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. 2021 Jul 16;6(29):18559–18565. doi: 10.1021/acsomega.1c00058

Development and Verification of the New Simplified Mechanism for CH4/O2/CO2 Laminar Premixed Flame under High Pressure

Ying Chen †,‡, Jingfu Wang †,‡,*, Conghao Li †,‡, Xiaolei Zhang †,‡
PMCID: PMC8319947  PMID: 34337196

Abstract

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To study the laminar premixed flame characteristics of methane under an O2/CO2 atmosphere in high pressure, a new simplified chemical mechanism (44 steps and 19 species) was extracted from the GRI-Mech 3.0 mechanism. The sensitivity coefficient analysis method is used to retain the elementary reactions that have great influence on the target parameters and remove other secondary elementary reactions. Meanwhile, the closeness of the simplified mechanism initially obtained was verified. The results of the laminar burning velocities, the distribution of the main species, and the ignition delay time were compared between the two mechanisms for the premixed flame and the ignition process. Overall, the simplified mechanisms performed fairly well over a wide range of pressure, equivalence ratio, and fuel mixture composition.

1. Introduction

The O2/CO2 combustion technology,1 as an important carbon capture technology and pollutant reduction,2,3 has become a hot subject for scholars in the study of fuel combustion in the recent decades. Compared with the traditional combustion atmosphere, CO2 replaces the position of N2 (partially or wholly) in air and therefore changes the combustion atmosphere of the fuel. Meanwhile, the physical and chemical properties of CO2 and N2 are very different,4 which makes the elementary reactions involving CO2 participation and the reaction rate change in the combustion process. Therefore, each elementary reaction needs to be reconsidered when simplifying the detailed mechanism in an O2/CO2 atmosphere. At present, the reaction mechanism of hydrocarbon fuel combustion in an air atmosphere has been studied by a large number of scholars using different mechanism simplification methods. However, there are few studies on the simplified mechanism process of fuel combustion in an O2/CO2 atmosphere, especially in a high pressure. The simplified mechanism can efficiently and accurately simulate and calculate the combustion flame.

Most of the previous studies on hydrocarbon fuels in O2/CO2 atmospheres focused on the effects of CO2 on the flame combustion characteristics caused by the physical properties, chemical properties, and radiation properties of CO2, but research studies on the mechanism of O2/CO2 atmospheres are extremely rare. Some scholars have developed and proposed a simplified mechanism for the total package of hydrocarbon fuel combustion in an O2/CO2 atmosphere. Leise5 proposed that the chemical mechanism of turnkey under an air atmosphere needs to be modified before it can be applied in an O2/CO2 atmosphere and also proposed a three-step mechanism. Andersen6 revised the WD two-step turnkey mechanism and the JL four-step turnkey mechanism to improve the prediction of CO concentration. Frassoldati7 constructed a simplified general package mechanism suitable for high-temperature oxygen-enriched flames, while Hjärtstam et al.8 analyzed three types of combustion mechanisms suitable for an O2/CO2 atmosphere through reaction kinetic calculations and numerical simulations of combustion fields which are one-step, four-step, and six-step turnkey mechanisms.5,6 Compared with the total package mechanism, the simplified mechanism is more complicated in terms of the number of components and the number of elementary reactions, but it can get more accurate results without time-consuming calculations under certain conditions.

Scholars have developed a series of mechanism simplification methods in recent years, such as the sensitivity analysis (SA) method,9 calculation of singular perturbation,10 and direct relationship graph method.11 As for the present work, this article adopts the SA method to accomplish the mechanism simplification based on the detailed chemical reaction mechanism of GRI-Mech 3.0. Because methane is the simplest hydrocarbon fuel and the most widely studied and is also the main component of natural gas, it was selected as the target fuel for this study. The flame temperature, the distribution of the main species, and the laminar burning velocities simulated by the reduced chemical mechanism were compared with the detailed chemical mechanism to verify the simplified mechanism. The new efficient and accurate simplified mechanism suitable for the combustion of CH4 in an O2/CO2 atmosphere is obtained.

2. Computational Method

2.1. Model of the Simulation

The numerical simulations and the reduced process were conducted by using the perfectly stirred reactor (PSR) code in ANSYS Chemkin PRO software version 19.1 with the detailed chemical reaction mechanism (GRI-Mech. 3.0). The PSR model12,13 assumes that the fuel and oxidizer are completely uniformly mixed in the control volume at the instant when the fuel and oxidizer enter the reactor at a steady flow rate. Therefore, the combustion parameters at any position in the reactor are consistent, and there is no difference between the reaction parameters at the outlet position. Due to the characteristics of the above-mentioned PSR model, it is often used to study the kinetic principles of the combustion chemical reaction of various fuels, flame structures, and NOX generation mechanisms.

