Theoretical Calculation of Reaction Rates and Combustion Kinetic

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Theoretical Calculation of Reaction Rates and Combustion Kinetic Modeling Study of Tri-Ethyl Phosphate (TEP) Sneha Neupane, Ramees K. Rahman, Artëm E. Masunov, and Subith S Vasu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00636 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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The Journal of Physical Chemistry

Theoretical Calculation of Reaction Rates and Combustion Kinetic Modeling Study of Triethyl Phosphate (TEP) Sneha Neupanea, Ramees K. Rahmana, Artëm E. Masunovb,c,d, Subith S. Vasua* a

Center for Advanced Turbomachinery and Energy Research, Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 b NanoScience Technology Center, University of Central Florida, Orlando, FL 32816 c Department of Chemistry, University of Central Florida, Orlando, FL 32816 d School of Modeling, Simulation, and Training, University of Central Florida, Orlando, FL 32816

*Corresponding Email: [email protected]

Abstract Tri-ethyl phosphate (TEP) is an organophosphorous compound (OPC) used as a simulant for highly toxic nerve agents such as Sarin GB. High temperature decomposition pathway during TEP pyrolysis has been proposed previously and takes place via seven concerted elimination reactions. Computational study to investigate the kinetics of these seven reactions is carried out at CBS-QB3 level of theory. The transition state optimization is done at B3LYP/6-311G(2d,d,p) theory level and CanTherm is used to derive the Arrhenius coefficients. The pre-exponential factors of the rate constant of these reactions are found to be up to 50 times lower than the estimated values from the literature. In addition, kinetics of reaction of trioxidophosphorus radical (PO3) with H2 (H2+PO3=HOPO2+H); which is one of the important reactions in predicting CO formation during TEP decomposition, is also investigated computationally at the same theory level. The new kinetic parameters derived from the computational study is used with TEP kinetic model proposed recently by our group. In addition, an alternative decomposition pathway for TEP decomposition

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via H-abstraction, radical decomposition and recombination reactions is added. The proposed mechanism was validated with literature’s experimental data i.e. intermediate CO time-history data from pyrolysis and oxidation experiments and ignition delay times. Fairly good agreement with experiments was obtained for pyrolysis and oxidation CO yield within 1400-1700K. The model was able to predict the ignition times of rich TEP mixture (phi=2) within 25% of the experimental results while the discrepancies for stoichiometric and rich mixtures were larger. Discussions on results of sensitivity and reaction pathway analysis are presented to identify the important phosphorous reactions and to understand the effect of addition of the alternative TEP decomposition pathway.

1. Introduction The United Nations mandated destruction of all chemical warfare (CW) stockpiles for its Convention signatories and the preferred method adopted by the United States is incineration1-7. Incineration involves heating the chemical agents to a high temperature in an enclosed reactor so that it decomposes completely into non-toxic products. A chemical kinetic model incorporating detailed chemistry of the CW agents is essential to predict their decomposition temperatures, pathways, end-products and to design an effective incinerator. Accuracy of chemical kinetic models can be determined by validating them against well calibrated experimental data. Since CW agents are too toxic for laboratory use, experiments are carried out using simulants. Once an accurate model for a simulant has been developed using theoretical and experimental approaches, the modeling techniques can be extrapolated to develop a kinetic model of CW agents. Tri-ethyl phosphate with the chemical formula PO[OET]3 (see Scheme I) is an organophosphorous compound (OPC), commonly used as a simulant for Sarin, GB.


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Scheme I- Triethyl phosphate (TEP) In the first report of our study on TEP kinetic mechanism construction8, we developed a kinetic model for TEP combustion. It was based upon AramcoMech2.09-10 mechanism for base hydrocarbon (C0-C2) chemistry and Lawrence Livermore National Lab (LLNL)’s OPC incineration mechanism11. TEP decomposition pathway consisting of seven molecular elimination reactions and their estimated rates coefficients were taken from Glaude et. al11. Thermochemistry of phosphorus containing species were updated using either theoretical calculations at CBS-QB3 level of theory, or by group additivity method. The proposed mechanism was used to predict CO time-histories during TEP pyrolysis and oxidation. The predicted yields were compared with experiments carried out using shock tube and laser absorption spectroscopy within 1200-1700K and near 1 atm. Although the proposed model showed some improvements in terms of predicting CO mole fraction yield, there were remaining discrepancies with experiments. For TEP pyrolysis, the predicted CO yield was lower and for oxidation predicted CO formation and destruction rates were slow as compared to experiments (Figure 1).



