CO2 mixtures using ReaxFF molecular dynamics simulation

J. of Supercritical Fluids 155 (2020) 104661

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The Journal of Supercritical Fluids journal homepage: www.elsevier.com/locate/supflu

Investigation of hydrogen oxidation in supercritical H2 O/CO2 mixtures using ReaxFF molecular dynamics simulation Guoxing Li a , Youjun Lu a,∗ , Suitao Qi b a b

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China Department of Chemical Engineering, School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China

g r a p h i c a l

a b s t r a c t

h i g h l i g h t s • • • •

SCW inhibits the oxidation rate of H2 due to both chemical effect and cage effect. The presence of CO2 has promotion effect on the conversion rate of H2 . H2 oxidation mechanisms under supercritical conditions are newly developed. The activation energy is smaller at higher CO2 concentration level.

a r t i c l e

i n f o

Article history: Received 26 July 2019 Received in revised form 8 October 2019 Accepted 8 October 2019 Available online 15 October 2019 Keywords: Hydrogen oxidation Supercritical mixtures

∗ Corresponding author. E-mail address: [email protected] (Y. Lu). https://doi.org/10.1016/j.supflu.2019.104661 0896-8446/© 2019 Elsevier B.V. All rights reserved.

a b s t r a c t Hydrogen oxidation kinetics in supercritical H2 O/CO2 mixtures is a fundamental topic in supercritical water oxidation (SCWO) technology. A series of reactive molecular dynamics (ReaxFF-MD) simulations were performed to investigate hydrogen oxidation process in supercritical mixtures. The results showed that HO2 and H2 O2 radicals played key roles in the reaction kinetics. High concentration H2 O suppressed the production of OH radical and increased steric hindrance for effective collisions, exerting negative influence on hydrogen oxidation. The presence of CO2 advanced the oxidation rate of hydrogen mainly through the elementary reaction CO2 + H → CO + OH. It was found that high O2 concentration promoted

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ReaxFF Molecular dynamics

the oxidation of hydrogen and also affected the reaction induction time. The hydrogen reaction mechanisms under supercritical conditions were illustrated, showing different characteristics from those at atmospheric condition. The results will facilitate the development of continuum-scale kinetic models for accurate prediction of hydrogen oxidation behavior in supercritical systems. © 2019 Elsevier B.V. All rights reserved.

1. Introduction

effects of H2 O and CO2 on hydrogen oxidation in supercritical mixtures stay unclear and fundamental reaction mechanism remains unknown. More detailed information about hydrogen oxidation reaction in supercritical H2 O/CO2 mixtures needs to be further revealed from an atomistic perspective. Quantum mechanical (QM) methods are the most accurate atomistic methods for predicting reaction energies and barriers. However, these methods are computationally expensive and are limited to small systems within a short time scale. Molecular dynamics (MD) simulations based on the ReaxFF force field have recently been developed to be a computationally inexpensive alternative to QM-based methods. ReaxFF, derived from first principles, can correctly simulate the formation and dissociation of bonds during chemical reactions and provide a reasonable approximation of QM results [17]. The ReaxFF has been used extensively to investigate complex combustion phenomena [18–22] and also H2 /O2 reaction systems. Agrawalla et al. [23] developed a set of optimized ReaxFF force field parameters and ran MD simulations for various H2 /O2 mixtures. Their results elucidated the reaction kinetics of hydrogen combustion under high-pressure and high-temperature conditions (T ≥ 3000 K, P > 40 MPa). Chen et al. [24] developed a new method to dramatically accelerate the ReaxFF based MD simulations by using the bond boost concept. Their work determined the detailed sequences of hydrogen combustion reaction over a wide temperature range. Alaghemandi et al. [25] performed the ReaxFF reactive MD simulations on hydrogen combustion and analyzed the reactive sequences of chemical species. Their work developed a chemically-informed symbolic dynamics method and reduced the description of complex chemistry from the atomistic level. Jain et al. [26] explored the mechanism of spontaneous combustion of H2 /O2 mixtures inside nanobubbles at low temperature using reactive MD simulations based on ReaxFF. The results demonstrated that spontaneous combustion inside nanobubbles had quite different characteristics from macroscopic combustion due to the large surface to volume ratio. These works show that the reactive MD simulations based on ReaxFF are a powerful tool for getting a detailed, statistically relevant description of the H2 /O2 reaction at various conditions. In this study, we carried out MD simulations based on the reactive ReaxFF force field to investigate the chemical events involved in hydrogen oxidation processes in supercritical H2 O/CO2 mixtures. Hydrogen oxidation in air was also studied for comparison. Results obtained at various input conditions were presented. A detailed analysis of the simulations was performed to gain a better understanding of the chemical roles of H2 O and CO2 on hydrogen oxidation in supercritical mixtures. The influence of temperature and stoichiometry was taken into consideration. An atomistic description of the details of initiation reactions, important elementary reactions and distributions of radicals was gained by analyzing the computed MD trajectories. Furthermore, the overall activation energies and reaction mechanisms of hydrogen oxidation reactions under different conditions were determined.

