Comparative Analysis of the Oxy-Fuel Kinetic Mechanisms by the Ignition Delay Time of Methane

Abstract

Supercritical oxy-fuel combustion, which allows for the high efficiency of power generation with near-zero CO₂ emissions, is considered a promising method to reduce the carbon footprint in the power energy sector. One of the problems in the widespread use of oxy-fuel combustion is a lack of comparative studies on the existing oxy-fuel combustion kinetic mechanisms depending on mixture composition, which complicates the choice of a kinetic mechanism for modeling oxy-fuel combustion. In this paper, a comparative verification of the kinetic mechanisms of GRI-Mech 3.0, UoS sCO₂ 2.0, OXY-NG, and Skeletal was performed using published experimental data on the ignition delay time of methane under conditions of oxy-fuel combustion. A comparative numerical study of the kinetic mechanisms in the wide range of pressures, CO₂ mass fractions in oxidizer (γ), and excess oxidizer ratios (α) by the ignition delay time is also carried out. It was found that the limits of applicability of all of the mechanisms studied are absent when modeling the ignition delay time, the most accurate mechanism to model the IDT of methane in oxy-fuel conditions being UoS sCO₂ 2.0, while the other three mechanisms are overall much inferior to it in terms of accuracy. However, Skeletal and GRI-Mech 3.0 mechanisms can be used to model the IDT during the oxy-fuel combustion of methane under both atmospheric and supercritical conditions, although only in a narrow range of γ.

1. Introduction

The significant increase in the CO₂ concentration in the atmosphere over the past 200 years is caused by the intensive combustion of hydrocarbons that produce energy leading to global warming, threatening the sustainable development of humanity. The power energy sector is the largest source of carbon pollution, providing approximately 34% of greenhouse gas emissions [1]. For this reason, an active search for ways to reduce CO₂ emissions released by power plants is currently underway.

A promising method to eliminate the carbon footprint in the power energy sector is to switch to oxygen-fuel power complexes (OFC) based on the Allam cycle. Any OFC is a modified Brayton cycle, in which pure oxygen is used to burn fuel, while flue gases, consisting mainly of carbon dioxide, are almost not released into the atmosphere, and are used as a working fluid in a semi-closed cycle. Of all the OFCs, the Allam cycle has the highest efficiency of up to 59% [2], which is significantly higher than traditional power plants—operating on Rankine and Brayton cycles—without carbon capture can provide (35–40%), and is comparable to the best CCGTs (up to 60%). The disadvantages of OFCs are the large area of the recuperative system due to the low heat transfer coefficient of CO₂ compared to steam, and the high energy cost to produce pure oxygen, which significantly reduces the net efficiency of oxy-fuel cycles, although it is still comparable to that of CCCGTs. However, the advantages of OFCs, such as near-zero CO₂ emissions, high net efficiency, and the ability to use traditional hydrocarbon fuels without harming the environment, outweigh their disadvantages.

Unfortunately, the widespread use of OFCs is currently hampered by technical difficulties in implementing oxy-fuel cycles. One of the problems is the design of an oxy-fuel combustion chamber. Unlike the standard Brayton cycle, in OFCs, combustion chamber fuel burns at supercritical pressures of up to 300 bar in a mixture of oxygen and carbon dioxide, rather than in atmospheric air (a mixture of oxygen and nitrogen). Supercritical CO₂ is a much stronger inhibitor than N₂, since the laminar burning velocity in a mixture diluted with CO₂ is 2–4 times lower than in a mixture diluted with N₂ [3]. The differences between air-fuel and oxy-fuel combustion require significant changes in the design of standard Brayton cycle combustion chambers to make them suitable for oxy-fuel combustion. In addition, most kinetic hydrocarbon combustion mechanisms were developed for modeling air-fuel combustion, so their use to model oxy-fuel combustion can significantly distort the results. Therefore, it is an urgent task to find a mechanism suitable for modeling oxy-fuel combustion. However, there is a lack of comparative studies of the presented oxy-fuel kinetic mechanisms.

In this paper, the authors address the problem of finding an optimal oxy-fuel kinetic mechanism. For this purpose, the authors performed a comparative verification of the known kinetic mechanisms developed for modeling oxy-fuel combustion on the experimental data on the ignition delay time of methane published in [4,5,6,7,8,9]. This paper also provides a numerical simulation for the ignition delay time (IDT) for various mixture compositions and kinetic mechanisms, since the IDT is one of the most important combustion characteristics sensitive to chemical kinetics. The main task of numerical simulation was to compare reduced oxy-fuel mechanisms to the most accurate mechanism identified during experimental verification.

Therefore, in this paper, the following tasks were set and solved:

1. Comparative verification of the known oxy-fuel combustion kinetic mechanisms was conducted using published experimental data on the ignition delay time of methane in order to identify the most accurate mechanism to model oxy-fuel combustion.

2. A comparison of reduced oxy-fuel kinetic mechanisms to the most accurate detailed oxy-fuel mechanism identified during the experimental verification was conducted to determine the limits of their applicability using numerical simulation.

2. Kinetic Mechanisms of Oxy-Fuel Combustion

As studies have shown, of the known air-fuel kinetic mechanisms, USC Mech and AramcoMech are the best at modeling oxy-fuel combustion. USC Mech II and AramcoMech 2.0 cope well with modeling the ignition delay time at pressures up to 200 atm for USC Mech II and 260 atm for AramcoMech 2.0 [10]. Both mechanisms also satisfactorily model the laminar burning velocity at pressures up to 3 atm [11] (there is a lack of experimental data at higher pressures). This is why the mechanisms of the USC and Aramco branches are being used as a basis for designing specified oxy-fuel kinetic mechanisms. USC Mech II was originally designed for the combustion of methane, hydrogen, and syngas, and it contains 784 reactions and 111 species [12], while AramcoMech 3.0 contains 3037 reactions and 581 species and is designed for the combustion of C1–C4 hydrocarbons [13].