2400

TEP pyrolysis

XCO (ppm)

XTEP = 0.25%

T = 1590 K P = 1.355 atm

1800

1200

600

0

0

1000 Time s)

2000

TEP oxidation T = 1437 K P = 1.269 atm

3000 XCO (ppm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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XTEP = 0.038%  = 0.078

2000

1000

0

0

500 Time s)

1000

Figure 1: Experiment and predicted CO time-histories during TEP pyrolysis and oxidation. Solid line: Experiments; Dashed line: LLNL OPC incineration mechanism with addition of TEP pyrolysis sub-mechanism from Glaude et. al11; Dot line: TEP mechanism proposed in our previous study8. In this paper, we aim to further improve our kinetic mechanism for TEP decomposition. We used conventional transition state theory based on CBS-QB3 quantum chemistry calculations to predict the reaction rates of eight phosphorous containing reactions, listed in Table 1. The reactions were 4 ACS Paragon Plus Environment

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chosen based on the results of sensitivity analysis shown in Figure 2. Sensitivity coefficient (S) for ith reaction rate (ki) for a species is defined as: 𝑆 𝑋

,𝑘 ,𝑡

Eqn. 1

H2+PO3=HOPO2+H PO[OET]3=PO[OH][OET]2+C2H4 PO[OH][OET]2=PO[OH]2[OET]+C2H4 PO[OH][OET]2=C2H5OPO2+C2H5OH PO[OH]2[OET]=HOPO2+C2H5OH PO[OH]2[OET]=C2H5OPO2+H2O PO[OH]2[OET]=PO[OH]3+C2H4 C2H5OPO2=HOPO2+C2H4

1.0 CO sensitivity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5 0.0 -0.5 0

100

200

300

400

500

Time (s) Figure 2: Sensitivity coefficients of important phosphorous reactions in TEP sub-mechanism. Sensitivity analysis was carried out for 0.25% TEP pyrolysis at 1462 K and 1.47 atm using TEP kinetic model from Neupane et al8. Only top phosphorous containing reactions are shown. Table 1: TEP reactions chosen for CBS-QB3 analysis based on results of CO sensitivity analysis shown in Fig. 2.

RXN #

RXN

R1 R2 R3 R4 R5 R6

PO[OET]3=PO[OH][OET]2+C2H4 PO[OH][OET]2=PO[OH]2[OET]+C2H4 PO[OH][OET]2=C2H5OPO2+C2H5OH PO[OH]2[OET] = PO[OH]3+C2H4 PO[OH]2[OET]=HOPO2+C2H5OH C2H5OPO2 = HOPO2+C2H4 5 ACS Paragon Plus Environment


R7 R8

PO[OH]2[OET]=C2H5OPO2+H2O H2+PO3=HOPO2+H

The TEP decomposition mechanism proposed in the literature11-12 and hence used in our previous kinetic model8 consists of seven unimolecular decomposition reactions (R1 - R7 listed in Table 1) that take place via six-center (R1, R5, R6 and R7) and four-center (R2, R3, R4) concerted eliminations of ethylene or ethanol/water respectively. The rates of these reactions were estimated by Glaude et. al.11 using Zegers and Fisher’s 12-14 experimental measurements (within temperature range of 706-854 K) and analogy with ester decompositions. The first step (R1) of TEP decomposition is via six center elimination to form ethylene and diethyl phosphate (PO[OH][OET]2). Hahn et. al.15 used results of ab initio calculations to predict rates of this reaction within temperatures 570-2000 K using CVT/SCT (canonical variational transition state theory/ small-curvature tunneling) and VTST-ISPE/SCT (variational transition state theory with interpolated single-point energies) levels of theory. To the best of our knowledge, rates of the remaining six four-center and six-center eliminations reactions have not been quantitatively investigated in the literature. The calculated rates at CBS-QB3 level of theory were used in the TEP kinetic model proposed in our previous study8. For TEP oxidation case, these reactions were not very sensitive to CO formation and to further improve CO prediction using the mechanism, we explored an alternative decomposition pathway for TEP decomposition via H-abstraction, radical decomposition and recombination reactions. Rates of H-abstraction reactions are much slower as compared to the molecular elimination reactions16 and most of the TEP is expected to decompose through the predominant molecular elimination pathway. However, in the presence of radicals such as H, O etc. or in a fuel lean combustion cases with high concentration of O2, H-abstraction


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pathways can play an important role in predicting intermediate species concentration. The effect of addition of this alternative decomposition pathway via H-abstraction at different temperatures is discussed using sensitivity, rate of production and reaction path analyses.

2. Methods 2.1 Computational methods All quantum chemical calculations were performed using Gaussian 0917 at CBS-QB3 level of theory,18 which includes transition state optimization at B3LYP/6-311G(2d,d,p) level. The transition states were confirmed to be the first-order saddle points by vibrational analysis. The intrinsic reaction coordinate (IRC) method19 was used to verify these transition states are connected to the reactants and products of the respective reactions by the minimum energy pathways (MEP). The reaction rates were predicted with conventional transition state theory (TST) and the rigid-rotor harmonic oscillator approximation, as implemented in Python script CanTherm.20 Frequencies obtained at the B3LYP/6-311G(2d,d,p) level have been scaled by 0.99 in rate constant calculations.21 Asymmetric Eckart tunneling corrections22 were employed to compute the effect of 1-D tunneling through the barrier. This correction is determined using three parameters: (i) the imaginary frequency of the transition state, (ii) the barrier height and (iii) the reaction exothermicity.

