Microsoft Word - 1.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 77, 2019 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Genserik Reniers, Bruno Fabiano Copyright © 2019, AIDIC Servizi S.r.l. ISBN 978-88-95608-72-3; ISSN 2283-9216 Experimental Determination of the Static Equivalent Pressures of Detonative Explosions of Cyclohexane/O2/N2- Mixtures in Long and Short Pipes (part 3 of 3) Hans-Peter Schildberg*, Julia Eble BASF SE, 67056 Ludwigshafen, Germany hans-peter.schildberg@basf.com The abstract of the third part of this paper is included in the abstract of part 1. Table 2: Compilation of precompression factors found for all tests conducted. The tests are listed in the same order as in Table 1. Omitted are those tests without DDT and those with a DDT location upstream of the first pressure sensor (tests 29, 26, 24). Note that tests 22, 32 and 35 were tests in the short pipe configuration. num- ber of test initial pressure of the gas mixture [bar abs] value of last pressure measurement of precompressed zone upstream of DDT location [bar abs] precom- pression factor [ - ] axial position of last pressure measure- ment [mm] location of DDT as inferred from pipe deformation [mm] speed of precom- pressed zone as inferred from the two last pressure signals upstream of DDT location [m/s] distance between two last pressure sensors upstream of DDT location [mm] 1 20,00 250 12,50 3300 3740 442 620 19 14,10 603 42,77 4440 4530 1280 320 20 14,00 470 33,57 2840 3060 578 630 21 14,00 > 1000 > 71,43 1580 1710 706 630 5 20,00 508 25,40 4580 4750 800 640 22 14,00 580 41,43 6040 6140 914 320 25 12,00 110 9,17 2840 3430 533 320 28 12,00 > 1000 > 83,3 2840 2980 1103 320 23 12,00 980 81,67 1580 1690 360 630 32 3,07 625 203,58 7760 7910 1736 330 35 3,17 500 157,72 7430 7540 1488 320 The final speeds of the precompressed zone relative to the pipe wall found for the long pipe configuration seem to be similar for Cyclohexane and the other mixtures. The values are in the range of 1000 m/s to 1300 m/s, which is about half of the speed of the stable detonation. The full width at half maximum of the pressure peaks corresponding to the compressed zone of unreacted gas ahead of the accelerating deflagrative flame front is of the order of 30 µs (see Figures 9, 10, 11) in the final stage of the run-up to detonation. This also holds for the other mixtures investigated in the past. If a final speed of 1150 m/s relative to the pipe wall is assumed, the extension of the compressed zone in axial direction is about 35 mm (34.5 mm = 1150 m/s * 30µs). Figure 12 provides a schematic sketch. To allow the precompressed unreacted gas to autoignite before it is consumed by the extremely fast deflagrative flame front, its ignition delay time must drop to values of about 10 µs or less. This results from the fact that in the final stage of flame acceleration the deflagrative flame front propagates into the unreacted, heated mixture with speeds of the order of 1000 m/s, meaning that within 10 µs a 1 cm thick slice (in axial direction) of the shock front is converted into hot reaction products. If the thin slice of unreacted mixture still DOI: 10.3303/CET1977177 Paper Received: 1 January 2019; Revised: 3 May 2019; Accepted: 3 July 2019 Please cite this article as: Schildberg H.-P., Eble J., 2019, Experimental Determination of the Static Equivalent Pressures of Detonative Explosions of Cyclohexane/O2/N2-Mixtures in Long and Short Pipes (part 3 of 3), Chemical Engineering Transactions, 77, 1057-1062 DOI:10.3303/CET1977177 1057 remaining ahead of the front would need longer than about 10 µs to autoignite – and thereby generating the DDT – it would be consumed in the next 10 µs in deflagrative manner and the DDT would not occur. Figure 12: Schematic sketch of the pressure distribution in a long pipe when the pressure peak corresponding to the compressed unreacted mixture ahead of the deflagrative flame front has attained its maximum height, i.e. an instant just before DDT occurrence. 5. Understanding the observed precompression factors by applying reaction kinetics The precompression factors, which are attained in the precompressed zone of unreacted mixture ahead of the deflagrative flame front at the instant of autoignition, should correlate with the values found experimentally for the ratio R. To understand quantitatively the reason why (1) the R-values of stoichiometric C6H12/O2/N2 mixtures with low O2 concentrations differ from the R-values found for the other three stoichiometric mixtures CH4/O2/N2, H2/O2/N2 and C2H4/O2/N2 at corresponding O2-concentrations and why (2) the R-values drop along the stoichiometric line with rising O2 concentrations, reaction kinetics will be applied. 