Thermodynamic assessment of hydrogen production via solar thermochemical cycle based on MoO₂/Mo by methane reduction

Abstract

Inspired by the promising hydrogen production in the solar thermochemical (STC) cycle based on non-stoichiometric oxides and the operation temperature decreasing effect of methane reduction, a high-fuel-selectivity and CH₄-introduced solar thermochemical cycle based on MoO₂/Mo is studied. By performing HSC simulations, the energy upgradation and energy conversion potential under isothermal and non-isothermal operating conditions are compared. In the reduction step, MoO₂: CH₄ = 2 and 1020 K<T_red<1600 K are found to be most favorable for syngas selectivity and methane conversion. Compared to the STC cycle without CH₄, the introduction of methane yields a much higher hydrogen production, especially at the lower temperature range and atmospheric pressure. In the oxidation step, a moderately excessive water is beneficial for energy conversion whether in isothermal or non-isothermal operations, especially at H₂O: Mo= 4. In the whole STC cycle, the maximum non-isothermal and isothermal efficiency can reach 0.417 and 0.391 respectively. In addition, the predicted efficiency of the second cycle is also as high as 0.454 at T_red = 1200 K and T_oxi = 400 K, indicating that MoO₂ could be a new and potential candidate for obtaining solar fuel by methane reduction.

Keywords

MoO₂/Mo based on solar thermochemical cycle / methanothermal reduction / isothermal and non-isothermal operation / syngas and hydrogen production / thermodynamic analysis

Introduction

Owing to the regenerative characteristic and abundant reserves, solar energy is considered as a promising energy resource. To date, solar energy plays an important role in a wide range of fields such as concentrating solar power, photovoltaic power generation and so on. Despite of the above applications, solar energy suffers intermittency and instability. Therefore solar energy storage is increasingly important. Recently, solar thermochemical technologies, which utilize the full spectrum of sunlight, attract wide attention due to prominent energy storage and fuel production capacities [¹]. In general, a typical two-step solar thermochemical process contains reduction and oxidation reactions, which could be described as

(1){\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_X\to {\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_{x-\delta }+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{O}}_{\mathrm{2}}(g),

(2){\mathrm{H}}_{\mathrm{2}}\mathrm{O}(g)+{\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_{x-\delta }\to {\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_x+{\mathrm{H}}_{\mathrm{2}}(g).

Equation (1) expresses the metal oxide reduction process and Eq. (2) represents water splitting reaction [²]. The solar thermochemical (STC) cycle is an interactive process which includes endothermic reduction of multivalent metal oxides and fuel production via H₂O-splitting and reoxidation of reduced material [³].

To date, mainstream metal-oxide redox pairs MO_x have been divided into three categories: volatile stoichiometric materials, nonvolatile stoichiometric ones, and non-stoichiometric ones [⁴–⁶].

Stoichiometric materials may encounter evaporation or sublimation, which usually leads to the decrement of the solar-to-fuel efficiency [⁷,⁸].

The disadvantage of non-stoichiometric materials is the relatively low reduction extent. As state-of-the-art non-stoichiometric materials, ceria and doped ceria suffer a high reduction temperature [⁹,¹⁰], which gives rise to larger energy penalties due to heat losses [³,⁵]. Perovskites have a lower operating temperature than ceria thanks to their better oxygen exchange ability [¹¹–¹⁴]. However, Yang et al. [¹⁵] found that the rate of hydrogen-generation was inferior at a lower water-splitting temperature.

When compared with conventional thermochemical processes, the superiority of the STC redox cycle is that the utilization of solar energy is environmental benign and the consumption of carbonaceous fuel used for combustion and heat addition would be substantially reduced [¹⁶,¹⁷]. Currently, the bottleneck of the STC technology is the extreme operating condition.

