¼ p0 ξ þ ⋅ (3) qtr e V0 vl Ce;V ⋅T0

Table 1 The fit parameters of linear correlations between the peak explosion pressure and the initial pressure for data at 298 K. Inert

-a/bar

Air* [16] Ar N2 CO2

0.153 � 0.277 � 0.191 � 0.235 �

0.026 0.055 0.037 0.033

b

r2n

8.718 � 0.030 8.978 � 0.041 8.723 � 0.027 8.223 � 0.025

0.9999 0.9999 0.9999 0.9999

* The stoichiometric propane-air mixture diluted with 10% air, i.e. propaneair mixture with [C3H8] ¼ 3.62 vol%.

mixtures can be explained by the decrease of density of the burning charge, which thus releases a lower heat amount [16]; other factors, determined by additive presence in these mixtures, is examined below. In Fig. 7, the pressure ratio πmax ¼ pmax/p0 of stoichiometric propaneair-inert is plotted against the reciprocal values of initial temperature for mixtures at ambient initial pressure. As found for other fuel-air mixtures [16,35,36,39], the data correlate well through:

π max ¼ α þ

β T0

where ξ ¼ ne=n is the molar ratio of combustion (n0 ¼ the initial number 0 of moles and ne ¼ the number of moles at the end of combustion), rl ¼ nl= is the mole fraction of the limiting component of the mixture, νl is n0 the stoichiometric coefficient of the limiting component in the mixture, V0 is the volume of explosion vessel, Ce;V is the molar heat capacity of the end gaseous mixture, averaged for the end components and for the temperature range T0 to Te;V , γe is the adiabatic compression coefficient

(2)

9.0

9.0

8.8

8.5

max

8.0

8.4

max

= pmax/p0

8.6

8.2

N2, adiab. pressures CO2, adiab. pressures

6.5

N2, exp. data CO2, exp. data

7.8 0.6

0.8

1.0

1.2

1.4

1.6

1.8

298 K, adiabatic 363 K, adiabatic 423 K, adiabatic

298 K, exp. data 363 K, exp. data 423 K, exp. data

7.0

8.0

0.4

7.5

6.0 0.4

2.0

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

p0 / bar

p0 / bar

(a)

(b)

Fig. 4. Initial pressure influence on adiabatic and on experimental pressure ratio πmax: (a) propane-air-inert mixtures at T0 ¼ 298 K; (b) propane-air-argon mixtures at various initial temperatures. 4

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Fire Safety Journal 111 (2020) 102939 2640

2600

2620

2550

Tf,V / K

Tf,V / K

2600 2500

Ar N2 CO2

2450

2580 2560

T0 = 298 K T0 = 363 K T0 = 423 K

2540

2400 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

2.0

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

p0 / bar

p0 / bar

(a)

(b)

Fig. 5. Initial pressure influence on adiabatic flame temperatures Tf,V: (a) propane-air-inert mixtures at T0 ¼ 298 K; (b) propane-air-argon mixtures at various initial temperatures. Table 2 Parameters of linear correlations between dimensionless explosion pressures and the reciprocal temperature, for the stoichiometric C3H8-air mixture diluted with 10% N2.

9.0 8.5 10% Ar 10% N2 10% CO2

pmax / bar

8.0 7.5 7.0 6.5 6.0 5.5

300

320

340

360

380

400

p0 (bar)

α

-β

0.50 0.75 1.00 1.25 1.50 1.75 2.00

0.546 � 0.093 0.780 � 0.168 0.676 � 0.208 0.661 � 0.103 0.725 � 0.154 0.739 � 0.158 0.380 � 0.238

2.350 � 2.298 � 2.349 � 2.367 � 2.352 � 2.353 � 2.479 �

r2n 0.033 0.059 0.073 0.037 0.054 0.056 0.084

0.9997 0.9990 0.9985 0.9996 0.9992 0.9992 0.9983

of the end products, Δc U’ is the molar heat of combustion (at constant volume and T0 ) corrected for the endothermic processes and qtr is the heat transferred to the vessel before the end of combustion. At constant initial temperature, the peak explosion pressures of diluted C3H8-air mixtures depend on initial pressures, on the nature of the inert additive (influencing Ce;V and γe ) and on lost heat by the burned gas, qtr , transferred to the explosion vessel before the end of combustion.