5.1 Computational model A detailed chemical kinetic mechanism taken from Silke (2007) was used to study the oxidation of cyclohexane both at high and low temperatures. The mechanism was validated against experimental data incorporating the temperature range 650-1150 K, and different pressures and equivalence ratios (Silke 2007). Based on this kinetic model, concentration-time profiles were calculated with the program package OpenSMOKE (Cuoci 2013, 2015) for an adiabatic batch reactor with constant volume. Besides, a homogenous reaction system with ideal gas behavior was assumed. The calculated ignition delay times were set equal to the times of the maximum slopes of the temperature profiles. To identify the most important reactions that influence the ignition delay times, sensitivity and reaction flux analyses were performed. 5.2 Results and discussion Kinetic mechanisms for combustion often consist of different parts, the so-called submechanisms, to describe the consumption of the combustible, the C1/C6 species or the H2/O2 system in different temperature regimes. At lower temperatures, the dominant reaction path for cyclohexane is the H atom abstraction by OH and other radicals, followed by successive additions of oxygen leading to chain branching pathways (Silke 2007). Through the degenerate chain-branching reactions OH radicals are formed, which, in turn, lead to the consumption of the combustible. At high temperatures, the mechanism includes unimolecular combustible decomposition, H atom abstraction, alkyl radical decomposition and the subsequent oxidation reactions of the fragments. The different reaction rates can indicate whether the low- or the high-temperature mechanism is more influential. 5.2.1 Temperature dependence of the mechanism To get an idea which mechanism is dominant in the different temperature regimes, reaction flux analyses were performed at 1100 K, 1200 K, 1300 K and 1400 K and 2000 bar for the stoichiometric C6H12/O2/N2 mixture used in tests 1 and 5 (mole fractions: 0.0228/0.20521/0.77199). The high pressure was chosen to roughly account for the pressure in the precompressed zone at the instance of DDT occurrence. The analyses were performed for the cyclohexane consumption at 90 % of the ignition delay time to get comparable results. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10 100 axial position x/L in pipe p re s s u re /p in iti a l 2 5 50 20 Final stage of pressure peak due to compressed unreacted mixture directly ahead of deflagrative flame front Full width at half maximum: Δt ≅ 30 µs Δx ≅ 35 mm (at 1150 m/s) Shockfront moving with ca. 1150 m/s relative to pipe, unreacted mixture gets highly compressed, temperature rises to values of ca. 1100 K, i.e. T >> Tinitial unreacted mixture downstream of initial shock wave moves with typically ca. 250 m/s relative to pipe, T > Tinitial Unreacted mixture still at rest and at pinitial and Tinitial Initial shock wave, moves with typically 400 m/s , i.e. typically 20 % faster than the speed of sound of the unreacted mixuture at Tinitial Extremely fast deflagrative flame front, hot reaction gases expand in direction to x/L = 0, thereby providing the momentum to drive shockfront further in opposite direction 1058 An indicator for the occurrence of the low-temperature mechanism is the addition of O2 to the cyclohexyl radical. For the high-temperature mechanism the indicator is the isomerization reaction of the cyclohexyl radical followed by decomposition. The temperature dependent competition between these two reaction pathways was analyzed in this study. At 1100 K the ratio between the reaction paths is nearly 1:1, whereas at 1400 K around 90 % of the cyclohexyl radicals are consumed by the high-temperature reaction path. Therefore, it can be concluded that the transition between the low- and high-temperature mechanisms proceeds between 1100 K and 1400 K. 5.2.2 Ignition temperature of cyclohexane The experimentally determined ignition temperature of cyclohexane in air at 1 bar abs is 533 K (=260 °C; CHEMSAFE database). The ignition temperature is the lowest temperature of a hot surface at which within 5 minutes an ignition of a flammable gas or vapor in mixture with an oxidiser (usually air) and, if applicable, an inert gas occurs. To determine the ignition temperature predicted by the kinetic mechanism, the simulations were performed with a simulation time of 5 minutes and 1 bar varying the temperature. As a result, the first ignition within 5 minutes at 1 bar occurs at 602 K. From sensitivity analyses and reaction flux analyses it becomes obvious that the most influential reactions are the low-temperature reactions (e.g. the O2-addition to the cyclohexyl radical). 