### Abstract

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

This article illustrates a method to predict flammability of mixtures containing methane, oxygen, and other inert gases like nitrogen and carbon dioxide based on chemical equilibrium. Calculated adiabatic flame temperature (CAFT) is used as a parameter to determine whether a fuel mixture is combustible or not. Our calculated results are obtained with initial conditions of 1 atm and 298 K. Compared with experimental data reported in the literature, we find that 1,450 K is an appropriate threshold of flammability. Mixtures with adiabatic flame temperatures higher than this value are considered flammable while those lower are judged as nonflammable. Using this criterion, it is convenient for us to predict the flammable zone and prevent the existence of flammable mixtures to ensure security. Showing the CAFT of fuel mixtures with various concentrations in a triangular flammability diagram, we can easily find out the influence of inert gases, oxygen, and soot formation on the mixture's flammability, respectively. © 2014 American Institute of Chemical Engineers Process Saf Prog 34: 31–35, 2015

### INTRODUCTION

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

Fugitive methane is the largest source of greenhouse gas emissions from coal mining operations. Considerable work has focused on the oxidation of methane in very low concentration processes, such as ventilation air methane mitigation system. To ensure the safety in plant operation, it is important to predict the flammability of fuel mixtures with various concentrations of some major components. In this article, attention is paid to the influence of inert gases, like carbon dioxide and nitrogen, on the calculated adiabatic flame temperature (CAFT).

In this article, mole fractions of methane, oxygen, carbon dioxide, and nitrogen are taken into consideration when we calculate the CAFT. To clearly demonstrate the relationship between flammability and mole fractions of fuel, oxidizer, and inert gases, a triangular flammability diagram is used, from which we can easily point out the flammable zone.

The calculation of adiabatic flame temperature is based on chemical equilibrium and minimization of Gibb's free energy. Equilibrium calculations considered the effects of 53 species, which refers to GRI 3.0 [1]. GRI 3.0 mechanism is the product of computational and experimental research sponsored by the Gas Research Institute. GRI 3.0 thermochemistry is based on standard databases, including the NASA-Lewis [2] and Technion [3] archives.

The calculation is based on the hypothesis of no heat losses and the CAFT is obtained at fixed enthalpy and pressure, where the enthalpy is determined indirectly by the initial thermophysical properties of the combustible mixture. The CAFT is a measure of the maximum temperature that could be reached by combusting a particular gas mixture under a specific set of conditions. In a real system which includes heat losses, chemical kinetic, and/or mass transport limitations, the flame temperature is likely to be lower than the CAFT [4].

To solve chemical equilibrium problems, the method of minimization of Gibbs free energy is used in this article, which is subject to atomic population constraints and non-negative moles. An established method for evaluating chemical equilibrium is the element-potential method embodied in the Stanford software STANJAN [5].

### NUMERICAL RESULTS FOR CH_{4}/O_{2}/N_{2}

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

The triangular diagram in Figure 1 shows the flammable limits of methane/oxygen/nitrogen mixtures, which gives consistent results with prior study [6]. It represents nearly all possible mixtures of a three-components system. Three vertexes of the triangle stand for each pure component, respectively. At any point in the diagram, concentration of each component in the mixture can be read out at the same time. Using a triangular flammability diagram is also convenient to find out the upper flammable limit (UFL) and lower flammable limit (LFL) with arbitrary initial mole ratio of nitrogen to oxygen. For example, on Line 1, the mole ratio of nitrogen to oxygen is 1.66, with which the mole fraction of methane can change between 4.91 and 33.34% to ensure that the mixture is flammable. UFL and LFL for Air Line, Line 1, Line 2, Line 3, and pure oxygen are listed in Tables 1 and 2. It shows that calculated results can fit well with experimental data in fuel-lean region while have a slight discrepancy in fuel-rich region. We can see from Table 2 that LFL has a slight reduction when the mole fraction of nitrogen increases gradually, which is also observed in experiments [[7], [8]]. This may be resulted from the difference of heat capacity between nitrogen and oxygen. Heat capacity of nitrogen is lower than that of oxygen and for the fuel-lean region, effects of extra N_{2} and O_{2} are essentially the same. Thus, mixtures with more nitrogen will have a higher CAFT compared with mixtures that have more oxygen while the same in the mole fraction of methane. Furthermore, it is obvious that along with the increase of the ratio of nitrogen to oxygen, the flammable zone becomes narrow.

