# Solar Thermochemical Hydrogen Production via Terbium Oxide Based Redox Reactions

Authors: Rahul Bhosale; Anand Kumar; Fares AlMomani
Journal: International Journal of Photoenergy
 (2016)

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## Abstract

The computational thermodynamic modeling of the terbium oxide based two-step solar thermochemical water splitting (Tb-WS) cycle is reported. The 1st step of the Tb-WS cycle involves thermal reduction of TbO2 into Tb and O2, whereas the 2nd step corresponds to the production of H2 through Tb oxidation by water splitting reaction. Equilibrium compositions associated with the thermal reduction and water splitting steps were determined via HSC simulations. Influence of oxygen partial pressure in the inert gas on thermal reduction of TbO2 and effect of water splitting temperature (TL) on Gibbs free energy related to the H2 production step were examined in detail. The cycle (ηcycle) and solar-to-fuel energy conversion (ηsolar-to-fuel) efficiency of the Tb-WS cycle were determined by performing the second-law thermodynamic analysis. Results obtained indicate that ηcycle and ηsolar-to-fuel increase with the decrease in oxygen partial pressure in the inert flushing gas and thermal reduction temperature (TH). It was also realized that the recuperation of the heat released by the water splitting reactor and quench unit further enhances the solar reactor efficiency. At TH=2280 K, by applying 60% heat recuperation, maximum ηcycle of 39.0% and ηsolar-to-fuel of 47.1% for the Tb-WS cycle can be attained.


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## Body

## 1. Introduction

H2 is considered as one of the most promising future energy sources as it is characterized by a very high energy density (143 MJ/kg) and environmentally clean utilization. H2 can be produced by gasification and reforming of fossil fuels [1–3], pyrolysis and reforming of biomass [4–7], ethanol and methanol decomposition [8–11], and so forth. Literature survey indicates that, in recent years, the researchers are attracted more towards production of H2 from water by using solar energy as the heat source.Solar radiation is an essentially inexhaustible energy source that delivers about 100,000 TW to the earth. Harvesting the solar radiation and converting it effectively into renewable H2 fuel from H2O provide a promising path for a future sustainable energy economy. Solar H2 production via metal oxide (MO) based thermochemical H2O splitting reaction is considered as one of the capable new technologies for fulfillment of future energy requirement. In comparison to the high temperature direct thermolysis of H2O, the MO based thermochemical cycle is advantageous as (a) this cycle needs lower temperatures as compared to thermolysis, (b) it has no explosive mixture formation as the production of H2 and O2 can be carried out in two different steps, and (c) it is environmentally and thermodynamically more feasible compared to thermolysis.Production of solar H2 via MO based thermochemical reactions is a two-step process. In the first step, the MO is reduced into a lower valence MO or metal with the help of solar energy. The reduced MO is further reoxidized in the second step via H2O splitting reaction. Several MO based redox systems were theoretically and experimentally studied towards thermochemical water splitting reaction which includes ZnO/Zn cycle [12–15], Fe3O4/FeO cycle [16–20], SnO2/SnO cycle [21–23], ferrite cycle [24–30], ceria cycle [31–36], and perovskite cycle [37–41]. Previous investigations indicate that these cycles are promising towards solar water splitting reaction but possess certain imitations also. The ZnO/Zn and SnO2/SnO cycles are volatile in nature and hence material loss during multiple cycles is inevitable. On the other hand, Fe3O4/FeO, ferrite, ceria, and perovskite cycles depend upon the nonstoichiometry of the redox materials and hence the complete reduction and oxidation were not observed which resulted in the fact that smaller amounts of H2 production were observed. Due to these reasons, investigations are underway to explore new thermochemical cycles for the production of H2 via water splitting reaction.In this study, computational thermodynamic modeling of a new terbium oxide based two-step solar thermochemical water splitting (Tb-WS) cycle was performed to determine its thermodynamic efficiency by using HSC Chemistry software and databases (HSC 7.1). Thermodynamic equilibrium composition of the solar thermal reduction of terbium oxide (step 1) and water splitting reaction (step 2) were determined. Effect of oxygen partial pressure in the inert flushing gas used inside the solar reactor during thermal reduction step on thermodynamic efficiency of the process was explored in detail. Furthermore, the effect of water splitting temperature (TL) on Gibbs free energy associated with the oxidation of Tb (via water splitting reaction) was also explored. In addition to the thermodynamic equilibrium analysis, the solar reactor thermodynamic modeling was also carried out. Absorption efficiency of the solar reactor, solar energy input required to run the Tb-WS cycle, heat losses due to radiation, rate of heat rejected by the quench unit and water splitting reactor, Tb-WS cycle efficiency, and solar-to-fuel energy conversion efficiency were estimated. Typical redox reactions involved in the Tb-WS cycle are presented in Figure 1.Figure 1
Typical redox reactions involved in the Tb-WS cycle.The redox reactions involved in the Tb-WS cycle are as follows:(1)TbO2⟶Tbg+O2g(2)Tb+2H2Og⟶TbO2+2H2gThermodynamic data associated with TbO2, Tb, O2, H2O, and H2 as the reactive species were taken from HSC and the analysis was performed by assuming continuous operation of the solar reactor with inlet molar flow rate of TbO2 equal to 1 mol/sec. The boiling and fusion points for Tb are 1629 and 3396 K, respectively. Similar to other lanthanides, Tb possesses low toxicity. According to Patnaik [42], the crust global abundance of Tb is estimated to be 1.2 mg/kg.