5.2.3 Ignition delay times of cyclohexane, ethylene, methane and hydrogen in mixture with air The ignition delay times (IDT) for stoichiometric cyclohexane, ethylene, methane and hydrogen mixtures with air (or with slightly O2-depleted air or slightly O2-enriched air) were calculated for different compression ratios and temperatures. The temperature after compression was calculated as follows: Tfinal= Tinitial· pfinalpinitial κ-1 κ and κ = Cp CV . (1) Here, p is the absolute pressure, T the absolute temperature and κ the isentropic exponent, calculated as the ratio between the heat capacity at constant pressure and the heat capacity at constant volume. For the different mixtures, the isentropic exponent was calculated by the thermodynamic rules of mixtures. The conditions before compression are labelled as “initial”, the conditions after compression as “final”. The ignition delay times calculated by the kinetic simulations for the different combustible/O2/N2 mixtures at different compression ratios are given in Tables 3 to 6. x denotes the mole fraction of the species. For methane, ethylene and hydrogen the gas mixture must be compressed by a factor of about 200 to heat the gas from Tinitial = 20 °C to about 1100 K. At this temperature the IDT has dropped to about 10 µs. For cyclohexane at Tinitial = 70 °C a compression ratio of about 100 is enough to heat it to a temperature at which the IDT has dropped to about 10µs. It becomes obvious, that at temperatures of greater than or equal to about 1100 K the ignition delay times are of the same order for all combustible/air mixtures. At lower temperatures the difference between the ignition delay times of the individual mixtures is much higher. In this low-temperature regime cyclohexane has the shortest ignition delay times and the lowest ignition temperature compared to the other combustibles of this study. By employing reaction flux analyses it could be shown that the low-temperature reactions of cyclohexane are most influential in this temperature regime. The typical low-temperature reaction path of the cyclohexane oxidation cannot occur for methane, ethylene or hydrogen. But, in the high temperature regime at temperatures above 1100 K, ignition is caused by similar reactions for the four different combustible/air mixtures and the ignition delay times converge. These findings show that if an explosive mixture M1 has a substantially lower AIT than an explosive mixture M2, it cannot yet be assumed that mixture M1 also exhibits an IDT sufficiently small for DDT occurrence at substantially lower temperatures (and henceforth at smaller precompression factors) than the mixture M2. The correct way to estimate whether an unknown mixture M1 exhibits smaller or larger R-values than a known mixture M2 is to compare the precompression ratios which generate temperatures for which the IDT drops to values of the order of 10 µs. Table 3: Ignition delay times of cyclohexane. Tinitial = 343 K = 70 °C, pinitial = 20 bar, x(C6H12) = 0.0228, x(O2) = 0.2052, x(N2) = 0.772. This is the mixture of test no. 1 in Table 1. pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] 25 500 776 1.70E-03 100 2000 1104 7.40E-06 50 1000 926 6.60E-05 125 2500 1168 4.10E-06 75 1500 1026 1.70E-05 150 3000 1223 2.60E-06 1059 Table 4: Ignition delay times of methane. Tinitial = 293 K = 20 °C, pinitial = 12 bar, x(CH4) = 0.125, x(O2) = 0.25, x(N2) = 0.625. This is the mixture of test no. 4 in Schildberg (2016a). pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] 25 300 646 3.30E+01 125 1500 958 6.10E-04 50 600 765 1.80E-01 150 1800 1002 2.30E-04 75 900 845 1.20E-02 200 2400 1075 5.70E-05 100 1200 907 2.10E-03 300 3600 1188 9.40E-06 Table 5: Ignition delay times of ethylene. Tinitial = 293 K = 20 °C, pinitial = 8 bar, x(C2H4) = 0.0733, x(O2) = 0.22, x(N2) = 0.7067. This is the mixture of test no. 10 in Schildberg (2018). pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] 25 200 651 3.60E-01 125 1000 971 1.90E-04 50 400 774 2.30E-02 150 1200 1016 8.70E-05 75 600 856 2.30E-03 200 1600 1091 2.30E-05 100 800 919 5.40E-04 300 2400 1207 5.10E-06 Table 6: Ignition delay times of hydrogen. Tinitial = 293 K = 20 °C, pinitial = 3.58 bar, x(H2) = 0.276, x(O2) = 0.138, x(N2) = 0.586. This is the mixture of test no. 22 in Schildberg (2015). pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] pfinal/pinitial pfinal [bar] Tfinal [K] IDT [s] 25 89.5 675 2.20E+02 125 447.5 1025 4.40E-04 50 179 808 2.00E-01 150 537 1075 1.60E-04 75 268.5 898 1.10E-02 200 716 1158 3.50E-05 100 358 966 1.70E-03 300 1074 1286 5.20E-06 5.2.4 Ignition delay times of stoichiometric cyclohexane/O2/N2 mixtures in dependence on the O2- concentration In the experiments it had been found that the ratio R slightly reduces when raising the C6H12 concentration in the stoichiometric C6H12/O2/N2 mixtures from 2.28 vol.