To decrease the operating temperature, carbothermal and methanothermal reduction have been proposed to promote the thermochemical process [¹⁰,¹⁸,¹⁹]. Kodama et al. [¹⁸] stated that the reduction temperature range was 1073–1173 K when introducing methane and using Ni_0.39Fe_2.61O₄/ZrO₂ as a working material. The reduction temperature could be greatly decreased via methanothermal reduction where the produced H₂ and CO can be used for the Fischer-Tropsch process [²⁰,²¹], as illustrated in Eqs. (3) and (4).

(3){\mathrm{CH}}_{\mathrm{4}}+{\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_x\to {\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_{x-\delta }+\mathrm{2}{\mathrm{H}}_{\mathrm{2}}+\mathrm{CO,}

(4){\mathrm{H}}_{\mathrm{2}}\mathrm{O}+{\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_{x-\delta }\to {\displaystyle \frac{\mathrm{1}}{\delta }}{\mathrm{MO}}_x+{\mathrm{H}}_{\mathrm{2}}.

The STC process with methane reduction can significantly decrease the operating temperature and avoid phase change, where the latent heat of metal oxide becomes energy penalty under the high reduction temperature condition [²¹]. Figure 1 compares the Gibbs free energy change of reactions with and without CH₄ reduction at different temperatures. It is clear that when CH₄ is introduced, the reaction temperature related to ∆G = 0 is much lower than that without CH₄ and lower than the melt points of MoO₂, Mo, and other solids.

Figure 2 shows the detailed process of the STC redox cycle with methane reduction. Concentrated solar energy provides heat input for the system.

At present, many researches concern about the temperature decreasing effect of methane reduction in the STC process, but it is unknown whether hydrogen production would be promoted by the previous step of methane reduction. Besides, the study about the incomplete recovery of redox material used is very scarce and the advantage and disadvantage of isothermal operation and non-isothermal operation are rarely studied. This paper aims to calculate the equilibrium composition, energetic upgrade factor and solar-to-fuel efficiency under isothermal and non-isothermal conditions, and analyze the optimal system operation condition based on the calculations proposed in this paper.

System model and computational details

The process of STC cycle based on MoO₂/Mo is demonstrated in Fig. 2. Concentrated solar energy is used for driving methane reduction. As shown in Eqs. (3) and (4) based on mass balance, one mole CH₄ and one mole H₂O could produce the syngas with a H₂:CO ratio of 3:1 [²²]. Generally, when evaluating system thermodynamic performance, the equilibrium composition analysis is of great significance. In this paper, the commercial thermodynamic HSC Chemistry software is used in calculating the thermodynamic property and equilibrium composition of the STC cycle [²³]. The name of the software is defined based on the calculations done by utilizing enthalpy (H), entropy (S), and heat capacity (Cp) for more than 28000 chemical species in the thermochemical database [²⁴]. Table1 lists the basic parameters and their nomenclatures. The primary formulas are

(5)Q_{\mathrm{r}\mathrm{e}\mathrm{d}}={\displaystyle {\sum }_i}{n}_i{\mathrm{\Delta }}_f{H}_i^{T_{\mathrm{r}\mathrm{e}\mathrm{d}}}-n_{\mathrm{C}{\mathrm{H}}_{\mathrm{4}},\mathrm{i}\mathrm{n}\mathrm{i}}\mathrm{\Delta }{H}_{\mathrm{C}{\mathrm{H}}_{\mathrm{4}}}^{T_{\mathrm{0}}}-n_{\mathrm{M}\mathrm{o}{\mathrm{O}}_{\mathrm{2},\mathrm{i}\mathrm{n}\mathrm{i}}}\mathrm{\Delta }{H}_{\mathrm{M}\mathrm{o}{\mathrm{O}}_{\mathrm{2}}}^{T_{\mathrm{o}\mathrm{x}\mathrm{i}}},

where n_i is the amount of substance i in equilibrium of methane reduction reaction, and Q_reactor can be described by