## 2. Equilibrium Thermodynamic Analysis

Previous investigations associated with the production of solar fuels via MO based thermochemical reactions indicate that the heat energy that is thermal reduction temperature (TH) required to achieve complete reduction of MOs can be decreased if ultra-high purity inert flushing gas with lower oxygen partial pressures in the range of 10−3 to 10−8 atm is used during the reduction step inside the solar reactor [43, 44]. The effect of oxygen partial pressure in the inert flushing gas on thermal reduction of TbO2 was examined in this study and the results are reported in Figure 2. The reported findings indicate that, similar to the previous MO cycles, TH required for the thermal reduction of TbO2 can be lowered due to the drop in the oxygen partial pressure in the inert flushing gas. For example, at oxygen partial pressure of 10−5 atm, TH required for the complete dissociation of TbO2 is equal to 2780 K. TH can be decreased by 80, 260, and 500 K if the oxygen partial pressure in the inert flushing gas is reduced to 10−6, 10−7, and 10−8 atm, respectively.Figure 2
Influence of oxygen partial pressure in the inert flushing gas onTH for Tb-WS cycle.In addition toTH, the effect of oxygen partial pressure in the inert flushing gas on equilibrium compositions associated with the thermal reduction of TbO2 was also investigated. HSC simulations reported in Figure 3 indicate that the slope of the decrease in the equilibrium concentration of TbO2 and increase in the equilibrium concentration of Tb(g) is shifted significantly towards the lower TH due to the decrease in the oxygen partial pressure in the inert flushing gas. The possible reason behind this shift is the reduction in the entropy of the product gases due to the drop in the oxygen partial pressure in the inert flushing gas used inside the solar reactor.Figure 3
Influence of oxygen partial pressure in the inert flushing gas on equilibrium compositions associated with the thermal reduction of TbO2.As per the HSC simulations, formation of Tb2O3 is an intermediate step in the thermal reduction of TbO2 into Tb(g) and O2(g). In addition, it was observed that the Tb formation is achieved only after decomposition of Tb2O3. Hence, as we are dealing with the final products, there is no need to consider Tb2O3 in the thermodynamic analysis. Therefore, Tb2O3 is not included in this study.Figure4 shows the variation in the Gibbs free energy related to the water splitting reaction as a function of TL. The Gibbs free energy change plot indicates that the hydrogen production via water splitting reaction and oxidation of Tb is feasible below 5400 K (pressure = 1 atm). It was also observed that ΔGWS decreases by 434.5 kJ/mol due to the drop in TL from 5400 to 300 K.Figure 4
Variation in Gibbs free energy as a function ofTL for Tb-WS cycle.