The complete mathematical description of the PSR model is as follows:

Mass conservation equation

2.1. 1

Energy conservation equation

2.1.

where ṁ is the mass flow into the control body, ωi is the mass fraction of the ith component, v̇i is the net production rate of the ith component, MWi is the molar mass of the ith component, and hi is the specific enthalpy of the ith component. The subscript in denotes the import parameter and the subscript out represents the export parameter.

The boundary conditions set in the PSR calculation model during the simplification process are residence time 0.2 s, initial temperature 1800 K, equivalence ratio range 0.6–1.2, and pressure range 1–16atm, and the reactant mole fraction composition is 0.5CH4 + 0.25O2 + 0.25CO2.

2.2. Method of Simplification

The SA14,15 was selected as the mechanism simplification method in this study. The so-called SA method is to analyze the influence degree of the small disturbance on the research system, which is denoted as the sensitivity coefficient (obtained by solving a set of partial differential equations). The sensitivity coefficient is defined as the influence of the small change of the chemical reaction rate constant of each elementary reaction on the target parameters of the system (such as temperature, flame speed, and main species concentration). By comparing the magnitude of the sensitivity of each elementary reaction to determine the primary and secondary reaction on the target parameter, and then eliminate the secondary reaction. SA methods are divided into global SA methods and local SA methods. In this paper, the local sensitivity coefficient analysis method is used to analyze and calculate the sensitivity coefficients of the target parameters which are the mole fractions of CH4, O2, CO2, H2O, OH, and CO (consist of the primary reactants, products, most important activated free radicals, and intermediate components).

The detailed chemical reaction mechanism of GRI-Mech 3.0 (53 species and 325 reactions) is currently the most widely used and common mechanism for scholars to study the combustion characteristics of CH4. This study also takes the detailed chemical reaction mechanism of GRI-Mech 3.0 as a simplified object. In most of the actual simplification work, the simplification of the chemical combustion mechanism adopts different simplification methods according to different reaction conditions or research purposes and pays attention to multiple factors at the same time as well. Due to the influence of many factors, we cannot get a set of methods that apply various mechanism simplifications. For this article, the simplification criteria and steps are as follows:

  • (1)

    Remove the C3 components and the elementary reaction involving C3 in the detailed mechanism.

  • (2)

    Calculate the sensitivity coefficient of each elementary reaction to the set target components and select the elementary reaction with a larger sensitivity coefficient.

  • (3)

    Change the equivalence ratio (Φ = 0.6–1.2) and pressure (2–5 atm) (4 × 4 = 16 boundary conditions in total), recalculate the sensitivity coefficient, and supplement the results of the previous step. For each set target component, 10 elementary reactions with greater sensitivity coefficients were retained. (The set target components are CH4, O2, CO2, H2O, OH, and CO, and 96 sensitivity coefficient analysis sets are obtained.)

  • (4)

    Remove those elementary reactions that only occur once or have a small sensitivity coefficient from the reaction sets obtained above.

  • (5)

    Verify the closure of the simplified mechanism.

  • (6)

    Perform the simulation to verify the simplified mechanism and compare with GRI-Mech 3.0.

  • (7)

    Under the condition where the mechanism meets the requirements of sealing and accuracy, carry out the final inspection of the reaction components and chemical reactions of the mechanism to minimize the components and chemical reactions as much as possible and then maximize the improvement under the premise of ensuring the calculation accuracy and computational efficiency.

2.3. Process of Simplification

The simplified calculation process of the mechanism in this paper is carried out in the PSR code in ANSYS Chemkin PRO software version 19.1, which is over the equivalence ratios ranging from 0.6 to 1.2 (0.2 as the increase step) and reactor pressures ranging from 1 to 16 atm (5 atm as the increase step). CH4, O2, CO2, H2O, OH, and CO are selected as the target species. Therefore, a total of 4 × 4 × 6 = 96 SA graphs are obtained (Figure 1).

Figure 1.

Figure 1

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Sensitivity coefficients of the important species.

Only parts of the sensitivity coefficient analysis graphs were listed in the following, which include the analysis under various boundary conditions. By summarizing 96 SA graphs, a reaction group consisting of 76 elementary reactions was obtained. After screening the elementary reactions that occurred more than 10 times in the reaction group, the 39-step simplified mechanism was extracted first, as shown in Figure 2.

Figure 2.

Figure 2

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Elementary reactions with a frequency of more than 10 times in the reaction group.

