Microscopic Analysis of Hydrogen Production from Methane Sono-Pyrolysis

Abstract

The sonolysis of certain substrates in water has proved its effectiveness for the enhancement of the sonochemical production of hydrogen. In this study, the sonolysis of methane has been investigated for the first time in a single acoustic bubble (microreactor) over a frequency from 140 to 515 kHz. The obtained findings have been compared to those available in the literature. Independently of the methane dose (inside the bubble), the yield of H₂ was improved especially with the decrease in wave frequency (from 515 to 140 kHz). For the driving frequencies 140, 213, 355, and 515 kHz, the production of hydrogen was maximized at 20, 15, 10, and 10% CH₄, respectively. For 213 kHz, and the presence of 10% methane, the yield of hydrogen goes up by 111 fold compared to the case where the gas atmosphere is saturated only by argon. On the other hand, the highest methane conversions (~100% for 2, 5 and 7% CH₄) were retrieved at 140 and 213 kHz. In terms of hydrogen formation and methane decay, the use of 140 kHz was found to be the best choice, whereas for a multi-bubble system, the number of acoustic bubbles should be taken into account for an optimal choice of frequency. Interestingly, it was observed that at 140 and 213 kHz and for methane mole fractions lower than or equal to 30 and 10%, respectively, a maximal formation of H₂ and a relatively important production of ^•OH could result simultaneously.

1. Introduction

In the ongoing energy transition from a fossil-based energy economy, new storable and transportable energy forms are readily required. This is possibly achieved via rechargeable batteries, biofuels and hydrogen technology. Hydrogen (H₂) is an attractive fuel source due to its rather high specific energy compared to other conventional fuels. In comparison to other conventional energy sources (methane, gasoline, diesel, ethanol and methanol), hydrogen has many advantages, such as: HHV (higher heating value) and LHV (lower heating value) values are 141.9 KJ g⁻¹ and 119.9 KJ g⁻¹ [1], respectively; it can be stored in various forms (such as liquid, gaseous, or in combination with metal hybrid); abundant; a clean fuel with no CO₂ emissions; and it can be used in fuel cells to produce electricity [2,3,4]. Hydrogen is therefore one of the best ways to lower greenhouse gas (GHG) emissions and reliance on oil. Contrary to fossil fuels, hydrogen must be produced because it is not freely available in nature [5], where it is typically found in mixtures with other elements, most notably with oxygen in water and with carbon, nitrogen, and oxygen in biological things and fossil fuels [6]. Hydrogen is mainly (~95%) produced from fossil fuel conversion [7], where most of H₂ is formed by steam reforming of natural gas [8,9]. Alternative solutions (e.g., water electrolysis [5], bio-photolysis of water by algae [10], dark-fermentation, photo-fermentation [10], gasification [1] and pyrolysis of biomass [1,5]) for hydrogen production were developed for a possible reduction in the fossil fuel use.

Recently, the sonolysis of water [11,12] has attracted the attention of many researchers as a new and clean technology for hydrogen production. Compared to other pyrolytic processes for H₂ production, sonolysis uses only ultrasound (physical means) so it is easy to manipulate, safe (water is the sonicated matrix), and produces clean hydrogen (without needing to add hazardous solvents to the sonicated medium). Furthermore, it is environmentally friendly (with no CO₂ emissions) and can be easily involved in combination with all other production techniques (electrolysis, photocatalysis, etc.) for an intensification strategy. By incorporating certain substrates into the sonicated media (e.g., alcohols in the liquid matrix or mono-, di- or polyatomic gases in the gas matrix), the sonolysis process can be speeded up.

Acoustic cavitation, i.e., the formation, growth and implosion of microbubbles, resulting from the ultrasonic irradiation of liquids, is the origin of sonochemical reactions [13]. These bubbles are real power microreactors within which pyrolytic reactions occur and generate free radicals and oxidants (i.e., ^●OH, H, HO₂^● and H₂O₂) and molecular hydrogen (H₂). These reaction products are the result of the bubbles’ high temperature of several thousand Kelvin and high pressure of 1000 atm during the violent implosion [14]. Experimental data indicated that the rate of H₂ generation is 1.25 times greater than that of H₂O₂ [11]. However, due to the relatively low energetic efficiency of the sonolytic process, alternative solutions were adopted, such as the sonolysis of some substrate (e.g., methanol), for the enhancement of the sono-hydrogen production [15,16,17,18]. According to the experimental works of Henglein et al. [19,20] and Hart et al. [21], hydrogen was found to be the main product of the sonolysis of methane and ethane gases. Furthermore, Arsentev [22] has recently shown the possibility of improving the yielding of formaldehyde from the sonolysis of methane and ethylene (and a mixture of both), where the accumulation of formaldehyde is dependent on the ultrasonic power and the dose of molecular oxygen injected into the medium. As it can be retrieved, a great scarcity is observed for the studies focusing on the analysis of the sonochemical field in the presence of methane.

