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Temperature and Pressure Influence on Ethane−Air Deflagration Parameters in a Spherical Closed Vessel Maria Mitu,† Venera Giurcan,† Domnina Razus,*,† and Dumitru Oancea‡ †

“Ilie Murgulescu” Institute of Physical Chemistry, Romanian Academy, 202 Splaiul Independentei, Post Office Box 12-194, 060021 Bucharest, Romania ‡ Department of Physical Chemistry, University of Bucharest, 4-12 Regina Elisabeta Boulevard, 030018 Bucharest, Romania ABSTRACT: The maximum (peak) pressures, maximum rates of pressure rise, times to reach the peak pressure, and severity factors, representing the most frequently used pressure-related phenomenological parameters for risk assessment connected with laminar deflagrations, are measured and reported for various ethane−air mixtures (3.42−7.58 vol %) at different initial pressures (30−130 kPa) and temperatures (298−423 K). The reported results are obtained from the pressure−time records during the laminar deflagration in a 0.52 L spherical vessel with central ignition and are compared to the available literature data. Their magnitudes and dependencies upon operational parameters are given and discussed on the basis of simple theoretical models.

1. INTRODUCTION The peak explosion pressure, the time to reach the peak explosion pressure (or the explosion time for short), the maximum rate of pressure rise, and the severity factor are basic pressure-related parameters characteristic for closed-vessel deflagration of fuel−air mixtures, directly measurable from pressure−time curves. These deflagration indices are important for risk assessment, appropriate pressure vessel design for explosion containment, and design of pressure relief systems. They are also necessary for analysis and prediction of various engine or combustor performances. Recent publications provide useful information on explosion pressures, rates of pressure rise, and related properties of various fuels mixed with air: hydrogen, carbon oxide, ammonia, C1−C4 alkanes [pure or as mixed blends, such as liquefied petroleum gas (LPG)], ethylene, and dimethyl ether,1−23 in various conditions. Many processes, especially in the petrochemical industry, operate at various initial temperatures and pressures; therefore, the dependencies of deflagration indices on the initial composition, temperature, and pressure of flammable mixtures are required for a correct evaluation of explosion risks and adequate safety measures. Ethane combustion is of interest for gas-turbine engines, high-speed propulsion, materials synthesis, and many other applications. In concentrations ranging up to 6 vol %, ethane is one of the two main components of natural-gas blends widely used in the power generation industry. The variation of ethane concentrations in natural gas can significantly change the ignition characteristics of the base fuel, which is particularly relevant to the performance of homogeneous charge compression ignition (HCCI) engines, while it is also useful for preventing knock in forced-ignition natural-gas engines and gas turbines. The issue is especially important for mobile applications, where using natural gas from completely different sources is mostly inevitable. Ethane is also separated from petroleum gas, a mixture of gaseous hydrocarbons that arises as a byproduct of petroleum refining. Explosion pressures of ethane−air mixtures measured in various closed vessels with © 2012 American Chemical Society

central ignition at ambient initial conditions were reported by Bartknecht (5 L sphere),3 Senecal et al. (22 L cylindrical vessel),5 Holtappels et al. (20 L sphere),12 and Van den Schoor et al. (4.2 L sphere).13 Data measured at 100 kPa and initial temperatures higher than ambient were reported by Maisey et al.1 (65 °C and 10 L sphere) and Holtappels et al. (100 and 200 °C and 20 L sphere). In this paper, experimental results for explosions of ethane− air mixtures at initial pressure from 30 to 130 kPa, temperature from 298 to 423 K, and various initial composition from 3.42 to 7.58 vol % ethane obtained in a spherical closed vessel (V = 0.52 L) with central ignition are reported. They are supplemented with computed adiabatic explosion pressures, for the same range of initial conditions. While the values of these flammability indices are essential to safety and reliable operations, where natural gas or pure ethane is involved, they are comparatively less available in the literature. In addition, explosion pressures are important input parameters for computation of the normal burning velocity, another basic physicochemical property of premixed combustible gases, necessary for vent design and risk mitigation.