Hydrogen has recently drawn increasing attention as an ideal renewable energy source. Its major advantages include high combustion value, low toxicity and zero CO2 emission [1]. Hydrogen is widely used as a fuel itself or a supplemental fuel in internal combustion engines and gas turbine combustors for energy conversion [2,3]. In order to utilize hydrogen safely and effectively, the reaction kinetics for hydrogen combustion has been studied extensively and various kinetic models have been proposed in the past decades. Mueller et al. [4] measured reaction profiles of dilute H2 /O2 /N2 mixtures in a variable pressure flow reactor at a wide range of conditions(850 k–1040 k, 0.03 MPa–1.57 MPa) and built an updated H2 /O2 kinetic model that could accurately predicted the experimental data. Strohle et al. [5] established a reduced mechanism based on the detailed reaction mechanism of Li et al. [6] to represent chemical kinetics for hydrogen combustion at elevated pressures under typical gas turbine conditions. Burke et al. [7] incorporated improvements in the rate constant and transport treatment into their updated kinetic model and identified major uncertainties affecting predictions of combustion behavior in both parameters and model assumptions. Olm et al. [8] tested the performance of 19 existing hydrogen combustion mechanisms against all published experimental data and investigated the dependence of accuracy on the experiment types and experimental conditions. These works mainly concentrate on regions around the classical extended second limit [9,10], which comprises high temperatures and low pressures (up to 3.3 MPa). The prospect of a hydrogen-based economy [11] has extended the use of hydrogen to wider application fields. Hydrogen is used as an auxiliary fuel under supercritical conditions in a novel power generation system proposed by our laboratory [12,13]. The system is based on supercritical water gasification (SCWG) of coal and supercritical multi-staged steam turbine. In the system, organics in coal are completely gasified and converted to H2 and CO2 . Hydrogen, as a primary gasification product, is supposed to be further oxidized in a combustor to reheat supercritical working medium and increase its capability for power generation. The hydrogen oxidation reaction occurs in supercritical H2 O/CO2 mixtures environment, which has been hardly studied. A better understanding of the reaction kinetics and mechanism is of fundamental meaning to the steady operation of the system. Additionally, hydrogen is a major intermediate during supercritical water oxidation (SCWO) processes and the elementary kinetics play a prominent role in determining the composition of the radical pool. The mechanism for hydrogen oxidation is a subset of all other oxidation mechanisms [14,15]. A deep understanding of the mechanism of hydrogen oxidation will yield insight into other oxidation mechanisms of complex organics. In our previous work, we conducted experiments in an isothermal, plug-flow reactor to investigate the oxidation kinetics of hydrogen in supercritical H2 O/CO2 mixtures and established an empirical rate expression [16]. However, the chemical

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Table 1 Input conditions of systems studied.

2. Computational methods 2.1. ReaxFF reactive force field and its reasonability for the studied systems ReaxFF is a reactive force field based on the concept of bond order [27]. It includes all the bond-order-dependent terms like bond, angle, torsion and penalty energy into the potential functions. ReaxFF also accounts for non-bonded interactions like Coulomb and van der Waals between every pair of atoms irrespective of the connectivity [17,18]. The potential energy of the system in ReaxFF is expressed as

system No.