2.2 Chemical kinetic mechanism Decomposition of TEP via molecular elimination reactions (R1 to R7, listed in Table 2) has been described in detail in our previous study8 and also in the literature11-12. In current study, alternative decomposition pathway via H-abstraction reactions followed by radical decomposition and



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recombination have been added to construct an updated kinetic model for TEP decomposition. The reactions were based on di-isopropyl methyl phosphonate (DIMP) proposed by Glaude et. al16. Thermochemistry of new species were calculated by group additivity method utilizing recently proposed group values from Khalfa et. al.23 The details on thermochemistry calculation via group additivity method is provided in our previous study8. Radicals (containing P=O), whose bond dissociation energies are not known, were estimated using analogy with C=O groups. Table 2 shows the computed thermochemical data of the new species added in the present study. Figure 3 shows the reactions involved in unimolecular decomposition of TEP as well as added Habstraction, decomposition and recombination reactions. Similar sets of H-abstraction, decomposition and recombination reactions for TEP intermediate products: diethyl phosphate PO[OH][OET]2, monomethyl phosphate PO[OH]2[OET] are also included in the proposed kinetic mechanism. Species dictionary and complete list of reactions are provided in supplementary information Table S1 and mechanism file respectively. Supplementary file “therm” contains thermochemistry data in Chemkin format.

Table 2: Thermochemistry of new species calculated using group additivity method

Species PO[OET]2[OsC2H4] PO[OET]2[OpC2H4] PO[OET]2O PO[OET]2 PO[OH][OET][OsC2H4] PO[OH][OET][OpC2H4] PO[OH][OET]O PO[OH][OET] PO[OH]2[OsC2H4] PO[OH]2[OpC2H4]

Hf Kcal.mol-2 -233.83 -227.69 -228.07 -223.92 -233.45 -227.31 -227.69 -223.54 -231.47 -225.33

Cp cal/mol.K

S cal.mol-1.K 137.24 138.93 140.06 134.71 119.58 121.27 122.41 118.43 101.93 103.61

300K

400K

500K

600K

800K

1000K

50.84 50.53 51.46 52.19 41.57 41.26 42.19 42.92 32.30 31.99

63.42 62.39 63.26 63.43 51.35 50.32 51.19 51.36 39.28 38.25

74.36 73.02 73.83 74.05 59.50 58.16 58.97 59.19 44.64 43.30

82.84 81.52 82.23 82.56 65.62 64.30 65.01 65.34 48.40 47.08

94.19 93.24 93.76 94.43 73.54 72.59 73.11 73.78 52.89 51.94

102.39 101.73 102.14 103.01 79.05 78.39 78.80 79.67 55.71 55.05


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PO[OH]2O

-203.09

78.69

21.58

23.83

25.66

27.14

29.28

30.63

Not a lot is known about the kinetics of these phosphorous reactions and hence rate coefficients were estimated based on analogy with similar reactions in the literature. TEP has three CH3 groups in β-site and three CH2 groups in α-site. Rate constants for abstraction of H-atoms were determined by analogy with H-atom abstraction from primary and tertiary sites in DIMP, respectively with some modifications noted below. A-factor of the abstraction reactions were scaled according to the number of abstractable H-atoms and activation energies were corrected based on EvansPolanyi principle proposed by Dean and Bozzelli24. For example, abstractable H–atoms in primary site of DIMP is 12 and that of TEP is 9. Hence, for primary H-abstraction reactions, A-factors of corresponding reactions were scaled by a factor of 0.75. Rate constants of decomposition and recombination reactions were assumed to be same as those of similar reactions in diisopropyl methyl phosphonate (DIMP), trimethyl phosphate (TMP) and diethyl carbonate (DEC) kinetic mechanisms16.



Figure 3: Reaction pathway for TEP consumption via molecular elimination and H-abstraction, radical decomposition and recombination reactions. Highlighted in red are molecular elimination reactions. 2.3 Simulations The proposed TEP mechanism is used to predict the CO time-histories during TEP pyrolysis and oxidation at conditions summarized in Table 3. Shock tube experiments data at these conditions are obtained from our previous work8. Closed homogenous reactor and constant pressure assumptions in ANSYS Chemkin Pro25 software were used to predict the CO profiles.

Table 3: Experiments conditions – CO time-history measurement during TEP combustion in shock tube8 from our prior work Mixture Temperature Pressure Experiment composition (K) (atm) Pyrolysis 1673 1.374 10 ACS Paragon Plus Environment