420

T0 / K Fig. 6. Initial temperature influence on experimental maximum explosion pressure; stoichiometric propane-air-inert mixtures at p0 ¼ 1 bar.

Equation (3) can be rewritten in the form of Eq. (2), with a ¼

qtr γeV0 1

and b ¼ ξ þ vrll ⋅CΔc U⋅T . The additive influence is seen both in the intercepts ’

e;V

9.0 8.5

10% Ar 10% N2 10% CO2

pmax rl Δc U ’ ¼ξþ ⋅ p0 vl Ce;V ⋅T0

8.0

max

qtr γe 1 1 ⋅ ¼ α þ β⋅ T0 p 0 V0

(4)

According to this correlation, the initial temperature increase results in lower explosion pressures. Using Eq. (4), the slope β of correlation between the dimensionless explosion pressures and the reciprocal of initial temperature is written as:

7.5 7.0

rl Δc U ’ β¼ξþ ⋅ vl Ce;V ⋅T0

6.5

2.4

2.6

2.8

3.0

3.2

(5)

The corrected heat of combustion Δc U’ of propane with air in the presence of various additives can be obtained from the slopes of vl ⋅Ce;V ⋅ðβ ξÞ versus 1/T0 plots, using the data recorded at various initial rl

6.0 5.5 2.2

0

and slopes of pmax versus p0 plots, through Δc U’Ce;V , qtr ,γe and ξ. Another equivalent form of Eq. (3) is:

3.4

temperatures. A set of results referring to stoichiometric propane-airinert mixtures is shown in Fig. 8 and Table 3. For comparison, the cor­ rected heats of combustion of stoichiometric alkane-air mixtures are 1280 kJ mol 1 (C2H6-air) [41], 1970 kJ mol 1 (C3H8-air) [16] and 2050 kJ mol 1 (n-C4H10-air) [42]. The corrected heats of combustion for inert-diluted propane-air are lower, as a consequence of fuel amount diminution and changes in the physical properties of flammable mix­ tures: the heat capacity of the burned gas Ce;V and its adiabatic

1000*K / T Fig. 7. Variation of dimensionless explosion pressures reached at p0 ¼ 1 bar, in correlation with the reciprocal temperature of stoichiometric propane-airinert mixtures.

5

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Fire Safety Journal 111 (2020) 102939

time depends on the initial properties of the flammable mixture (con­ centration, pressure, temperature and nature of diluents), which influ­ ence the amount and rate of heat release and through them, the mass burning rate (or laminar burning velocity), with shorter explosion times corresponding to higher burning velocities. Representative results referring to the stoichiometric propane-air10% CO2 mixture at various initial pressures (constant T0) and tem­ peratures (constant p0) are given in Fig. 9(a) and (b). As shown in Fig. 9 (a), at all initial temperatures, the increase of initial pressure entails the increase of explosion time (time from ignition to peak explosion pres­ sure), θmax. At constant initial pressure, the explosion times decrease when the initial temperature increases, as seen from Fig. 9(b). Both trends of θmax variation correspond to the trends of variation observed for the laminar burning velocity under the pressure or temperature increase. This behaviour is consistent with data reported for non-diluted propane-air [16] and other fuel-air mixtures, namely, ethane [41] and n-butane [42]. A comparison between the explosion times of the stoichiometric propane-air mixture diluted with 10% inert gases (Ar, N2 or CO2) is shown in Fig. 10, where data measured at ambient initial pressure and various initial temperatures are plotted. The highest inerting effect, at all temperatures, is determined by CO2 addition, as seen from significant increase of explosion times in comparison with Ar- or N2-diluted flam­ mable mixtures.