2. EXPERIMENTAL SECTION The experimental setup consists of the following important parts: the vacuum and gas-feed line, the combustion vessel, the ignition controller, the data acquisition system connected with the pressure transducer, and the ionization probe. A scheme of the experimental setup is given in Figure 1. Experiments were performed in a stainless-steel combustion vessel: a spherical vessel S of diameter Φ = 10 cm (V = 0.524 L), which can withstand an internal pressure of 4 MPa under static conditions. The vessel was equipped with several ports for the gas feed and evacuation valve, the ionization probe (tip mounted 3 mm away from the side wall), ignition electrodes, and a pressure transducer. A vacuum and gas-feed line, tight at pressures between 50 Pa and 450 kPa, connected Received: May 17, 2012 Revised: July 10, 2012 Published: July 10, 2012 4840

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initial condition of the explosive mixture. The standard error in measured explosion pressures was ≤2%.

3. DATA EVALUATION The derivatives (dp/dt) were obtained after smoothing the experimental p(t) data by the Savitsky−Golay method based on least-squares quartic polynomial fitting across a moving window within the data. In all cases, we used a 10% smoothing level. The calculations of adiabatic explosion pressures were made with the program ECHIMAD24 based on a general algorithm meant to compute the equilibrium composition of products for any fuel−oxidizer gaseous mixture. The algorithm is based on the thermodynamic criterion of chemical equilibrium: the minimum of Gibbs free energy, at constant temperature and pressure, or the minimum of Helmholtz free energy, at constant temperature and volume. A total of 15 compounds, among them one solid compound (Cgraphite) were considered as products: the fuel (C2H6), Cgraphite, CO2, CO, H2O, O2, N2, CH4, C2H2, C2H4, H2, NO, H, OH, and O. Their heat capacities (expressed as functions of temperature with the form Cp = a + bT + cT2 + dT−2), the standard enthalpies of formation at 298 K, and the standard entropies at 298 K were taken from refs 25 and 26. The adiabatic flame temperatures were also calculated for each system, for both the isobaric and isochoric combustions.

Figure 1. Schematic diagram of the test equipment. the combustion vessels with the gas cylinders containing fuel and air, with a metallic cylinder for mixture storage and a vacuum pump. The fuel−air gaseous mixtures were obtained in a metallic cylinder by the partial pressure method and used 24 h after mixing the components, at a total pressure of 400 kPa. The initial pressures of ethane−air mixtures were measured by a strain gauge manometer (Edwards type EPS-10HM). Before each test, the combustion vessel was evacuated down to 50 Pa; the explosive mixture was admitted and allowed 15 min to become quiescent and thermally equilibrated. Ignition was made with inductive−capacitive sparks produced between stainless-steel electrodes (1 mm diameter, round tips). The spark gap of constant width (3 mm) was located in the geometrical center of the vessel (Figure 2).

4. RESULTS AND DISCUSSION The pressure−time history for centrally ignited explosions propagating in the spherical vessel is shown in Figure 3, for a

Figure 2. Scheme of the combustion vessel. Spark energies were adjusted to a minimum value, between 1 and 5 mJ, to avoid the turbulence produced by an excessive energy input at initiation. The pressure variation during explosions was recorded with piezoelectric pressure transducers (Kistler 601A), connected to charge amplifiers (Kistler 5001SN). Each charge amplifier was calibrated by means of a Kistler calibrator type 5357. For experiments at elevated temperatures, the spherical vessel S was electrically heated; its piezoelectric pressure transducer was mounted in a special adapter, maintained at 25 ± 0.1 °C by a water jacket. The temperature of vessel S was adjusted by ±1 °C using a controller type AEM 1RT96 and monitored by a K-type thermocouple. The signals from the charge amplifier and ionization probe were recorded with an acquisition data system TestLabTM Tektronix 2505, by means of an acquisition card type AA1, usually at 5000 signals per second. Using a spherical test vessel with central ignition, having a volume significantly smaller than that frequently recommended (20 L), offers some advantages arising from the minimization of asymmetrical heat losses associated with the flame buoyancy. Ethane−air mixtures with fuel concentration between 3.42 and 7.58 vol % were investigated, at total initial pressures between 30 and 130 kPa and initial temperatures between 298 and 423 K. Ethane (99.99%) (SIAD, Italy) was used without further purification. Several tests performed in spherical vessel S with a 5.70 vol % ethane−air mixture at ambient initial conditions were used to examine the reproducibility of results. A minimum of three experiments was performed for each