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Oxidation

TEP = 0.247%; Ar =99.759% TEP = 0.038%; O2 = 3.381%; Ar=96.581% TEP = 0.0757%; O2=9.105%; Ar= 90.8193%

1590 1462 1437

1.355 1.473 1.269

1508

1.17

1213

1.424

1387

1.329

In addition, the new TEP chemical kinetic model is compared with data from Mathieu et al26, who recently published shock tube ignition delay times for TEP combustion within 1100 to 2100 K and near 1.5 atm. The experiments were conducted at three equivalence ratios: 0.5, 1 and 2. Neat mixtures (TEP, Ar and O2) and hydrogen and methane mixtures seeded with TEP were investigated. The reported ignition times based on peak or maximum rising slope of the measured OH* signals are compared with corresponding model prediction results. Further, sensitivity and rates of production (ROP) analyses are carried out to explain the discrepancies between the measured and predicted values. 3. Results 3.1 Quantum chemical and kinetics calculations The structures of the transition states were optimized at B3LYP/6-311G(2d,d,p) theory level and their ball-and-stick models are shown on Figure 4. Four of the reactions considered (R1, R2, R4, R6) present elimination of ethylene from PO[OET]3, PO[OH][OET]2, PO[OH]2[OET], and C2H5OPO2 respectively. They correspond to intramolecular hydrogen transfer from the β-carbon atom of the ethoxy group to the terminal oxygen atom via six-membered ring transition states. Alternative mechanisms with hydrogen transfer to the oxygen of the same ethoxy group via fourmembered ring transition states had considerably higher energy barrier due to the ring strain and were neglected. Elimination of ethanol (R3, R5) from PO[OH][OET]2, and PO[OH]2[OET] 11 ACS Paragon Plus Environment


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respectively proceeds by hydrogen transfer from hydroxyl to the oxygen of the ethoxy group via four-membered ring transition states. Similar four-member ring transition state is observed in reaction of water elimination (R7) from PO[OH]2[OET]. It is taking place by hydrogen transfer from one hydroxyl group to another oxygen. Finally, intermolecular hydrogen abstraction from H2 molecule by PO3 radical (R8) has a linear transition state.

R2

R1

2.066 1.289

1.341

1.326

1.306

1.992

R3

R4

1.345 1.175

1.332

1.302

1.824

2.075


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R5

R6

1.352

1.280 1.366

1.173

1.811 2.137

R7

R8

1.874

1.289

0.871

1.180

1.338

Figure 4. Structure of the Transition states for all reactions considered here. Dotted lines denote the chemical bonds being broken and formed, the bond lengths (Ǻ) are also shown. Check numbering The theoretical Arrhenius parameters of each reaction, obtained with TST, are compared with the literature values in Table 4, and predicted rate constants are compared in Table 5. The computed A-factors of all eight reaction were lower than estimated values in the literature by factor of 1.01 to ~ 50. The calculated activation energies of these reactions were 6-14% lower than Glaude et al11 estimations. The activation energy for R8, which involves intermolecular hydrogen abstraction from H2 molecule by PO3 radical by forming a linear transition state is calculated to be 16.890 kcal/mol. Tables 5 compares the rates of all eight reactions within 1000 – 2000K (also shown in Supplementary Figure S1). Table 4: The Arrhenius expression for the rate constants calculated at CBS-QB3 level of theory (present work) and estimated by Glaude et. al.11 Activation energy (Ea): kcal/mol. RXN #

RXN

Glaude et. al.


CBS QB3 (Arrhenius)

CBS QB3 (Modified Arrhenius)


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R1

PO[OET]3=PO[OH][OET]2+C2H4

A 2.8E+13

Ea 45.30

A 3.3E+12

Ea 41.51

A 4.8E+03

n 2.73

Ea 38.51

R2

PO[OH][OET]2=PO[OH]2[OET]+C2H4

1.9E+13

45.30

3.7E+12

42.11

2.8E+05

2.20

39.69

R3

PO[OH][OET]2=C2H5OPO2+C2H5OH

2.5E+13

44.00

4.1E+12

40.96

7.5E+07

1.36

37.50

R4

PO[OH]2[OET] = PO[OH]3+C2H4

9.6E+12

45.30

9.5E+12

42.12

1.2E+06

2.14

39.78

R5

PO[OH]2[OET]=HOPO2+C2H5OH

2.5E+13

44.00

1.3E+12

40.21

1.1E+06

1.87

38.16

R6

C2H5OPO2 = HOPO2+C2H4

1.9E+13

45.30

1.1E+13

38.67

4.4E+07

1.67

36.84

R7

PO[OH]2[OET]=C2H5OPO2+H2O

5E+13

45.00

9.8E+11

41.98

2.2E+05

2.05

39.73

R8

H2+PO3=HOPO2+H

2E+12

0.00

7.0E+11

16.89

2.4E+07

1.38

15.38

Table 5: Comparison of reaction rates (CBS-QB3 calculations vs. Glaude et. al. estimation) at 1000, 1500 and 2000 K. Unit of k : R1 to R7 = s-1; R8 = cm3mol-1s-1 a CBS-QB3 – present work; bGlaude et al11 Rxn # 1 2 3 4 5 6 7 8

k (T=1000K) CBS‐QB3 3.16E+03 2.56E+03 5.74E+03 6.44E+03 2.25E+03 4.17E+04 7.29E+02 1.51E+08

k (T=1500K)

Glaude et. al.

ka/kb

CBS‐QB3

3.52E+03 2.39E+03 6.05E+03 1.21E+03 6.05E+03 2.39E+03 7.31E+03 2.00E+12

0.90 1.07 0.95 5.34 0.37 17.46 0.10 0.00

5.06E+06 4.27E+06

5.38E+06 1.07E+07 2.51E+06 3.68E+07 1.11E+06 3.19E+09

k (T=2000K)

Glaude et. al.