The UoS sCO₂ detailed mechanism was created based on USC Mech II by adding reactions involving CH₃O₂ and CH₃O₂H species from AramcoMech 2.0. These reactions were found to have high significance for oxy-fuel combustion at pressures over 200 atm. UoS sCO₂ 1.0 was presented in the paper [10], it contains 798 reactions and 113 species, and it was experimentally verified by the ignition delay time of methane at pressures of 0.7–266.3 atm, equivalence ratios from 0.5 to 2.0, and CO₂ dilutions from 30 to 86.17%. UoS sCO₂ 2.0 was presented in the paper [14], and its only difference from UoS sCO₂ 1.0 was the increase in the third-body efficiency of CO₂, from 2.0 to 3.8, in the reaction of H + O₂ (+M) ↔ HO₂ (+M). UoS sCO₂ 2.0 was verified for the combustion of hydrogen [14] and syngas [15] at pressures up to 40 bar, CO₂ dilutions up to 85%, and equivalence ratios from 0.25 to 2.0. Finally, the UoS sCO₂ 2.1 mechanism was presented in [16]. It included all possible reactions involving CH₃O₂ and CH₃O₂H species, with their rate coefficients being determined in accordance with the newest measurements. Overall, the UoS sCO₂ 2.1 mechanism contains 812 reactions and 113 species, but it turned out to be less accurate than the unmodified UoS sCO₂ 1.0 mechanism when modeling the ignition delay time of methane at pressures over 200 atm [16]. Therefore, in this paper, the UoS sCO₂ 2.0 mechanism was studied, since this mechanism only slightly differs from the UoS sCO₂ 1.0 mechanism, which was designed specifically for modeling the oxy-fuel combustion of methane, and was verified by the IDT at pressures up to 260 atm.

Another detailed kinetic mechanism for modeling oxy-fuel combustion, OXY-NG, was developed based on AramcoMech 1.3. In papers [7,17,18,19,20], researchers consistently measured the ignition delay time for methane, ethane, propane, methane–propane mixtures, and natural gas (methane–ethane–propane mixture) using a shock tube and modified AramcoMech 1.3 for better modeling oxy-fuel combustion based on the measurements; overall, 55 reactions were modified. The final OXY-NG mechanism presented in [20] includes 2824 reactions and 495 species and is the most detailed of the kinetic mechanisms designed specifically for modeling the oxy-fuel combustion of hydrocarbons. Taking into account all stages of development, the OXY-NG mechanism was verified by the ignition delay time of C1–C3 hydrocarbons oxy-fuel combustion at pressures up to 10 atm and some high pressures up to 260 atm, CO₂ dilutions up to 80%, and equivalence ratios from 0.5 to 2.0, as well as by the laminar burning velocity at atmospheric pressure. The advantages of the OXY-NG mechanism compared to UoS sCO₂ are the presence of verification for the combustion of ethane and propane, which comprise natural gas, together with methane, and the presence of the laminar burning velocity verification, albeit only at atmospheric pressure, while the disadvantage is the fragmentary verification at pressures above 10 atm. The OXY-NG mechanism was chosen for this study since this mechanism contains the largest amount of reactions and species among all of the mechanisms designed for modeling oxy-fuel combustion of hydrocarbons.

Based on USC Mech II, three reduced oxy-fuel kinetic mechanisms presented in papers [11,21] were also developed. The authors did not assign any names to these mechanisms, so in this paper, the mechanisms from paper [11] are called Skeletal and R-A (Reduced-Atmospheric), and the mechanism from paper [21] is called R-SC (Reduced-Supercritical).

The Skeletal mechanism was derived from USC Mech II using skeletal reduction, and it contains 155 reactions and 34 species. The R-A mechanism is the further reduction of USC Mech II and was derived from the Skeletal mechanism using time-scale reduction; it contains 19 reactions and 22 species. Both mechanisms were experimentally verified by the ignition delay time, the laminar burning velocity, and CO measurements at pressures of no more than 10 atm [11]. The main disadvantage of both mechanisms is the lack of verification at supercritical pressures, while the advantage is the wide range of combustion characteristics used for verification. The Skeletal and R-A mechanisms were chosen for the study, since they are both reduced mechanisms designed specifically for modeling oxy-fuel combustion.

The R-SC mechanism was also derived from USC Mech II using skeletal reduction. It contains 150 reactions and 27 species, and was verified by the ignition delay time, the laminar burning velocity, and an adiabatic combustion temperature at pressures up to 300 atm, but only by comparing simulation results to the original USC Mech II, not on experimental data [21]. The R-SC mechanism was included in the study, together with R-A and Skeletal mechs, as another reduced mechanism designed for modeling oxy-fuel combustion.

Thus, there are seven presented kinetic mechanisms suitable for modeling the oxy-fuel combustion of methane, of which four—USC Mech, UoS sCO₂, AramcoMech, and OXY-NG—are detailed, and three—Skeletal, R-A, and R-SC—are reduced. In addition to these mechanisms, the GRI-Mech 3.0 air-fuel mechanism was also included in this study, since this mechanism, consisting of 325 reactions and 53 species and designed for the combustion of natural gas and ammonia [22], is widely used in engineering and scientific practice, so studying its applicability for modeling the oxy-fuel combustion of methane is of practical interest.

Table 1. Kinetic mechanisms suitable for modeling oxy-fuel combustion of methane.

Mechanism	Source	Species	Reactions	Scope
Detailed mechanisms
GRI-Mech 3.0	[22]	53	325	Natural gas and ammonia
USC Mech II	[12]	111	784	C1–C4, CO, H2
UoS sCO2 2.0	[10,14,15,16]	113	798	C1–C4, CO, H2
AramcoMech 3.0	[13]	581	3037	C1–C4
OXY-NG	[7,17,18,19,20]	495	2824	C1–C4
Reduced mechanisms
Skeletal	[11]	34	155	C1–C4, CO, H2
R-A	[11]	22	19	C1–C4, CO, H2
R-SC	[21]	27	150	C1–C4, CO, H2

presents brief characteristics of all known kinetic mechanisms suitable for modeling the oxy-fuel combustion of methane.