In this work, the sono-conversion of methane within the acoustic bubble for hydrogen production is investigated with respect to the variation in ultrasound frequency (from 140 to 515 kHz). In addition, the bubble chemistry and dynamics are analyzed at the indicated wave frequencies. Our findings are contrasted with those found in the literature. With a particular emphasis on the production of hydrogen from the pyrolytic processes, the current research is regarded as the first theoretical attempt at elucidating the sonolysis of methane by acoustic cavitation

2. Model

To simulate the single-bubble sonochemistry in the presence of CH₄, the detailed mathematical model developed early by our research team for CCl₄ pyrolysis [23,24] has been partially modified here via involving a new pyrolytic reaction scheme for methane within the acoustic bubble. The sonicated medium (water) is saturated with argon containing different proportions of methane. Therefore, the initial content of the bubble is argon, water vapor and CH₄. When the bubble starts to oscillate, mass and heat transfer take place across the bubble wall (in addition to the chemical reactions). The key points of our model are provided in this section. Based on ordinary differential equations, our model incorporates non-equilibrium water molecule vaporization and condensation at the bubble wall, heat transmission both within and outside the bubble, and chemical reactions.

Table 1. Principal equations of the model (see detail in Refs. [23,24]) *.

Bubble dynamics:
$\left(1-\frac{\dot{R}}{C}+\frac{\dot{m}}{C{\rho }_L}\right)R\ddot{R}+\frac{3}{2}{\dot{R}}^2\left(1-\frac{\dot{R}}{3C}+\frac{2\dot{m}}{3C{\rho }_L}\right)$ $=\frac{1}{{\rho }_L}\left(1+\frac{\dot{R}}{C}\right)\left[P_B\left(t\right)-P_A\mathit{sin}\left(2\pi f\left(t+\frac{R}{C}\right)\right)-P_{\infty }\right]+\frac{\ddot{m}R}{{\rho }_L}\left(1-\frac{\dot{R}}{C}+\frac{\dot{m}}{C{\rho }_L}\right)+\frac{\dot{m}}{{\rho }_L}\left(\dot{R}+\frac{\dot{m}}{2{\rho }_L}+\frac{\dot{R}\dot{m}}{2C{\rho }_L}\right)$ $+\frac{R}{C{\rho }_L}\frac{d{P}_B}{dt}$	(1)
- Pressure at the external bubble wall:
$P_B\left(t\right)=P\left(t\right)-\frac{2\sigma }{R}-\frac{4\mu \dot{R}}{R}$	(2)
- Bubble pressure and Temperature:
$P\left(t\right)=\frac{{\mathit{nR}}_{g}T}{V-\mathit{nb}}+\frac{{\mathit{an}}^2}{V^2}$	(3)
$T=\frac{\left(E+\frac{{\mathit{an}}^2}{V}\right)}{C_v{n}_t}$	(4)
2. Mass transfer (water vapor and methanol condensation and evaporation):
$\dot{m}=\alpha \frac{\left\{P_{sat},i\left[R\right]-Pi\right\}}{\sqrt{\frac{2\pi T_{\left[R\right]}{R}_g}{M_i}}} i=H_{2}O$	(5)
3. Heat transfer (thermal conduction):
$\dot{Q}=4\pi R^2{\lambda }_{\mathit{mix}}\frac{\left(T_{liq}-T\right)}{L_{th}}$	(6)
$L_{th}=min\left\{\frac{R}{\pi },\sqrt{\frac{R\chi }{\dot{R}}}\right\}$	(7)
${\lambda }_{\mathit{mix}}{=\lambda }_{H_{2}O}\left(T\right)\left(\frac{n_{H_{2}O}}{n_t}\right){+\lambda }_{\mathit{Ar}}\left(T\right)\left(\frac{n_{\mathit{Ar}}}{n_t}\right){+\lambda }_{{\mathit{CH}}_4}\left(T\right)\left(\frac{n_{{\mathit{CH}}_4}}{n_t}\right)$	(8)
4. Internal bubble energy:
$\mathrm{\Delta }E=-P\left(t\right)\mathrm{\Delta }V\left(t\right){+4\pi R}^2\mathrm{\Delta }t\frac{\dot{ m},H_{2}O}{M_{H_{2}O}}{e}_{H_{2}O}{+4\pi R}^2\mathrm{\Delta }t\lambda \frac{\left(T_{\mathit{liq}}-T\right)}{L_{\mathit{th}}}-\frac{4}{3}{\pi R}^3\mathrm{\Delta }t{\displaystyle {\displaystyle \sum }_{i=1}^n}\mathrm{\Delta }{H}_i{r}_i$	(9)
5. Change in species quantities (mol)
- For H2O:
$n_{H_{2}O}\left(t+\mathrm{\Delta }t\right)=n_{H_{2}O}\left(t\right)+4\pi R^2\mathrm{\Delta }t\frac{\dot{m},H_{2}O}{M_{H_{2}O}}+V\mathrm{\Delta }t{\dot{U}}_{H_{2}O}$	(10)
- For other species k (except Ar):
${ n}_k\left(T+\mathrm{\Delta }t\right){=n}_k\left(T\right)+V \mathrm{\Delta }t{\dot{ U}}_k$	(11)
where:
$\dot{U_k}=\frac{1}{V}\frac{{\mathit{dn}}_k}{\mathit{dt}}{\displaystyle {\displaystyle \sum }_{i=1}^I}\left(\upsilon ″-\upsilon \prime \right)r_i \left(k=1, \dots , K\right)$	(12)
${ r}_i{=k}_{\mathit{fi}}{\displaystyle {\displaystyle \prod }_{k=1}^K}{\left[X_k\right]}^{{\upsilon \prime }_{\mathit{ki}}}{-k}_{\mathit{ri}}{\displaystyle {\displaystyle \prod }_{\mathrm{k}=1}^K}{\left[X_k\right]}^{{\upsilon ″}_{\mathit{ki}}}$	(13)
${ k}_{\mathit{fi}}{=A}_{\mathit{fi}}{T}^{b_{\mathit{fi}}} \mathit{exp}\left(-\frac{E_{a_{\mathit{fi}}}}{R_{g}T}\right)$	(14)
$k_{\mathrm{ri}}{=A}_{\mathit{ri}}{T}^{b_{\mathit{ri}}} \mathit{exp}\left(-\frac{E_{a_{\mathrm{ri}}}}{R_{g}T}\right)$	(15)

