CALCULATION OF THE UPPER EXPLOSION LIMIT OF METHANE-AIR MIXTURES AT ELEVATED PRESSURES AND TEMPERATURES

CALCULATION OF THE UPPER EXPLOSION LIMIT OF METHANE-AIR MIXTURES AT ELEVATED PRESSURES AND TEMPERATURES F. Van den Schoor 1, F. Verplaetsen 2 and J. Berghmans 1 1 Katholieke Universiteit Leuven, Department of Mechanical Engineering, Celestijnenlaan 300A, 3001 Heverlee (Leuven), Belgium; Tel.: þ32 16 32 25 49, Fax: þ32 16 32 29 85, e-mail: Filip.VandenSchoor@mech.kuleuven.be 2 Adinex N.V., Brouwerijstraat 5/3, 2200 Noorderwijk (Herentals), Belgium Four different existing methods to calculate the upper explosion limit of methane-air mixtures at initial pressures up to 10 bar and initial temperatures up to 2008C are evaluated by comparison with experimental data. Planar freely propagating flames are calculated with the inclusion of a radiation heat loss term in the energy conservation equation to numerically obtain explosion limits. Three different reaction mechanisms are used in these calculations. At atmospheric pressure, the results of these calculations are satisfactory. At elevated pressures, however, large discrepancies are found. The spherically expanding flame calculations only show a marginal improvement compared with the planar flame calculations. On the other hand, the application of a limiting burning velocity with a pressure dependence S u,lim p 21/2 is found to give good agreement with the experimental data, whereas the application of a limiting flame temperature is found to underestimate the pressure dependence of the upper explosion limit. KEYWORDS: explosion limits, methane, pressure, temperature INTRODUCTION The explosion limits of a combustible substance in air determine the range of concentrations of this substance in air, within which an explosion can occur. Knowledge of these limits, thus, allows industrial processes to be run safely and economically. Primarily, explosion limits are determined experimentally. These experiments are, however, cumbersome and time-consuming, especially at the elevated conditions of pressure and temperature at which many industrial processes are operated. Therefore, it is necessary to seek other methods with which safe and accurate values of the explosion limits can be obtained. To guarantee a safe operation, these estimates should at the least be higher (lower) than the experimentally determined upper (lower) explosion limit values. The differences between the estimated and the experimental values cannot, however, be too large, since this could lead to a non economic operation. The aim of this study is to evaluate existing methods to calculate the upper explosion limit of methane-air mixtures at initial pressures up to 10 bar and initial temperatures up to 2008C. The methods that will be evaluated are the numerical calculation of planar (Lakshmisha et al., 1990; Law and Egolfopoulos, 1992) and spherical (Sibulkin and Frendi, 1990) freely propagating flames with the inclusion of a heat loss term in the energy conservation equation and the application of a limiting flame temperature (Wierzba et al., 1996; Shebeko et al. 2002) and of a limiting burning velocity (Bui-Pham and Miller, 1994) below which flames are unable to propagate. The evaluation of these different approaches will be based upon a comparison with experimental data (Van den Schoor and Verplaetsen, 2007). Since it is expected that the chemical kinetics play an important role in the limit flame behaviour, different reaction mechanisms will be used in the planar flame calculations: the GRI 3.0 mechanism (Smith et al.), the Konnov 0.5 mechanism (Konnov, 2000), the Leeds 1.5 mechanism (Hughes et al., 2001) and a mechanism by Appel et al. (2000), which will be called the Berkeley mechanism in the remainder of this manuscript. All these mechanisms are available on the Internet. In the next section the determination of explosion limits from numerical calculations of both planar and spherical flames is explained. In Section 3 the different reaction mechanisms which are used in the numerical calculations are presented. Section 4 gives the main results of this study, whereas Section 5 gives a discussion of these results from a physical point of view. NUMERICAL CALCULATIONS The numerical calculations are performed using CHEM1D, a one-dimensional (1D) flame code capable of solving 1D mass, energy and species conservation equations with detailed transport and chemical kinetics models. Two different flame geometries are used, namely 1D planar premixed flames, both steady and unsteady, and quasi 1D spherically expanding premixed flames. By introducing a heat loss term into the energy conservation equation it is possible to numerically calculate limits of flame propagation. Since flames will always lose part of their energy by radiation heat transfer, a radiation heat loss term was chosen. Four radiating species are considered, namely CO 2,H 2 O, CO and CH 4. To simplify the numerical calculations, the radiation is modelled by means of the optically thin limit, 1