H2 a

O2

H2 O

CO2

ϕb

density (g/cm3 )

1 2 3 4 5 6

100 100 100 100 100 100

50 50 50 50 30 100

0 300 255 210 255 255

0 0 45 90 45 45

1 1 1 1 1.7 0.5

0.067c 0.267 0.365 0.505 0.337 0.434

a

Quantity of H2 molecules in the system. ϕ represents fuel equivalence ratio and is defined as ([H2 ]/[O2 ])actual /([H2 ]/[O2 ])stoich . c The density is chosen to guarantee that the simulation box of system 1 has the same size as that of system 2. b

E system =E bond +E over +E under +E val +E pen +E tors +E conj +E vdWaals +E Coulomb

(1)

where Ebond , Eover , Eunder , Eval , Epen , Etors , Econj , EvdWaals and ECoulomb represent bond energy, overcoordination energy penalty, energy contribution for undercoordinated atoms, valence angle energy, additional penalty energy, torsion angle energy, energy contributed by conjugation effects, van der Waals energy and Coulomb energy, respectively. The ReaxFF reactive force field allows the valence interaction between a pair of atoms to change continuously and determines their connectivity by the bond order, which is updated at every calculation iteration. ReaxFF provides accurate description of bond formation and breaking between atoms and can be applied to simulate dynamics of a large system of atoms by solving Newton’s equations of motion. Recent reviews on the ReaxFF method and its applications to combustion or other large-scale reactive systems can be seen in Ref. [28–30]. ReaxFF has been applied successfully to simulate chemical processes occurring in supercritical systems [31,32]. The reactive force field is able to capture the details of evolution and extinction of radicals and produce results comparable to experimental data. Manzano et al. [33] systematically tested the validity of the ReaxFF force field to reproduce the basic properties of supercritical water (SCW), including density, static dielectric constant, microstructure, hydrogen bonding and diffusivity. They concluded ReaxFF could satisfactorily describe the structure and dynamics of SCW and proved the reasonability of ReaxFF to simulate chemical reactions in the supercritical regime. The particular ReaxFF force field used in our study was developed by Agrawalla et al. [23]. The force field was designed to investigate the reaction mechanisms of H2 /O2 system at high-pressure and high-temperature conditions (T ≥ 3000 K, P ≥ 100 MPa) and could predict all aspects of H2 /O2 chemistry. 2.2. Simulation details The MD simulations were performed in LAMMPS using the ReaxFF reactive force field. We studied reactive systems of hydrogen oxidation in supercritical H2 O/CO2 mixtures for a wide range of input conditions with the canonical ensemble (NVT). Additionally, simulations of H2 /O2 mixtures seeded with one OH radical were performed with the micro-canonical ensemble (NVE). The simulations began with creating input structure in a cubic periodic box. Then reaction models were constructed employing the Amorphous Cell module in Materials Studio software by assigning the initial position of molecules randomly. The simulation time step was set as 0.1 fs, which could guarantee both accuracy and acceptable computational cost. Each system was heated up from 0 K to 1000 K with a rising rate of 50 K/ps and then equilibrated at 1000 K for 2 ps. Next, the temperature was increased from 1000 K to the target temperature with a rising rate of 100 K/ps. Finally, equilibrium calculations at the target temperature were conducted for 500 ps. The temper-

ature was controlled by a Nose/Hoover thermostat [34,35] with a damping constant of 100 fs. Table 1 displays details of the input conditions. The density of pure SCW was fixed at 0.20 g/cm3 and the density of each system was determined accordingly. In order to save simulation time, we selected a relatively high temperature range from 3200 K to 4000 K with an interval of 200 K. According to previous works [36], high simulation temperature might affect product distributions but had little influence on the reaction processes and mechanisms. Increased temperatures during ReaxFF-MD simulations were adopted by earlier studies [37,38] and good agreement with experiments in the initial reaction mechanisms and kinetics was obtained. Three parallel simulations with different initial configurations were performed to ensure the results more reasonable. 3. Results and discussion 3.1. Initiation reactions The detailed chemical mechanism for hydrogen oxidation is a perplexing issue even though hydrogen is the simplest fuel molecule. The process from reactants to products involves five or so unstable intermediates and more than twenty elementary reactions. It is recognized that the oxidation of hydrogen can only occur after an initiation stage. Getting a deeper insight into initiation reactions and the formation of the first radical is critical for understanding the overall H2 /O2 chemistry. For simulated reaction systems under supercritical conditions, we observed the predominant initiation reaction as reaction Eq. (R1). H2 + O2 + H2 O → H + HO2 + H2 O

(R1)

This is consistent with the conclusion obtained by Michael et al. [39] except a little difference. In the high-temperature and low-pressure experiments conducted by Michael et al., initiation reaction tended to occur through the direct collision of H2 and O2 molecules. However, the termolecular reaction Eq. (R1) with H2 O as a third body is the most likely initiation reaction under highpressure and high-density conditions with the presence of high concentration H2 O. Reaction Eq. (R2) was also observed as the initiation reaction sometimes under fuel-lean conditions (system 6). The reaction requires a symmetric structure of one H2 and two O2 molecules to form two HO2 radicals simultaneously. The energy barrier of reaction Eq. (R2) is lower than that of reaction Eq. (R1) [40]. Reaction Eq. (R2) can be competitive with reaction H2 + O2 + O2 → 2HO2

(R2)

H2 + M → H + H + M

(R3)

Eq. (R1) at high O2 concentration conditions.