* Variables description: dots denoted here time derivative (d/dt), R is the bubble radius, C is the sound speed in the medium (water), ρ_L is the liquid density, $\dot{m }$ is the net rate of evaporation per unit area and unit time and P_∞ is the ambient static pressure. P_A is the acoustic amplitude (linked to the acoustic intensity I_a by: P_A = (2I_aρ_LC)^1/2), P_B(t) is the liquid pressure at the liquid side of the bubble, P(t) is the pressure inside the bubble. σ is the surface tension, μ is the liquid viscosity), f is the sound frequency, P_v is the vapor pressure within the bubble, a and b (in Equations (3) and (4)) are the Van der Waals constants (given in [29]), Rg is the universal gas constant. V is the volume of the bubble [V = 4/3(πR³)], T is the temperature inside the bubble, E is the internal bubble energy, P_sat[R] is the saturated vapor pressure (calculated by using Antoine’s equation) at the interface temperature T_[R] = T_liq,, M_H2O is the molecular weight of water vapor. ‘α’ is the accommodation coefficient (given in [17]). λ_mix, χ and L_th are the heat conductivity, thermal diffusivity of the gas mixture and the thickness of the thermal boundary layer, respectively. [Individual λ_i of gases [29,30,31]: λ_H2O(T) = 9.967213 × 10⁻⁵T − 1.1705 × 10⁻², λ_Ar(T) = 3.5887 × 10⁻⁵T + 6.81277 × 10⁻³, λ_CH4 (T) = −0.0017 + 1.0 × 10⁻⁴T + 7.0 × 10⁻⁸T² , χ = [λ_mix/Cp]. C_p is the heat capacity concentration (J m⁻³ K⁻¹) for H₂O, Ar and CH₄ mixture, C_v is the molar heat of gases and vapor in the bubble [C_v = (3/2)R_g for monoatomic gases (Ar, H…), (5/2)R_g for diatomic gases (O₂, N₂, …) and (6/2)R_g for triatomic gases]. ΔH_i and r_i are the enthalpy change and the rate of the ith reaction, respectively, and e_H2O is the energy transported by 1 mole of an evaporating or condensing water vapor [e,_H2O = C_v,H2OT], ${\dot{ U}}_i$ (${\dot{ U}}_k$) is the production rate of H₂O (kth species) within the bubble.

outlines the equations that govern the model. Each equation in this table is fully described in our previous papers [23,24]. All numerical simulations were carried out for a bubble oscillating in Ar or Ar–CH₄-saturated water with different quantities of methane (X_CH4 varies from 0 to 1). The bubble–bubble interactions are neglected.

Table 2. Scheme of the possible chemical reactions inside a collapsing Argon bubble [32,33]. M is the third Body. A is in (m³ mol⁻¹ s⁻¹) for two-body reaction [(m⁶ mol⁻² s⁻¹) for a three-body reaction], and E_a is in (KJ mol⁻¹) and ∆H in (KJ mol⁻¹).