## 3. Tb-WS Solar Reactor Thermodynamic Modeling

Solar reactor operating the Tb-WS cycle was thermodynamically modeled by using the principles of the second law of thermodynamics. Figure5 shows the process flow configuration of the Tb-WS cycle which includes a solar reactor, a quench unit, a water splitter, and an ideal H2/O2 fuel cell. Like the previous studies, for the solar reactor thermodynamic modeling, several assumptions were made such as the following [20]:(a)
The Tb-WS solar reactor considered as a perfectly insulated blackbody absorber with effective emissivity and absorptivity equal to 1 and negligible conductive convective heat losses.(b)
Atmospheric H2 production and steady state conditions with negligible viscous losses and kinetics/potential energies.(c)
Complete conversion of all the reactions associated with the Tb-WS cycle.(d)
Products separating naturally without laying out any work.(e)
Omission of heat exchanger required for recovering the sensible latent heat from the thermodynamic modeling.Figure 5
Process flow diagram for H2 production via Tb-WS cycle.Previously reported methodology was employed to perform the solar reactor modeling [20]. HSC Chemistry software and databases were used to get the thermodynamic properties of the reactive species and the calculations are normalized to the TbO2 molar flow rate (1 mol/sec) entering the solar reactor.The solar reactor absorption efficiency (ηabsorption), which is defined as the net rate at which energy is being absorbed by the solar reactor divided by the solar energy input through the aperture, can be calculated as per(3)ηabsorption=1-σTH4IC,where  I is direct-normal solar irradiance (normal bean insolation) (W/m2), C is solar flux concentration ratio (ratio of the solar flux intensity achieved after concentration to the normal beam insolation, dimensionless number) (suns), TH is solar reactor temperature required for the thermal reduction of TbO2 (K), and σ is Stefan-Boltzmann constant which is equal to 5.6705×10-8 (W/m2·K4).Figure6 indicates a significant improvement in ηabsorption due to the reduction in TH and oxygen partial pressure in the inert flushing gas used inside the solar reactor decreases. At oxygen partial pressure in the inert flushing gas of 10−5 atm, the required TH is 2780 K and corresponding ηabsorption is 66.1%. As the oxygen partial pressure in the inert flushing gas is further lowered to 10−7 atm, TH can be decreased to 2520 K and ηabsorption can be increased up to 77.1%. As per the conditions employed in this study, the maximum ηabsorption that can be achieved is equal to 84.7% (oxygen partial pressure in the inert flushing gas is 10−8 atm and TH is 2280 K).Figure 6
Effect ofTH on ηabsorption.In addition to the oxygen partial pressure in the inert flushing gas andTH, C also has a significant impact on ηabsorption. At oxygen partial pressure of 10−8 atm and TH of 2280 K, the lower values of C (2000 suns) yield ηabsorption of 23.4%. As the value of C increases up to 3000 to 5000 suns, ηabsorption can get enhanced up to 48.9% and 69.3%, respectively.The net energy required to operate the Tb-WS solar reactor can be determined according to the following equations:(4)Qreactor-net=QTbO2-heating+QTbO2-reduction(5)QTbO2-heating=n˙ΔHTbO2@TL→TbO2@TH(6)QTbO2-reduction=n˙ΔHTbO2@TH→Tb+O2(g)@TH.The variation in Qreactor-net with respect to the change in TH is presented in Figure 7. Presented results indicate that the required Qreactor-net decreases with the drop in TH and oxygen partial pressure in the inert flushing gas. As TH is reduced from 2780 K (oxygen partial pressure in the inert flushing gas of 10−5 atm) to 2280 K (oxygen partial pressure in the inert flushing gas of 10−8 atm), Qreactor-net is also lowered from 1543.0 kW to 1499.2 kW, respectively.Figure 7