-% to about 4.5 vol.-% (see Fig. 7). The change in R would require that IDT-values small enough to allow for a DDT are obtained at ever smaller precompression ratios when raising the C6H12-concentrations to about 4.5 vol.-%. As shown by Tab. 7, the recompression ratios yielding the same IDT value actually exhibit a slight reduction in this concentration range. At higher combustible concentrations R suddenly drops to 1 (see Fig. 7), which is most probably due to directly triggering the detonative mode of combustion in these highly reactive mixtures by the ignition source, i.e. there is no longer an initial deflagrative stage. 5.2.5 Qualitative variation of R to be expected as function of initial temperature of the explosive mixture Until now no tests have been conducted to determine the variation of R with the initial temperature of the explosive mixture. In this section it will be shown what can be expected for the variation of R, when certain simplifying assumption are made. Under the assumption that the DDT occurs as soon as the precompressed zone of unreacted mixture ahead of the flame front has reached a temperature for which the IDT is equal to 10 µs and under the assumption that an IDT of 10 µs is always attained at 1100 K, the required precompression ratios can be specified in dependence on the mean isentropic exponent κ of the mixture. Furthermore it is assumed that the formula for adiabatic compression as used in section 5.2.3 holds. Then the required precompression ratio pfinal/pinitial as function of Tinitial is given by: = Tinitial κκ-1 and κ = CpCV . (2) In fact, the last assumption is presumably not perfectly justified because to some extent the compression process might be better described by the formula for temperature rise caused by shock (see e.g. Schildberg 2016a), but this formula is extremely difficult to handle for the run-up from deflagration to detonation because the ratio pfinal/pinitial and the Mach number M are permanently changing. Since only a qualitative understanding is sought for, the simple equation (2) is used. 1060 Although different combustibles will have different values of κ, the mean κ value of the explosive mixture is dominated by the κ values of O2 and N2, which are close to 1.4. Therefore, the κ values of stoichiometric explosive combustible/O2/N2 mixtures with low O-concentrations (18 to 30 vol.-%) are usually in range from 1.3 to 1.4 in the temperature interval from 20 °C to about 1000 °C. For cyclohexane/O2/N2 the average κ value in this interval is about 1.34. Table 7: Ignition delay times (IDT) calculated for different precompression ratios of the stoichiometric C6H12/O2/N2 mixtures investigated in tests 5, 22, 25, 23, 29 and 26 (see Table 1). All mixtures were at same Tinitial = 130 °C but at different initial pressures between 12 and 20 bar abs. In the last 8 lines the IDT’s calculated for stoichiometric mixtures with even higher O2-concentrations are given. These mixtures were not investigated in the tests. (Note that the IDT also drops when the final pressure rises but the temperature is kept constant. Thus, the effect of rising O2-concentration on the IDT can be compensated for or even overcompensated by conducting the experiment at a lower initial pressure. This explains that the IDT’s in test 22 are slightly longer than in test 5). pfinal/pinitial Test 5, O2=20,5 vol.-%, 20 bar Test 22, O2=24,3 vol.-%, 14 bar Test 25, O2=29,0 vol.-%, 12 bar pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] 25 500 912 1,50E-04 350 912 1,90E-04 300 912 1,70E-04 50 1000 1088 2,30E-05 700 1088 2,90E-05 600 1088 2,70E-05 75 1500 1206 6,30E-06 1050 1206 7,40E-06 900 1206 7,20E-06 100 2000 1297 2,50E-06 1400 1297 2,80E-06 1200 1297 2,80E-06 125 2500 1372 1,30E-06 1750 1372 1,40E-06 1500 1372 1,40E-06 150 3000 1437 7,20E-07 2100 1437 7,90E-07 1800 1437 7,70E-07 pfinal/pinitial Test 23, O2=38,3 vol.-%, 12 bar Test 29, O2=47,3 vol.