	Reaction	A	n	Ea	ΔH
1	H2O + M → H• + •OH + M	1.912 × 107	−1.83	28.35	508.82
2	O2+M → O + O + M	4.515 × 1011	−0.64	28.44	505.4
3	•OH + M → O + H•+ M	9.88 × 1011	−0.74	24.43	436.23
4	H• + O2 → O + •OH	1.915 × 108	0.0	3.93	69.17
5	H• + O2 + M → HO2• + M	1.475	0.6	0.0	−204.80
6	O + H2O → •OH + •OH	2.97	2.02	3.21	72.59
7	HO2• + H• → H2 + O2	1.66 × 107	0.0	1.97 × 10−1	−239.67
8	HO2• + H• → •OH + •OH	7.079 × 107	0.0	7.06 × 10−2	−162.26
9	HO2• + O → •OH + O2	3.25 × 107	0.0	0.0	−231.85
10	HO2• + •OH → H2O + O2	2.89 × 107	0.0	−1.19 × 10−1	−304.44
11	H2+M → H• + H• + M	4.577 × 1013	−1.4	24.98	444.47
12	O + H2 → H• + •OH	3.82 × 106	0.0	1.9	8.23
13	•OH + H2 → H• + H2O	2.16 × 102	1.52	8.25 × 10−1	−64.35
14	H2O2 + O2 → HO2• + HO2•	4.634 × 1010	−0.35	12.12	175.35
15	H2O2 + M → •OH + •OH +M	2.951 × 108	0.0	11.59	217.89
16	H2O2+H• → H2O+•OH	2.410 × 107	0.0	9.5 × 10−1	−290.93
17	H2O2 + H• → H2 + HO2•	6.025 × 107	0.0	1.9	−64.32
18	H2O2 + O → •OH + HO2•	9.550	2.0	9.5 × 10−1	−56.08
19	H2O2 + •OH → H2O + HO2•	1.0 × 106	0.0	0.0	−128.67
20	H• + •OH + M → H2O + M	2.2 × 1010	−2.0	0.0	−508.82
21	O + O + M → O2 + M	6.165 × 103	−0.5	0.0	−505.4
22	O + H• + M → •OH + M	4.714 × 106	−1.0	0.0	−436.23
23	O + •OH → H• + O2	5.481 × 105	0.39	−7.01 × 10−2	−69.17
24	HO2• +M → H• + O2 + M	3.09 × 106	0.53	11.7	204.80
25	•OH+•OH → O + H2O	1.465 × 10−1	2.11	−6.94 × 10−1	−72.59
26	H2 + O2 → HO2•+ H•	3.164 × 106	0.35	13.3	239.67
27	•OH + •OH → HO2• + H•	2.027 × 104	0.72	8.8	162.26
28	•OH+O2 → HO2• + O	3.252 × 106	0.33	12.75	231.85
29	H2O + O2 → HO2• + •OH	5.861 × 107	0.24	16.53	304.44
30	H• + H• + M → H2 + M	1.146 × 108	−1.68	1.96 × 10−1	−444.47
31	H• + •OH → O + H2	2.667 × 10−2	2.65	1.17	−8.23
32	H• + H2O → •OH + H2	2.298 × 103	1.40	4.38	64.35
33	HO2• + HO2• → H2O2 + O2	4.2 × 108	0.0	2.87	−175.35
34	•OH + •OH + M → H2O2 + M	1.0 × 102	−0.37	0.0	−217.89
35	H2O + •OH → H2O2 + H•	1.269 × 102	1.31	17.08	290.93
36	H2 + HO2• → H2O2 + H•	1.041 × 105	0.70	5.74	64.32
37	•OH + HO2• → H2O2 + O	8.66 × 10−3	2.68	4.45	56.08
38	H2O + HO2• → H2O2 + •OH	1.838 × 104	0.59	7.4	128.67

and

Table 3. Scheme of the possible chemical reactions inside a collapsing Ar–CH₄-bubble [32,33]. M is the third Body. A is in (m³ mol⁻¹ s⁻¹) for two-body reaction [(m⁶ mol⁻² s⁻¹) for a three-body reaction], and E_a is in (KJ mol⁻¹) and ∆H in (KJ mol⁻¹).

	Reaction	A	n	Ea	ΔH
1	H2O+M → H• + •OH + M	1.912 × 107	−1.83	28.35	508.82
2	O2 + M → O + O + M	4.515 × 1011	−0.64	28.44	505.4
3	•OH + M → O + H• + M	9.88 × 1011	−0.74	24.43	436.23
4	H• + O2 + M → HO2• + M	1.475	0.6	0.0	−204.80
5	H2 + M → H• + H•+ M	4.577 × 1013	−1.4	24.98	444.47
6	H2O2 + M → •OH + •OH + M	2.951 × 108	0.0	11.59	217.89
7	CH4 + •OH → CH3• + H2O	0.19	2.4	8.81	−57.69
8	CH4 + H• → CH3• + H2	1.313 × 10−2	3.0	33.61	3.33
9	CH4 + M → CH3• + H+ M	1.04 × 1012	0.0	402.97	439.27
10	CH3• + CH3• +M → C2H6 + M k0               k∞	1.27 × 1029 3.614 × 107	−7.0 0	11.55 0.0	−376.66
11	CH3• + CH3• → C2H4 + H2	1.0 × 108	0.0	133.76	−240.34
12	C2H4+ M → C2H2 + H2 + M	9.33 × 1010	0.0	38.8	175.74
13	O + C2H2 → CH2• + CO	4.086 × 102	1.5	7.07	−197.51
14	CH2• + O → CO + H2	4.818 × 107	0.0	0.0	−750.09
15	CO + O2 → CO2 + O	2.529 × 106	0.0	199.44	−33.83
16	C2H2 + •OH → CO + CH3•	4.84 × 10−10	4.0	8.39	−229.51
17	CH2• + CH2• → C2H2 + 2H•	2.0 × 108	0.0	44.99	−116.64
18	CH3• + H• → CH2• + H2	2.0 × 108	0.0	63.1	26.02
19	O + O + M → O2 + M	6.165 × 103	−0.5	0.0	−505.4
20	HO2• + M → H• + O2 + M	3.09 × 106	0.53	11.7	204.80
21	H• + H• + M → H2 + M	1.146 × 108	−1.68	1.96 × 10−1	−444.47
22	•OH + •OH + M → H2O2 +M	1.0 × 102	−0.37	0.0	−217.89
23	CH3• + H• + M → CH4 + M k0              k∞	1.42 × 1021 1.27 × 1010	−4.8 −0.6	10.22 1.6	−439.27

indicate the reaction pathways utilized to visualize the internal bubble chemistry for the cases of Ar-bubble (0% CH₄, Table 2, 38 irrev. reactions), and Argon–CH₄ bubble (Table 3, 23 irrev. reactions). Table 1 provides the following main equations:

• Equation (1) (the modified Keller–Miksis equation [25]) describes the radial dynamics, R(t), of the bubble during its oscillation in compressible medium (water);
• Equations (3) and (4) provide the internal bubble pressure and temperature during oscillation;
• Equation (5) (the Hertz–Knudsen formula [26]) describes the mass flux, dm/dt, of water evaporation and condensation at the bubble–liquid interface;
• Equations (6)–(8) (heat dissipation by conduction [27]) describe the heat exchange dQ/dt inside and outside the bubble during oscillation;
• Equation (9) describes the temporal variation in the internal energy of a bubble;
• Equations (10)–(15) describe the change, with time, in quantities of H₂O, CH₄ and all other species ‘k’ within the bubble during oscillation.

In our prior works [23,24], we explained the approach for solving the differential equations in Table 1 (time step = 10⁻⁴ µs) in conjunction with the reaction scheme during the bubble oscillation. The variation in bubble temperature, pressure, radius, and wall velocity, as well as the quantities (moles) of all species (except argon, which is chemically inert) in the bubble, are all outputs of these equations, which are applied throughout the bubble oscillations (with respect to time). The initial bubble composition varies with the mole fraction of methane (varied from 0 and 1) inside the acoustic cavitation. The initial pressures of Ar, CH₄ and H₂O within the bubble were determined using the equilibrium stress at the bubble wall: P₀ = P_∞ + 2σ/R₀, where P₀ is the initial pressure in the cavity (P_v,0 + P_CH4,0 + P_Ar,0). P_v,0 of the water vapor is determined by Antoine’s equation [28]. P_Ar,0 is deduced as P_Ar,0 = P₀ − (P_v,0 + P_CH4,0). The entire computation algorithm is available in [23,24].

3. Results and Discussions

3.1. Kinetics of Bubble in Presence of Methane

In Figure 1a,b, the molar production and the temperature evolution inside the acoustic cavitation bubble are shown for Ar and Ar–CH₄ (90%/10%) saturated water irradiated at 213 kHz and 1 W/cm². The time scale in Figure 1a,b is shown at around the end of bubble collapse (~3.4885 and 3.490 µs, respectively), when the initial bubble radius (R₀ = 3.9 µm) is taken as that determined experimentally by Brotchi et al. (i.e., the mean ambient bubble radius of the bubble population) [34]. As it can be seen in Figure 1a, the main species produced (at the end of collapse) within an argon bubble are H^• (2.95 × 10⁻¹⁷ mol), ^•OH (4.19 × 10⁻¹⁸ mol), O (2.36 × 10⁻¹⁷ mol), and H₂ (1.15 × 10⁻¹⁷ mol) molecules. The predominance of these species was also observed in the different theoretical works for argon-saturated water [35,36,37]. Under these conditions (213 kHz, 1 W/cm²), the peak temperature of the bubble is 6788 K. On the other hand, in Figure 1b it can be seen that the important products are in the order: H₂ (1.28 × 10⁻¹⁵ mol) > CH₂ (4.79 × 10⁻¹⁶ mol) > CH₃^• (3.55 × 10⁻¹⁶ mol) > C₂H₂ (2.24 × 10⁻¹⁶ mol) > H^• (1.23 × 10⁻¹⁶ mol) > ^•OH (4.88 × 10⁻¹⁸ mol) > C₂H₄ (4.87 × 10⁻¹⁸ mol) > CO (1.09 × 10⁻¹⁸ mol) > C₂H₆ (6.13 × 10⁻¹⁹ mol). Whereas, in this case, the maximal bubble temperature goes down to 3650 K (46.22% of decrease in the presence of 10% CH₄). This decrease in the peak temperature is owing to the increase in heat capacity of the bubble as well as the endothermal dissociation of methane. In the presence of 10% methane (Figure 1b), the yield of hydrogen goes up by 111 fold compared to the case where the gas atmosphere is saturated only by argon (Figure 1a). This enhancement in H₂ production could be ascribed mainly to the thermolysis of CH₄ (Reaction 9, Table 3) and the reaction of methane with hydrogen atoms (Reaction 9, Table 3). According to Figure 1b, a slight enhancement (16%) was retrieved for ^•OH radicals in the presence of methane, Figure 1a,b. The explication of this outcome is detailed in Section 3.3. The confrontation of the findings of Figure 1b to those of Hart et al. [21] (real system) indicates a clear discrepancy in the molar formation of C₂H₂, C₂H₄, C₂H₆, and CO (for Hart’s group: CO > C₂H₂ > C₂H₆ > C₂H₄). This difference is primarily explained by the different acoustical conditions, i.e., in the present study: 213 kHz and 1 W/cm² and for Hart’s team: 300 kHz, 2 W/cm². In addition, in our work the simulation task is performed for a single bubble (single micro-reactor) whereas Hart et al.’s obtained results are for a multi-bubble system (multiple interactions). It should be stressed here that the chemistry of the sonicated medium is affected by the solubility of the generated species from the collapsing bubbles. This means that the resulting kinetics in Figure 1b are plausibly modified, especially for the more soluble species which undergo more sonolysis before escaping outside the irradiated solution. This could be understood by knowing that the solubilities of acetylene (1.08 g/1 kg H₂O, at 25 °C [38]) and ethylene in water are 39 and 5 times greater than that of carbon monoxide (0.0276 g/1 kg H₂O, at 25 °C [38]), respectively. More clarifications about the bubble chemistry are given in Section 3.3 with respect to the variation in the driving ultrasound frequency. This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