Figure 3. Typical p(t) and dp/dt = f(t) diagrams characteristic to explosion of a lean ethane−air mixture obtained in a spherical vessel with central ignition, at ambient initial conditions.

lean ethane−air mixture ([C2H6] = 4.80 vol %), at p0 = 101.3 kPa and T0 = 298 K. The p(t) diagram has a S shape, where p(t) reaches the peak value pmax and then decreases. The time θmax is the time where the peak (maximum) explosion pressure is reached, a moment when the rate of heat generation by combustion is equal to the rate of heat losses. Much earlier, the p(t) diagram has its first inflection point, corresponding to the peak value of the pressure rise rate (dp/dt). 4.1. Maximum Explosion Pressures. The maximum explosion pressures pmax reached during explosions at ambient initial temperature and various initial pressures of ethane−air mixtures are reported in Figure 4 for several lean ethane−air mixtures (3.42−4.80 vol %) and the stoichiometric mixture 4841

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(5.71 vol %). Similar plots were obtained for rich mixtures ([C2H6] = 6.33−7.58 vol %).

Table 2. Fit Parameters of Linear Correlations between the Maximum Explosion Pressure and the Initial Pressure (eq 1) for Ethane−Air Mixtures with Various Initial Compositions at Ambient Initial Temperature [C2H6] (vol %)

φ

−a (kPa)

3.42 4.04 4.80 5.71 6.33 6.96 7.58

0.59 0.70 0.84 1.01 1.13 1.25 1.37

12.85 9.18 11.33 15.92 9.51 15.51 9.33

± ± ± ± ± ± ±

r2n

b

10.80 2.04 3.43 1.94 1.70 3.22 2.90

6.086 7.284 8.126 8.950 9.254 9.207 9.073

± ± ± ± ± ± ±

0.110 0.024 0.038 0.023 0.020 0.037 0.034

0.999 0.999 0.999 0.999 0.999 0.999 0.999

observed differences can be assigned mainly to differences in volume and shape of explosion vessels. Table 3. Measured Explosion Pressure of Ethane−Air Mixtures, at Ambient Initial Pressure and Temperature

Figure 4. Maximum explosion pressures of ethane−air mixtures at various initial pressures.

At a constant initial temperature, the measured maximum explosion pressures are correlated to the initial pressure (within the range of 30−130 kPa) by a linear equation, for all ethane− air mixtures. pmax = a + bp0

number

pmax (kPa)

[C2H6] (vol %)

explosion vessel

reference

1 2 3 4 5

915 880 840 885 790

6.3 6.3 6.3 6.0 6.0−7.0

sphere, 0.5 L sphere, 5 L cylinder, 22 L sphere, 20 L sphere, 4.2 L

present data 3 5 12 13

(1)

The slope and intercept of these equations are listed in Tables 1 and 2, together with the coefficients of determination, r2n. Table 1. Fit Parameters of Linear Correlations between the Maximum Explosion Pressure and the Initial Pressure for Data Obtained at Various Initial Temperatures T0 (K)

−a (kPa)

r2n

b a

298 333 363 393 423 298 333 363 393 423 298 333 363 393 423

[C2H6] = 4.04% (φ = 0.70) 9.18 ± 2.04 7.284 ± 0.024 7.58 ± 1.76 6.596 ± 0.021 4.41 ± 1.73 6.118 ± 0.021 3.53 ± 1.57 5.745 ± 0.019 3.86 ± 2.23 5.401 ± 0.026 [C2H6] = 5.71% (φ = 1.01) 15.92 ± 1.94 8.950 ± 0.023 5.25 ± 6.02 7.852 ± 0.070 6.87 ± 5.55 7.328 ± 0.065 5.15 ± 1.25 6.839 ± 0.016 6.83 ± 1.10 6.434 ± 0.014 [C2H6] = 6.96% (φ = 1.25) 15.51 ± 3.22 9.207 ± 0.037 5.06 ± 2.08 8.216 ± 0.024 10.65 ± 2.06 7.610 ± 0.026 6.08 ± 1.21 7.152 ± 0.015 6.82 ± 1.88 6.744 ± 0.023

0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999

Figure 5. Maximum explosion pressures of ethane−air mixtures at p0 = 101.3 kPa and various initial concentrations.