(6)Q_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}}={\displaystyle \frac{Q_{\mathrm{r}\mathrm{e}\mathrm{d}}}{{\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}}}={\displaystyle \frac{Q_{\mathrm{r}\mathrm{e}\mathrm{d}}}{\mathrm{1}-{\displaystyle \frac{\sigma {(T_{\mathrm{r}\mathrm{e}\mathrm{d}})}^{\mathrm{4}}}{I{C}_{\mathrm{0}}}}}}\mathrm{.}

It is assumed that the system is performed under the standard atmospheric pressure and in a well-insulated cavity-type reactor where the absorbed energy is diminished mainly by radiation. In Eq. (6), the normal beam solar insolation I is 1000 W/m², the mean flux concentration ratio labeled as C₀ is 3000 suns, s is the Stefan-Boltzmann constant [²⁵], and h_abs is defined as the absorbed solar energy efficiency. The theoretical summation of energy for the whole solar thermochemical cycle is expressed as Eq. (7):

(7)Q_{\mathrm{total}}=Q_{\mathrm{reactor}}+Q_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}=Q_{\mathrm{reactor}}+n_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}{\displaystyle {\int }_{T_{\mathrm{0}}}^{T_{\mathrm{oxi}}}{C}_{p,{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}(T)\mathrm{d}T}.

The definitions of the conversion ratio and production selectivity S_i are expressed as

(8){\chi }_{{\mathrm{CH}}_{\mathrm{4}}}={\displaystyle \frac{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}-n_{{\mathrm{H}}_{\mathrm{2}}\mathrm{,eq}}}{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

(9)S_{{\mathrm{H}}_{\mathrm{2}}}={\displaystyle \frac{n_{{\mathrm{H}}_{\mathrm{2}}\mathrm{,eq}}}{\mathrm{2}{n}_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

(10)S_{\mathrm{CO}}={\displaystyle \frac{n_{\mathrm{CO,eq}}}{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

(11)S_{{\mathrm{CO}}_{\mathrm{2}}}={\displaystyle \frac{n_{{\mathrm{CO}}_{\mathrm{2}}\mathrm{,eq}}}{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

(12)S_{\mathrm{C}}={\displaystyle \frac{n_{\mathrm{C,eq}}}{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

(13)S_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}={\displaystyle \frac{n_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O,eq}}}{\mathrm{2}{n}_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}},

where S_i means the production selectivity of i at equilibrium when reduction step is completed [²⁶], S_i can reflect the conversion extent of syngas production. In this paper, it is assumed that there is no additional consumption for producing H₂ and CO as the value of selectivity is very high.

Results and discussion

Effects of reactant ratio on chemical equilibrium and thermodynamic properties

Previous theoretical studies of solar thermochemical reactions indicate that equilibrium composition and thermodynamic analyses are the prior and feasible means of setting the practical reaction conditions and evaluating solar-to-fuel efficiency [²⁷]. Figure 3 presents the equilibrium composition analysis under different R_red and temperature conditions, in which Fig. 3(a) depicts the equilibrium compositions of MoO₂, MoO₃ and Mo at the temperature range of 800 K to1200 K, R_red = 2. Only Mo is produced when operation temperature is more than 940 K, labeled as T_Mo. In reduction step, the optimal operation of Mo production is located at T_Mo≥940 K and R_red = 2. Figure 3(b) reveals the relationship between T_Mo and R_red. As seen, at R_red = 1, MoO₂ is completely dissociated at T_Mo≥1160 K, according to which, apparently, T_Mo decreases with the increase of R_red and reaches the minimum value of 820 K at R_red = 10.