3. Methodology

The present study was carried out using Chemkin 18.2. USC Mech II and AramcoMech 3.0 were excluded from the study, since the UoS sCO₂ 2.0 and OXY-NG mechanisms are their modified versions, designed specifically for modeling oxy-fuel combustion. The R-A and R-SC mechanisms were also excluded, since the latter could not be found in open sources, and the former could not be run for calculation in Chemkin 18.2 in the form in which it is presented in the appendix of the original paper [11]. Therefore, in this paper, the kinetic mechanisms of GRI-Mech 3.0, UoS sCO₂ 2.0, OXY-NG, and Skeletal were studied.

The comparative experimental verification of the kinetic mechanisms was performed using the ignition delay time. The IDT was chosen as the verified parameter, since this combustion characteristic has the largest number of experimental measurements under the conditions of the oxy-fuel combustion of methane in a wide range of mixture compositions, while other combustion characteristics, such as laminar burning velocity (LBV), lack experimental data at pressures higher than 1 atm in highly CO₂-diluted mixtures. The experimental data used in this work were presented in papers [4,5,6,7,8,9], and include 132 datapoints combined into 25 datasets with similar mixture parameters; together, they cover pressures in the range of 0.528–285.5 atm, CO₂ dilutions from 30 to 86.17%, and equivalence ratios from 0.5 to 2.0. The experimental data in all datasets were obtained using a shock tube; the experimental conditions are presented in

Table 2. Conditions for obtaining the experimental data on the ignition delay time of methane in CO₂-diluted mixtures.

Dataset	Source	Number of Points	P, atm	T, K	ϕ	CO2 Molar Fraction, %	Method of Measuring	Uncertainty
1	[4]	6	0.8	1876	1	30	max [CH*]	±12%–±18%
2	[4]	6	3.8	1782	1	30	max [CH*]	±12%–±18%
3	[4]	6	0.8	1846	0.5	30	max [CH*]	±12%–±18%
4	[4]	6	3.9	1735	0.5	30	max [CH*]	±12%–±18%
5	[4]	7	0.7	1859	2	30	max [CH*]	±12%–±18%
6	[4]	8	3.6	1749	2	30	max [CH*]	±12%–±18%
7	[4]	5	0.6	1963	1	60	max [CH*]	±12%–±18%
8	[5]	3	0.9	1822	1	60	max [CH*]	20%
9	[5]	6	7.2	1658	1	60	max [CH*]	20%
10	[5]	4	8.9	1613	1	30	max [CH*]	20%
11	[5]	3	29.6	1444	1	85	max [CH*]	20%
12	[6]	3	0.9	1822	1	60	6 methods	20%
13	[6]	1	0.6	2038	1	89.5	6 methods	20%
14	[6]	5	1	1823	1	85	6 methods	20%
15	[7]	10	1.9	1636	0.5	75	max [OH*]	±16%–±20%
16	[7]	11	0.9	1671	0.5	75	max [OH*]	±16%–±20%
17	[8]	4	32.4	1394	1	77.5	max [OH*]	25%
18	[8]	4	106.3	1329	1	77.5	max [OH*]	25%
19	[8]	4	260	1072	1	77.5	max [OH*]	25%
20	[8]	4	31.4	1503	1.27	86.17	max [OH*]	25%
21	[8]	5	74.7	1394	1.27	86.17	max [OH*]	25%
22	[8]	3	266.3	1104	1.27	86.17	max [OH*]	25%
23	[9]	11	99	1357	1	85	max [OH*]	±15%–±18%
24	[9]	3	97	1341	2	80	max [OH*]	±15%–±18%
25	[9]	4	201.9	1194	1	85	max [OH*]	±15%–±18%

(CH* and OH* are excited CH and OH radicals).

.

The Closed Homogeneous Batch Reactor model with the “Constraint Volume And Solve Energy Equation” Problem Type, which allowed us to get as close as possible to the experimental conditions of shock tubes, was used to simulate the IDT of methane.

The method of measuring the ignition delay time for each dataset was chosen based on the conditions of the corresponding experiment, which are as follows: the IDT was determined by max [CH] emissions for datasets 1–11 and by max [OH] emissions for datasets 15–25. In paper [6], presenting datasets 12–14, the ignition delay time was measured in six different ways, including max emissions; however, the paper did not specify what exact species was used for the measurements. However, the paper compared the experimental data to the simulated IDT measured by max dT/dτ. Therefore, in this paper, the ignition delay time for datasets 12–14 was determined by max dT/dτ and compared to the experimental data obtained by max emissions. For the Skeletal mechanism, the IDT in datasets 1–11 was also determined by max dT/dτ, since this mechanism does not contain a CH species. A selective comparison of simulated IDTs obtained using different methods showed that IDTs measured by max dT/dτ or max [CH] emissions are equal or differ only slightly, while measuring by max [OH] emissions overestimates IDT compared to the previous two methods. For example, the UoS sCO₂ 2.0 mechanism for point 1 from dataset 10 showed the IDT 608.5 μs by max [CH], 608.5 μs by max dT/dτ, and 611.3 μs by max [OH]. If the ignition delay time could not be determined by max emissions, or if the discrepancy between IDTs measured by max [OH] and max dT/dτ was too high (more than 20%), the ignition delay time was taken by max dT/dτ (for example, the UoS sCO₂ 2.0 mechanism for point 1 from dataset 21 showed IDT 2500 μs by max [OH] and 265.7 μs by max dT/dτ; the last value was taken).