Effect ofTH on (a) Qsolar and (b) Qreactor-net.By using the calculatedηabsorption and Qreactor-net, total amount of solar energy required for the operation of the Tb-WS cycle can be estimated as(7)Qsolar=Qreactor-netηabsorption.The decrease in Qsolar as a function of reduction in TH and oxygen partial pressure in the inert flushing gas is shown in Figure 7. 2333.2 kW of solar energy is required for the operation of Tb-WS cycle when the oxygen partial pressure in the inert flushing gas is equal to 10−5atm (TH = 2780 K). Qsolar is reduced to 1970.3 kW as the oxygen partial pressure in the inert flushing gas is lowered to 10−7atm (TH = 2520 K). As per the modeling conditions employed in this study, the minimum Qsolar (1770.5 kW) is possible at oxygen partial pressure in the inert flushing gas of 10−8atm (TH = 2280 K). The reason behind this drop in Qsolar is the elevation in ηabsorption due to the fall in TH from 2780 to 2280 K as the oxygen partial pressure in the inert flushing gas is reduced from 10−5 to 10−8 atm.Radiation heat losses from the Tb-WS solar reactor are unavoidable as the operating temperatures are very high. These losses can be calculated as(8)Qreradiation=Qsolar-Qreactor-net.The radiation heat losses associated with the Tb-WS cycle are presented in Figure 8(a). The plot shown indicates that, at TH = 2780 K, 790.2 kW of heat is lost from the solar reactor due to the reradiation. However, the radiation losses are decreased due to the lowering of TH. For instance, at TH = 2280 K, only 271.3 kW of reradiation losses is reported as per the thermodynamic modeling. This is again due to the fact that ηabsorption of the Tb-WS solar reactor is higher at lower TH.Figure 8
Effect ofTH on (a) Qreradiation and (b) Qquench.
(a)
(b)Solar thermal reduction of TbO2 yields Tb(g) and O2(g). As the operating temperatures are very high, these compounds will try to recombine and reform the TbO2. Therefore, it is highly essential to quench these compounds from TH to TL to avoid any recombination. During quenching, it is assumed that the chemical composition of the products remains unaltered. Due to quenching Tb(g) is cooled down to solid Tb and automatically gets separated from O2(g). Also, during quenching, latent and sensible heat will be lost to the surroundings from the quench unit which can be estimated as(9)Qquench=-n˙ΔHTbg+O2g@TH→Tbs+O2g@TL.The data reported in Figure 8(b) indicates that higher amount of heat is lost due to quenching (571.4 kW) when TH is 2780 K (oxygen partial pressure in the inert flushing gas is 10−5 atm). However, as TH is decreased to 2280 K due to the lowering of oxygen partial pressure in the inert flushing gas (10−8 atm), the heat lost is reduced by 43.8 kW.Because of the irreversible chemical transformations and reradiation losses, the irreversibilities generated in the solar reactor and the quench unit can be determined as(10)Irrreactor=-QsolarTH+Qreradiation298+n˙ΔSTbO2@TL→Tbg+O2(g)@TH(11)Irrquench=Qquench298+n˙ΔSTbg+O2(g)@TH→Tbs+O2(g)@TL.Table 1 lists the Irrreactor and Irrquench values as a function of TH. From the reported numbers, it can be seen that, in case of both the Tb-WS solar reactor and quench unit, Irrreactor and Irrquench values are maximum at higher TH and decrease with the reduction in TH. For instance, Irrreactor and Irrquench can be lowered by 73.8% and 7.8% due to the drop in TH from 2780 to 2280 K.Table 1
Irrreactor and Irrquench as a function of TH for Tb-WS cycle.
T
H (K)
Irrreactor (kW/K)
Irrquench  (kW/K)
2780
2.3
1.6
2700
1.9
1.6
2520
1.2
1.5
2280
0.6
1.5H2 generation via water splitting reaction can be carried out at TL of 298 K by transferring the Tb obtained after the quench unit to the water splitting reactor. The water splitting is an exothermic reaction and hence the rate of heat rejected to the surroundings from the water splitting reactor is estimated as being equal to 399.8 kW according to (12)QTb  oxidation=-n˙ΔHTb+2H2O→TbO2+2H2(g)@TL.Similarly, the irreversibility associated with the water splitting reaction is estimated (1.5 kW/K) by solving (13)IrrSm  oxidation=QSm  oxidation298+n˙ΔSTb+2H2O→TbO2+2H2(g)@TL.To determine the maximum work that can be extracted from the H2 generated, an ideal H2/O2 fuel cell with 100% work efficiency is added to the Tb-WS cycle. According to (14) and (15), it was observed that the theoretical work performed and heat energy released by the ideal fuel cell are equal to 473.9 and 97.3 kW:(14)WFC-Ideal=-n˙ΔG2H2g+O2g→2H2Ol@298K(15)QFC-Ideal=-298n˙ΔS2H2g+O2g→2H2Ol@298K.The cycle (ηcycle⁡) and solar-to-fuel conversion (ηsolar-to-fuel) efficiency of the Tb-WS cycle can be defined as(16)ηcycle⁡=WFC-IdealQsolar(17)ηsolar-to-fuel=HHVH2Qsolar.Variation inηcycle⁡ and ηsolar-to-fuel of the Tb-WS cycle as a function of TH is presented in Figure 9. The data reported indicate ηcycle⁡ of 20.3% and ηsolar-to-fuel of 24.5% at TH of 2780 K. However, at lower TH (2280 K), higher ηcycle⁡ (26.8%) and ηsolar-to-fuel (32.3%) can be achieved. ηsolar-to-fuel of the Tb-WS cycle at TH of 2280 K is comparable to the efficiency values reported by previous investigators in case of ZnO/Zn cycle (29%), SnO2/SnO cycle (29.8%), Fe3O4/FeO cycle (30%), and ceria cycle (20.2%).Figure 9