The linear variation of pmax against the initial pressure p0 was reported for both experimental and calculated adiabatic explosion pressures of other fuel−air gaseous mixtures: methane−air (Pekalski et al.,9 standard 20 L sphere; Van den Schoor et al.,13 4.2 L sphere; Kindracki et al.,15 17.2 L cylinder; Cammarota et al.,21 5 L cylinder), biogas−air (Dupont and Arccosi,21 20 L sphere), propane−air (Razus et al.,22,23 0.52 L sphere; Desoky et al.,27 14 L sphere), LPG−air (Huzayyin et al.,17 2.56 L cylinder; Razus et al.,19,20 0.52 L sphere), and dimethyl ether−air (Huang et al.,14 cuboid vessel with V = 1.57 L). The peak explosion pressures of ethane−air are close to the characteristic values reported for methane−air,28 propane− air,22 and butane−air,16 as seen from data in Table 4, measured in the same spherical vessel with V = 0.52 L and central ignition, at various initial pressures and ambient initial temperature.

0.999 0.999 0.999 0.999 0.999

φ is the equivalence ratio of the fuel−air mixture, defined as φ = ([fuel]/[O2])/([fuel]/[O2])stoich.

a

The same variation was found for all examined systems. The highest value of maximum explosion pressures is observed in the range of ethane-rich mixtures, at φ = 1.13. In comparison to this result, the maximum explosion pressures of ethane−air mixtures reported in the literature are slightly lower, as seen from data listed in Table 3 and from plots in Figure 5. The 4842

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Table 4. Maximum Explosion Pressures for Stoichiometric Alkane−Air Mixtures, at Various Initial Pressures and T0 = 298 K, Reached in Spherical Vessel with Central Ignition pmax (kPa) p0 (kPa)

9.58 vol % [CH4]

5.71 vol % [C2H6]

4.08 vol % [C3H8]

3.14 vol % [C4H10]

40 60 80 100 120

336 508 679 854 1030

345 521 704 879 1060

355 537 719 901 1083

346 531 717 903 1090

The influence of initial temperature on maximum explosion pressures is shown in Figure 6, where data referring to the

Figure 8. Maximum explosion pressures of ethane−air mixtures at p0 = 101.3 kPa and various initial temperatures. Experimental: (■) 298 K, (●) 333 K, (▲) 363 K, (▼) 393 K, and (◆) 423 K. Calculated: lines (1) 298 K, (2) 333 K, (3) 363 K, (4) 393 K, and (5) 423 K.

Figure 6. Maximum explosion pressures of 5.71 vol % ethane−air mixture at various initial pressures and temperatures.

For explosions at ambient initial temperature, the maximum adiabatic explosion pressure is 940 kPa (experimental explosion pressure is 915 kPa) reached for 6.3 < [C2H6] < 7.0 vol %. For each concentration and/or initial temperature, the adiabatic explosion pressures are higher in comparison to experimental values measured in systems with heat losses. The experimental data, plotted as dimensionless explosion pressures πmax = pmax/p0 against the reciprocal values of initial temperature, are linear, as seen from Figure 9. Similar plots were obtained for rich mixtures (6.33−7.58 vol % [C2H6]). The data in Figure 9 are well-fitted by equation

stoichiometric ethane−air mixture ([C2H6] = 5.71 vol %) are plotted. The increase of initial temperature entails the decrease of the maximum explosion pressure pmax, as already reported for other fuel−air mixtures.9−12,17,18,21,22 Diagrams of maximum explosion pressures reached at ambient initial pressure in preheated ethane−air mixtures are given in Figure 7 for several lean ethane−air mixtures (3.42− 4.80 vol %) and the stoichiometric mixture (5.71 vol %). A comparison of experimental and calculated (adiabatic) explosion pressures referring to explosions at initial ambient pressure and various initial temperatures is given in Figure 8.