After the experimental verification of the kinetic mechanisms, which allowed us to identify the most accurate mechanism to model the IDT of methane in oxy-fuel conditions, the numerical simulation for the ignition delay time, as one of the most important combustion characteristics, was performed for various mixture compositions using different kinetic mechanisms. The objective of the numerical simulation was to determine the limits of the reduced mechanisms’ applicability for modelling oxy-fuel combustion by comparing them to the reference mechanism identified during the experimental verification. The modeling was carried out in the range of pressures 1–300 atm, mass fractions of CO₂-diluent in the oxidizer (γ) 0–0.95 ($\mathsf{\gamma }={\displaystyle \frac{{\mathrm{C}\mathrm{O}}_2}{{\mathrm{C}\mathrm{O}}_2+{\mathrm{O}}_2}}$), and oxidizer excess ratios of (α) 0.5–2.0 (oxidizer excess ratio is the reciprocal of equivalence ratio). To obtain the IDT, the same reactor model as the one employed during experimental verification was used, and the IDT was measured by max dT/dτ.

The numerical simulation was divided into three stages. In the first stage, the influence of pressure on the ignition delay time was investigated, as follows: the oxidizer excess ratio (α) was taken as equal to 1 (stoichiometry), the pressure range was 1–300 atm (from atmospheric to supercritical conditions), and the measurement was carried out for γ 0, 0.6, 0.82, and 0.95. In the second stage, the influence of γ (i.e., CO₂ dilution) was investigated, as follows: α was also taken as equal to 1, the range of γ was 0–0.95, and the measurement was carried out at pressures of 1 atm and 300 atm. Finally, in the third stage, the influence of α (i.e., oxygen concentration) was investigated, as follows: the measurement was carried out for two pressures—1 atm and 300 atm—and for four γ—0, 0.6, 0.82, and 0.95—for which the range of α was 0.5–2.0. Throughout all three stages, the temperature of a mixture was taken as 1500 K, which corresponds to conditions in a shock tube after the reflected shock wave [4,5,6,7,8,9].

When determining the composition of a mixture, the mass flow-rate of methane was taken as 1 kg/s. With the known methane flow-rate, and given α and γ, the mass flow-rates of oxygen and CO₂ were determined using Formulas (1) and (2), which are as follows:

$${\mathrm{O}}_2=4·\mathsf{\alpha }·{\mathrm{C}\mathrm{H}}_4$$

(1)

$${\mathrm{C}\mathrm{O}}_2={\displaystyle \frac{\mathsf{\gamma }}{1-\mathsf{\gamma }}}·{\mathrm{O}}_2$$

(2)

The known mass flow-rates of the mixture components made it possible to determine the mass fraction of each component in a mixture using Formula (3), which is as follows:

$$\left[\mathrm{S}\right]={\displaystyle \frac{\mathrm{S}}{{\mathrm{C}\mathrm{H}}_4+{\mathrm{O}}_2+{\mathrm{C}\mathrm{O}}_2}},$$

(3)

where S is a component of a mixture, comprising methane, oxygen, or carbon dioxide.

Table 3. Compositions of the mixtures studied at varying pressure using numerical methods.

P, atm	γ	α	[CH4]	[O2]	[CO2]	T, K
1, 5, 10, 50, 100, 150, 300	0	1	0.2	0.8	0	1500
	0.6	1	0.0909	0.3636	0.5455	1500
	0.82	1	0.0431	0.1722	0.7847	1500
	0.95	1	0.0123	0.0494	0.9383	1500

,

Table 4. Compositions of the mixtures studied at varying CO₂ dilutions using numerical methods.

γ	α	P, atm	[CH4]	[O2]	[CO2]	T, K
0	1	1, 300	0.2	0.8	0	1500
0.1	1		0.184	0.735	0.0816	1500
0.2	1		0.1667	0.6667	0.1667	1500
0.3	1		0.1489	0.5957	0.2553	1500
0.4	1		0.1304	0.5217	0.3478	1500
0.5	1		0.1111	0.4444	0.4444	1500
0.6	1		0.0909	0.3636	0.5455	1500
0.7	1		0.0698	0.2791	0.6512	1500
0.8	1		0.0476	0.1905	0.7619	1500
0.82	1		0.0431	0.1722	0.7847	1500
0.85	1		0.0361	0.1446	0.8193	1500
0.872	1		0.031	0.1240	0.845	1500
0.9	1		0.0244	0.0976	0.878	1500
0.95	1		0.0123	0.0494	0.9383	1500

and

Table 5. Compositions of the mixtures studied at varying O₂ concentrations using numerical methods.

