A Reduced Kinetics Model for the Oxidation of Transcritical/Supercritical Gasoline Surrogate/Ethanol Mixtures Using Real Gas State Equations

Figures & data

Table 1. Hydrocarbon and alcohol fuels, oxygen, and nitrogen critical properties (Poling, Prausnitz, and O’Connell 2001). $P_c$ and $T_c$ are the critical pressure and temperature.

Formula	Name	Tc [$\mathit{K}$]	Pc [$\mathit{bar}$]
$C_8{H}_{18}$	iso-octane	543.9	25.70
$C_8{H}_{16}$	diisobutylene	559.9	25.85
$C_7{H}_{16}$	n-heptane	540.2	27.40
$C_7{H}_8$	toluene	591.7	41.08
$C_2{H}_5\mathit{OH}$	ethanol	513.9	61.48
$O_2$	oxygen	154.6	50.43
$N_2$	nitrogen	126.2	33.98

Figure 1. Numerical stoichiometric IDT at different pressure points (a) the TRF/DIB reduced mechanism against the original TRF/DIB mechanism Andrae and Kovács (2016) (1, 10, 50, 100 atm) for a mixture of toluene, n-heptane, iso-octane, diisobutylene (surrogate D) (Fikri et al. 2008), (b) the ethanol reduced mechanism versus the original one (Burke et al. 2014; Kéromnès et al. 2013; Metcalfe et al. 2013) (1, 10, 100 atm).

Table 2. Gasoline surrogate (TRF/DIB) and ethanol mechanisms.

Name	Species	Reaction	Type	Ref${ }^{\ast }$
Ethanol OM	114	1999	Detailed	Burke et al. (2014); Kéromnès et al. (2013); Metcalfe et al. (2013)
TRF/DIB OM	159	734	Detailed	Andrae and Kovács (2016)
Ethanol RM	37	564	Reduced	–
TRF/DIB RM	121	592	Reduced	–
TRFE/DIB MM	129	1015	Merged	–

Figure 2. Numerical original, reduced and merged (1st and 2nd) IDT of individual components against experimental data: (a) iso-octane (Davidson, Gauthier, and Hanson 2005), (b) n-heptane (Gauthier, Davidson, and Hanson 2004), and (c) toluene (Davidson, Gauthier, and Hanson 2005). The symbol represents experiments from the literature.

Figure 3. Temperature sensitivity analysis of TRFE/DIB_1st model for single components: (a) iso-octane, (b) n-heptane, and (c) toluene at temperatures equal and lower than 1000 K.

Table 3. Modifying gasoline surrogates (iso-octane, n-heptane, toluene) key reactions constant rate (k).

Reaction	Previous (k)	Modified (k)	Reference
iso-octane $\mathbf{(}{\mathbf{C}}_{\mathbf{8}}{\mathbf{H}}_{\mathbf{18}}\mathbf{)}$ 1000 K and 50 atm :
R. [423] C${ }_8$H${ }_{18}$ + HO${ }_2$ $\iff$ AC${ }_8$H${ }_{17}$ + H${ }_2$O${ }_2$	{A: 1.12e+13, b: 0.0, Ea: 1.695e+04}	{A: 3.50e+13, b: 0.0, Ea: 1.69e+04}	Cancino et al. (2011)
R. [413] AC${ }_8$H${ }_{16}$OOH-B + O${ }_2$ $\iff$ AC${ }_8$H${ }_{16}$OOH-BO${ }_2$	{A: 1.86e+11, b: 0.0, Ea: 0.0}	{A: 1.16E+11, b: 0.0, Ea: 0.0}	Liu et al. (2013)
n-heptane $(C_7{H}_{16})$ 950 K and 55 atm:
R. [391] C${ }_7$H${ }_{15}$O${ }_2$ $\Rightarrow$ C${ }_7$H${ }_{14}$O${ }_2$H	{A: 2.0e+11, b: 0.0, Ea: 1.701e+04}	{A: 2.5e+12, b: 0.0, Ea: 2.51e+04}	Burke et al. (2014)
toluene $(C_6{H}_5\mathit{C}{H}_3)$ 1000 K and 50 atm:
R. [43] H + OC${ }_6$H${ }_4$CH${ }_3$ $\iff$ HOC${ }_6$H${ }_4$CH${ }_3$	{A: 1.0e+14, b: 0.0, Ea: 0.0}	{A: 2.5e+14, b: 0.0, Ea: 0.0}	Andrae (2008)
R. [49] C${ }_6$H${ }_5$CH${ }_3$ + OC${ }_6$H${ }_4$CH${ }_3$ $\iff$ C${ }_6$H${ }_5$CH${ }_2$ + HOC${ }_6$H${ }_4$CH${ }_3$	{A: 1.6e+11, b: 0.0, Ea: 1.51e+04}	{A: 1.05e+11, b: 0.0, Ea: 9.50e+4}	Andrae (2008)

Table 4. The IDT RMSE for various kinetics models were compared to experimental data of single components of gasoline surrogates (toluene, n-heptane, or iso-octane). The bolded data in each row indicates the model with the lowest values of RMSE compared with the same row experimental data.