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3.2. Effect of O2 concentration

Fig. 1. Water formation vs simulation time at different fuel equivalence ratio conditions: (a) system 5, ϕ = 1.7; (b) system 3, ϕ = 1; (c) system 6, ϕ = 0.5 s.

Additionally, we observed that reaction Eq. (R3) occurred as the initiation reaction at high temperatures. H2 dissociation, which occurs after colliding with a third body, is another way for H radical production except reaction Eq. (R1). According to previous study [41], the energy barrier for breaking of H H bond at 298 K and 1 bar is 437 kJ/mol. Under our simulation conditions, the value varies a little [42,43] but is still much higher than the energy barriers of reaction Eq. (R1) and Eq. (R2). So this reaction is only preferred at temperatures above 3800 K and occurs in a low frequence.

The effect of O2 concentration on hydrogen oxidation in 85%H2 O/15%CO2 environment was studied by performing a series of ReaxFF-MD simulations covering a range of fuel equivalence ratios from 0.5 to 1.7 at the temperature range of 3200 K–4000 K. Fig. 1 shows the water formation profile obtained as a function of temperature and fuel equivalence ratio. Results indicate that the hydrogen oxidation reaction becomes faster for progressively higher O2 levels and higher temperatures. O2 concentration also affects the reaction induction time. Increased O2 concentration greatly shortens the induction times at temperatures above 3600 K. The oxidation reactions even begin before the temperature reaches the target values under fuel-lean conditions at high temperatures, as shown in Fig. 1(c). However, the reaction induction times seem to be lengthened by increasing the O2 concentration at temperatures below 3600 K. This differs from the hydrogen oxidation characteristics in air observed by previous researchers [44], signifying the mechanism controlling the induction time in supercritical H2 O/CO2 mixtures is very different from that in gas phase. Fig. 2 displays the time evolution of CO molecules and OH, HO2 radicals under different temperature and fuel equivalence ratio conditions. It can be seen that high O2 concentration facilitates the production of OH and HO2 radicals but inhibits the production of CO molecule. Increased O2 concentration promotes the production of HO2 radicals mainly through reaction Eq. (R4). Then HO2 radicals can be further converted to OH radicals through reaction Eq. (R5) and Eq. (R6). In addition, the accelerated reaction Eq. (R4) consumes more H radicals, suppressing the reduction of CO2 to produce CO. The produced CO molecules can also be further oxidized to CO2 molecules with the presence of high O2 concentration.

H + O2 + H2 O → HO2 + H2 O

(R4)

H + HO2 → OH + OH

(R5)

H2 O + HO2 → H2 O2 + OH

(R6)

Fig. 2. Time evolution of CO molecule and OH, HO2 radicals at temperatures of 3200 and 4000 K under fuel-rich, stoichiometric and fuel-lean conditions.

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high-pressure conditions [7,46]. Fig. 4 displays the time evolution of HO2 and H2 O2 radicals in system 1 and system 2 at 3600 K. It is observed that the presence of H2 O increases the generation of both HO2 and H2 O2 radicals. The promotion effect on H2 O2 radical is more obvious. According to Dagaut et al. [47], H2 O had high third body efficiency to facilitate the production of HO2 through reaction Eq. (R4). Additionally, our simulation results suggest that H2 O can directly react with O2 to produce HO2 through reaction Eq. (R7) and consume HO2 through reaction Eq. (R6). H2 O + O2 → HO2 + OH

Fig. 3. Time evolution of H2 molecules during simulations at different temperatures in system 1 and system 2.