Figure 9. Variation of dimensionless explosion pressures reached at p0 = 101.3 kPa, in correlation with the reciprocal temperature of lean and stoichiometric ethane−air mixtures.

Figure 7. Maximum explosion pressures of ethane−air mixtures, at various initial temperatures and p0 = 101.3 kPa. 4843

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n T0

Table 6. Data for the Linear Correlation (νl/rl)C̅ e,V(b − ξ) versus 1/T0 at Ambient Initial Pressure

(2)

5.65 vol % ethane−air; νl = 1; rl = 0.0565

The slopes and intercepts of the correlations found for data measured in the spherical vessel at ambient initial pressure are given in Table 5. Data measured at other initial pressures fit well (eq 2), for all examined ethane−air mixtures.

298 333 363 393 423 ΔcU′ (kJ mol−1)

Table 5. Parameters of Linear Correlations between Dimensionless Explosion Pressures and the Reciprocal Temperature, for Ethane−Air Mixtures with Various Initial Compositions and Ambient Initial Pressure [C2H6] (vol %)

φ

m

1000n (K)

r2n

3.42 4.04 4.80 5.71 6.33 6.96 7.58

0.59 0.70 0.84 1.01 1.13 1.25 1.37

1.778 1.020 1.157 0.712 0.764 0.986 0.691

1.263 1.843 2.033 2.398 2.494 2.396 2.480

0.993 0.999 0.999 0.999 0.999 0.999 0.998

(3)

where ξ = ne/n0 is the ratio of final (end)/initial mole numbers in the isochoric combustion, rl = nl/n0 is the ratio of the number of moles corresponding to the limiting component of the mixture and the total initial number of moles, νl is the stoichiometric coefficient of the limiting component in the mixture, ΔcU′ is the combustion heat (at constant volume and T0) corrected by taking into account the endothermic processes, C̅ e,V is the molar heat capacity of the end gaseous mixture, averaged for the end components and the temperature range from T0 to T̅ e,V, qtr is the total amount of heat losses, transferred by the gas to the vessel before the end of combustion, γe is the adiabatic coefficient at the end of combustion, and V0 is the volume of the vessel. Equation 3 accounts for both the initial pressure and temperature influence on pmax, expressed by eqs 1 and 2. A note of caution should be added regarding the explicit form of eq 3: it is based on the simplifying assumption that qtr is pressure- and temperatureindependent, equivalent with using its average value within a limited range of p0 and T0 variation. Using eq 3, the slope b from eq 1 can be written as b=ξ+

rl ΔcU ′ νl T0Ce,V ̅

C̅ e,V (J mol−1 K−1)

b

1.045 1.046 0.968 1.133 1.049

27.741 27.640 27.523 27.462 27.346 1283 ± 66

8.95 7.85 7.33 6.84 6.43

heat capacities C̅ e,V are calculated as average values for the end (burned) gas, from T0 to Tf,V, using CV(T) polynomials according to Knacke et al.26 Using eq 5, the combustion heat at constant volume and T0, ΔcU′ = 1283 ± 84 kJ/mol, is obtained. This can be compared to the calculated heat effect at constant volume and 298 K, ΔcU0298 = 1427 kJ/mol, obtained with the resulted water in the gas state;33 the observed difference accounts for the endothermic processes in the burned gas. 4.2. Explosion Times. The explosion time, θmax, easily available from pressure−time curves, indicating the time scale of the combustion development, depends upon many fundamental and operational parameters. It is expected to be closely related to the mass burning rate (or the normal burning velocity): the higher the mass burning rate, the shorter the explosion time. The reported results are significantly dependent upon the initial temperature and concentration of the mixture and exhibit only a slight increase with the initial pressure, within the studied range (as seen from Table 7). The influence of the initial temperature and concentration of ethane−air mixtures on explosion times measured at p0 = 101.3 kPa is shown in Figure 10. The increase of the initial temperature determines the decrease of the time necessary to reach the peak explosion pressure, as already reported for various fuel−air mixtures.17,22 This is the consequence of the burning velocity increase when the initial temperature increases, at a constant initial pressure and composition. For all examined initial temperatures, the minimum values of explosion times are observed in the concentration range of 5.7−6.9 vol % (stoichiometric to rich mixtures). 4.3. Maximum Rates of Pressure Rise. For systems with a constant initial concentration and temperature, linear correlations were found between the maximum rates of pressure rise and the initial pressures.