As one of the key performance parameters for the STC system, the equilibrium composition selectivity related to a range of temperature is calculated and presented in Fig. 4. The change of selectivity curve in Fig. 4(a) indicates that the value of S_{{\mathrm{H}}_2} increases with the temperature at the relevant temperature region and reaches the maximum (73.88%) at a temperature of 1000 K. When R_red = 2, 3, and 4, as seen in Figs. 4(b), 4(c), and 4(d), the values of S_{{\mathrm{H}}_2} increase with temperature and approach to 1 when T_red≥1200 K, indicating that H₂ could be produced with a high selectivity in the operation condition of R_red>1 and T>1200 K. S_CO is also of great significance in the production of syngas. As seen from Fig. 4(b), only when R_red = 2 and T≥1600 K, the value of S_CO increases to 1 whereas S_C and S_{{\mathrm{C}\mathrm{O}}_2} are the smallest ones. The reason for this is that more carbon element in constant amount of CH₄ changes into CO, but less carbon atoms becomes C and CO₂. To prevent the deactivation of metal oxide caused by carbon deposition, it is necessary to limit the production of solid C. As seen in Fig. 4, a higher temperature restrains the generation of solid C. When R_red = 2, illustrated as the dash-dot line in Fig. 4(b), {\chi }_{{\mathrm{CH}}_{\mathrm{4}}} reaches 1 at T_red≥1400 K. Even at T_red = 1100 K, R_red = 2, the ratio is still 0.987. In Figs. 4(a)–4(d), it is clearly observed that {\chi }_{{\mathrm{CH}}_{\mathrm{4}}} is not sensitive to R_red at the high temperature range.

In summary, R_red = 2 should be the optimum selection because of the higher selectivity of H₂ and CO but the lower production of solid carbon or water. Thus R_red = 2 will be applied in the follow-up oxidation step discussion of the STC redox cycle based on MoO₂/Mo.

According to Eq. (14), the water-splitting can be fully completed when the reactant ratio R_oxi is 2 in theory.

(14)\mathrm{Mo}+\mathrm{2}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}(g)={\mathrm{MoO}}_{\mathrm{2}}+\mathrm{2}{\mathrm{H}}_{\mathrm{2}}(g).

Figure 5 exhibits the variation of equilibrium compositions related to different temperature of oxidation step in the STC under the initial condition of H₂O: Mo= 2: 1.

As seen in Fig. 5, the oxidation products, H₂ and MoO₂, decrease gradually as the temperature rises at R_oxi = 2. This indicates that the low temperature operation in the oxidation step is more beneficial to obtain MoO₂ and H₂. This phenomenon can be explained by the fact that if the exothermic reaction releases more energy to the reaction temperature, the splitting reaction could be efficient. Thus, the low temperature region provides an advantageous thermochemical condition for H₂ production and MoO₂ recovery. As seen in Fig. 5, there is a H₂ production loss of 0.78 mol at T_oxi = 1200 K but no H₂ production loss at T_oxi = 400 K. Hence, R_oxi = 2 is not preferable for H₂ production. In Fig. 5, when T_oxi>1380 K and R_oxi = 4, the H₂ and MoO₂ productions decrease while the equilibrium amount of Mo increases. This indicates that excessive water is favorable to hydrogen production and MoO₂ recovery at a wider oxidation temperature range. However, the equilibrium amount of H₂, MoO₂, and Mo remain unchanged under 400 K<T_oxi<1600 K, and R_oxi≥6. This indicates that a water vapor of 6 mol is abundant for 1 mol MoO₂ recovery at 400 K<T_oxi<1600 K. Meanwhile, H₂O almost does not coexist with H₂ and MoO₂ as splitting temperature ranges from 400 to 600 K. Even though a small amount of water remains, it can be removed by some mature technologies such as condensation separation and drying agent. In addition, according to calculations, MoO₃, which is the by-production generated at T_oxi>1800 K, may have an impact on the stability of materials over many cycles of the two-step STC system and aiming at this, the calculations based on the data of the first cycle will continuously be checked. The following calculations of the second STC redox cycle indicates that a small amount of MoO₃ produced in the oxidation step can also be recycled into the pure Mo production in the solar reactor around T_Mo.