η
cycle
⁡ and ηsolar-to-fuel as a function of TH.η
cycle
⁡ and ηsolar-to-fuel of Tb-WS cycle can be increased further by reutilizing the heat released by the water splitting reactor and quench unit. The amount of heat that can be recuperated is calculated as(18)Qrecuperable=Qquench+QSm  oxidation.As the heat released by the water splitting reactor and quench unit is recycled to run the Tb-WS cycle, the amount of solar energy required will be decreased as(19)Qsolar,with  recuperation=Qsolar-%recuperationQrecuperable.In case of TH of 2280 K, Figure 10 shows that as the % heat recuperation increases, Qrecuperable enhances whereas Qsolar,withrecuperation diminishes. At 10% heat recuperation, Qsolar,withrecuperation is equal to 1677.8 kW, which can be decreased to 1306.8 kW due to the increase in the heat recuperation up to 50%.Figure 10
Effect of % heat recuperation onQsolar,withrecuperation and Qrecuperable (TH = 2280 K).
(a)
(b)After applying the heat recuperation,ηcycle⁡ and ηsolar-to-fuel associated with the Tb-WS cycle can be calculated as(20)ηcycle⁡=WFC-IdealQsolar,with  recuperation(21)ηsolar-to-fuel=HHVH2Qsolar,with  recuperation.Table2 reports ηcycle⁡ and ηsolar-to-fuel of Tb-WS cycle for different TH and by applying 10 to 50% heat recuperation. For the data listed, it can be seen that, due to the inclusion of heat recuperation, both ηcycle⁡ and ηsolar-to-fuel of Tb-WS cycle are significantly improved. For instance, by applying 20% heat recuperation at TH of 2280 K, ηcycle⁡ and ηsolar-to-fuel can be increased up to 23.5 and 28.4%. Likewise, at heat recuperation of 60% and TH of 2280 K, ηcycle⁡ and ηsolar-to-fuel can get enhanced up to 39.0 and 47.1%.Table 2
η
cycle
⁡ and ηsolar-to-fuel of Tb-WS cycle.
T
H (K)
η
cycle
⁡ (%)
η
solar-to-fuel (%)
Recuperation = 0%
2780
20.3
24.5
2700
21.4
25.9
2520
24.0
29.0
2280
26.7
32.3
Recuperation = 20%
2780
22.1
26.7
2700
23.5
28.3
2520
26.6
32.1
2280
29.9
36.0
Recuperation = 40%
2780
24.3
29.4
2700
26.0
31.4
2520
29.7
35.9
2280
33.8
40.8
Recuperation = 60%
2780
27.0
32.6
2700
29.1
35.1
2520
33.8
40.8
2280
39.0
47.1According to the previous studies, the heat recuperation is highly essential to achieve higher efficiency values in case of metal oxide based solar thermochemical cycles [12, 14, 15, 17, 18, 43, 44]. In the past, attempts were made to achieve the heat recuperation in a real-life solar reactor system. For instance, Diver et al. [45] developed a heat recovery system for iron oxide cycle by using a stack of counter-rotating rings with the reactive material along the perimeter of each ring. In this system, the reactive surfaces act as extended heat transfer surfaces to achieve heat recuperation. Similarly, in case of Tb-WS cycle, heat exchangers can be coupled with the quench unit and water splitting reactor to recover the latent and sensible heat rejected by these units. Suitable heat exchanger fluid needs to be selected and the heat rejected by quench unit (due to the cooling of the thermal reduction products) and water splitting reactor (due to the exothermic splitting of water) can be stored in this fluid. This fluid can be recirculated throughout the process configuration shown in Figure 5 and the captured heat can be reutilized to run the Tb-WS cycle.The solar reactor thermodynamic modeling performed in this paper is also verified by performing an energy balance and by evaluating the maximum achievable efficiency from the total available work and from the total solar power input. The energy balance performed in case of Tb-WS cycle (for allTH) confirms that(22)WFC-Ideal=Qsolar-Qreradiation+Qquench+QSm  oxidation+QFC-Ideal.As an example, at TH of 2280 K, (22) indicates WFC-Ideal of 473.9 kW which is equal to WFC-Ideal determined by (14). Furthermore, the maximum cycle efficiency is also calculated according to(23)ηcycle⁡,maximum=WFC-Ideal+TLIrrreactor+Irrquench+IrrSm  oxidationQsolar.For all TH, it was observed that ηcycle,maximum is equal to the Carnot heat engine operating between hot and cold temperature reservoirs:(24)ηcycle,maximum=1-TLTH=ηcarnot.For instance, at TH of 2280 K and TL of 298 K, ηcycle,maximum is 86.9% which is equal to ηcarnot = 86.9%.