The explosion pressures of preheated ethane−air mixtures, measured in the closed spherical vessel, were examined by means of the equation of energy balance in closed-vessel combustion29 and also described in a recent publication22 ⎛ γ −1 r ΔcU ′ ⎞ ⎟⎟ − qtr e pmax = p0 ⎜⎜ξ + l νl T0Ce,V V0 ̅ ⎠ ⎝

ξ

T0 (K)

(dp /dt )max = α + βp0

(6)

A set of representative data is given in Figure 11. This correlation was observed within the studied pressure range (30−130 kPa) for all examined ethane−air mixtures. In Table 8, the intercept α, slope β, and coefficients of determination r2n for the linear correlations between the maximum rate of pressure rise and the initial pressure are given, for ethane−air mixtures (3.04−7.58 vol % [C2H6]), at ambient initial temperature. The linear correlation between the maximum rate of pressure rise and the initial pressure of the flammable mixture holds at all initial temperatures within the examined range, as seen in panels a and b of Figure 12 for a lean and rich ethane−air mixture. In lean and rich ethane−air mixtures, the increase of the initial temperature entails a slight increase of the maximum rate of pressure rise at all initial pressures. For near-stoichiometric

(4)

The rearrangement of eq 4 gives the possibility to evaluate the temperature influence on the explosion pressure. νl 1 c Ce,V ̅ (b − ξ ) = Δ U ′ rl T0 (5) Equation 5 was used to examine the data referring to preheated fuel−air mixtures, to check the predictions of eq 3. The data referring to the stoichiometric ethane−air mixture are given in Table 6, where the limiting component is ethane; ξ is calculated from data obtained in ethane−air isochoric combustion. The 4844

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Table 7. Initial Pressures Influence on Explosion Time for the Stoichiometric Ethane−Air Mixtures at Various Initial Temperatures θmax (ms) p0 (kPa)

T0 = 298 K

T0 = 333 K

T0 = 363 K

T0 = 393 K

T0 = 423 K

60 80 100.2 120.2

54 56 58 59

47 49 50 51

43 45 45 47

39 41 43 43

34 36 37 39

Figure 10. Time to peak pressure, measured at ambient initial pressure and various initial temperatures: (■) 298 K, offset 40 ms; (●) 333 K, offset 30 ms; (▲) 363 K, offset 20 ms; (▼) 393 K, offset 10 s; and (◆) 423 K.

Figure 12. Maximum rates of pressure rise of ethane−air explosions at various initial temperatures and pressures for (a) a lean mixture: (■) 298 K; (●) 333 K, offset 1 MPa/s; (▲) 363 K, offset 2 MPa/s; (▼) 393 K, offset 3 MPa/s; and (◆) 423 K, offset 4 MPa/s and (b) a rich mixture: (■) 298 K; (●) 333 K, offset 10 MPa/s; (▲) 363 K, offset 20 MPa/s; (▼) 393 K, offset 30 MPa/s; and (◆) 423 K, offset 40 MPa/s.

Figure 11. Maximum rates of pressure rise of ethane−air mixtures at various initial pressures.