3.2. Model Efficiency

To check the viability of our model, numerical simulations of bubble sonochemistry in the presence of different CH₄ proportions in argon (i.e., the saturation gas matrix) have been performed under the same experimental operating conditions of Hart et al. [f = 300 kHz, I_n = 2 W/cm²] [21]. Then the results of the main produced species (H₂, CO, C₂H₂, C₂H₄, and C₂H₆) are compared with the experimental profiles using normalized yields (Figure 2a–f). The ambient bubble radius adopted for all these calculations was 3.2 µm, which is the typical value of R₀ for frequencies around 300 kHz (~300–360 kHz) [18,34,39,40,41].

As can be seen in Figure 2a–f, a Gaussian tendency was retrieved for the molar yield of H₂, CO, C₂H₂, C₂H₄, and C₂H₆, and the conversion of CH₄, which is in accordance with the experimental results of Hart’s group. The same trend was also obtained in the experimental study of Henglein et al. [19,20] for the sonolysis of methane under an argon atmosphere. The Gaussian shape of the different graphs could be explained by the impact of the methane amount within the collapsing cavitation. This is because even with the decrease in bubble temperature (will be seen later) with the rise in CH₄ mole fraction (increases the bubble heat capacity), the production of the various species (H₂, CO, C₂H₂, C₂H₄, and C₂H₆) and methane conversion are found to be increased (competing effect), whereas over an optimum value [e.g., 20% CH₄ for H₂ formation, Figure 2a], the yield of these substances and CH₄ conversion are proportionally decreased with the peak temperature of the bubble. This means that above this optimum the low bubble temperature is unable to ensure high molar production and methane conversion at the end of the bubble implosion. The same tendencies were previously retrieved in the literature works [18,23,42] at the different initial bubble compositions. For the molar production of H₂, CO, C₂H₂, C₂H₄, C₂H₆ and CH₄ conversion, our maximal values are found at 20%, 5%, 20, 50%, 50% and 30% of CH₄ in the gas matrix, respectively; whereas those obtained experimentally by Hart’s group were at 15%, 10%, 20%, 30%, 30% and 20%, respectively. It should be noted that a total matching between our theoretical findings and those of Hart’s team is not expected because our results (expressed in moles) are based on a single-bubble system (micro-reactor), whereas those of Hart et al. (molar rates) are given for a real system (multi-cavitation system) where many phenomena (bubble–bubble interaction, bubbles coalescence …) are taking place. Despite that, our outcomes are very acceptable with slight discrepancies observed for the formation of ethylene and ethane, Figure 2e,f. Based on the results of Figure 2a–f, it can be concluded that the present model is accepted for modelling the effect of methane on bubble sonochemistry with the change in ultrasound frequency.

3.3. Effect of Methane Dose on the Bubble Chemistry and Dynamics

In this section, the impact of methane concentration (in the gas phase) on the sonoactivity and dynamics of a single bubble is explored with respect to the change in the wave frequency in the range from 140 to 515 kHz (Figure 3 and Figure 4). The choice of this frequency range (140–515 kHz) is based on the findings of the different experimental and theoretical works [43,44,45], indicating that the maximal sonoactivity in this is situated in this frequency range (140–515 kHz). In these simulations, the typical initial bubble radii are taken as a function of frequency as R₀ = 5 µm for 140 kHz, R₀ = 3.9 µm for 213 kHz [34], 3.2 µm for 355 kHz [34], 3 µm for 515 kHz [46]. These typical values are reported experimentally (in the indicated references) and confirmed theoretically in several numerical studies [37,39,41,42,47].

As it can be seen in Figure 3a, independently of the used frequency (140–515 kHz), the presence of methane (X_CH4 = 0.02–1) within the oscillating bubble has a positive effect on the formation of hydrogen, where this yield (H₂) is increased with the decrease in ultrasound frequency (from 515 to 140 kHz). Additionally, it is observed at 140, 213, 355, and 515 kHz that the maximal production of H₂ is obtained at 20 (5.54 × 10⁻¹⁵ mol), 15 (1.37 × 10⁻¹⁵ mol), 10 (8.35 × 10⁻¹⁷ mol), and 10% (8.27 × 10⁻²⁰ mol) CH₄, respectively. Above these optimums (10–20% CH₄) the production of hydrogen goes down with the rise in CH₄ mole fraction in the gas phase (bubble interior). These optimums (especially that at 355 kHz (10%)) are in good concordance with those obtained experimentally by Hart et al. [21] and Henglein et al. [19,20]. The same trend observed in Figure 3a was obtained previously via the sonolysis of methanol and carbon tetrachloride [18,23,48]. It is worth mentioning that the increase (at the optimum values) in molar yield of hydrogen at low frequencies (four orders of magnitude at 10% CH₄, for f = 515 kHz) is greater than that retrieved at high frequencies (two orders of magnitude at 20% CH₄ for f = 140 kHz), Figure 3a.