Here a comparison of maximum hydrogen production is made between methane reduction and direct dissociation at different values of T_red. For the direct dissociation reaction, the partial oxygen pressure labeled as {\mathit{p}}_{{\mathrm{O}}_2} is decreased by 10⁻⁴ to 10⁻⁷ bar. Moreover, T_red ranges from 1000 K to 3000 K with a temperature step of 500 K. Although decreasing {\mathrm{p}}_{{\mathrm{O}}_2} is favorable for dissociation reaction, there is no H₂ generating at T_red<2000 K. In addition, the further incremental temperature would lead to the melting of MoO₂ and Mo. However, as expressed in Eq. (3), the operating condition of a lower temperature range and atmospheric pressure would be achieved because of the declining temperature effect after introducing CH₄.

In Fig. 6, the maximum n_{{\mathrm{H}}_2} is equal to 2 mol at different values of T_red with the methane reduction. Although the maximum n_{{\mathrm{H}}_2} can reach 1.82 mol at p_{{\mathrm{O}}_2} = 10⁻⁷ bar without methane reduction, it is difficult to separate hydrogen from gas mixture of MoO₂/Mo because T_red is very high. Therefore, it can be verified that introducing methane in MoO₂ reduction step could increase hydrogen production and decrease the reduction temperature.

Evaluation of energetic upgrade factors

Because the chemical characteristic of STC system is net endothermic, the solar energy in radiation received from solar reactor would be transformed to chemical energy. The energetic upgrade factor, U, often used to evaluate the solar fuel HHV, is defined by

(15)U={\displaystyle \frac{n_{\mathrm{CO}}\cdot {\mathrm{HHV}}_{\mathrm{CO}}+n_{{\mathrm{H}}_{\mathrm{2}}}\cdot {\mathrm{HHV}}_{{\mathrm{H}}_{\mathrm{2}}}}{n_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}\cdot {\mathrm{HHV}}_{{\mathrm{CH}}_{\mathrm{4}}}}}.

Figure 7 displays the computational U at a wide temperature range of 600 K<T_red<1600 K, 400 K<T_oxi<1600 K, R_red = 2, and R_oxi = 2, 4, 6, and 8. By analyzing the temperature region of U>1 in Fig. 7 (a), it is known that the value of U can be influenced by T_red at R_oxi = 2 and R_red = 2. Besides, U>1.2 needs a low oxidation temperature (400 K≤T_oxi≤980 K) but an inversely high reduction temperature (1200 K≤T_red≤1600 K), which may go against the oxidation rate. By observing Figs. 7 (a) and 7(b), temperature distribution of U>1.2 is found to expand by T_oxi≤1580 K when R_oxi increases to 4, indicating that excessive water can enlarge the temperature range of U>1.2. In addition, a prominent feature is that U does not change with oxidation temperature when T_red>1220 K, R_oxi≥6. This could be explained by the fact that the amount of H₂ production does not change when 400 K<T_oxi<1600 K. And this is same reason for the fact that U does not change with T_oxi in Figs. 7(c) and 7(d), suggesting that the yields of H₂ and CO are stable at R_oxi≥6 and the same temperature, that is, the excess water has little effect on fuel production.

Evaluation of solar-to-fuel efficiencies

Besides the achievement of a high value of U, the maximization of solar-to-fuel efficiency, h_{solar-to-fuel}, is also essential for optimization of the STC system. Solar-to-fuel efficiency as an important evaluation criterion of economy is defined as the rate of the heat value of the fuel production and the solar energy input [²⁸].

(16){\eta }_{\mathrm{solar-to-fuel}}={\displaystyle \frac{(U-\mathrm{1}){\mathrm{HHV}}_{{\mathrm{CH}}_{\mathrm{4}}}{n}_{{\mathrm{CH}}_{\mathrm{4}}\mathrm{,ini}}}{Q_{\mathrm{total}}}},