## 4. Summary and Conclusions

Solar reactor efficiency analysis of the Tb-WS cycle for the production of H2 via water splitting reaction was conducted by using HSC Chemistry software and databases. Simulation results indicate that the heat energy required for the complete reduction of TbO2 into Tb and O2 can be reduced significantly from 2780 to 2280 K by decreasing the oxygen partial pressure in the inert flushing gas from 10−5 to 10−8 atm. According to the simulations, the water splitting reaction via Tb oxidation is feasible below 5400 K.Exergy analysis shows thatηabsorption of the Tb-WS solar reactor can be increased by a factor of 1.28 due to the decrease in TH from 2780 to 2280 K. It was also observed that Qreactor-net and Qsolar can be reduced by 43.8 and 562.7 kW with the lowering of TH from 2780 to 2280 K. Similarly, due to the similar fall in TH, the quenching and reradiation heat losses can be dropped by 7.7 and 65.7%, respectively. The reason for the lower amounts of solar energy requirement and reduction in the heat loss via quenching and reradiation is due to the fact that ηabsorptionof the Tb-WS solar reactor improves with the decrease in TH. ηcycle⁡ of 23.5% and ηsolar-to-fuel of 28.4% of Tb-WS cycle at TH of 2280 K are observed to be comparable to the previously investigated MO cycles. Furthermore, ηcycle⁡ and ηsolar-to-fuel can be further increased up to 39.0% and 47.1% by recuperating 60% of the heat rejected by the quench unit and water splitting reactor.



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