ka/kb

CBS‐QB3

7.03E+06 4.77E+06 9.70E+06 2.41E+06 9.70E+06 4.77E+06 1.39E+07 2.00E+12

0.72 0.90 0.55 4.44 0.26 7.72 0.08 0.00

3.03E+08 2.36E+08

1.85E+08 6.05E+08 1.10E+08 1.34E+09 5.94E+07 1.78E+10

Glaude et. al.

ka/kb

3.14E+08 2.13E+08 3.89E+08 1.08E+08 3.89E+08 2.13E+08 6.05E+08 2.00E+12

0.96 1.11 0.48 5.62 0.28 6.28 0.10 0.01

3.2 Comparison of experimental data in literature with model predictions 3.2.1 CO time-histories measured in shock tube Plots in Figure 5 show the experimental CO time-histories during TEP pyrolysis and oxidation taken from our previous work8 and model predictions. The green dotted lines represent predictions using TEP kinetic model proposed in our previous study. This model contains the most up-to-date hydrocarbon chemistry (from AramcoMech2.0) and updated thermochemistry of phosphorous species. The TEP submechanism in this model consists of seven molecular elimination reactions (R1 - R7 in Table 4) proposed by Glaude et al11 and Zegers and Fisher12 for decomposition of TEP


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during its pyrolysis. The red dashed lines are the CO predictions by TEP kinetic model proposed in the present work. In this model, the rate coefficients of the pyrolysis reactions (R1 - R7) are updated using calculated rates from CBS-QB3 (Table 4). In addition, alternative TEP decomposition pathway via H-abstraction, radical decomposition and molecular elimination reactions (Figure 3) are included. For TEP pyrolysis (Figures 5, a-c), the current model predicts higher CO yield and for TEP oxidation (Figures 5, d-g), CO formation rate predicted by the present model is faster. Overall, better agreement with the literature experimental data is obtained from the new mechanism.

Figure 5: Experimental and predicted CO yield during TEP pyrolysis (a-c) and oxidation (d-g)



Sensitive reactions to CO formation In order to understand CO formation during TEP pyrolysis and oxidation, sensitivity analyses (defined in eqn. 1) were performed using the proposed mechanism. The results for TEP pyrolysis (0.25% TEP in Ar; T = 1462 K and P = 1.473 atm) and TEP oxidation (0.03% TEP in Ar; ϕ= 0.075; T = 1213 K and P = 1.424 atm) are shown in Figure 6. The first reaction is the six-center elimination reaction of parent TEP molecule to form ethylene and diethyl phosphate (R1). At high temperatures (conditions studied here), the rate of this reaction is very fast and thus proceeds rapidly as compared to any H-abstraction reactions. As seen in Figure 6, CO formation has very high sensitivity to this reaction near time zero. The sensitivity is reduced to zero after ~20 µs for TEP pyrolysis at 1462 K, this is when all TEP has decomposed into PO[OH][OET]2 and C2H4.

CO Sensitivity coefficient

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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CO Sensitivity coefficient

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Figure 6: CO sensitivity analysis for TEP pyrolysis (1462 K) and b. TEP oxidation (1213 K) using the proposed kinetic model. Diethyl phosphate (which is a direct product from six-center elimination of TEP) decomposition has three possible pathways: six-center molecular elimination of ethylene (R2); four-center molecular elimination of ethanol (R3) and via H-abstraction reactions. Both R2 and R3 are highly sensitive to CO formation during TEP pyrolysis. The rates of these reactions are very important in determining the ratio of ethanol to ethylene formed during TEP decomposition. Since CO formation pathway during TEP pyrolysis is via formation of ethylene or ethanol8, the rates of these reaction show very high sensitivity to CO yield. Also, from ROP analyses of TEP (Figure 7), it was found that virtually 100% of TEP decomposes via molecular elimination pathway and Habstraction channel does not play an important role in initial TEP decomposition (Figure 7). However, appearance of H-abstraction reaction (R9) of TEP by H-atom to form PO[OET]2[OsC2H4], radical decomposition reaction (R10) and recombination reaction (R11) in the top sensitive reactions show the importance of this pathway to accurately predict the



intermediate product concentration during TEP pyrolysis. Further analyses on effect of addition of H-abstraction pathway in TEP mechanism is given in Section 4.

PO[OET]3+H=PO[OET]2[OsC2H4]+H2

R9

PO[OET]2[OsC2H4]=PO[OET]2+CH3CHO

R10

PO[OET]2[OsC2H4]+H=PO[OET]3

R11

For oxidation, CO formation was found to be sensitive to six center elimination reactions (R1 and R2) that forms C2H4 and the subsequent C2H4 chemistry (Figure 6). At lower temperature (1213K), radicals recombination reaction as a result of H-abstractions was also among the sensitive reactions, while at higher temperatures, this reaction is not sensitive.