3.3. Effect of H2 O Simulations of hydrogen oxidation in air (system 1) and pure SCW (system 2) environments under stoichiometric conditions (ϕ = 1) at the temperature range of 3200 K–4000 K were performed to investigate the effect of H2 O. Fig. 3 shows the time evolution of number of H2 molecules at different temperatures in system 1 and system 2. As can be seen, the consumption rates of H2 in system 2 are lower than those in system 1 at all given temperatures. It is clear that the presence of high concentration H2 O inhibits the oxidation rate of H2 . This is qualitatively consistent with experimental results. It was reported that H2 conversion in air at 0.3 MPa and 934 K achieved 98% at a residence time of 0.3 s [4]. However, it took around 18.5 s for H2 conversion to reach 98% in SCW at 25 MPa and 923 K [45]. The hydroperoxyl (HO2 ) and hydrogen peroxide (H2 O2 ) radicals play important roles in hydrogen oxidation reactions under

(R7)

Thus H2 O enhances both the generation and consumption of HO2 . The change of the number of HO2 is a result of the concurrent function of reaction Eq. (R4), Eq. (R6) and Eq. (R7). Reaction Eq. (R6) is also the main pathway for the generation of H2 O2 , which illustrates the promotion effect of H2 O on H2 O2 production [48]. For hydrogen oxidation under high-pressure conditions, OH radical is produced mainly through reaction Eq. (R5). Reaction Eq. (R6) competes with reaction Eq. (R5) and greatly decreases the occurrence frequence of reaction Eq. (R5). Many HO2 radicals are converted to H2 O2 rather than OH, causing the reduction of the number of OH. H2 is mainly consumed by OH to form H2 O through reaction Eq. (R8) and the reduction of the number of OH certainly decreases the consumption rate of H2 . H2 O also hinders the oxidation of H2 by enhancing the reverse reaction of reaction Eq. (R8) because of equilibrium reasons. H2 + OH → H2 O + H

(R8)

In addition, the SCW environment acts as a physical barrier that retards the oxidative process of hydrogen. SCW can form a solvent cage around the reactive species, hindering the diffusion of radicals. Such cage effects suppress fission-type reactions in SCW by detaining the nascent products within the cage. If the products cannot escape the cage, they are more likely to recombine and regenerate the reactant. A solvent cage can also reduce the reaction rate by

Fig. 4. Time evolution of HO2 , H2 O2 and OH radicals during simulations at 3600 K in (a) system 1 and (b) system 2.

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Fig. 6. Time evolution of CO molecules during simulations at different temperatures in system 3 and system 4.

ulations, as shown in Fig. 7. In path I, an H radical attacks CO2 and forms O-H bond with an O atom. Then the single C–O bond breaks and the HOCO intermediate is split to CO molecule and OH radical. In path II, an OH radical attacks CO2 and forms C–O bond with the C atom. Later the HOCO2 intermediate is converted to CO molecule and HO2 radical. Path I dominates the reduction reaction of CO2 while path II occurs in a relatively low frequence. Two reaction pathways can be expressed as reaction Eq. (R9) and Eq. (R10). CO2 + H → CO + OH CO2 + OH → CO + HO2

Fig. 5. (a) Number of unconsumed H2 molecules at the steady state and (b) mean time to reach the steady state at 3200–4000 K in different systems.

isolating the reactant molecules [49,50]. Thus the presence of SCW slows down the overall rate of hydrogen oxidation. 3.4. Chemical role of CO2 For the purpose of studying the chemical role of CO2 , we carried out simulations of hydrogen oxidation in 85%H2 O/15%CO2 (system 3) and 70%H2 O/30%CO2 (system 4) environments under stoichiometric conditions (ϕ = 1) at a temperature range from 3200 K–4000 K. Fig. 5 shows the number of unconsumed H2 molecules at the steady state and mean time to reach the steady state at different temperatures in different systems. Detailed data obtained from three parallel simulations are listed in Table S1 and Table S2, Supplementary Materials. The steady state is defined as a period where the number of H2 molecules only fluctuates in a narrow range with a maximum fluctuation amplitude of two. It can be seen that the presence of CO2 advances the conversion of H2 at all given temperatures. And a higher oxidation rate of H2 is found at higher CO2 concentration conditions, signifying the promotion effect becomes more obvious as CO2 concentration increases. CO was observed in system 3 and 4 as the simulations proceeded. Fig. 6 displays the time evolution of CO molecules at different temperatures in system 3 and system 4. CO is the reduction product of CO2 . It can be seen that the CO concentration in system 4 is higher than that in system 3. CO2 molecules have high reactivity at high temperatures and nearly half of them are reduced to CO at 4000 K. Two reaction pathways of CO2 reduction was observed during sim-

(R9) (R10)