α	P, atm	[CH4]	[O2]	[CO2]	T, K	α	P, atm	[CH4]	[O2]	[CO2]	T, K
γ = 0						γ = 0.6
0.5	1, 300	0.3333	0.6667	0	1500	0.5	1, 300	0.1667	0.3333	0.5	1500
0.6		0.2941	0.7059	0	1500	0.6		0.1429	0.3429	0.5143	1500
0.7		0.2632	0.7368	0	1500	0.7		0.125	0.35	0.525	1500
0.8		0.2381	0.7619	0	1500	0.8		0.1111	0.3556	0.5333	1500
0.9		0.2174	0.7826	0	1500	0.9		0.1	0.36	0.54	1500
1		0.2	0.8	0	1500	1		0.0909	0.3636	0.5455	1500
1.1		0.1852	0.8148	0	1500	1.1		0.0833	0.3667	0.55	1500
1.2		0.1724	0.8276	0	1500	1.2		0.0769	0.3692	0.5538	1500
1.3		0.1613	0.8387	0	1500	1.3		0.0714	0.3714	0.5571	1500
1.4		0.1515	0.8485	0	1500	1.4		0.0667	0.3733	0.56	1500
1.5		0.1429	0.8571	0	1500	1.5		0.0625	0.375	0.5625	1500
1.6		0.1351	0.8649	0	1500	1.6		0.0588	0.3765	0.5647	1500
1.7		0.1282	0.8718	0	1500	1.7		0.0556	0.3778	0.5667	1500
1.8		0.122	0.878	0	1500	1.8		0.0526	0.3789	0.5684	1500
1.9		0.1163	0.8837	0	1500	1.9		0.05	0.38	0.57	1500
2		0.1111	0.8889	0	1500	2		0.0476	0.381	0.5714	1500
γ = 0.82						γ = 0.95
0.5	1, 300	0.0826	0.1651	0.7523	1500	0.5	1, 300	0.0244	0.0488	0.9268	1500
0.6		0.0698	0.1674	0.7628	1500	0.6		0.0204	0.049	0.9306	1500
0.7		0.0604	0.1691	0.7705	1500	0.7		0.0175	0.0491	0.9333	1500
0.8		0.0533	0.1704	0.7763	1500	0.8		0.0154	0.0492	0.9354	1500
0.9		0.0476	0.1714	0.781	1500	0.9		0.0137	0.0493	0.937	1500
1		0.0431	0.1722	0.7847	1500	1		0.0123	0.0494	0.9383	1500
1.1		0.0393	0.1729	0.7878	1500	1.1		0.0112	0.0494	0.9393	1500
1.2		0.0361	0.1735	0.7904	1500	1.2		0.0103	0.0495	0.9402	1500
1.3		0.0335	0.174	0.7926	1500	1.3		0.0095	0.0495	0.9410	1500
1.4		0.0311	0.1744	0.7945	1500	1.4		0.0088	0.0496	0.9416	1500
1.5		0.0291	0.1748	0.7961	1500	1.5		0.0083	0.0496	0.9421	1500
1.6		0.0274	0.1751	0.7976	1500	1.6		0.0078	0.0496	0.9426	1500
1.7		0.0258	0.1754	0.7989	1500	1.7		0.0073	0.0496	0.9431	1500
1.8		0.0244	0.1756	0.8	1500	1.8		0.0069	0.0497	0.9434	1500
1.9		0.0231	0.1758	0.801	1500	1.9		0.0065	0.0497	0.9438	1500
2		0.022	0.176	0.802	1500	2		0.0062	0.0497	0.9441	1500

show compositions of all of the mixtures studied at each of the three stages of numerical simulation ([CH₄], [O₂], and [CO₂] are mass fractions of the corresponding components in a mixture).

The discrepancy between the simulation results and experimental data was considered acceptable if it was no more than 20%. The discrepancy of 20% was adopted as the convergence threshold, since it is the average uncertainty value for the experimental data on the IDT used in the study (see Table 2). Although the uncertainty varies for different datasets, the use of the average uncertainty value for verification is justified due to the large amount of experimental data. The discrepancy δ for each datapoint was determined using Formula (4), which is as follows:

$$\mathsf{\delta }=\left|{\displaystyle \frac{I_{\mathrm{r}\mathrm{e}\mathrm{f}}-I_{\mathrm{s}\mathrm{t}}}{I_{\mathrm{r}\mathrm{e}\mathrm{f}}}}\right|·100\%,$$

(4)

where I_ref is experimental data on the ignition delay time during experimental verification and I_st is the simulation results for the mechanism under study.

During the experimental verification, Formula (6) was used to calculate the simulation error E for each dataset, as follows:

$$E={\displaystyle \frac{1}{N}}{\sum }_i^N\left(\left|{\displaystyle \frac{{I_{\mathrm{r}\mathrm{e}\mathrm{f}}}_i-{I_{\mathrm{s}\mathrm{t}}}_i}{{I_{\mathrm{r}\mathrm{e}\mathrm{f}}}_i}}\right|·100\%\right),$$

(5)

where N is the number of datapoints in each dataset and i is the number of a point.

During both the experimental verification and the numerical simulation, the standard solver settings were used, which are high enough to ensure the independence of the solution. For example, at the pressure of 300 atm, α = 1, and γ = 0.95, Skeletal showed the ignition delay time of 74.7 μs with the standard solver settings (absolute tolerance 1 × 10⁻²⁰, relative tolerance 1 × 10⁻⁸, maximum 4 iterations); increasing the quality of the solver (absolute tolerance 1 × 10⁻³⁰, relative tolerance 1 × 10⁻¹², maximum 10 iterations) only decreased the IDT to 70.6 μs.

It should be noted that the appendix of the original paper [20] presenting the OXY-NG mechanism did not contain a transport properties file, so the similar file from the OXYMECH 2.0 mechanism was used. OXYMECH 2.0 includes the same number of reactions and species as OXY-NG and is its earlier version presented in the paper [18].

4. Comparative Verification of the Kinetic Mechanisms on Experimental Data

Table 6. Comparative verification of the mechanisms studied on experimental data on the ignition delay time of methane.

Dataset					Simulation Error (E, (%))
No.	P, atm	T, K	φ	CO2 Molar Fraction, %	GRI-Mech 3.0	UoS sCO2 2.0	OXY-NG	Skeletal
1	0.8	1876	2	30	6.63	8.57	12.18	22.85
2	3.8	1782	2	30	16.14	16.95	19.87	21.03
3	0.8	1846	0.5	30	17.92	20.41	20.79	36.56
4	3.9	1735	0.5	30	13.51	16.73	27.44	27.66
5	0.7	1859	2	30	8.66	9.97	12.79	12.84
6	3.6	1749	2	30	14.01	13.58	31.69	21.99
7	0.6	1963	1	60	9.12	10.99	5.24	44.29
8	0.9	1822	1	60	12.96	12.85	24.60	42.05
9	7.2	1658	1	60	19.56	14.59	22.65	19.50
10	8.9	1613	1	30	20.48	15.87	13.1	7.49
11	29.6	1444	1	85	35.33	13.75	18.31	30.3
12	0.9	1822	1	60	9.15	8.8	14.26	31.88
13	0.6	2038	1	89.5	3.31	7.94	3.33	59.7
14	1	1823	1	85	21.08	21.48	16.96	6.8
15	1.9	1636	0.5	75	11.22	12.41	28.04	14.89
16	0.9	1671	0.5	75	26.75	21.84	47.22	38.26
17	32.4	1394	1	77.5	23.35	23.61	50.58	49.95
18	106.3	1329	1	77.5	41.59	22.61	21.7	26.44
19	260	1072	1	77.5	207.98	22.15	13.87	326.55
20	31.4	1503	1.27	86.17	33.42	73.89	90.87	82.77
21	74.7	1394	1.27	86.17	51.34	12.78	23.86	12.01
22	266.3	1104	1.27	86.17	31.43	28.21	26.36	153.03
23	99	1357	1	85	51.89	15.91	23.23	21.21
24	97	1341	2	80	56.3	10.92	5.78	21.88
25	201.9	1194	1	85	31.29	11.55	22.39	56.4
Average Error (by datasets), %					30.98	17.93	23.88	47.53
No. Good Convergences (by datasets)					12	17	11	6
No. Best Fits (by datasets)					9	8	5	3
Total number of datasets					25
Average Error (by datapoints), %					29.33	17.56	25.51	39.74
No. Good Convergences (by datapoints)					68	91	73	64
No. Best Fits (by datapoints)					34	45	28	25
Total number of datapoints					132