However, the maximal yields of H₂ at low frequencies (8.27 × 10⁻²⁰ mol at 10% CH₄ for f = 515 kHz) are very low compared to those retrieved at higher ones (6.54 × 10⁻¹⁵ mol at 20% for f = 140 kHz).

In Figure 3b, the conversion (%) of methane inside the acoustic cavitation is depicted over the frequency range from 140 to 515 kHz as a function of its (CH₄) initial mole fraction (from 0 to 1) within the bubble. It is found that the highest conversions (in %) are obtained at 140 and 213 kHz (compared to those at 355 and 515 kHz), where the same methane conversion (~100%) is obtained at 140 and 213 kHz for the mole fractions of 2, 5 and 7% CH₄ inside the bubble (initially). These results are corroborated in Figure 3c in terms of the molar conversion of methane, where the gap between the frequencies (especially for f > 213 kHz) is increased with the rise of the initial mole fraction of CH₄ (X_CH4) inside the bubble. For X_CH4 > 0.5, the molar conversion of methane (inside the bubble) is suppressed. It should be stressed here that for a single-bubble system the choice of a frequency of 140 kHz is more beneficial for maximal hydrogen production and methane conversion. However, for a multi-bubble system (real system) this might not be true, because in this case (a multi-bubble system) the number density should be taken into account; therefore, the total yields of hydrogen and methane conversion are affected. In general, it is known that for a constant acoustic amplitude the number of active bubbles increased with the rise in ultrasound frequency [40,49,50,51]; this means that for a frequency greater than 140 kHz (213–515 kHz), higher production of hydrogen and conversion of methane are possibly obtained. This trend is like that found for CCl₄ sonopyrolysis within acoustic bubbles, where the single-bubble conversion decreased with increasing frequency, while the bubble density increased [40]. The compromise between these two factors yields a continued increase in the overall CCl₄ conversion (in solution) because of the frequency impact’s dominance on the bubbles’ number against the single-bubble yield (please see [40]).

In Figure 3d, the variation in the maximal bubble temperature is evaluated as a function of methane mole fraction over the ultrasound frequency range from 140 to 515 kHz. At first sight, it can be retrieved that the peak temperature of a bubble goes down either with the rise of wave frequency (at a fixed mole fraction of CH₄), or with the increase in methane dose (at a constant frequency) inside the acoustic cavitation. Furthermore, it is found that the effect of methane mole fraction on bubble temperature (T_max) is intensified with the decrease in ultrasound frequency. At 140, 213, 355, and 515 kHz the peak temperature goes down by 68.79 (from 9168 to 2861 K), 61.48 (from 6767 to 2606 K), 52.66 (from 4205 to 1990 K), and 44.18% (from 2741 to 1530 K), respectively. The decrease in bubble temperature with the rise in methane mole fraction inside the bubble is explained by the increased heat capacity of the bubble in the presence of methane and its endothermal dissociation (Reaction 9, Table 3) during bubble collapse. Therefore, the decrease in ultrasound frequency (more expansion) increases the encapsulated quantity of CH₄, which means that its negative effect on bubble temperature is accelerated in this case. The same tendency was previously observed [18,52] in the presence of different volatile species within the implosive cavitation.

In Figure 4a, remarkably, it is seen that at each driving frequency the compression ratio is increased (35.71, 39.33, 49.73, and 58.43% at 140, 213, 355, and 515 kHz, respectively) with the rise in CH₄ mole fraction (from 0 to 1), but despite that the bubble temperature was found to be decreased (Figure 3d). This outcome could be explained by the decrease in bubble internal energy (in the presence of CH₄) as a result of the increase in its heat capacity (Equation (4), Table 1), enhancement of heat conduction outside the bubble (Equation (8), Table 1), and the endothermal dissociation of methane (Table 1 and Equation (9)). Therefore, according to Equation (4) (Table 1), the bubble temperature is found to be reduced proportionally with the increase in CH₄ concentration. On the other hand, we observe that the compression ratio increased with the decrease in ultrasound frequency (at a constant CH₄ mole fraction), so obviously this is a logical result because in this case (low frequencies) the expansion and compression of bubble are maximized with the longer acoustic period. It should be noted that of the energetic evaluation of the sono-cavitation process is of great importance for understanding the sonochemical efficiency. An entire study on the energetic efficiency of the sonolytic process (single- and multi-bubble systems) has been performed and published in our recent papers [53,54]. The single-bubble energy increased with frequency decrease and applied power increase, whereas some difference was found for the multi-bubble system [53,54].

In Figure 4b it is shown that the bubble’s total yield is enhanced in the presence of methane until an optimum threshold (depending on the applied frequency), above which this production goes down proportionally with the rise in CH₄ dose inside the bubble. This decrease in the total production is clearly explained by the decrease in bubble temperature [Figure 3d]; thus, in these regions (where the total yield is decreased) the peak temperature is unable to ensure the increase in the overall production (i.e., low dissociation of water vapor and methane). However, the reduction in the total yield of bubble is amortized at low frequencies as a result of the relatively high temperatures under these circumstances.