PO[OET] 3 ROP, mole/m 3-sec

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 7: ROP analysis of TEP oxidation at 1213 K


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3.2.2 Ignition times measured in shock tube The proposed kinetic model was used to predict OH time-histories during TEP combustion at conditions reported by Mathieu et al26. The simulated OH profiles showed a two-stage ignition behavior (Fig. 8). However, no such behavior was reported by Mathieu et al26 in their shock tube study of TEP ignition. The model predicts the first stage rise time to be very fast (within 20 μs) for the range of temperatures studied and in fuel lean and stoichiometric conditions, the first stage ignitions are weak. In Mathieu et al26 study, for neat TEP mixture, ignition times based on peak OH* signals (τmax) are reported and for CH4 and H2 mixtures seeded with TEP, ignition delay times corresponding to maximum positive slope in OH* (τign) signals are reported. To calculate ignition delay time using the proposed kinetic model, we used corresponding peak and maximum slope of predicted OH time-histories as shown in Figure 8.



T=1361 K Normalized OH concentration

1.2 max

1 0.8 0.6 0.4 0.2 0

0

200

400

600

800

1000

500

600

Time, s T=1713 K

10-4

8

6

XOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

ign

2

0

0

100

200

300

400

Time, s

Figure 8: Ignition time calculation from predicted OH profile. OH profiles are simulated using proposed TEP mechanism showing two stage ignition


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As seen in Figure 9a, predicted ignition delay time for rich TEP mixture (φ=2) is in very good agreement with the experiments data. For stoichiometric mixture, fairly good agreement with experiments is observed. However, for lean mixture, the predicted ignition times are faster than the experiment. Model predictions show a clear trend of increasing ignition delay time with equivalence ratio. However, no significant difference in ignition times for stoichiometric and lean mixtures were observed from the experiments. Similarly Figures 9b and 9c show the measured and predicted ignition delay times of H2 and CH4 mixtures seeded with 1% TEP. For H2 mixture, while the model deviates from experiment at extreme temperatures (1132 K and 1522 K), fairly good agreement is obtained within temperature 1210 to 1425 K. However, for CH4 mixture, the predicted ignition times is significantly lower than experiments at all three equivalence ratios.



  

max [s]

1000

100

10

0.00060

0.00065

0.00070

0.00075

1/T [1/K]

ign [s]

10000

1000

100

0.000675 0.000750 0.000825 0.000900 1/T [1/K]

1000

  

ign [s]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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100

0.00045

0.00050

0.00055

0.00060

0.00065

1/T [1/K]

Figure 9: Ignition times comparison: experiments results by Mathieu et al (symbols) and model prediction (dashed lines)


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Brute force sensitivity analyses of ignition delay time Brute force sensitivity analysis of important reactions was carried out to further understand their effects on ignition delay time prediction and the results obtained are plotted in Figure 10. As evident from Fig. 8, two-stage ignitions were observed for TEP. Thus, sensitivity analysis was carried out for first stage (Figure 10a) and second stage ignition (Figure 10b). The results of the brute force sensitivity analysis show that Reactions R2 and R3 have the highest sensitivity coefficients for the first stage ignition while the reaction “O2+HO+OH” has the highest sensitivity coefficient for the second stage ignition times. This indicates that first stage ignition is dominated by TEP decomposition reactions while second stage ignition was less sensitive to TEP decomposition reactions. For example, Reaction R1, the first step in TEP decomposition mechanism, showed a very low sensitivity coefficient to second stage ignition delay time at stoichiometric condition. Changing the rate of this reaction by a factor of two did not affect ignition delay time of TEP in rich and lean conditions.



a

  

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O2+HO+OH HOPO2+OH=H2O+PO3 PO2+H+M=HOPO+M HPO2+OH=H+HOPO2

PO[OH]2[OET]=PO[OH]3+C2H4 (R4) PO[OH][OET]2=C2H5OPO2+C2H5OH (R3) PO[OH][OET]2=PO[OH]2[OET]+C2H4 (R2) PO[OET]3=PO[OH][OET]2+C2H4 (R1) -0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Brute force sensitvity coefficient

b

   O2+HO+OH HOPO2+OH=H2O+PO3 PO2+H+M=HOPO+M HPO2+OH=H+HOPO2 PO[OH]2[OET]=PO[OH]3+C2H4 (R4) PO[OH][OET]2=C2H5OPO2+C2H5OH (R3) PO[OH][OET]2=PO[OH]2[OET]+C2H4 (R2) PO[OET]3=PO[OH][OET]2+C2H4 (R1) -2.5

-2.0

-1.5

-1.0

-0.5

0.0

Brute force sensitvity coefficient

Figure 10: Brute force sensitivity analysis (absolute) of important reactions to ignition times for a) first stage and b) second stage.