presents the simulation errors for all datasets. It also presents simulation errors averaged both by all datasets and by all datapoints without combining them in datasets. Averaging simulation errors directly by datapoints is more correct, since each dataset includes a different number of points (see Table 2). Simulation errors for each individual datapoint are not presented because of the large amount of data.

Table 6, “No. Good Convergences”, shows the number of datasets or datapoints for which the mechanism under study showed the discrepancy with the experimental data of no more than 20%, i.e., it did not exceed the convergence threshold, and “No. Best Fits” is the number of datasets or datapoints for which the mechanism under study showed the smallest discrepancy with the experimental data compared to other mechanisms.

As can be seen from the data in Table 6, the more correct averaging of simulation results directly by datapoints, compared to the averaging by datasets, shows a higher accuracy of modeling, wherein the average error decreases for all mechanisms except OXY-NG.

As for the comparison of different mechanisms to each other, it is obvious that the UoS sCO₂ 2.0 mechanism performed best in modeling the ignition delay time. This mechanism has the smallest average error and the largest number of good convergences and best fits, both when averaging by datasets and when averaging by datapoints (highlighted in bold in Table 6). Furthermore, UoS sCO₂ 2.0 is the only mechanism which did not exceed the convergence threshold of 20%.

The OXY-NG mechanism turned out to be less accurate overall compared to UoS sCO₂ 2.0, showing a significantly higher average error (25.51% versus 17.56% when averaging by datapoints) and a smaller number of good convergences and best fits. At the same time, OXY-NG contains significantly more reactions and species than the UoS sCO₂ 2.0 mechanism (see Table 2). For that reason, it requires much more computing power for calculation, so using the OXY-NG mechanism to model the oxy-fuel combustion of methane seems unjustified compared to the more accurate UoS sCO₂ 2.0 mechanism.

Skeletal and GRI-Mech 3.0 turned out to be the worst mechanisms to model oxy-fuel combustion, as expected, with Skeletal showing the largest simulation error and the smallest number of good convergences and best fits. GRI-Mech 3.0 is overall more accurate than the Skeletal mechanism, but it is inferior to both the UoS sCO₂ 2.0 and OXY-NG mechanisms by its average simulation error. Therefore, according to the results of the experimental verification, using Skeletal or GRI-Mech 3.0 to model the IDT of methane in oxy-fuel conditions cannot be justified, even though, of all the mechanisms studied, they have the smallest number of reactions and species, and thus do not require much time or computing resources for calculation.

Thus, it is established that UoS sCO₂ 2.0 is the most accurate kinetic mechanism to model the ignition delay time during the oxy-fuel combustion of methane, as OXY-NG, Skeletal, and GRI-Mech 3.0 are significantly inferior to it in accuracy. However, the obtained verification results are insufficient to accurately determine the applicability limits of the mechanisms for modeling the oxy-fuel combustion of methane. First, the verification was carried out only by ignition delay time, since there is a lack of experimental data on other combustion characteristics at pressures higher than 1 atm in highly CO₂-diluted mixtures. Second, the experimental data used, although they cover a nominally wide range of mixture parameters, are in fact very fragmentary.

Table 7. Average simulation errors across datasets grouped by pressure.

Experimental Data			Kinetic Mechanism, Simulation Error (%)
Datasets	Number of Datasets	Average P, atm	GRI 3.0	UoS sCO2 2.0	OXY-NG	Skeletal
1, 3, 5, 7, 13	5	0.7	9.13	11.58	10.87	35.25
8, 12, 14, 16	4	0.9	17.48	16.24	25.76	29.75
15	1	1.9	11.22	12.41	28.04	14.89
2, 4, 6	3	5.6	21.84	23.63	39.50	35.34
9, 10	2	8.0	20.02	15.23	17.88	13.49
11, 17, 20	3	31.2	30.7	37.08	53.25	54.34
21	1	74.7	51.34	12.78	23.86	12.01
18, 23, 24	3	100.8	49.93	16.48	16.90	23.18
25	1	201.9	31.29	11.55	22.39	56.4
19, 22	2	263.1	119.71	25.18	20.11	239.79

, which averages the simulation errors across datasets grouped by pressure, allows us to better understand this. (In Table 7, errors that do not exceed, or only slightly exceed, the convergence threshold of 20% are highlighted in bold).