	Experiments			kinetics models
Fig	Authors	Pressure	TRF/DIB Origin M.	TRF/DIB Reduced M.	TRFE/DIB_1st	TRFE/DIB_2nd
iso-octane
Figure 2(a)	Davidson, Gauthier, and Hanson (2005)	50 atm	9.290e-04	9.280e-04	3.620e-04	2.340e-04
n-heptane
Figure 2(b)	Gauthier, Davidson, and Hanson (2004)	55 atm	3.100e-05	3.100e-05	8.900e-05	4.400e-05
toluene
Figure 2(c)	Davidson, Gauthier, and Hanson (2005)	50 atm	1.655e-03	1.653e-03	6.080e-04	4.400e-05

Figure 4. Temperature sensitivity analysis of TRFE/DIB_1st model for ethanol at a temperature equal to 1100 K (a). Numerical IDT of ethanol of distinct models against experimental data. The symbol represents experiments (Heufer et al. 2011).

Table 5. Modifying ethanol key reactions constant rate (k).

Reaction	Previous (k)	Modified (k)	Reference
Ethanol $(C_2{H}_5\mathit{OH})$ 1100 K and 40 atm :
R. [889] C${ }_2$H${ }_5$OH + HO${ }_2$ $\iff$ SC${ }_2$H${ }_4$OH + H${ }_2$O${ }_2$	{A: 2.45e-05, b: 5.26, Ea: 7475.1}	{A: 0.028, b: 4.32, Ea: 8530.0}	Heufer et al. (2012)

high-P, high-P-rate-constant; low-P, low-P-rate-constant.

Table 6. RMSE of IDT for various kinetics models compared to ethanol experimental data. Bold data represents the mechanisms with the lowest RMSE values in each row.

Fig	Experiments		kinetics models
	Authors	Pressure	TRF/DIB Origin M.	TRF/DIB Reduced M.	TRFE/DIB_1st	TRFE/DIB_2nd
ethanol
Figure 2a	Heufer et al. (2011)	40 atm	5.500e-04	5.500e-04	1.470e-04	1.200e-04

Table 7. Composition of selected experimental gasoline surrogate and ethanol (by liquid vol.%).

		Liquid volume composition (%)					RON	Experimental	Ref.
	Surr.	ethanol	iso-octane	n-heptane	toluene	diisobutylene		Conditions
Gasoline Surr	I		63	17	20		88	ST, IDT (850–1140 K; 15–55 atm)	Gauthier, Davidson, and Hanson (2004)
	II		69	17	14		87	ST, IDT (850–1140 K; 15–55 atm)	Gauthier, Davidson, and Hanson (2004)
	III		25	20	45	10	94.6	ST, IDT (690–1230 K; 10–50 atm)	Fikri et al. (2008) Cancino et al. (2009)
	IV	40	37.8	10.2	12		98.8	ST, IDT (690–1200 K; 10–50 atm)	Cancino et al. (2011)
	VI	10	30	22	25	13	95.1	ST, IDT (980–1200 K; 10–30 atm)	Heufer et al. (2011)
Single Fuels	–	100					–	ST, IDT (900–1300 K; 13–75 atm)	Gauthier, Davidson, and Hanson (2004)

Table 8. Predicted critical properties of stoichiometric gasoline surrogate mixtures ($\mathit{\varphi }$ = 1) without and with air concerning the literature mixtures available in Table 7.

	Estimated critical Properties
	Surrogate	$T_c$ [K]	$V_c$ [cm${ }^3$/mol]	$P_c$ [bar]	$\mathit{\varphi }$
Gasoline Surr	I	550.28	410.08	28.85	–
	II	553.24	389.73	30.20	–
	III	566.09	338.94	35.18	–
	IV	522.97	275.64	31.66	–
	VI	552.80	366.33	33.56	–
Gasoline Surr + Air	I+Air	166.04	76.45	87.79	1.00
	II+Air	166.12	76.65	87.37	1.00
	III+Air	166.74	77.68	85.72	1.00
	IV+Air	167.75	77.67	84.76	1.00
	VI+Air	166.89	77.22	87.37	1.00
Pure ethanol + Air	–	176.79	84.10	72.02	1.00

Table 9. Literature values for n-heptane properties (Poling, Prausnitz, and O’Connell 2001) versus Joback’s heptane estimated properties.

	Formula	Name	Mol. Wt	$T_{\mathit{fp}},\mathit{K}$	$T_b,\mathit{K}$	$T_c,\mathit{K}$	$P_c,\mathit{bar}$	$V_c,\mathit{c}{m}^3/\mathit{mol}$	$Z_c$	$\mathit{\omega }$
Literature	C7H16	Heptane	100.204	182.590	371.570	540.20	27.40	428.00	0.261	0.350
Estimated	C7H16	Heptane	100.204	168.150	359.56	522.71	27.99	427.5	0.275	0.350
Relative S. deviation (%)	–	–	–	5.82	2.30	2.30	1.51	0.10	3.69	0.00

Figure 5. 2D heptane chemical structure: a model of heptane, the white balls represent hydrogen atoms, and the grey balls represent carbon atoms.