Table 1. Differences of UFL. | Air Line | 1 | 2 | 3 | Pure O_{2} |
---|

N_{2}/O_{2} (Vol) | 79/21 | 62.5/37.5 | 50/50 | 25/75 | 0 |

Experiment (UFL) | 16.14% | 33.22% | 42.91% | 56.42% | 65.10% |

Calculation (UFL) 1,450 K | 18.77% | 33.34% | 41.45% | 52.97% | 60.52% |

Absolute error | 2.63% | 0.12% | −1.46% | −3.45% | −4.58% |

Relative error | 16.29% | 0.36% | −3.40% | −6.11% | −7.04% |

Table 2. Differences of LFL. | Air Line | 1 | 2 | 3 | Pure O_{2} |
---|

N_{2}/O_{2} (Vol) | 79/21 | 62.5/37.5 | 50/50 | 25/75 | 0 |

Experiment (LFL) | 4.85% | 4.85% | 4.95% | 4.95% | 4.95% |

Calculation (LFL) 1,450 K | 4.80% | 4.91% | 5.12% | 5.12% | 5.45% |

Absolute error | −0.05% | 0.06% | 0.17% | 0.17% | 0.50% |

Relative error | −1.03% | 1.24% | 3.43% | 3.43% | 10.10% |

In Figure 1, the thick line represents critical flammable mixtures in experiment. The Stoichiometric Line represents mixtures that the mole ratio of methane to oxygen is 0.5. The CAFT contours of 1,000, 1,450, and 1,700 K are labeled in this diagram.

To choose a proper CAFT as the criterion to predict whether a mixture is flammable or nonflammable, calculated and experimental values for LFL, UFL, and Minimum Oxygen concentration are listed in Table 3. From this table, we can see that 1,450 K fits better with the experimental result than 1,300, 1,400, and 1,500 K. Hence, in this article, 1,450 K is chosen as the CAFT criterion to predict flammability zone.

Table 3. Comparison between experiment and calculation. | LFL in Air (Vol%) | UFL in Air (Vol%) | LFL in Pure O_{2} (Vol%) | UFL in Pure O_{2} (Vol%) | Minimum Oxygen |
---|

Experiment | 4.85 | 16.14 | 4.95 | 65.10 | 11.60 |

1,300 K | 4.14 | 20.52 | 4.60 | 61.82 | 11.09 |

Relative error | 14.64 | 27.14 | 7.07 | 5.04 | 4.40 |

1,400 K | 4.49 | 19.30 | 4.90 | 60.85 | 11.37 |

Relative error | 7.42 | 19.58 | 1.01 | 6.53 | 1.98 |

1,450 K | 4.80 | 18.77 | 5.45 | 60.52 | 11.88 |

Relative error | 1.03 | 16.29 | 10.10 | 7.04 | 2.41 |

1,500 K | 5.03 | 18.06 | 5.63 | 60.13 | 12.29 |

Relative error | 4.67 | 11.90 | 13.74 | 7.63 | 5.95 |

Utilizing 1,450 K as the CAFT criterion, effects made by the mole fraction change of a certain component on the flammability of a mixture can be predicted from Figure 1. For instance, we can see that the Air Line goes across with the critical CAFT line (1,450 K). On the Air Line, volume ratio of nitrogen to oxygen is a constant value. When the mole fraction of methane changes from 3 to 30% gradually, the flammability of the mixture will change from nonflammable to flammable first and then to nonflammable. On the Stoichiometric Line, keep the mole ratio of methane to oxygen constant while change the mole fraction of nitrogen from low to high, the CAFT will descend gradually, which means that the flammability of mixture will change from flammable to nonflammable with the increasing volume concentration of nitrogen.

### NUMERICAL RESULTS FOR CH_{4}/O_{2}/CO_{2}

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

For CH_{4}/O_{2}/CO_{2} mixtures, the CAFT contour is shown in Figure 2. To predict the flammability of CH_{4}/O_{2}/CO_{2} mixtures, we also use 1,450 K as the critical flame temperature.

It is shown in Figure 2 that, in pure oxygen, the LFL is 5.45% and the UFL is 60.52%, which is same to the result of CH_{4}/O_{2}/N_{2} mixture. The calculated LFL and UFL under different volumetric ratio of CO_{2} to O_{2} are listed in Table 4 and Figure 3. We can see that the LFL changes from 5.86 to 6.78% gradually accompany with the increase of the mole ratio of CO_{2} to O_{2} from 1.5 to 2.3, different from that rule in CH_{4}/O_{2}/N_{2} mixtures. This is because the heat capacity of CO_{2} is higher than O_{2} and for the fuel-lean region, the effects of extra CO_{2} and O_{2} are essentially the same. Similar to the tendency of CH_{4}/O_{2}/N_{2} mixtures, the flammable zone of CH_{4}/O_{2}/CO_{2} mixtures also narrows down when the mole fraction of CO_{2} grows.