where h_{solar-to-fuel} is meaningful when U>1, correspondingly at T_red>1020 K. Figure 8 shows the calculated values of h_{solar-to-fuel} related to 1020 K<T_red<1200 K, 400 K<T_oxi<1600 K, and a temperature step of 20 K. Hao et al. [²²] indicated the impact of high temperature on H₂ generation. In Fig. 8(a), the values of h_{solar-to-fuel} at T_red = 1200 K are larger than those at other T_red columns. h_{solar-to-fuel} at T_oxi = 400 K and T_red = 1200 K is almost the same as that at T_oxi = 600 K and T_red = 1200 K. For instance, h_{solar-to-fuel} is more sensitive to T_red than T_oxi around 0.0014≤h_{solar-to-fuel}≤0.4677. Comparing Figs. 8(a) and 8(b), the distributions of h_{solar-to-fuel} at R_oxi = 4 are almost entirely different from those at R_oxi = 2. Furthermore, the temperature distribution of h_{solar-to-fuel}>0.3 at R_oxi = 2 is 1100 K≤T_red≤1200 K and 400 K≤T_oxi≤740 K, whereas it locates at 1120 K≤T_red≤1200 K and 400 K≤T_oxi≤1360 K at R_oxi = 4. This indicates that a higher h_{solar-to-fuel} can be achieved under a wider oxidation temperature condition at R_oxi = 4. The corresponding cycle temperature range of h_{solar-to-fuel}≥0.3 (seen as the wine-colored part in Fig. 8) at R_oxi = 6 and 8 are smaller than that at R_oxi = 4. This can be explained by the fact that the excessive water consumes lots of transformation latent heat. The solar-to-fuel efficiency (h_{solar-to-fuel}<0.4) at R_oxi = 6 and 8 is lower than that at R_oxi = 2 and 4. Therefore R_oxi = 2 and 4 are preferable for energy conversion. Based on the calculations, the maximum h_{solar-to-fuel} at R_oxi = 2 and 4 is 0.468 and 0.417 respectively. This indicates that a higher efficiency is obtained at R_oxi = 2. However, as seen in Figs. 8(a) and 8(b), compared with the results at R_oxi = 2 and 4, h_{solar-to-fuel} decreases rapidly when T_oxi varies from 1200 K to 400 K at R_oxi = 2. These findings indicate that it is feasible to pursue a high h_{solar-to-fuel} and a smaller temperature interval between reduction and oxidation steps at R_oxi = 4.

Besides, the h_{solar-to-fuel} at isothermal operation is also analyzed. Isothermal operation means that the reduction step and the water splitting step are operated at the same temperature. Compared with the non-isothermal process, the isothermal cycle excludes the solid-phase heat recuperation and simplify the operation [²⁹]. However, isothermal operation is impractical and ineffcient for H₂ production [³⁰]. As seen in Fig. 9, which compares the results under the isothermal condition and at R_oxi = 2, 4, 6 and 8, the highest h_{solar-to-fuel} is 0.391 at R_oxi = 4 when T = 1200 K. From the calculations, when R_oxi = 2, h_{solar-to-fuel} can reach the maximum 0.180 at T = 1200 K, which is lower than the non-isothermal operation efficiency maximum (0.468) at the same R_oxi and R_red. Hence the non-isothermal operation discussed here is preferable to the utilization of energy. To sum up, H₂O: Mo= 4: 1 in the oxidation step is a desirable condition for the isothermal and non-isothermal STC redox cycle based on MoO₂/Mo.

Because part of Mo is transformed into MoO₃ instead of MoO₂ at the oxidation step, the energy conversion efficiency in the second STC redox cycle could be less than that in the first STC redox cycle. According to the equilibrium composition analyses of the reduction step in the second STC redox cycle, it could be determined that the same amount of pure Mo would be produced at T_red although a small amount of MoO₃ produced from the last oxidation step is recycled to reactants. Moreover, since R_oxi remains to be 4, the Mo-containing products at the second oxidation step are the same as those at the first oxidation step. Simultaneously, the Mo-containing reactants at the third reduction step, also the production at the second oxidation step, are exactly the same as those at the second reduction step. Logically, it can be concluded that the solar-to-fuel efficiency could remain constant from the third STC redox cycle under the ideal condition.