5500

/K

5000 Ar N2 CO2

4500

4000 2.4

2.6

2.8

3.0

3.2

3.4

1000*K / T0 Fig. 8. Variation of slopes β (defined by eq. (5)) versus the reciprocal initial temperatures for propane-air-inert mixtures. Table 3 The molar heat of combustion for the stoichiometric C3H8-air in the presence of additives. Additive - ΔcU’ (kJ mol

1

)

Ar

N2

CO2

no additive

1778 � 56

1814 � 37

1720 � 10

1970 � 48

4.3. Maximum rates of pressure rise and severity factors

compression coefficient γe . The lowest corrected heat of combustion, Δc U’ ¼ 1720 kJ mol 1, is found for the CO2-diluted C3H8-air mixture, determined by the action of CO2 as a heat sink (the heat capacities range as CO2 > N2 > Ar) and by CO2 dissociation in the flame. The corrected heats of combustion for Ar- and N2-diluted C3H8-air mixtures, higher when compared to Δc U’ of C3H8-air- CO2 mixture, are close (within experimental errors). Studies on CH4–O2 and H2–O2 flames diluted by N2 and CO2 [43] confirmed that the main effect of CO2 on explosion characteristic properties is not on kinetics and diffusive transport rates, but rather on the specific heat of the flammable mixture.

For systems with a constant initial concentration and temperature, linear correlations were found between the maximum rates of pressure rise and the initial pressures. A set of representative data describing the examined propane-air-inert mixtures is given in Fig. 11(a) and (b), where the linear correlations are fitted by:

where m and n are empirical coefficients. Equation (6) was found to be valid within the studied pressure range (0.5–2.0 bar) for all studied C3H8-air-additive gaseous mixtures. The intercepts, slopes and coefficients of determination for the linear cor­ relations between the maximum rate of pressure rise and the initial pressure of C3H8-air-additive mixtures are given in Table 4 for data at ambient initial temperature. Similar results, found for data at temper­ atures higher than ambient, are given in the Appendix in Table A3. Such linear correlations of maximum rates of pressure rise versus the initial

4.2. Explosion times The explosion time, θmax, obtained from pressure-time diagrams, indicates the time scale of the combustion development under given conditions of shape and volume of the explosion vessel. The explosion 70

/ ms

60

55 50

55 50

45

45

40

40

0.4

0.6

0.8

0.50 bar 1.00 bar 1.50 bar 2.00 bar

65

max

/ ms

60

max

70

298 K 333 K 363 K 393 K 423 K

65

(6)

ðdp=dtÞmax ¼ m þ n⋅p0

1.0

1.2

1.4

1.6

1.8

35

2.0

300

320

340

360

380

400

420

T0 / K

p0 / bar

(a)

(b)

Fig. 9. Time to maximum pressure for propane-air-CO2 explosions: (a) initial pressure influence; (b) initial temperature influence. 6

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60

mixtures were found in larger explosion vessels. Experiments at ambient initial conditions, using a rich propane-air mixture ([C3H8] ¼ 5.0 vol%; equivalence ratio φ ¼ 1.25) diluted with 10 vol% CO2 in a 20 L sphere with central ignition delivered (dp/dt)max ¼ 25 bar s 1 [20]. Azatyan studied an even richer propane-air mixture ([C3H8] ¼ 7.0 vol%; equiv­ alence ratio φ ¼ 1.59) and reported (dp/dt)max ¼ 4.7 bar s 1 for this mixture diluted with 10 vol% CF3H, from experiments in a cylindrical vessel of volume V ¼ 3.14 L [24]. A better comparison of their data with the present results can be made by means of severity factors, frequently discussed in literature and defined as: pffiffiffiffiffi KG ¼ ðdp = dtÞmax ⋅ 3 V0 (7)

10% Ar 10% N2 10% CO2

55 50

max

/ ms

45 40 35 30 25

The severity factors KG characteristic of the stoichiometric C3H8-airadditive mixtures at various initial temperatures and ambient initial

20 300

320

340

360

380

400

420 Table 4 Intercepts and slopes of linear correlations of (dp/dt)max versus p0, experiments at T0 ¼ 298 K.

T0 / K Fig. 10. Initial temperature influence on time to maximum explosion pressure; propane-air-inert mixtures at p0 ¼ 1 bar.