When verifying the closure of the 39-step reaction mechanism, it was found that the elementary reaction containing H2O2 in the product, the elementary reaction of CH in the reactant, and the elementary reaction of CH2OH in the product should be supplemented in the mechanism. In the detailed chemical reaction mechanism of GRI-Mech 3.0, the elementary reactions containing H2O2 in the product are R[85], R[115], R[116], R[121], and R[306], the reactant elementary reactions with CH are R[6], R[49], R[91], R[125], R[126], R[127], R[132], and R[289], and the products including the elementary reactions of CH2OH are R[18], R[56], R[64], R[68], R[104], R[162], and R[311]. In order to satisfy the closeness of the simplified mechanism, the elementary reactions proposed above need to be selected or deleted. The supplementary principles are as follows:

  • (1)

    Preferentially select the elementary reactions that appear in the previous reaction group.

  • (2)

    Select the elementary reaction with a large sum of the absolute value of the elementary reaction sensitivity coefficient.

  • (3)

    Try to avoid adding new components.

A positive sensitivity coefficient indicates that the elementary reaction promotes the formation of the target component, and a negative sensitivity coefficient indicates that the elementary reaction inhibits the formation of the target component. In order to comprehensively consider the promotion and inhibition effects of the elementary reaction on the components, the sum of the absolute values of sensitivity coefficients of the previously specified reaction is taken into consideration when choosing. The specific supplementary data are shown in Figures 3 and 4. It can be clearly seen that the elementary reaction containing CH should supplement R[49] and the elementary reaction containing CH2OH should supplement R[68]. In addition, R[85] as the only elementary reaction containing H2O2 in the previous reaction group should be added. After supplementing R[49] and R[68], CH3OH and C were added to the reaction species as new components. Based on the principle where no new components were added, the elementary reactions R[49] (corresponding to reaction R[122]) and R[95] (corresponding to reaction R[68]) should be added, both of which are not included in the previously pooled reaction group.

Figure 3.

Figure 3

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Preselected supplementary elementary reactions including CH radicals.

Figure 4.

Figure 4

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Preselected supplementary elementary reactions including CH2OH radicals.

In summary, after supplementary reactions, the final 44-step, 19-species simplified mechanism can be obtained.

3. Results and Discussion

In order to verify the accuracy of the 44-step, 19-species simplified mechanism, the study calculated the laminar flame velocity, the important species distributions in the CHEMKIN PRO one-dimensional premixed flame model, the flame temperature, and the ignition time in the Chemkin-Pro Open zero-dimensional (0D) PSR model in a CO2/O2 atmosphere with the simplified mechanism and compared with the results obtained by GRI-Mech 3.0. The conditions of the verification in the two models are listed in Table 1.

Table 1. Conditions of the Verification in the Two Simulation Reactors.

  equivalence ratio   XO2:XCO2 pressure (atm) residence time (ms)
premixed laminar flame model 0.6 0.8 0.25:0.75 1  
  1.0 1.2 0.3:0.70    
      0.35:0.65    
0D closed homogeneous model 0.6 0.9 0.24:0.76 1, 5, 9, 13, 17 3
  1.0 1.2 0.29:0.71   5
      0.34:0.64    
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3.1. Laminar Flame Velocity

Figure 5 shows the comparison of laminar flame velocity between the simplified mechanism and GRI-Mech 3.0 under the conditions that the O2/CO2 volume fraction ratios are 0.25/0.75, 0.3/0.7, and 0.35/0.65 and the equivalent ratios are 0.6, 0.8, 1.0, and 1.2. It can be seen from the figure that the results of the simplified mechanism and GRI-Mech 3.0 are in good agreement under the lean burn condition when the CO2 mole fraction is less than 70%.

Figure 5.

Figure 5

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Comparison of laminar flame velocity between the simplified mechanism and GRI-Mech 3.0.

However, under the rich combustion conditions, there are obvious errors in the results of the simplified mechanism and detailed mechanism. The simplified mechanism overestimates the laminar flame velocity compared to the GRI-Mech mechanism in the rich combustion. When the CO2 molar volume fractions are 0.75, 0.7, and 0.65, the maximum relative errors of flame velocity are 7.1, 5.7, and 2.4%, respectively. What is more, when the CO2 volume fraction is higher than 70%, the simplified mechanism underestimates the laminar flame velocity compared to GRI-Mech 3.0 in the lean combustion. Figure 5 also depicts that the increase in the CO2 volume fraction inhibits laminar flame velocity, which is mainly caused by the high specific heat and low diffusion of CO2.

3.2. Main Species

The distributions of the molar fraction of important combustion species with the axial distance are shown in Figure 6. It can be seen from the figures that the simplified mechanism can well predict the starting position of combustion and the composition distribution of the products after the combustion is completed. Moreover, Figure 6c also depicts that the simplified mechanism overestimates the reactants and underestimates the products during the combustion process in the rich combustion. The error of the prediction between the two mechanisms is less than 0.3%, which can be ignored. Meanwhile, the two mechanisms maintain a high degree of consistency in the prediction on the combustion region which lays at 0.5–0.75 cm.