meaning that no reabsorption of emitted radiation is considered. Estimates for the explosion limits are obtained from the planar flame calculations by considering whether an unsteady flame calculation reaches a steady state or not. In the latter case, the maximum flame temperature and burning velocity will decrease continuously in time. Before doing unsteady flame calculations, an initial guess for the upper explosion limit is sought by doing a series of steady flame calculations in which the equivalence ratio is stepwise increased until a steady solution cannot be found upon further increase of the equivalence ratio. Next, steady solutions in the neighbourhood of this initial guess are calculated with 90 98% (depending on the initial pressure) of the total radiation heat loss included. Finally, these solutions serve as initial conditions for the unsteady calculations, which are done from their start with the radiation heat loss restored to the full 100%. In the spherical flame calculations, mixtures in which flames propagate over a distance of 100 mm, are considered to be flammable. Due to the large computational time and the absence of a good initial guess, the equivalence ratio at which calculations are performed is changed in steps of 0.1. The ignition source is modelled as an energy input of 10 J during a period of 40 ms in a spherical volume with a diameter of 10 mm. These parameters are chosen to resemble the ignition source that was used to obtain the experimental data with which the numerical estimates will be compared (Van den Schoor and Verplaetsen, 2007). Beside estimates for the explosion limits the steady planar flame calculations will also give values for the maximum flame temperatures and the burning velocities which enable evaluation of the limiting flame temperature and limiting burning velocity approaches. REACTION MECHANISMS The GRI mechanism contains 325 elementary reactions and 53 species. It can be used for the calculation of methane and natural gas flames and it is validated for temperatures of 1000 2500 K, pressures up to 10 bar and equivalence ratios up to 5. The Konnov mechanism contains 1027 elementary reactions and 127 species. Compared to the GRI mechanism, it can also be used for calculating the combustion of C 2 and C 3 hydrocarbons and their derivatives. To reduce computational times the nitrogen chemistry is stripped from both these mechanisms, since it is unimportant for the highly rich flames under consideration. To allow a better comparison between the GRI mechanism and the Konnov mechanism, the C 3 C 6 species other than C 3 H 8 and n-c 3 H 7 also present in the GRI mechanism are stripped from the Konnov mechanism, thereby further reducing the number of elementary reactions and species. The Leeds mechanism contains 175 elementary reactions and 37 species. It can be used for the calculation of methane, hydrogen, carbon monoxide, ethane and ethylene flames. The Berkeley mechanism contains 544 elementary reactions and 101 species. It can be used for the calculation of methane, ethane, ethylene and acetylene flames at 1 bar. It also includes aromatic species in order to better model soot formation. There also exists a modification of this mechanism for simulating flames at 10 bar, which contains a different set of 546 elementary reactions. Table 1 shows the number of elementary reactions and species for the different reaction mechanisms used in this study. These reaction mechanisms were all validated against a variety of experimental data, including burning velocities, ignition delay times and species concentration profiles. The most important parameter of these with respect to the calculation of explosion limits is the burning velocity. Therefore, the different mechanisms are tested on their capability of reproducing burning velocities of rich methane/air flames. To this end, 1D planar freely propagating adiabatic premixed flames were simulated at 1 atm and 258C. As can be seen in Figure 1, the numerically calculated burning velocities obtained with the Leeds mechanism are in poor agreement with the experimentally determined values. Consequently, this mechanism was not used in any of the further calculations, as it would underestimate the upper explosion limit. RESULTS NUMERICAL 1D PLANAR FLAME CALCULATIONS At an initial pressure of 1 atm, the 1D planar flame calculations show a satisfactory agreement with the experiments (Figure 2). All of the tested reaction mechanisms predict the slope of the temperature dependence of the upper explosion limit (UEL) well, whereas the observed differences between the numerically and experimentally determined values is approximately 2 mol%. At higher initial pressures, however, larger differences are found between the numerical and experimental results, as well as large discrepancies between the different reaction mechanisms. Whereas the results of the Konnov mechanism reproduce the slope of the pressure dependence at an initial temperature of 258C fairly well with a difference between numerical and experimental results of about 5 mol% at an initial pressure of 10 bar, the results of the GRI mechanism substantially diverge from the experimental ones, with differences over 10 mol% at 10 bar (Figure 3). Figure 4 shows Table 1. Number of elementary reactions and species for the different reaction mechanisms # elementary reactions # species GRI 3.0 219 36 Konnov 0.5 776 93 Konnov 0.5 (reduced) 456 54 Leeds 1.5 175 37 Berkeley (1 bar) 544 101 Berkeley (10 bar) 546 101 not including the nitrogen chemistry 2