As can be seen in Table 7, the UoS sCO₂ 2.0 mechanism confirms its status as the best mechanism to model the IDT of methane under oxy-fuel combustion conditions, since it satisfactorily copes with modeling in the widest pressure range, from subatmospheric up to 200 atm. GRI-Mech 3.0 does not exceed the convergence threshold at pressures only up to 8 atm, while for the OXY-NG and Skeletal mechanisms, the simulation error changes chaotically with increasing pressure. However, as we said, the experimental data are fragmentary. For example, at pressures about and below 1 atm, there are nine datasets, covering CO₂ dilution from 30 to 89.5%, and equivalence ratios from 0.5 to 2.0. At the same time, at pressures above 200 atm there are only three datasets, which do not cover CO₂ dilutions lower than 85% and equivalence ratios lower than 1.0. For these reasons, it was decided to carry out the second stage of the study, which consisted of a comparative numerical simulation of the ignition delay time for various mixture compositions and kinetic mechanisms. The aim of the numerical simulation was to fill the gaps in the experimental data and to determine the applicability limits of the GRI-Mech 3.0 and Skeletal mechanisms in terms of physicality and accuracy, compared to UoS sCO₂ 2.0.

During the numerical simulation, UoS sCO₂ 2.0 was adopted as the reference mechanism, since it demonstrated the highest modeling accuracy and the largest number of good convergences with the experimental data compared to other mechanisms. However, the authors understood that the UoS sCO₂ 2.0 mechanism is not absolutely accurate, since it was verified using experimental data with significant gaps, and even in comparison to them, it has an average simulation error of about 17%. For these reasons, during numerical simulation, the convergence threshold between the reference mechanism and the mechanism under study was reduced from 20% to 7%. In that case, the average simulation error of GRI-Mech 3.0 and Skeletal compared to the experimental data will not exceed 25% ($1.17\times 1.07=1.25)$, which is the largest uncertainty value for the experimental data used in the study (see Table 2). It was also decided to abandon the further study of the OXY-NG mechanism, since this mechanism is not only inferior to UoS sCO₂ 2.0 in accuracy, but also, unlike GRI-Mech 3.0 and Skeletal, contains significantly more reactions and species (see Table 2), and is therefore more demanding of computational and time resources.

5. Effect of Mixture Composition on the Ignition Delay Time of Methane in Oxy-Fuel Combustion Conditions

Simulated ignition delay times, as a function of mixture composition, obtained using kinetic mechanisms GRI-Mech 3.0, UoS sCO₂ 2.0, and Skeletal, are shown in Figure 1.

As can be seen in Figure 1, in their behavior, all mechanisms show an increase in the IDT with increasing CO₂ dilution (Figure 1b), and a decrease in the IDT with increasing pressure (Figure 1a). As for the effect of the oxygen concentration, the ignition delay time decreases with increasing α at atmospheric pressure (Figure 1c). At the same time, at a supercritical pressure of 300 atm (Figure 1d), a minimum of the IDT is observed at a certain oxygen concentration. Its value depends on the mechanism and γ; for example, the minimum is reached at α 1.3–1.6 for γ = 0 (except for the Skeletal mechanism, which predicts a constant decrease in the IDT) and at α 0.8–1.2 for γ = 0.6. However, with a further increase in γ, this rule is violated, as follows: at γ = 0.82, this behavior is typical only for the GRI-Mech 3.0 and Skeletal mechanisms (the minimum is at α 0.7–0.8), while UoS sCO₂ 2.0 shows the constant increase in the IDT. At γ = 0.95, all mechanisms predict growth in the IDT, except Skeletal, which shows the constant decrease.

The ignition delay time is the duration of the pre-flame oxidation phase of combustion, during which the flame does not yet exist, and mostly incomplete oxidation reactions occur. There are few falloff reactions among them, so the catalytic effect of high pressure is stronger than the inhibitory one, which causes the IDT to decrease. In the case of increasing CO₂ dilution, the inhibitory effect, on the contrary, dominates, since most third-body reactions involving CO₂ occur during active combustion and afterburning. Therefore, their acceleration with increasing γ cannot reduce the IDT. Thus, in regard to the effect of pressure and CO₂ dilution on the ignition delay time, it can be concluded that the simulation results are physical.

The effect of oxygen concentration on the behavior of mechanisms requires a more detailed explanation. Under atmospheric conditions, decreasing α causes the sharp increase in fuel underburning because of a lack of oxygen for complete oxidation. This significantly reduces heat generation, which causes the combustion temperature to decrease and the oxidation reactions to slow down, so the ignition delay time increases. Increasing α also has an inhibitory effect, as this creates an inert ballast in a mixture. However, with an increase in O₂ concentration, the number and size of the reactor zones in which there is not enough oxygen for complete oxidation decrease. As a result, the critical concentration of incomplete combustion products, at which the flame ignites and the pre-flame oxidation phase ends, is achieved faster, so the ignition delay time decreases. Thus, the mechanisms’ behavior at atmospheric pressure and varying α is also physical.

Switching to the effect of α under supercritical conditions, we need to pay attention to the following circumstance. The catalytic effect of increasing pressure is caused by the decreasing volume of a mixture, which increases molar concentrations of the reagents. In the case of oxygen concentration, mixture compression also leads to a sharp decrease in the size and reduction in the number of underburning zones, as well as accelerates incomplete oxidation reactions. For these reasons, under supercritical conditions, the inhibitory effect of the inert ballast becomes more noticeable; therefore, from a certain value of α, the ignition delay time begins to increase. With increasing γ, the minimum IDT shifts towards lower α, since the inhibitory effect of oxygen is supplemented by the inhibitory effect of CO₂. As CO₂ dilution increases, the cumulative inhibitory effect begins to prevail over the entire α range; therefore, at the highest γ = 0.95, all mechanisms predict an increase in the ignition delay time. The exception to this is the Skeletal mechanism, which, at γ = 0.95, shows a decrease in the IDT, the clear violation of physicality. At γ = 0, Skeletal also shows a decrease in the IDT, but given that it shows the same trend as the other mechanisms before the start of IDT growth, it is likely that a sufficiently high α value, from which it would show an increase in the ignition delay time, like the rest of the mechanisms, was not reached during the study. Thus, at the supercritical pressure of 300 atm and varying α, all mechanisms show physical behavior, except for the Skeletal mechanism at γ = 0.95.