Figure 6.

Figure 6

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Comparison of important species distribution with axial distance between the simplified mechanism and GRI-Mech 3.0 at (a) XO2:XCO2 = 0.25:0.75, Φ = 0.8, (b) XO2:XCO2 = 0.3:0.7, Φ = 1.0, and (c) XO2:XCO2 = 0.35:0.65, Φ = 1.2.

In the process of simplifying the mechanism, important combustion components are selected as the target parameters. As can be seen from Figure 6, the simplified mechanism is very consistent with the detailed mechanism in terms of composition prediction. This indicates that the elementary reactions involving the species remained in the simplified mechanism can be efficiently applied to simulate and calculate the premixed combustion of CH4 in an O2/CO2 atmosphere whether the lean combustion or the rich combustion.

3.3. Flame Temperature

The 0D closed homogeneous model was used to calculate the flame temperature distribution with the conditions of equivalence ratios from 0.6 to 1.2, residence times from 3 to 5 ms, and pressure from 1 to 17 atm. It can be clearly seen from Figure 7 that when the ratio of CO2 in the oxidant is less than 70%, the simplified mechanism performs very well on the prediction of the temperature for the 0D premixed laminar flame under the high pressure of up to 17 atm. However, the discrepancies appear between the simplified mechanism and GRI-Mech 3.0 on the prediction of the flame temperature when the CO2 fraction in the oxidant is greater than 70%, especially in a high pressure (≥10 atm). The ignition time of the simplified mechanism is slightly earlier than that of the GRI-Mech3.0 mechanism. The important fact that can be observed in Figure 7 is that the above-mentioned discrepancies can be enlarged along with the increase of the reactor pressure. Also, the enlarged phenomenon is especially obvious in the short residence time.

Figure 7.

Figure 7

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Comparison of laminar flame temperature between the simplified mechanism and GRI-Mech 3.0 at (a) XO2:XCO2 = 0.24:0.76, (b) XO2:XCO2 = 0.29:0.71, and (c) XO2:XCO2 = 0.34:0.66 under stoichiometric conditions.

3.4. Ignition Time Delay

The comparison of the ignition delay time between the GRI 3.0 mechanism and the simplified mechanism is shown in Figure 8. The simulated results from Figure 8 indicate that the simplified mechanism can qualitatively predict the ignition delay time trends with the GRI 3.0 detailed mechanism. Moreover, the prediction of the ignition delay time of the simplified mechanism is slightly over than that of the GRI 3.0 detailed mechanism; meanwhile, the discrepancies between the two mechanism increase as the pressure increases. It is necessary to note that the average errors between the reduced and the detailed mechanism in Figure 5a–c are less than 4.7% that is acceptable at the present work.

Figure 8.

Figure 8

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Comparison of the ignition time with pressure between the simplified mechanism and GRI-Mech 3.0 at (a) XO2:XCO2 = 0.24:0.76, (b) XO2:XCO2 = 0.29:0.71, and (c) XO2:XCO2 = 0.34:0.66.

4. Conclusions

In this study, the local SA method is applied to simplify the detailed chemical reaction mechanism GRI-Mech 3.0. Also, a set of simplified mechanisms (44 reactions and 19 species) which are suitable for the combustion of CH4 in an O2/CO2 atmosphere are extracted. The process of simplification based on the SA method is newly developed by the authors with respect to the specified combustion atmosphere. The results of laminar flame velocity, flame temperature, and important species calculated by the simplified mechanism are compared with the results of GRI-Mech 3.0. The applicability and accuracy of the simplified mechanism have been verified in the one-dimensional laminar premixed flame and 0D homogeneous flame. The extensive selection of simulate conditions and their comparisons show a very good agreement over the entire range of conditions considered (including the high CO2 fraction in the oxidant and high pressure of up to 17 atm). It is necessary to note that the high-pressure conditions involved during the calculation are relevant for the gas turbine. To the best of our knowledge, the attempt of the simplified mechanism in a high pressure is rare. Even though the little discrepancies exist between the simplified mechanism and GRI-Mech 3.0, the simplified mechanism obtained in this study can be used to calculate the high-pressure combustion of CO4 in an O2/CO2 atmosphere.

Acknowledgments

This research was funded by the National Natural Science Foundation of China (grant no. 50876002). The authors gratefully acknowledge them for the financial support of this work.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c00058.

  • Simplified mechanism (44 steps and 19 species) (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao1c00058_si_001.pdf (88.4KB, pdf)

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Associated Data

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Supplementary Materials

ao1c00058_si_001.pdf (88.4KB, pdf)

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