In addition, in order to figure out whether MoO₂ is recovered at the end of the first cycle, or affects the subsequent energy efficiency, the solar-to-fuel efficiency, h′_{solar-to-fuel}, of the second STC redox cycle is calculated and plotted in Fig. 10. It can be found that at T_red = 1200 K and T_oxi = 400 K, the largest value of h′_{solar-to-fuel} (0.454) is slightly larger than h_{solar-to-fuel} (0.417) in Fig. 8(b), indicating that the STC redox cycle presented here can be achieved at a high efficiency for a long time. The difference between h′_{solar-to-fuel} and h_{solar-to-fuel} could be explained by the C_p difference between MoO₂ and MoO₃, and the change of H₂ and CO production because of the generation of MoO₃. Apparently, since C_{\mathrm{p},\mathrm{M}\mathrm{o}{\mathrm{O}}_3} is less than C_{\mathrm{p},\mathrm{M}\mathrm{o}{\mathrm{O}}_2} at 400 K<T_oxi<1200 K and parts of MoO₂ are replaced by MoO₃ at the second reduction step, and the input solar energy could be reduced at the second STC redox cycle, optimizing the solar-to-fuel efficiency of STC cycle. However, compared with the first cycle, the fuel production could decrease because the mixture of MoO₂ and MoO₃ has a smaller capacity at the second reduction step. This indicates that less solar energy is transformed into chemical energy relatively.

Conclusions

In this paper, a two-step STC system with CH₄ reduction based on MoO₂/Mo is studied. The thermal properties of the equilibrium components at different temperatures and reactant ratios, energetic upgrade factor, and comparison between the isothermal and non-isothermal solar-to-fuel efficiency are underscored.

The results show that methanothermal reduction can greatly reduce the operating temperature and is favorable for hydrogen production. R_red = 2 and 940 K<T_red<1600 K are beneficial for system performance and higher values of S_H2 and S_CO. By analyzing the effect of excessive water vapors on the oxidation step, it is found that it is not necessary to input water more than six times the amount of solid Mo because fuel production is stable at R_oxi≥6. In addition, by investigating the distribution of the U value with temperature at R_oxi = 2, 4, 6, and 8, it is found that T_red>1220 K is productive and consistent to U>1.2 when R_oxi≥6. Comparing the U distribution in the oxidation step, it is found that excessive water is beneficial for increasing fuel production, but the effect is diminished when R_oxi≥6 at the same temperature. However, by analyzing the solar-to-fuel efficiency at 1020 K<T_red<1200 K and 400 K<T_oxi<1600 K, it is found that h_{solar-to-fuel} is more influenced by T_oxi at R_oxi = 2 than that at R_oxi = 4, 6, and 8. Besides, the distributions of 0.3<h_{solar-to-fuel}<0.4 at R_oxi = 6 and 8 are smaller when compared with the results at R_oxi = 4. Moreover, comparing the effects of isothermal and non-isothermal operation on efficiency, it can be concluded that the non-isothermal efficiency at R_oxi = 4 and T_red = 1200 K, T_oxi = 400 K is the highest efficiency (0.417) while solar-to-fuel efficiency at isothermal operation is no more than 0.391 at T = 1200 K. Hence, it is preferable to choosing R_oxi = 4 and non-isothermal operation as the working conditions. Furthermore, the solar-to-fuel efficiency of the second STC cycle is calculated. When oxidation temperature is equal to 1200 K, h_{solar-to-fuel} (0.391) is smaller than h'_{solar-to-fuel} (0.422). Additionally, the h'_{solar-to-fuel} of the second cycle can reach 0.454 under non-isothermal operation, which is more than the h_{solar-to-fuel} (0.417) of the first cycle at T_red = 1200 K and T_oxi = 400 K. These findings show that the proposed STC cycle based on MoO₂/Mo paired with the methane reduction is practicable for hydrogen production.

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