pressure were already found for other gaseous fuel-air mixtures [14,17, 41,42,44]. They can be used for evaluating the maximum rate of pres­ sure rise reached from any initial pressure within (or close to) the examined range in processes running as deflagrations. The data of Fig. 11(a) reveal the effectiveness of the three examined inert gases. At constant temperature, the rates of pressure rise change in the order of Ar < N2 < CO2, in parallel to the changes of heat capacities of these compounds and of their burning velocities, dependent on the rates of heat release in their flames [27]. For stoichiometric propane-air mixtures with 10 vol% inert additive, the increase of the initial temperature results in a slight increase of the maximum rate of pressure rise at all initial pressures, as seen in Fig. 11 (b) for stoichiometric propane-air-10 vol% N2. The weak temperature influence on the maximum rates of the pressure rise was already observed for closed vessel explosions of lower alkanes in air [17,41,42, 45] and qualitatively assigned to two opposite phenomena influencing the reaction rate (and the laminar burning velocity). The acceleration of the reaction rate was determined by the increase of initial temperature and the decrease of both reaction rate and released heat amount caused by diminution of the fuel amount in the burning charge. The good cor­ relation of pressure rise rates with the rates of heat release is confirmed by the data from Fig. 12, where experimental maximum rates of pressure rise are plotted versus computed volumetric rates of heat release in propane-air-inert flames, delivered by the kinetic modelling of these flames [27]. Much lower rates of pressure rise of inert-diluted propane-air

)

– Ar N2 CO2

137.4 � 25.6 198.2 � 63.9 196.7 � 20.9 148.8 � 22.9

n/(s 1)

r2n

1063.0 � 20.1 626.2 � 47.4 495.0 � 15.5 267.3 � 16.9

0.9986 0.9860 0.9976 0.9901

1600 298 K

-1

(dp/dt)max / (bar s )

1400 1200

Ar N2 CO2

1000 800 600 400 0

2

4

6

8

10 -9

12 -3

14

16

-1

-dQ/(V*dt)*10 / (J m s ) Fig. 12. Influence of volumetric rates of heat release on maximum rates of pressure rise, for propane-air-inert mixtures at T0 ¼ 298 K and various initial pressures.

-1

1200

(dp/dt)max / (bar s )

10% Ar 10% N2 10% CO2

1400 -1

m/(bar.s

1200

1600

(dp/dt)max / (bar s )

1

Additive

1000 800 600

298 K 363 K 423 K

1000

800

600

C3H8-air-10% N2

400 200

400

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

p0 / bar

p0 / bar

(a)

(b)

Fig. 11. Initial pressure influence on maximum rates of pressure rise: (a) propane-air-inert mixtures at T0 ¼ 363 K; (b) propane-air-N2 mixtures at various initial temperatures. 7

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pressure are given in Table 5. For the same inert additive and a constant initial temperature, the severity factors increase with increasing initial pressure, in accord with the rates of the pressure rise plotted in Fig. 11(a). For the same inert additive and a constant initial pressure, the severity factors decrease slightly with temperature, in accord with the data plotted in Fig. 11(b). At constant initial pressure and temperature, the severity factors of the inert-diluted C3H8-air stoichiometric mixtures follow the order of Ar > N2 > CO2. The severity factors obtained from experimental data can be compared with the adiabatic severity factors, calculated from the maximum explosion pressures and normal burning velocities, according to the model of Dahoe et al. [46] further developed by van der Bulck [47] and discussed by Cammarota et al. [48]: 1

=

KG;ad ¼

ð36πÞ 3 ðpmax 1:041

� �1 pmax =γu p0 Þ ⋅Speak p0

Table 6 Comparison between experimental and computed adiabatic severity factors; stoichiometric propane-air-inert gaseous mixtures (10% inert) at p0 ¼ 1 bar and T0 ¼ 298 K.