As for the limits of applicability of the various mechanisms, as can be seen in Figure 1, they are absent; data breaks or deviations from physical results are not detected for any mixture. Only Skeletal showed a non-physical result at γ = 0.95 under supercritical conditions, but this is an insignificant exception.

Comparing the simulation results of the GRI-Mech 3.0 and Skeletal mechanisms to UoS sCO₂ 2.0 shows that the discrepancy between the GRI-Mech 3.0 and UoS sCO₂ 2.0 mechanisms when modeling the ignition delay time does not exceed 7% only at pressures of 1 atm and low γ that is no more than 0.7 for stoichimetric or oxidizer-poor mixtures. At the pressure of 300 atm, the GRI-Mech 3.0 mech satisfactorily copes with modeling the IDT only at γ = 0, regardless of α. Therefore, the GRI-Mech 3.0 mechanism is not suitable for modeling the IDT of methane during oxy-fuel combustion, as in the oxy-fuel cycles, fuel burns at much higher pressures of up to 300 atm, and much higher γ of no less than 0.6 [3].

The discrepancy between the Skeletal and UoS sCO₂ 2.0 mechanisms increases with decreasing pressure at low γ that is no more than 0.6, and decreases with increasing γ at high pressures. Overall, Skeletal does not exceed the convergence threshold at the pressure of 1 atm and γ of no more than 0.7 for stoichiometric and oxidizer-poor mixtures. At the same time, under conditions of real oxy-fuel cycles (300 atm.), Skeletal satisfactorily predicts the IDT, only in the narrow range of γ from 0.82 to 0.85 for stoichiometric and oxidizer-rich mixtures. Therefore, the Skeletal mechanism can be used to simulate the IDT of methane during oxy-fuel combustion under both atmospheric and supercritical conditions, although, in both cases, only in a narrow range of γ. If a simulation problem falls within the established limitations, then it is recommended to use the Skeletal mechanism for simulation, since it contains the smallest number of reactions and species among all of the mechanisms studied (see Table 1).

6. Summary of Simulation Results

Table 8. Mixture compositions showing simulation physicality and completeness or convergence with the reference mechanism UoS sCO₂ 2.0.

Kinetic Mechanism	Simulation Results	Ignition Delay Time
UoS sCO2 2.0	Physicality and completeness	Any parameters
GRI-Mech 3.0	Convergence with UoS sCO2 2.0	1 atm at γ ≤ 0.7 and α ≤ 1; γ = 0 at 300 atm and any α
	Physicality and completeness	Any parameters
Skeletal	Convergence with UoS sCO2 2.0	1 atm at γ ≤ 0.7 and α ≤ 1; 0.82 ≤ γ ≤ 0.85 at 300 atm and α ≥ 1
	Physicality and completeness	Any parameters, excluding γ = 0.95 at 300 atm

summarizes the comparative simulation results of the ignition delay time during the oxy-fuel combustion of methane obtained using UoS sCO₂ 2.0, GRI-Mech 3.0, and Skeletal kinetic mechanisms. Table 8 allows us to determine the mixture compositions at which all mechanisms studied show physical and complete simulation results for the IDT and (for GRI-Mech 3.0 and Skeletal mechanisms) convergence with the reference mechanism of UoS sCO₂ 2.0.

As can be seen from Table 8, when modeling the ignition delay time, there are no limitations on a mixture composition, excluding a minor exception for Skeletal at γ = 0.95 and 300 atm.

Comparing simulation results of the relatively light GRI-Mech 3.0 and Skeletal mechanisms to the heavier reference mechanism UoS sCO₂ 2.0 (see Table 1 for the number of reactions and species in all mechanisms) shows that both mechanisms can simulate the IDT of methane in oxy-fuel combustion conditions in a narrow range of mixture compositions. At the same time, the Skeletal and GRI-Mech 3.0 mechanisms contain less reactions and species than UoS sCO₂ 2.0 mech; therefore, it is preferable to use them instead of UoS sCO₂ 2.0 if the relevant limitations are met.

7. Conclusions

1. The comparative verification of the kinetic mechanisms of GRI-Mech 3.0, UoS sCO₂ 2.0, OXY-NG, and Skeletal, based on published experimental data on the ignition delay time of methane in oxy-fuel combustion conditions, showed that UoS sCO₂ 2.0 is the best mechanism to model the IDT, as it has the lowest average simulation error and is in good agreement with the largest number of published experimental data.

2. The OXY-NG and GRI-Mech 3.0 mechanisms are much inferior to the UoS sCO₂ 2.0 mechanism in terms of accuracy; OXY-NG also contains many more reactions and species than UoS sCO₂ 2.0. Therefore, these two mechanisms are not suitable for modeling the IDT of methane during oxy-fuel combustion.

3. The Skeletal mechanism is also not suitable overall for modeling the IDT of methane in oxy-fuel combustion conditions. However, unlike GRI-Mech 3.0, it can be used to model the IDT at a supercritical pressure of 300 atm, but only in the narrow range of γ from 0.82 to 0.85 at α more than 1.

4. Numerical simulation and the IDT for various mixtures and kinetic mechanisms, GRI-Mech 3.0, UoS sCO₂ 2.0, and Skeletal, showed that there are no any limits of applicability for the mechanisms studied when modeling the IDT.

Therefore, the only mechanism that is suitable overall for modeling the IDT of methane in oxy-fuel combustion conditions is UoS sCO₂ 2.0. Skeletal and GRI-Mech 3.0 can be used instead of UoS sCO₂ 2.0 only in a narrow range of mixture compositions. However, the high accuracy of modeling the ignition delay time does not mean that modeling other combustion characteristics, primarily the laminar burning velocity, will be equally accurate, since different combustion characteristics are influenced by different groups of reactions. Therefore, to design better mechanisms for modeling the oxy-fuel combustion of methane, additional experimental measurements of the IDT and the LBV in supercritical, highly CO₂-diluted mixtures are needed, especially the LBV at pressures above 1 atm.