Hydroxyl radical (^•OH) plays a central role in H₂ production inside the bubble (via the pyrolytic reaction). Merouani et al. [32] demonstrated that H₂ is primarily produced in the gas phase of bubbles via recombination of primary radicals (H^• + ^•OH → O + H₂, Reaction 31 of Table 2) formed by splitting water vapor molecules at the high temperature developed during the bubble’s collapse phase. This reaction is responsible for H₂ generation over a wide range of sonication conditions [2,11,42,55,56]. Furthermore, when methane is present, ^•OH is a major precursor of CH₃^• formation inside the bubble (CH₄ + ^•OH → CH₃^• + H₂O, Reaction 7 of Table 3). This latter, CH₃^•, is considered a principal source of H₂ production as per Reactions 11 and 18 of Table 3 (CH₃^• + CH₃^• → C₂H₄ + H₂ and CH₃^• + H^• → CH₂^• + H₂).

The evolution of hydroxyl radicals as a function of methane mole fraction (inside the bubble) and the ultrasound frequency is shown in Figure 4c. First, a maximal improvement in the ^•OH production is observed at 2% (5% for 140 kHz) CH₄ for all the driving frequency, whereas over these optimums the yield of hydroxyl radicals is drastically decreased. The confrontation of Figure 4c to Figure 3a indicates that at 355 and 515 kHz and independently of CH₄ mole fraction, the yield of ^•OH radical is very low compared to that of hydrogen. For example, at 5% CH₄, the molar formation of H₂ is 285- and 80-fold higher than that of ^•OH radicals, respectively, at 355 and 515 kHz. This gap goes up to three orders of magnitude at 20% CH₄ for both frequencies (355 and 515 kHz). Our outcomes are in good concordance with those obtained by Hart et al. and Henglein et al. [19,20,21] at 300 kHz, where a very low production of H₂O₂ (resulting from the recombination of ^•OH radicals) was obtained compared to that of H₂ during the sonolysis of methane. Interestingly, at 140 and 213 kHz a relative enhancement was observed for the production of ^•OH radicals compared to the case of 355 and 515 kHz. For example, at 140 kHz the molar yield of H₂ is ~3 times greater than that of ^•OH radicals at 2% CH₄, whereas this difference goes up rapidly to 4-, 10-fold and 3 orders of magnitude, respectively, at 7, 10, and 20% CH₄. Similarly, at 213 kHz, the increase in CH₄ mole fraction from 2 to 20% gives an increase of ~2 fold and 3 orders of magnitude, respectively, for the formation of H₂ compared to ^•OH radicals. The analysis of Figure 3a and Figure 4c indicates the possibility of ensuring a simultaneous high production of H₂ and a relatively important yield of ^•OH radicals for methane mole fractions lower than or equal to 30 and 10% for 140 and 213 kHz, respectively. This outcome was never discussed previously in the literature. According to Table 3 (Reaction 7), the improvement of ^•OH production at 140 and 213 kHz (in parallel to that of H₂) seems to be controversial because ^•OH radicals are supposed to be scavenged by CH₄ molecules. To explain this trend, it should firstly be noted that for CH₄ mole fraction ≤30% at 140 kHz and ≤10% at 213 kHz (Figure 3d) the bubble temperature under these conditions is between 3000 and 10,000 K. According to Figure 4d, it can be seen that with the increase in bubble temperature the scavenging mechanism of ^•OH radicals (Reaction 7, Table 3) is increasingly competed by the decomposition of methane (Reaction, Table 3), thermal decomposition of water vapor (Reaction 1, Table 3), and accompanied by the decomposition of hydroxyl radicals (Reaction 3, Table 3) at a low extent. Therefore, it can be concluded that the main source of enhancing the yield of hydroxyl radicals at high bubble temperatures is the decomposition of methane, and as a result, less scavenging of ^•OH radicals is achieved under these conditions.

4. Conclusions

In this study, the sono-formation of hydrogen from methane sonolysis in single acoustic cavitation was analyzed for the first time over a frequency range from 140 to 515 kHz, as a function of CH₄ mole fraction within the oscillating bubble. It was found that independently of the adopted frequency (140–515 kHz), the presence of methane inside the bubble positively affects the formation of hydrogen (increased), which is enhanced with the decrease in the driving frequency. The production of hydrogen was found to be maximal at 20, 15, 10, and 10% CH₄ at the driving frequency of 140, 213, 355, and 515 kHz, respectively. The highest conversions of methane (~100% for 2, 5 and 7% CH₄) were obtained at 140 and 213 kHz. For a single-bubble system (microreactor), the adoption of 140 kHz frequency was found to be the best choice for maximal hydrogen production and methane conversion, whereas for the multi-bubble system (real process), the parameter of number density should be considered for an optimal choice of the irradiation frequency. In accordance with the experimental findings, independently of CH₄ mole fraction, very low production of ^•OH radicals was obtained at 355 and 515 kHz. Interestingly, a relative improvement in the formation of hydroxyl radicals was retrieved at 140 and 213 kHz. It has been found that for methane mole fractions lower than or equal to 30 and 10% for 140 and 213 kHz, respectively, a maximal production of H₂ and a relatively important yielding of ^•OH could be obtained simultaneously.