(8)

where Su,0 is the laminar burning velocity at initial conditions (p0 and T0) and μ and ν are its thermal and baric coefficients, respectively. The laminar burning velocities Su,0 were computed from the cubic law co­ efficients of the pressure rise in the early stage of explosion in the spherical vessel [49]. Their thermal and baric coefficients μ and ν were determined from Su variation against temperature (at constant p0) and pressure (at constant T0), respectively [27]. The adiabatic explosion pressures were used in both Eqs. (8) and (9). Table 6 shows a comparison between the experimental and computed adiabatic severity indices, for explosions of stoichiometric propane-air-inert gaseous mixtures (10% inert) at ambient initial conditions.

(10)

and K ’G pmax=p

(11)

�1=γu

0

Table 5 Severity factors KG (bar m s 1) of stoichiometric propane-air mixtures at ambient initial pressure and various initial temperatures. T0/K Additive

298

333

363

393

423

– Ar N2 CO2

95.9 69.9 57.1 34.8

94.3 66.1 59.0 34.8

91.9 69.9 59.7 36.5

91.9 71.4 59.3 33.6

92.7 73.9 59.7 31.3

Ar N2 CO2

69.9 57.1 34.8

92.5 75.6 57.1

The explosion of a stoichiometric propane-air mixture in the pres­ ence of 10 vol% Ar, N2 or CO2 as diluents was studied under different initial pressures (0.5–2.0 bar) and temperatures (298–423 K). The ex­ plosion propagation in a small spherical vessel (V ¼ 0.52 L) with central ignition was characterised by several measured or computed indices: maximum explosion pressures (experimental and adiabatic), flame temperatures, explosion times, maximum rates of pressure rise and severity factors. The results complete the few experimental data avail­ able in the literature for this composition and these initial conditions (initial pressures and temperatures different from ambient). For each added inert gas, linear correlations were found between both the peak explosion pressure and the maximum rate of pressure rise with the initial pressure, when the initial temperature was constant. The obtained correlations allow the calculation of peak pressure or of the maximum rate of pressure rise at any initial pressure within the exam­ ined range or beyond this range, when direct measurements are not available, as long as the propagation is laminar and the explosion takes place as a deflagration. A good correlation was found between the computed volumetric rates of heat release and the maximum rates of

As acknowledged by many authors [2–4,9,10], the severity factors KG depend not only on the fuel type and its initial state (pressure, temperature and mole ratio to oxidiser) but also on the size and aspect ratio of the explosion vessel. A way to minimise the dependence of KG on the vessel’s size and the initial state of the flammable mixture was suggested by Kunz [50], who introduced two dimensionless severity factors:

K }G ¼ �

KG,adiab/(bar m s 1)

5. Conclusions

4.4. Dimensionless severity factors

KG Δpmax ⋅Su;exp

KG,exp/(bar m s 1)

These factors rely on several experimental properties (pmax and (dp/ dt)max), supposed to be influenced in the same way by vessel’s size and its aspect ratio. Su,exp is independent of the vessel’s characteristics, but depends on the fuel type and on the initial state of the flammable mixture. Representative results regarding the stoichiometric propane-air mixture at ambient initial conditions, in vessels of various dimensions and shapes are given in Tables 7 and 8, based on data from the present study and from the literature. Unfortunately, no similar data were found for inert-diluted stoichiometric propane-air mixtures. The variation range of “primary” severity factors, KG, observed for either spherical or elongated vessels, is greatly reduced by using the “corrected” severity factors KG’ and KG”. This aspect is confirmed by recent data on H2–N2O–N2 mixtures [54,55] at various initial pressures. However, a steady increase of “corrected” severity factors KG’ and KG” is observed in Tables 7 and 8 when the volume of explosion vessel increases. The dimensionless severity factors of inert-diluted stoichiometric propane-air mixtures at various initial temperatures are given in Ap­ pendix in Table A4. Their plots against the initial temperature of flam­ mable mixtures are shown in Fig. 13(a) and (b). The temperature increase within 300 and 420 K results in an important decrease of both KG’ and KG”. In accordance with the data from Fig. 11(a), the lowest corrected severity factors are found for the propane-air-CO2 mixture, revealing its higher inerting effect when compared to Ar or N2.

where γ u is the adiabatic compression coefficient of unburned gaseous mixture and Speak is the laminar burning velocity of the flammable mixture at peak (maximum) explosion pressure, pmax. Speak was calcu­ lated as: � � � �μ � �ν � �μ 1 1= þν γu Tmax pmax pmax Speak ¼ Su;0 ¼ Su;0 (9) T0 p0 p0

K ’G ¼

Inert

Table 7 KG obtained in spherical vessels and dimensionless severity factors KG’ and KG” for the stoichiometric C3H8-air mixture at ambient initial conditions.