Reaction Eq. (R9) greatly advances the production of OH, thus increasing the consumption rate of H2 [51]. CO can be further reduced to CHO and even formaldehyde (CH2 O). However, these reactions are highly reversible because of the low oxidability of CO, causing little influence on the overall reaction. Fig. 8 shows the time evolution of HOCO, total C-related (namely HOCO, HOCO2 , CHO and CH2 O) and OH radicals in system 3 and system 4 at 3600 K. It can be seen that the total number of C-related radicals is only slightly higher than the number of HOCO in both systems, proving that path I is the dominating way for CO2 reduction. The number of radicals in system 4 is higher than that in system 3, especially the OH radical. This explains the more advanced oxidation rate of H2 in system 4. We also performed electronic structure calculations to characterize the critical points on the potential energy surfaces (PES) of reaction Eq. (R9) at 0 K using Gaussian09 package. All calculations are based on the coupled-cluster singles and doubles theory with perturbational triples corrections methods [CCSD(T)] and the aug-cc-pVTZ basis set. In addition, the basis set superposition error is taken into consideration to correct the energies obtained from calculations, using the Boys and Bernardi counterpoise correction. Intricate reaction pathways on the complicated PES are observed, as reported in previous studies [52,53]. There are two pathways for the formation of HOCO intermediate from the CO2 + H reactants, with kinetic barriers as 107.5 and 131.4 kJ/mol, respectively. Each pathway is gated by a transition state. In addition, decomposition of HOCO complex to the OH + CO products is also controlled by two transition states. Both transition states in the entrance and exit channels are responsible for the kinetic behaviors of the reaction. Details about the energetics of two pathways and vibrational frequencies of transition states are shown in Fig. S1 and Table S3, Supplementary Materials, respectively.

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Fig. 7. Reaction pathways of CO2 reduction in supercritical H2 O/CO2 environment (grey, carbon; red, oxygen; black, hydrogen).

Fig. 8. Time evolution of HOCO, total C-related and OH radicals during simulations at 3600 K in (a) system 3 and (b) system 4.

Table 2 Elementary reactions of different species obtained from ReaxFF-MD at 3600 K in system 2 and system 3. Species

H2

H

HO2

H2 O2

OH

H2 O

a

system 2

system 3 a

elementary reactions

t1

H2 + OH → H2 O + H H2 + O2 → H + HO2 H2 + M → H + H + M H + OH → H2 O H + O2 + M → HO2 + M H + H2 O2 → H2 O + OH HO2 → H + O2 HO2 + H → OH + OH HO2 + H2 → H2 O2 + H HO2 + H2 O → H2 O2 + OH HO2 + OH → H2 O + O2 HO2 + HO2 → H2 O2 + O2 H2 O2 + M → 2OH + M H2 O2 + H → H2 O + OH OH + H2 → H2 O + H OH + H → H2 O OH + HO2 → H2 O + O2 OH + O → HO2 H2 O + H → H2 + OH H2 O → H + OH H2 O + O2 → HO2 + OH H2 O + O → OH + OH H2 O + HO2 → H2 O2 + OH

21.1 2.3 7.4 40.4 46.2 43.1 8.8 13 17.6 10.5 18.7 19.3 15.2 43.1 21.1 40.4 18.7 60.5 50.4 75.6 70.9 64.8 10.5

percentage

elementary reactions

t2

percentage

95.3% 3.4% 1.3% 2.3% 83.5% 14.2% 25.4% 45.3% 8.3% 18.6% 1.4% 1.0% 60.1% 39.9% 89.0% 4.5% 3.7% 2.8% 74.2% 5.7% 9.2% 8.3% 2.6%

H2 + OH → H2 O + H H2 + O2 → H + HO2 H2 + M → H + H + M H + O2 + M → HO2 + M H + CO2 → CO + OH H + H2 O2 → H2 O + OH HO2 → H + O2 HO2 + H → OH + OH HO2 + H2 → H2 O2 + H HO2 + H2 O → H2 O2 + OH HO2 + OH → H2 O + O2 HO2 + HO2 → H2 O2 + O2 H2 O2 + M → 2OH + M H2 O2 + H → H2 O + OH OH + H2 → H2 O + H OH + CO2 → CO + HO2 OH + CO → CO2 + H OH + HO2 → H2 O + O2 H2 O + H → H2 + OH H2 O + O → OH + OH H2 O + O2 → HO2 + OH H2 O + HO2 → H2 O2 + OH

19.8 2.6 8 51.7 22.4 41.6 8.1 14.2 15.3 9.8 20.5 22.6 17 41.6 19.8 52.4 28.6 20.5 9.8 57.9 66.5 9.8

97.1% 2.0% 0.9% 72.3% 16.2% 11.5% 34.3% 37.6% 5.7% 19.7% 1.1% 1.6% 67.4% 32.6% 78.8% 6.4% 10.5% 4.3% 63.7% 18.4% 9.6% 8.3%

t1 and t2 represent the first occurrence times of the elementary reactions in system 2 and system 3, respectively. The unit is ps.