Table 8. Intercepts and Slopes of Linear Correlations of (dp/dt)max versus p0, Experiments at 298 K [C2H6] (vol %)

φ

3.42 4.04 4.80 5.71 6.33 6.96 7.58

0.59 0.70 0.84 1.01 1.13 1.25 1.37

α (MPa/s) 4.13 9.29 15.48 16.51 15.02 12.70 13.12

± ± ± ± ± ± ±

1.86 0.97 1.23 1.48 2.28 2.51 1.96

β (s−1) 85 300 608 1020 1193 1107 827

± ± ± ± ± ± ±

19 12 14 17 27 29 23

r2n 0.878 0.993 0.998 0.999 0.998 0.997 0.997

temperature increases, as seen in Figure 13. Similar results were observed for other hydrocarbon−air mixtures (methane, ethylene, ethane, and n-propane) as well,12,23,30 at initial pressures between 100 kPa and 1 MPa. For adiabatically propagating spherical flames, the rate of pressure rise depends upon both the laminar burning velocity and the maximum explosion pressure.21,31,32 The temperature increase determines the increase of the laminar burning velocity Su and the decrease of the maximum explosion pressure pmax; the balance of these

ethane−air concentrations, the maximum rates of pressure rise seem to decrease or at least be nearly constant when the initial 4845

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Figure 13. Maximum rates of pressure rise of several ethane−air mixtures at ambient initial pressure and various initial temperatures.

Figure 15. Effect of the initial concentration on maximum rates of pressure rise of ethane−air explosions, at various initial pressures.

factors determines the overall influence of the temperature on the maximum rates of pressure rise.18,23 The plots of maximum rates of pressure rise at various initial temperatures (at constant initial pressure) and various initial pressures (at constant initial temperature) of ethane−air mixtures with various initial concentrations are given in Figures 14 and 15. The maximum rates of pressure rise of ethane−air

Table 9. Severity Factor of Ethane−Air Mixtures, at Ambient Initial Pressure and Temperature number

KG (bar m s−1)

[C2H6] (vol %)

explosion vessel

reference

1 2 3 4

105 106 78 127

6.3 6.0 5.7 6.0

sphere, 0.5 L sphere, 5 L cylinder, 22 L sphere, 20 L

present data 3 5 12

severity factors reported for a cylindrical vessel, where energy losses appear before the combustion ended. All plots from Figures 11−15 can be converted into plots of the severity factors against initial pressure, temperature, or composition. As long as the same spherical vessel was used, these plots would not bring additional information. It is, however, interesting to examine the maximum “adiabatic” deflagration index KG,ad of ethane−air mixtures in comparison to the deflagration index KG determined from experimental rates of pressure rise, according to eq 8. The adiabatic deflagration index KG,ad can be calculated according to an equation derived by Dahoe and co-workers,31 improved by van den Bulck32 and recently discussed by Cammarota and coworkers34 Figure 14. Effect of the fuel concentration on the maximum rate of pressure rise, in explosions of ethane−air at various initial temperatures: (■) 298 K; (●) 333 K, offset 20 MPa/s; (▲) 363 K, offset 40 MPa/s; (▼) 393 K, offset 60 MPa/s; and (◆) 423 K, offset 80 MPa/s.

K G,ad

(9)

where pmax is the adiabatic explosion pressure reached from initial pressure p0, γu is the adiabatic coefficient of the unburned gaseous mixture, and Speak is the normal burning velocity of the fuel−air mixture, at peak (maximum) explosion pressure. The normal burning velocity at peak explosion pressure, pmax, was calculated as

mixtures reach peak values at ethane concentrations slightly higher than the stoichiometric mixture, as observed earlier for the peak explosion pressures. From maximum rates of pressure rise, the severity factors KG were calculated with equation

⎛ dp ⎞ KG = ⎜ ⎟ 3 V ⎝ dt ⎠max

⎛ p ⎞1/ γu (36π )1/3 (p − p0 )⎜⎜ max ⎟⎟ Speak = 1.041 max ⎝ p0 ⎠

Speak

(8)

Severity factors characteristic to closed-vessel explosions of the most reactive ethane−air mixture, from our experiments (spherical vessel; φ = 10 cm; V = 0.52 L; and central ignition) and from the literature, measured in the same initial conditions (p0 = 101.3 kPa and T0 = 298 K),3,5,12 are given in Table 9. As expected, the severity factors of ethane−air mixtures obtained from experiments in spherical vessels are higher compared to