8

pmax (bar)

Δpmax (bar)

KG (bar*m/s)

Vessel’s volume (m3)

8.74 8.75 9.20

7.74 7.75 8.20

85 110 150

0.52*10 0.020 0.120

3

KG’

KG "

Reference

25.5 32.9 42.5

5.21 6.72 8.37

[16,17] [51] [10]

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Fire Safety Journal 111 (2020) 102939

Table 8 KG obtained in elongated vessels and dimensionless severity factors KG’ and KG” for the stoichiometric C3H8-air mixture at ambient initial conditions.(c) pmax (bar)

Δpmax (bar)

8.1 8.2(a) 8.0(b) 8.9 8.2 9.3

KG (bar*m/s)

7.1 7.2(a) 7.0(b) 7.9 7.2 8.3

Vessel’s volume (m3)

Vessel’s geometry

38 43(a) 92(b) 100 76 159

3

Cylindrical Cuboid Cylindrical Cylindrical Cylindrical Cylindrical

1.12*10 1.84*10 3 2.56*10 3 5.0*10 3 22*10 3 0.500

KG’

KG "

Reference

12.4 14.9 30.6 29.4 24.5 44.6

2.68 3.22 6.68 5.93 5.25 8.72

[16,17] [50] [5] [6] [7] [6]

a

Data corresponding to φ ¼ 0.95. Data corresponding to φ ¼ 1.15–1.20. c Su ¼ 43 cm s 1 was taken from Ref. [52]; γu ¼ 1.3659 according to specific heats from Knacke and Kubaschewski [53]. b

30

6.0 4.02% C3H8-air 4.02% (C3H8-air)+10% Ar 4.02% (C3H8-air)+10% N2 4.02% (C3H8-air)+10% CO2

28 26

5.8 5.6 5.4 5.2

KG"

KG'

24 22 20

5.0 4.8 4.6 4.4

18

4.2

16 300

320

340

360

380

400

4.0 280

420

4.02% C3H8-air 4.02% (C3H8-air)+10% Ar 4.02% (C3H8-air)+10% N2 4.02% (C3H8-air)+10% CO2

300

320

T0 / K

340

360

380

400

420

440

T0 / K

(a)

(b)

Fig. 13. Temperature influence on dimensionless severity factors K’G and K}G for stoichiometric propane-air-inert mixtures at p0 ¼ 1 bar.

pressure rise. At constant initial pressure and composition, the temperature in­ crease determines the decrease of peak explosion pressure and of ex­ plosion time, but only a slight variation of maximum rates of pressure rise and of severity factors. The heat balance in the constant volume combustion of propane-airadditive mixtures was used to explain the found correlations of peak explosion pressures with the initial pressure (at constant T0) and with the reciprocal initial temperatures (at constant p0). From such correla­ tions, the molar heat of combustion of propane, ΔcU0 , corrected for endothermic processes, was determined. The larger extent of endo­ thermic processes (mainly dissociation reactions) of propane combus­ tion in the presence of CO2 explains the largest decrease of the molar heat of combustion for the C3H8-air mixture diluted with CO2 as compared to C3H8-air-Ar and C3H8-air-N2. This effect is confirmed by the decrease of adiabatic flame temperatures Tf,V, in the order of Ar > N2 > CO2. The dilution effect is significant for all flammability indices, when constant initial pressure and temperature are maintained. The inerting efficiency of the examined gases varies in order of Ar < N2 < CO2, in parallel to the heat capacities of these compounds. However, other factors, such as the thermal conductivity and the chemical reactivity of added gases, influence the explosion propagation, through the processes of heat and mass transfer and of reaction evolution (development) in propane flames. The corrected severity factors K’G and K}G were used to minimise the dispersion of severity factor KG, observed for vessels of various di­ mensions and shapes, and to examine the influence of temperature and type of added inert on explosion severity.