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Fig. 9. State diagrams for hydrogen reaction pathways at 3600 K in (a) system 2 and (b) system 3.

3.5. Overall reaction mechanism The hydrogen oxidation process primarily consists of five radicals: H, O, OH, HO2 and H2 O2 , among which HO2 and H2 O2 play more important roles. The reaction pathways are shown illustratively in Fig. 9 for simulations of system 2 and system 3 at 3600 K. The thickness of the arrows indicates the percentages of observed branching reactions. Detailed elementary reactions of different species shown in the figure along with their percent contribution to the destruction of a certain species and the times of their first occurrence are listed in Table 2. H radicals produced by the initiation reaction are consumed by O2 molecules to form HO2 radicals. The HO2 radicals are then converted to OH radicals directly by H radicals or via the formation of H2 O2 . Finally, OH radicals consume H2 molecules to form H2 O through reaction Eq. (R8). This mechanism is similar to hydrogen oxidation mechanism in air conditions lying above the extended second explosion limit [54] except that the H2 O-involved reactions are enhanced. The reaction pathway in supercritical H2 O/CO2 mixtures is quite different due to the presence of CO2 . CO2 mainly reacts with H radicals to prompt the yield OH radicals, thus facilitating the consumption rate of H2 molecules. 3.6. Overall activation energy of the hydrogen oxidation reaction The overall hydrogen oxidation reaction is expressed as H2 + 1/2O2 → H2 O

(R11)

ReaxFF-NVT MD simulations of H2 /O2 mixtures under different conditions were run at a temperature range of 3200 K to 4000 K. According to experimental results [16,45,55], the oxidation kinetics of hydrogen under supercritical conditions exhibited a first-order dependence on hydrogen concentration and were independent of oxygen concentration. The overall rate constant is calculated by the following equation. k=−

d [H2 ] 1 dt [H2 ]

(2)

where [H2 ] is the average concentration of H2 . Simply replacing the H2 concentration with its molecular number, Eq. (2) evolves into kt = lnN 0 –lnN t

(3)

where N0 and Nt are the molecular number of H2 at the beginning and at time t, respectively. By fitting a curve of the ln Nt as a function of evolution time t and evaluating its slope, the rate constants for each temperature are calculated. Then based on the empirical Arrhenius formula

 E  a

k = A · exp −

RT

(4)

the overall activation energies are calculated by fitting a curve of the Napierian logarithm of rate constant k as a function of the inverse of temperature. Fig. 10 displays the fitted Arrhenius plots for hydrogen oxidation under different conditions. Detailed data shown in the figures are

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Fig. 10. Napierian logarithm of H2 oxidation rate constant versus inverse temperature under different conditions. Table 3 Arrhenius parameters for hydrogen oxidation at different conditions obtained from present work and experiments. Reaction medium

ReaxFF Mueller et al. [8] Holgate et al. [55] Kallikragas et al. [45] Li et al. [16] a b

/ H2 O 85%H2 O/15%CO2 70%H2 O/30%CO2 N2 SCW SCW SCW/CO2 b

Temperature (K)

3200–4000 850–1040 768–873 773–923 778–873

Ea (kJ/mol)

lnA (s−1 )

245.1 127.1 113.3 89.7 255.3 372 96.4 104.6

30.3 26.0 25.8 25.6 40.2a 52.5 11.1 13.4

The kinetics of H2 oxidation reaction is first order in hydrogen concentration and one-half order in oxygen concentration. The mole fractions of CO2 at the initial stage are around 0.8%.