Figure 1. Comparison between experimentally determined and numerically calculated adiabatic burning velocities of rich methane-air flames at 1 atm and 258C that at an initial pressure of 10 bar, the calculated upper explosion limits are significantly higher than the experimentally determined ones. These large differences imply that the estimates of the upper explosion limits obtained by 1D planar flame calculations are of limited value at elevated pressures and temperatures. NUMERICAL 1D SPHERICAL FLAME CALCULATIONS Only a limited number of 1D spherical flame calculations have been done. They show a slight lowering (of about 1.5 mol%) of the estimates of the UEL, when referred to those of the 1D planar flame calculations, using the GRI mechanism. Additional calculations are being done to ascertain whether these findings also hold for the other mechanisms. LIMITING BURNING VELOCITY Figure 5 shows estimates of the burning velocities at the experimentally determined upper explosion limits. These estimates are obtained from the numerical calculation of 1D steady nonadiabatic planar flames using the reduced Konnov mechanism. At atmospheric pressure and ambient temperature a value of 4.8 cm/s is found. This value is Figure 3. Comparison between experimentally determined and mixtures at 258C in the range of theoretically derived (Buckmaster and Mikolaitis, 1982; Ronney, 1998) and experimentally determined (Ronney and Wachman, 1985) values for the limiting burning velocity. The theoretical derivation also gives the pressure dependence of the limiting burning velocity: S u,lim p 21/2 (Ronney, 1998). Through the data points a relationship of the form S u,lim ¼ ap b is fitted by means of the least squares method, with p the initial pressure (Figure 5). The exponent b is found to be 20.51, 20.50 and 20.48, respectively at initial temperatures of 258C, 1008C and 2008C. These values are in excellent agreement with the theory. It must, however, be noted that the estimates for the burning velocity strongly depend on the reaction mechanism. For example, calculations at 258C with the full Konnov mechanism give a value for the exponent b of 20.47. Given the inaccuracies in the experimental determination of the explosion limits and in the numerical calculation of burning velocities, as well as the assumptions made in the derivation of the limiting burning velocity (Buckmaster and Mikolaitis, 1982), the agreement is promising. LIMITING FLAME TEMPERATURE Often cited in literature is the modified law of Burgess and Wheeler (Zabetakis et al., 1958), which describes a linear Figure 2. Comparison between experimentally determined and mixtures at 1 atm Figure 4. Comparison between experimentally determined and mixtures at 10 bar 3

Table 2. Calculated values of the maximum flame temperature at the experimentally determined upper explosion limits of methane-air mixtures (K) 298 K 373 K 473 K 1 atm 1692 1678 1667 3 bar 1648 1622 1612 6 bar 1597 1583 1584 10 bar 1545 1533 1524 Figure 5. Calculated values of the burning velocity at the experimentally determined upper explosion limits of methaneair mixtures as a function of pressure. The plot shows a least squares fit based upon the relationship S u,lim ¼ ap b experimental data than the limiting flame temperature approach, since it is less dependent on flame chemistry. relationship between the explosion limits and initial temperature. This law is based upon a constancy of the adiabatic flame temperature at the limits, independent of initial temperature. Table 2 shows estimates of the maximum flame temperatures at the experimentally determined UEL values. These estimates are obtained from the numerical calculation of 1D steady nonadiabatic planar flames using the reduced Konnov mechanism. As can be seen, they are nearly constant for a given initial pressure. This corroborates the experimental finding that the UEL increases linearly with initial temperature. The concept of a constant limiting flame temperature, however, cannot, be used to estimate the pressure dependence of the upper explosion limit, as the flame temperatures decrease by approximately 150 K in the pressure range 1 10 bar. This corroborates the experimental finding that the slope of the linear dependence of the UEL on initial temperature increases with increasing initial pressure. The application of a constant limiting flame temperature, thus, leads to underestimation of the upper explosion limits at elevated pressures. DISCUSSION The large differences between the experimental data and the estimates of the numerical planar flame calculations are not surprising, since the laboratory flames are far from planar. Upon igniting the mixture a flame kernel is initiated which spreads out spherically. At the same time it starts to rise as a result of natural convection. This causes the flame to become stretched as a result of its spherical expansion and of the interaction with the flow field caused by its buoyancy. This flame stretch obviously needs to be taken into account. By doing spherical flame calculations only part of this stretch especially the stretch upon igniting the mixture is included. From a physical point of view, the most promising approach would be the concept of a limiting burning velocity, since its expression was derived by equating the stretch experienced by a flame propagating upwards in a cylindrical tube with the stretch necessary to extinguish the flame (Buckmaster and Mikolaitis, 1982). Moreover, it is expected to give better agreement with the CONCLUSIONS. At atmospheric pressure the estimation of the UEL by numerically calculating 1D planar flames with the inclusion of a radiation heat loss term into the energy conservation equation is satisfactory. The differences between the different reaction mechanisms are minimal.. At elevated pressures, however, large discrepancies are found. The estimated UEL values are significantly too high and large differences are found between the different reaction mechanisms. The results obtained with the (reduced) Konnov mechanism show the best agreement with the experimental UEL data.. The 1D spherical flame calculations only show a marginal improvement compared with the 1D planar flame calculations.. The application of a limiting burning velocity with a pressure dependence S u.lim p 21/2 gives good agreement with the experimental UEL data.. The application of a limiting flame temperature underestimates the pressure dependence of the UEL. Overall, the limiting burning velocity approach shows the best potential for estimating the upper explosion limits at elevated pressures and temperatures and it would certainly be interesting to further explore it. REFERENCES Appel, J., Bockhorn, H., Frenklach, M., 2000, Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C 2 hydrocarbons, Combust Flame, 121: 122 136. Available from: http://www.me. berkeley.edu/soot/mechanisms/mechanisms.html. Bosschaart, K.J., de Goey, L.P.H., 2004, The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method, Combust Flame, 136: 261 269. Buckmaster, J. Mikolaitis, D., 1982, A flammability limit model for upward propagation through lean methane/air mixtures in a standard flammability tube, Combust Flame, 45: 109 119. 4

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