ν ⎛ p ⎞ μ(1 − 1/ γu) + ν ⎛ Tmax ⎞ μ⎛ pmax ⎞ ⎟⎟ = Su,0⎜⎜ max ⎟⎟ = Su,0⎜ ⎟ ⎜⎜ ⎝ T0 ⎠ ⎝ p0 ⎠ ⎝ p0 ⎠

(10)

where Su,0 is the normal burning velocity at initial conditions (p0 and T0) and μ and ν are the thermal and baric coefficients of normal burning velocity. In the present case, we used the adiabatic explosion pressures pmax calculated with ECHIMAD package and given in Figure 8. The normal burning velocities Su,0 were computed from the cubic law coefficients of pressure 4846

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rise in the early stage of explosion;35 their thermal and baric coefficients μ and ν were determined from Su variation against temperature (at constant p) and pressure (at constant T), respectively. A comparison of adiabatic deflagration indices KG,ad to experimental deflagration indices KG,exp determined from maximum rates of pressure rise by means of eq 8 for preheated ethane−air mixtures is given in Figure 16, together with the

concerning explosion evolution of confined ethane−air explosions. Such results are basic input data for scaling explosions in chemical reactors and the design of venting devices.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone: +40-21-3167912. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The donation of scientific equipment from the Alexander von Humboldt Foundation from Germany to its former fellow, Dr. Domnina Razus, is gratefully acknowledged by the authors.

■ Figure 16. Experimental and adiabatic deflagration indices of ethane− air explosions, at p0 = 101.3 kPa and 298 K.

corresponding best-fit equations (second-order polynomials). As already observed for propane−air, 21 the adiabatic deflagration index largely exceeds the experimental deflagration index; the trend was found at all examined temperatures.

5. CONCLUSION Explosion protection and prevention is based on permanently updated values of flammability indices of fuel−air mixtures, measured or computed in various conditions. In the present paper, maximum explosion pressures (experimental and adiabatic), explosion times, maximum rates of pressure rise, and severity factors of ethane−air mixtures with various initial pressures, temperatures, and fuel/air ratios are reported. Explosions of ethane−air quiescent mixtures in a spherical closed vessel with central ignition are characterized by linear correlations between both the peak explosion pressure and maximum rate of pressure rise with the initial pressure, when initial composition and temperature are constant. The obtained correlations allow for the calculation of peak pressure or maximum rate of pressure rise at any initial pressure within the examined range or even beyond this range, as long as the propagation is laminar and the process takes place as a deflagration. This is important in formulating safety recommendations for ambient conditions different from the standard. At constant initial pressure and composition, the temperature increase determines the decrease of peak explosion pressure and explosion time and a complex variation of maximum rates of pressure rise and severity factors. The peak pressures, the maximum rates of pressure rise, and the deflagration index of ethane−air mixtures have maxima at concentrations higher than stoichiometric. The reported data were measured in a spherical vessel different from the actual international standards [V = 0.52 L, in comparison to V = 20 L as recommended by European Union (EU) standards]. However, they provide useful information

NOMENCLATURE a and b = slope and intercept of the correlation pmax against p0 C = heat capacity h = height of the vessel K = severity factor m and n = slope and intercept of the correlation πmax against 1/T0 p = pressure rl = ratio of the number of moles corresponding to the limiting component of the mixture and the total initial number of moles S = normal burning velocity t = time T = temperature V = volume

Greek Letters

α and β = slope and intercept of the correlation (dp/dt)max against p0 γ = adiabatic coefficient (Cp/CV) φ = equivalence ratio μ = thermal coefficient of the normal burning velocity ν = stoichiometric coefficient of the limiting component in the flammable mixture; baric coefficient of the normal burning velocity π = dimensionless pressure ξ = ratio of final (end)/initial mole numbers θ = time to peak pressure Subscripts and Superscripts

■

ad = adiabatic value c = combustion e = end value G = gas explosions l = limiting component max = maximum value peak = peak value u = unburned gas V = isochoric process 0 = initial value

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