listed in Table S4, Supplementary Materials. The Arrhenius parameters derived through the fitted plots along with those obtained by experiments are shown in Table 3. It can be seen that the activation energies of hydrogen oxidation are greatly affected by the presence of H2 O and CO2 . The overall activation energies in air and pure SCW environments obtained from ReaxFF-MD simulations are 245.1 and 127.1 kJ/mol, respectively. The results are in good agreement with the experimental values of 255.3 and 96.4 kJ/mol, considering the temperatures and pressures in simulation conditions are much greater than those in experiments. The activation energy in 70%H2 O/30%CO2 (system 4) is lower than that in 85%H2 O/15%CO2 (system 3), which proves higher CO2 concentration can enhance the hydrogen oxidation reaction as discussed above. It should be noticed that the CO2 concentration in our previous experiments [16] is much lower than that in simulations. Considering this reason, the activation energy values of system 3

and system 4 are reasonably comparable with the experimental measurements. 3.7. Mixtures seeded with one OH radical Hydrogen oxidation in air may become uncontrollable and cause detonations under improper operating conditions, which is very dangerous and should be avoided. To evaluate the hydrogen oxidation behavior in supercritical systems under adiabatic conditions, we seeded one OH radical in system 2 and system 3 and performed MD simulations with the micro-canonical ensemble (NVE). The simulations were performed for a period of 500 ps with an initial temperature of 3200 K. Fig. 11 displays the time evolution of H2 , O2 and H2 O molecules and temperature profile for the simulation cases. It is observed that the induction times are shortened by the presence of OH radical

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G. Li, Y. Lu and S. Qi / J. of Supercritical Fluids 155 (2020) 104661

at higher CO2 concentration. CO2 mainly takes part in the reaction of CO2 + H → CO + OH, leading to the production of more OH radical. Furthermore, the effect of O2 concentration is studied. It is observed that high concentration O2 not only enhances the oxidation rate but also shortens the induction time at high temperatures. For H2 /O2 reaction under supercritical conditions, the predominant initiation reaction is observed as reaction Eq. (R1) H2 + O2 + H2 O → H + HO2 + H2 O

(R1)

The formation and consumption reactions of HO2 and H2 O2 are found to be dominant in the overall reaction process. Most O2 molecules are converted to OH radical through the formation of HO2 rather than the chain-branching reactions. The main elementary reactions are studied by analyzing the computed trajectories of atoms during simulations. Reactions mechanisms for hydrogen oxidation in pure SCW and supercritical mixtures are obtained and a transition in the reaction mechanism is observed because of the presence of CO2 . The activation energies of hydrogen oxidation in different simulation systems are obtained based on the Arrhenius equation. The results are reasonably comparable with experimental values, illustrating that the ReaxFF is able to accurately simulate the kinetic behavior of H2 /O2 reaction. Additionally, no explosion behavior occurs during hydrogen oxidation process in supercritical systems under adiabatic conditions, suggesting using hydrogen as an auxiliary fuel at such conditions is safe and feasible. The simulation results can also benefit the development of continuumscale kinetic models for prediction of hydrogen oxidation kinetics in supercritical H2 O/CO2 mixtures. Declaration of Competing Interest Fig. 11. Time evolution of H2 , O2 and H2 O molecules and temperature profile for NVE MD simulations of different reaction systems seeded with one OH radical with an initial temperature of 3200 K: (a) system 2; (b) system 3.

and the oxidation reactions occur at a very early time. So it can be regarded as an effective way to save simulation time before an initiation reaction by seeding an OH radical in reaction mixtures. The overall oxidation rate of H2 in system 3 is higher than that in system 2 even though the reaction proceeds very slowly at the initial stage. The values of total temperature rise in both systems are lower than 1800 K and no sudden rise in water molecule number or temperature is observed. This is different from the hydrogen oxidation behavior in air under adiabatic conditions. The system temperature can increase more than 3000 K within 100 ps in an NVE MD simulation for H2 /O2 reaction in air [23]. Our simulation results suggest that there is no obvious explosion and shock behavior occurring during the oxidation reaction process. Utilizing hydrogen oxidation to release heat in supercritical systems can be considered safe and feasible since the reaction is moderate and controllable. 4. Conclusion A series of NVT MD and NVE MD simulations based on the ReaxFF reactive force field were performed to elucidate the reaction kinetics and mechanism of hydrogen oxidation in supercritical H2 O/CO2 mixtures. The effects of H2 O and CO2 on hydrogen oxidation are revealed. The simulation results show that the presence of high concentration H2 O inhibited the oxidation rate of H2 . The chemical reactivity of H2 O is mainly expressed by several H2 Oinvolved elementary reactions, through which the production of OH radical is suppressed. High concentration H2 O also decreases the diffusion rates of H2 , O2 and other radicals and increases steric hindrance for effective collisions. The presence of CO2 promotes hydrogen oxidation rate and the promotion effect is more obvious

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