The parameters (a), (b), and ($\mathit{\omega }$) for p–R and R-K EoS were implemented in the developed reduced chemical kinetics mechanism file.

Figure 6. IDT simulations compared with (a) a transcritical data at 20 atm and a supercritical ST data at 75 atm (Heufer and Olivier 2010); (b) a transcritical data at 13, and 40 atm (Heufer et al. 2011) of a stoichiometric mixture of ethanol, $O_2$, and $N_2$; symbols represent experiments by Heufer and Olivier (2010); Heufer et al. (2011); solid and dashed lines are the TRFE/DIB_2nd mechanism, respectively, using the ideal (IES) and the real cubic gas R-K and the p-R EoS.

Table 10. IDT RMSE of the TRFE/DIB_2nd model against quinary, quaternary, and ternary mixtures of gasoline surrogates and ethanol experimental data. In addition, the relative deviations (%) of IDT simulations were analyzed between the same kinetics model that used distinct equations of states (redlich-kwong and peng-robinson), compared to the IDT simulations that relied on the ideal equation of state.

	Experiments			Kinetics model
Fig	Authors	Pressure	Ideal gas (s)	Real gas (R-K) (s)	Real gas (p-R) (s)	Rel. D. (R-K)	Rel. D. (p-R)
Ethanol
Figure 6b	Heufer et al. (2011)	13 atm	8.370e-04	8.270e-04	8.230e-04	0.789%	1.044%
Figure 6a	Heufer et al. (2011)	20 atm	1.430e-04	1.390e-04	1.370e-04	1.193%	1.570%
Figure 6b	Heufer et al. (2011)	40 atm	1.200e-04	1.170e-04	1.170e-04	2.184%	3.198%
Figure 6a	Heufer et al. (2011)	75 atm	1.670e-04	1.840e-04	1.890e-04	3.059%	4.290%
				Ternary Mixture
Figure 7a	Gauthier, Davidson, and Hanson (2004)	25 atm	2.610e-04	2.360e-04	2.280e-04	2.408%	3.154%
Figure 7a	Gauthier, Davidson, and Hanson (2004)	55 atm	6.200e-05	4.000e-05	4.000e-05	6.005%	8.384%
Quaternary Mixture
Figure 7b	Cancino et al. (2009)	10 atm	1.560e-04	1.610e-04	1.630e-04	0.855%	1.126%
Figure 7b	Cancino et al. (2009)	30 atm	1.708e-03	1.747e-03	1.769e-03	3.294%	4.999%
Figure 8a	Fikri et al. (2008)	10 atm	4.540e-04	4.410e-04	4.370e-04	0.916%	1.182%
Figure 8a	Fikri et al. (2008)	30 atm	8.290e-04	9.000e-04	9.520e-04	2.851%	4.593%
Figure 8a	Fikri et al. (2008)	50 atm	5.410e-04	5.900e-04	6.660e-04	5.038%	7.974%
				Quinary Mixture
Figure 8b	Cancino et al. (2011)	10 atm	5.680e-04	5.580e-04	5.550e-04	0.874%	1.147%
Figure 8b	Cancino et al. (2011)	30 atm	6.540e-04	5.620e-04	5.120e-04	3.245%	5.192%
Figure 8b	Cancino et al. (2011)	80 atm	–	–	–	9.041%	13.616%
Figure 8b	Cancino et al. (2011)	150 atm	–	–	–	17.603%	24.097%

Figure 7. IDT simulations compared with (a) a transcritical data at 25 atm and a transcritical data at 55 atm testing a TRF, $O_2$, and $N_2$ stoichiometric mixture (Gauthier, Davidson, and Hanson 2004); (b) a transcritical data at 10 and 30 atm using TRF/ethanol (Cancino et al. 2009). Symbols represent experiments by Cancino et al. (2009); Gauthier, Davidson, and Hanson (2004); solid and dashed lines are the TRFE/DIB_2nd mechanism, respectively, using the ideal (IES) and the real cubic gas RK and the p-R EoS.

Figure 8. IDT simulations compared with (a) a transcritical ST data at 10, 30, and 50 atm utilizing a stoichiometric mixture of TRF/DIB, $O_2$, and $N_2$ (Fikri et al. 2008); (b) a transcritical data at 10 and 30 atm with a stoichiometric mixture of TRF/DIB and ethanol (Cancino et al. 2011); c) a numerical transcritical IDT condition at 80 and a numerical supercritical IDT condition at 150 atm. Symbols represent experiments by (Cancino et al. 2011; Fikri et al. 2008); solid and dashed lines are the TRFE/DIB_2nd mechanism, respectively, using the ideal (IES), the real cubic gas R-K and the p-R EoS.

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