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Among the phosphorous reactions, reactions R2 and R3 show the highest brute force sensitivity coefficients for second ignition. The magnitude of sensitivity coefficient of these reactions is equal and in opposite direction to each other. Note that negative sensitivity means decreasing ignition delay time i.e. reaction promoting activity. For lean and stoichiometric conditions, R3, the fourcenter elimination reaction that forms C2H5OH showed positive sensitivity while the reaction R2 which involves elimination of C2H4 showed negative sensitivity. This trend was opposite for the rich mixture (φ=2). Also, the absolute sensitivity coefficients of these reactions to ignition times decreased with increase in equivalence ratio. On the other hand, the sensitivity coefficient of reaction R4 involving decomposition of monoethyl phosphate (PO[OH]2[OET]) to form C2H4 increased with increase in equivalence ratio. Reactions involving smaller phosphorous species such as HOPO2, HOPO and PO2 were also among the sensitive reactions that significantly affects the ignition delay times of TEP. 4. Effect of addition of H-abstraction pathway To understand the effects of H-abstraction pathway added in this work, the reaction pathway analyses were carried out using a 0-D closed homogeneous reactor simulation within the temperature range of 1200-1800 K for two cases, a) 0.1% TEP pyrolysis in N2 bath gas b) 0.1% TEP oxidation, 1% each of O2, H, OH and balance N2. Former case helps in understanding the important reactions involved in TEP decomposition while latter helps in understanding the role of H, OH and O2 in TEP decomposition. Kinetic model with only TEP sub-mechanism was used for this purpose. This provides a better understanding of the decomposition pathways by isolating the effects of hydrocarbon reactions and smaller phosphorous species reactions. Figure 11 shows the concentration profiles of species PO[OET]3, PO[OH][OET]2 and C2H5OPO2 for a residence time of about 10s. Here, TEP pyrolysis (case (a)) is shown by dotted lines while the solid lines show



the TEP oxidation mixture in case (b). In general, TEP decomposition is highly sensitive to temperature and undergoes six-center molecular elimination to form PO[OH][OET]2 and C2H4 (reaction R1). However, it can be observed that TEP decomposition is faster at low temperature (1200K) for mixture containing H, OH and O2. This can be attributed to H-abstraction reactions of TEP with H or OH to form PO[OET]2[OsC2H4] or PO[OET]2[OpC2H4] along with H2 or H2O respectively. These reactions are shown below in the decreasing order of their influence on TEP decomposition. PO[OET]3+OH=PO[OET]2[OsC2H4]+H2O PO[OET]3+OH=PO[OET]2[OpC2H4]+H2O PO[OET]3+H=PO[OET]2[OsC2H4]+H2 PO[OET]3+H=PO[OET]2[OpC2H4]+H2

R12 R13 R9 R14

2E‐3

4E‐4 1200 K pyro 1500 K pyro 1800 K pyro 1200 K 1500 K 1800 K

1E‐3

0E+0 1E‐10 2E‐4

1E‐07

1E‐04

Time (s)

Mole fraction

Mole fraction

PO[OET]3

Mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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PO[OH][OET]2

2E‐4 1E‐4 0E+0 1E‐10

1E‐01

1200 K pyro 1500 K pyro 1800 K pyro 1200 K 1500 K 1800 K

3E‐4

1E‐07

1E‐04

1E‐01

Time (s)

C2H5OPO2 1200 K pyro 1500 K pyro 1800 K pyro 1200 K 1500 K 1800 K

2E‐4 1E‐4 5E‐5 0E+0 1E‐10

1E‐07

1E‐04

Time (s)

1E‐01

Figure 11: Mole fraction vs time plot for important intermediates in TEP decomposition in a 0-D closed homogeneous reactor for a pyrolysis feed (0.1 mol% TEP and balance N2) and a simplified feed containing 0.1 mol % TEP,1 mol % each of O2, H, OH and balance N2. PO[OET]2[OsC2H4], formed from reactions R12 and R9, decomposes to PO[OET]2 which then forms C2H5OPO2 as shown in reactions R10 and R15. This explains the increased formation of 26 ACS Paragon Plus Environment

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C2H5OPO2 in oxidation mixture case (b) as compared to the pyrolysis mixture case (a) in Figure 11. PO[OET]2[OpC2H4] decomposes to PO[OET]2O, which undergoes H addition to form PO[OH][OET]2 as shown in reaction R16 and R17: PO[OET]2[OsC2H4]=PO[OET]2+CH3CHO

R10

PO[OET]2=C2H5OPO2+C2H5

R15

PO[OET]2[OpC2H4]=PO[OET]2O+C2H4

R16

PO[OET]2O+H=>PO[OH][OET]2

R17

At high temperature, TEP decomposition reaction via molecular elimination of C2H4 (R1) dominates over H-abstraction reactions R9, R12-14. Hence the contribution of H-abstraction reactions by H and OH are insignificant at high temperatures, which explains the overlapping of TEP profiles at 1800K in both the cases. Figure 11 indicates an increased formation of the intermediate product PO[OH][OET]2 with temperature for both the cases. At 1200 K, the lower peak concentration for oxidation mixture compared to the pyrolysis mixture is because of H-abstraction pathway. Due to the formation of PO[OET]2[OsC2H4] in reactions R12 and R9, less TEP is available for dissociation via molecular elimination reaction R1. As the temperature increases, PO[OH][OET]2 concentration profile in oxidation case moves closer to the pyrolysis case indicating that H-abstraction pathway has decreased role at higher temperatures.