The found correlations, even if based on several simplifying as­ sumptions, indicate the trend of variation for the flammability indices for propane-air-additive mixtures with the initial pressure and temper­ ature. The data were obtained in a small-scale vessel, in order to reduce the buoyancy effects common for larger vessels and the possibility of flames to develop a cellular structure. In addition, in large-scale enclo­ sures, there is also the possibility of flame acceleration and transition to a turbulent combustion regime. This recommends a careful use of the present results, limited to small scale explosions; they are suited mostly for determining fundamental laminar burning parameters without the effects of flame instability. Only quantitative values obtained by largescale experiments should be used in formulating safety recommenda­ tions requested by explosion protection and prevention. CRediT authorship contribution statement Venera Giurcan: Investigation, Validation, Formal analysis. Maria Mitu: Investigation, Visualization, Formal analysis, Writing - original draft, Writing - review & editing. Codina Movileanu: Investigation, Validation. Domnina Razus: Supervision, Writing - review & editing. Dumitru Oancea: Methodology, Conceptualization. Acknowledgement The present study was partially financed by the Romanian Academy under research project “Dynamics of fast oxidation and decomposition reactions in homogeneous systems” of “Ilie Murgulescu” Institute of Physical Chemistry.

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Appendix Table A.1 The fit parameters of linear correlations between the peak explosion pressure and the initial pressure obtained at various initial temperatures. T0/K

Inert

-a/bar

b

298

– Ar N2 CO2

0.2245 0.2767 0.1905 0.2354

� 0.0344 � 0.0547 � 0.0368 � 0.0334

9.353 8.978 8.723 8.223

� 0.027 � 0.041 � 0.027 � 0.025

0.9999 0.9999 0.9999 0.9999

333

– Ar N2 CO2

0.2003 0.1955 0.1695 0.1397

� 0.0385 � 0.0318 � 0.0109 � 0.0387

8.534 8.173 7.940 7.458

� 0.030 � 0.024 � 0.008 � 0.029

0.9999 0.9999 1.0000 0.9999

363

– Ar N2 CO2

0.1766 0.2384 0.1648 0.1456

� 0.0454 � 0.0498 � 0.0270 � 0.0244

7.856 7.628 7.332 6.896

� 0.036 � 0.037 � 0.020 � 0.019

0.9999 0.9999 0.9999 0.9999

393

– Ar N2 CO2

0.1538 0.1597 0.1389 0.1659

� 0.0225 � 0.0299 � 0.0135 � 0.0460

7.276 6.999 6.802 6.442

� 0.018 � 0.022 � 0.010 � 0.034

0.9999 0.9999 0.9999 0.9999

423

– Ar N2 CO2

0.1313 0.1574 0.1308 0.1897

� 0.0200 � 0.0267 � 0.0181 � 0.0585

6.774 6.547 6.336 6.063

� 0.016 � 0.020 � 0.014 � 0.044

0.9999 0.9999 0.9999 0.9998

r2n

Table A.2 Parameters of linear correlation between dimensionless explosion pressures and the reciprocal temperature, for stoichiometric propane-airþ10% inert (Ar, N2, CO2) at p0 ¼ 1 bar. p0 (bar)

α

4.02% C3H8-aer 0.50 0.75 1.00 1.25 1.50 2.00

0.974 0.560 0.775 0.858 0.985 0.288

-β

r2n

� 0.196 � 0.595 � 0.092 � 0.150 � 0.374 � 0.356

2.390 2.573 2.496 2.482 2.442 2.670

� 0.069 � 0.211 � 0.033 � 0.053 � 0.375 � 0.126

0.9988 0.9901 0.9997 0.9993 0.9956 0.9968

(4.02% C3H8-aer) þ 10% Ar 0.50 0.801 � 0.232 0.75 1.060 � 0.236 1.00 0.851 � 0.124 1.25 0.913 � 0.160 1.50 0.871 � 0.271 1.75 1.015 � 0.328 2.00 0.752 � 0.164