Table 4. LFL/UFL under different ratios of CO_{2} to O_{2}.Line | 0 | 1 | 2 | 3 | Pure O_{2} |
---|

CO_{2}/O_{2} (Vol) | 79/21 | 62.5/37.5 | 50/50 | 25/75 | 0 |

LFL 1,450 K | 6.90 | 6.51 | 6.31 | 5.71 | 5.45 |

UFL 1,450 K | 13.89 | 29.87 | 39.26 | 52.05 | 60.52 |

### NUMERICAL RESULTS FOR CH_{4}/O_{2}/CO_{2}/N_{2}

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

For CH_{4}/O_{2}/CO_{2}/N_{2} mixtures, we fix the concentration of CO_{2} and change the other three components' concentration to calculate the CAFT. Different flammable limits are obtained under conditions with various volume fractions of CO_{2}, which are listed in Table 5.

Table 5. Flammable limits (1450 K) with different CO_{2} concentrations.CO_{2} Concentration | 10% | 20% | 30% | 40% | 50% |
---|

LFL (N_{2}% = 0) | 6.69% | 6.63% | 6.42% | 6.45% | 6.39% |

UFL (N_{2}% = 0) | 53.65% | 46.31% | 39.26% | 32.45% | 24.04% |

Min. Oxygen | 10.77% | 12.00% | 11.86% | 12.06% | 12.59% |

To compare the influence of CO_{2} with that of N_{2} on flammable limits, we can refer to Figures 1 and 4. For example, in Figure 1, we can find out the effect of pure nitrogen while in Figure 4 we can obtain the influence of 10% CO_{2}. Similarly, we can adjust the volume percentage of CO_{2} from 10 to 50% to see the tendency. Detailed data are listed in Table 6. It shows in this table that fixing the sum mole fraction of CO_{2} and N_{2} at 60%, the UFL decreases while the LFL grows with increasing CO_{2}, that is to say, the flammable zone becomes smaller.

Table 6. Influences of N_{2} and CO_{2} on UFL and LFL. | LFL | UFL |
---|

N_{2} (60%) + CO_{2} (0%) | 4.89% | 21.35% |

N_{2} (50%) + CO_{2} (10%) | 5.33% | 21.05% |

N_{2} (40%) + CO_{2} (20%) | 5.57% | 20.46% |

N_{2} (30%) + CO_{2} (30%) | 5.71% | 20.07% |

N_{2} (20%) + CO_{2} (40%) | 6.04% | 19.95% |

N_{2} (10%) +CO_{2} (50%) | 6.40% | 19.48% |

In Figure 5, fixing mole fraction of CO_{2} at 10 and 20%, respectively, the flammable limits are plotted based on the mole fraction of nitrogen. It is clear that UFL and LFL both decline with the increasing volume percentage of nitrogen. However, the influence of CO_{2} is not like that. Increasing of CO_{2} leads to a slight augment of LFL while decrease of UFL.

### SOOT FORMATION

- Top of page
- Abstract
- INTRODUCTION
- NUMERICAL RESULTS FOR CH
_{4}/O_{2}/N_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2} - NUMERICAL RESULTS FOR CH
_{4}/O_{2}/CO_{2}/N_{2} - SOOT FORMATION
- CONCLUSIONS
- LITERATURE CITED

Computations mentioned above did not take soot formation into consideration. While in practice, soot formation is observed.

For CH_{4}/N_{2}/O_{2} mixtures, we mark the soot formation region in Figure 6 in black dots. It is interesting to find that in our computation, the boundary of soot formation region where the mole fraction of C(s) in products is greater than 1% is in consistent with the CAFT critical line (1,450 K). In this figure, it shows that in regions where the CAFT is less than 1,450 K the temperature contour has a slight deflection in fuel-rich region, while those in Figure 7 are straight lines. It means that soot formation can make the CAFT to have a slight drop.

To have a more detailed vision of the mole fraction of soot in products with different initial constituent, we plot the C(s) contour in Figure 8.We can see that the greatest mole fraction of C(s) can reach as much as 29.8%. In regions where the CAFT is greater than 1,450 K, the soot formation is negligible. It is mentioned in some documents [4] that the soot formation has less influence on the flammable limits of methane-air mixtures.