Figure 12 shows the major H-abstraction reaction products in the TEP dissociation pathway. It can be seen that all species except sDEP have concentrations above 1E-8 and hence can have a direct impact on the overall pathway. For sDEP, the reaction R18 is very fast in the reverse direction and decomposes to PO[OH][OET] rapidly which forms HOPO and HOPO2 as per reactions R19 and 27 ACS Paragon Plus Environment


R20. The trend on these species profiles also confirms that the role of H-abstraction reactions and its products decreases with increase in temperature. PO[OH][OET] +CH3CHO = sDEP PO[OH][OET]=HOPO2+C2H5 PO[OH][OET]=HOPO+C2H5O

R18 R19 R20

2E‐4

1E‐4

1E‐4

0E+0 1E‐10

PO[OET]2[OpC2H4]


1E‐07

1E‐04

Time (s)

0E+0 1E‐10

1E‐01

3E‐24

1E‐07

1E‐04

Time (s)

1E‐01

7E‐8

sDEP

6E‐8


2E‐24

1E‐24

Mole fraction

Mole fraction


Mole fraction

Mole fraction

PO[OET]2[OsC2H4]

pDEP


5E‐8 4E‐8 3E‐8 2E‐8 1E‐8

0E+0 1E‐10

1E‐07

1E‐04

Time (s)

0E+0 1E‐10

1E‐01

6E‐6

3E‐8


4E‐6 3E‐6 2E‐6 1E‐6 0E+0 1E‐10

1E‐07

1E‐04

Time (s)

1E‐01

4E‐8

PO[OH]2[OsC2H4]

Mole fraction

5E‐6

Mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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PO[OH]2[OpC2H4]


3E‐8 2E‐8 2E‐8 1E‐8 5E‐9

1E‐07

1E‐04

Time (s)

0E+0 1E‐10

1E‐01

1E‐07

1E‐04

Time (s)

1E‐01

Figure 12: Plots showing profiles of H- abstraction reaction products in the TEP decomposition pathway. Figure 13 displays the profiles of H, O2 and OH atoms for the case (b) mixture. It can be observed that both H and OH atoms were consumed in considerable amount at 1200 K emphasizing the


Page 29 of 33

importance of H-abstraction reactions at low temperatures. However, O2 profile maintains a constant trend indicating that neither H-abstraction nor oxidation of TEP or its intermediates takes place directly by O2 molecules. 2E‐2

0E+0 1E‐10

O2

1E‐2

1200 K 1500 K 1800 K 1E‐05

Time (s)

5E‐3

0E+0 1E‐10

1200 K 1500 K 1800 K 1E‐05

Time (s)

Mole fraction

1E‐2 5E‐3

2E‐2

2E‐2

H atoms

Mole fraction

Mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


OH 1E‐2 5E‐3

0E+0 1E‐10

1200 K 1500 K 1800 K 1E‐05

Time (s)

Figure 13: Plot showing the profiles of H, O2 and OH for 0-D closed homogenous reactor simulation for a mixture containing 0.1 mol % TEP,1 mol % each of O2, H, OH and balance N2. 5. Conclusions This study presents an improved TEP combustion chemical kinetic model. Reaction rates of seven molecular elimination reactions in TEP sub-mechanism were updated using CBS-QB3 quantum chemical theory level. Alternative TEP decomposition pathway via H-abstraction, radical decomposition and recombination reactions are added. The model was used to predict CO time histories during TEP pyrolysis and oxidation within 1400-1700 K and near 1.4 atm. The experimental data were adapted from our recent shock tube study of TEP combusiton8. The predicted CO profiles using the proposed model are in better agreement with the experiments The model is also used to simulate shock tube ignition delay time data26 and fair agreement was obtained for rich (phi =2) mixture. However, for lean and stoichiometric cases deviation from the experiments were larger. Reaction path and ROP analyses showed that the H-abstraction pathway plays an important role only at low temperature while at high temperatures, the molecular elimination pathway remains predominant. The molecular elimination reactions are very fast compared to any H-abstraction reactions at high temperature, hence most to the TEP 29 ACS Paragon Plus Environment


decomposition proceeds via this pathway. The newly calculated reactions rates, discussions on results of sensitivity and reaction path analysis presented in the present work will be critical in development of more comprehensive detailed mechanism for TEP combustion.

6. Acknowledgements The project or effort depicted was sponsored by the Department of the Defense, Defense Threat Reduction Agency (grant number: HDTRA1-16-1-0009). The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred. We would also like to acknowledge Dr. William J. Pitz (LLNL) and Prof Mani Sarathy (KAUST) for providing valuable insights regarding addition of H-abstraction pathway to TEP submechanism.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.xxxxxx. TEP mechanism and thermo files in Chemkin format, and species dictionary.

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23. Khalfa, A.; Ferrari, M.; Fournet, R.; Sirjean, B.; Verdier, L.; Glaude, P., Quantum chemical study of the thermochemical properties of organophosphorous compounds. The Journal of Physical Chemistry A 2015, 119 (42), 10527‐10539. 24. Dean, A. M.; Bozzelli, J. W., Combustion chemistry of nitrogen. In Gas‐phase combustion chemistry, Springer: 2000; pp 125‐341. 25. ANSYS Chemkin‐Pro, http://www.ansys.com/products/fluids/ansys‐chemkin‐pro: San Diego, CA., 2018. 26. Mathieu, O.; Kulatilaka, W.; Petersen, E., Shock‐tube studies of Sarin surrogates. Shock Waves 2018, 1‐9.


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Theoretical Calculation of Reaction Rates and Combustion Kinetic

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