2.326 2.253 2.344 2.351 2.371 2.344 2.432

� 0.082 � 0.083 � 0.050 � 0.057 � 0.096 � 0.116 � 0.058

0.9981 0.9980 0.9993 0.9991 0.9976 0.9964 0.9992

(4.02% C3H8-aer) þ 10% N2 0.50 0.546 � 0.093 0.75 0.780 � 0.168 1.00 0.676 � 0.208 1.25 0.661 � 0.103 1.50 0.725 � 0.154 1.75 0.739 � 0.158 2.00 0.380 � 0.238

2.350 2.298 2.349 2.367 2.352 2.353 2.479

� 0.033 � 0.059 � 0.073 � 0.037 � 0.054 � 0.056 � 0.084

0.9997 0.9990 0.9985 0.9996 0.9992 0.9992 0.9983

(4.02% C3H8-aer) þ 10% CO2 0.50 0.824 � 0.335 0.75 1.025 � 0.278 1.00 0.652 � 0.138 1.25 0.716 � 0.123 1.50 1.021 � 0.116 1.75 0.672 � 0.057 2.00 0.420 � 0.548

2.105 2.058 2.188 2.187 2.114 2.215 2.577

� 0.119 � 0.098 � 0.049 � 0.044 � 0.041 � 0.020 � 0.194

0.9953 0.9966 0.9993 0.9994 0.9994 0.9999 0.9916

10

Fire Safety Journal 111 (2020) 102939

V. Giurcan et al.

Table A.3 Intercepts and slopes of linear correlations of (dp/dt)max versus p0. 1

n/s

1

T0/K

Additive

m/bar.s

298

– Ar N2 CO2

137.4 198.2 196.7 148.8

� 25.63 � 63.88 � 20.92 � 22.88

1063.0 � 20.13 626.2 � 47.42 495.0 � 15.52 267.3 � 16.92

0.9986 0.9860 0.9976 0.9901

333

– Ar N2 CO2

147.4 260.5 225.0 154.8

� 42.94 � 46.44 � 23.71 � 17.63

1036.3 � 33.73 552.1 � 34.38 481.0 � 17.60 269.6 � 13.02

0.9979 0.9904 0.9967 0.9942

363

– Ar N2 CO2

183.5 173.5 215.9 148.6

� 30.35 � 26.29 � 20.20 � 20.03

972.1 � 23.95 669.0 � 19.51 500.6 � 14.98 273.7 � 15.72

0.9988 0.9979 0.9978 0.9903

393

– Ar N2 CO2

231.9 251.8 201.3 137.7

� 17.03 � 43.31 � 37.27 � 33.15

884.0 � 13.43 601.7 � 32.04 499.6 � 27.64 252.4 � 24.75

0.9995 0.9930 0.9924 0.9768

423

– Ar N2 CO2

131.5 221.2 207.5 86.84

� 62.3 � 39.66 � 21.77 � 16.05

1025.6 � 58.5 647.3 � 28.99 514.4 � 16.24 324.4 � 12.15

0.9952 0.9940 0.9975 0.9965

r2n

Table A.4 Experimental severity factors KG, and dimensionless severity factors K’G and K}G of stoichiometric propane-air and propane-air-inert mixtures at ambient initial pressure T0/K

Additive

KG (bar s

298

– Ar N2 CO2

333

1

m 1)

KG’

KG"

96.74 66.44 55.74 33.53

29.01 25.09 24.92 22.59

5.75 5.25 5.20 4.88

– Ar N2 CO2

95.39 65.48 56.89 34.20

27.03 22.45 23.61 21.45

5.67 4.96 5.24 4.89

363

– Ar N2 CO2

93.13 67.89 57.74 34.03

24.96 22.58 22.28 20.01

5.52 5.24 5.21 4.81

393

– Ar N2 CO2

89.93 68.78 56.48 31.44

22.98 21.63 20.29 17.15

5.35 5.28 4.95 4.32

423

– Ar N2 CO2

90.95 69.99 58.18 33.14

22.06 19.90 19.60 16.14

5.37 5.08 5.05 4.25

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