-%, 17 bar Test 26, O2=56,2 vol.-%, 17 bar pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] 25 300 896 1,40E-04 425 896 8,30E-05 425 896 7,20E-05 50 600 1064 2,00E-05 850 1064 7,80E-06 850 1064 6,00E-06 75 900 1177 6,40E-06 1275 1177 2,70E-06 1275 1177 2,00E-06 100 1200 1264 2,80E-06 1700 1264 1,50E-06 1700 1264 1,20E-06 125 1500 1336 1,50E-06 2125 1336 9,00E-07 2125 1336 7,30E-07 150 1800 1398 8,60E-07 2550 1398 5,60E-07 2550 1398 4,80E-07 pfinal/pinitial (no test), O2=70 vol.-%, 12 bar (no test), O2=80 vol.-%, 12 bar (no test), O2=90 vol.-%, 12 bar pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] pfinal [bar] Tfinal [K] IDT [s] 25 300 896 7,61E-05 300 880 9,00E-05 300 863 1,14E-04 50 600 1064 6,88E-06 600 1041 6,59E-06 600 1017 7,12E-06 75 900 1177 2,47E-06 900 1148 2,10E-06 900 1120 1,98E-06 100 1200 1264 1,39E-06 1200 1231 1,15E-06 1200 1199 9,74E-07 125 1500 1336 8,47E-07 1500 1299 7,75E-07 1500 1264 6,40E-07 150 1800 1398 5,39E-07 1800 1358 5,42E-07 1800 1319 4,77E-07 In Table 8 the required precompression ratios are presented. Furthermore, a relative R-value is calculated. This value describes the relative change of the ratio R when the initial temperature of the investigated mixture is changed from 20 °C to a lower or to a higher value. To calculate the relative R-values, it was assumed that R is proportional to the precompression factor of the precompressed zone at the instant when the DDT occurs. Presumably a strict proportionality cannot be expected but rather a soft correlation in the sense that larger precompression factors entail larger R-values. We still assumed strict proportionality because only a qualitative understanding is sought for. Furthermore, to specify the relative R values it has to be recalled that R was defined as the ratio between the static equivalent pressure at the location where the DDT occurs and the static equivalent pressure in the region of the stable detonation (pstat_stable). Because pstat_stable is inversely proportional to the absolute temperature of the mixture, this effect has to be compensated for in the calculation of the relative R values. Thus, to give an example, the relative R-value at 100 °C for a mixture with κ = 1.38 is calculated as 50.71/121.79 * (273.15 +100)/(273.15+20) = 0.53. 1061 Table 8: Precompression ratios required to heat a gas mixture, which is present at different initial temperatures Tinitial and which can have different values of κ = cp/cv, to a temperature of 1100 K. Tinitial [°C] Precompression ratios (PR) required for different values of κ = cp/cv and relative R-values PR for κ = 1,4 rel. R- value PR for κ = 1,38 rel. R- value PR for κ = 1,36 rel. R- value PR for κ = 1,34 rel. R- value -20 171,02 1,44 207,49 1,47 257,20 1,50 289,01 1,52 0 131,06 1,19 157,43 1,20 192,98 1,22 215,55 1,22 20 102,34 1,00 121,79 1,00 147,77 1,00 164,12 1,00 40 81,23 0,85 95,84 0,84 115,16 0,83 127,24 0,83 60 65,41 0,73 76,54 0,71 91,15 0,70 100,21 0,69 80 53,34 0,63 61,94 0,61 73,13 0,60 80,03 0,59 100 43,98 0,55 50,71 0,53 59,39 0,51 64,71 0,50 120 36,64 0,48 41,95 0,46 48,76 0,44 52,91 0,43 140 30,80 0,42 35,03 0,41 40,42 0,39 43,69 0,38 160 26,10 0,38 29,51 0,36 33,81 0,34 36,41 0,33 180 22,29 0,34 25,04 0,32 28,51 0,30 30,59 0,29 200 19,16 0,30 21,41 0,28 24,22 0,26 25,90 0,25 6. Conclusions The pstat-values determined for C6H12/O2/N2 confirm what had been found for other mixtures (CH4/O2/N2, C2H4/O2/N2, H2/O2/N2) in the past. In particular the estimation formulae for the pstat-values of the short pipe scenarios are reassured. The smaller R-values found for C6H12 at low O2-concentrations (3.7 instead of about 5.5 for other mixtures) are with high probability only due to the elevated initial temperature at which the tests were conducted and not a consequence of the AIT of C6H12 being much lower than the AIT of the other mixtures. The autoignition process starting the DDT, which requires an IDT of not larger than about 10 µs, is due the high temperature oxidation mechanism whereas the “classical” autoignition in air at 1 bar abs is due to the low temperature oxidation mechanism. For the four mixtures investigated by reaction kinetics the IDT values became very similar at temperatures ≥1100 K. At this temperature the AIT dropped to about 10 µs. If other common combustibles exhibited the same AIT-behaviour, the precompression factor required for triggering the DDT would be the same and, consequently, similar R values could be expected for corresponding O2-concentrations. 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