Solar Thermochemical Hydrogen Production via Terbium Oxide Based Redox Reactions

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 TbO 2 into Tb and O 2 , whereas the 2nd step corresponds to the production of H 2 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 TbO 2 and effect of water splitting temperature (T L ) on Gibbs free energy related to the H 2 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 (T H ). 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 T H = 2280K, 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.


Introduction
H 2 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.H 2 can be produced by gasification and reforming of fossil fuels [1][2][3], pyrolysis and reforming of biomass [4][5][6][7], ethanol and methanol decomposition [8][9][10][11], and so forth.Literature survey indicates that, in recent years, the researchers are attracted more towards production of H 2 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 H 2 fuel from H 2 O provide a promising path for a future sustainable energy economy.Solar H 2 production via metal oxide (MO) based thermochemical H 2 O 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 H 2 O, 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 H 2 and O 2 can be carried out in two different steps, and (c) it is environmentally and thermodynamically more feasible compared to thermolysis.
Production of solar H 2 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 H 2 O splitting reaction.Several MO based redox systems were theoretically and experimentally studied towards thermochemical water splitting reaction which includes ZnO/Zn cycle [12][13][14][15], Fe 3 O 4 /FeO cycle [16][17][18][19][20], SnO 2 /SnO cycle [21][22][23], ferrite cycle [24][25][26][27][28][29][30], ceria cycle [31][32][33][34][35][36], and perovskite cycle [37][38][39][40][41].Previous investigations indicate that these cycles are promising towards solar water splitting reaction but possess certain imitations also.The ZnO/Zn and SnO 2 /SnO cycles are volatile in nature and hence material loss during multiple cycles is inevitable.On the other hand, Fe 3 O 4 /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 H 2 production were observed.Due to these reasons, investigations are underway to explore new thermochemical cycles for the production of H 2 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 (  ) 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.
The redox reactions involved in the Tb-WS cycle are as follows: Tb Thermodynamic data associated with TbO 2 , Tb, O 2 , H 2 O, and H 2 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 TbO 2 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.

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 (  ) 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 TbO 2 was examined in this study and the results are reported in Figure 2. The reported findings indicate that, similar to the previous MO cycles,   required for the thermal reduction of TbO 2 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,   required for the complete dissociation of TbO 2 is equal to 2780 K.   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.
In addition to   , the effect of oxygen partial pressure in the inert flushing gas on equilibrium compositions associated with the thermal reduction of TbO 2 was also investigated.HSC simulations reported in Figure 3 indicate that the slope of the decrease in the equilibrium concentration of TbO 2 and increase in the equilibrium concentration of Tb(g) is shifted significantly towards the lower   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.
As per the HSC simulations, formation of Tb 2 O 3 is an intermediate step in the thermal reduction of TbO 2 into Tb(g) and O 2 (g).In addition, it was observed that the Tb formation is achieved only after decomposition of Tb 2 O 3 .Hence, as we are dealing with the final products, there is no need to consider Tb 2 O 3 in the thermodynamic analysis.Therefore, Tb 2 O 3 is not included in this study.Figure 4 shows the variation in the Gibbs free energy related to the water splitting reaction as a function of   .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 Δ WS decreases by 434.5 kJ/mol due to the drop in   from 5400 to 300 K.

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.Figure 5 shows the process flow configuration of the Tb-WS cycle which includes a solar reactor, a quench unit, a water splitter, and an ideal H 2 /O 2 fuel cell.Like the previous studies, for the solar reactor thermodynamic modeling, several assumptions were made such as the following [20]: (e) Omission of heat exchanger required for recovering the sensible latent heat from the thermodynamic modeling.
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 TbO 2 molar flow rate (1 mol/sec) entering the solar reactor.
The solar reactor absorption efficiency ( absorption ), 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 where  is direct-normal solar irradiance (normal bean insolation) (W/m 2 ),  is solar flux concentration ratio (ratio of the solar flux intensity achieved after concentration to the normal beam insolation, dimensionless number) (suns),   is solar reactor temperature required for the thermal reduction of TbO 2 (K), and  is Stefan-Boltzmann constant which is equal to 5.6705 × 10 −8 (W/m 2 ⋅K 4 ). Figure 6 indicates a significant improvement in  absorption due to the reduction in   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   is 2780 K and corresponding  absorption is 66.1%.As the oxygen partial pressure in the inert flushing gas is further lowered to 10 −7 atm,   can be decreased to 2520 K and  absorption can be increased up to 77.1%.As per the conditions employed in this study, the maximum  absorption that can be achieved is equal to 84.7% (oxygen partial pressure in the inert flushing gas is 10 −8 atm and   is 2280 K).
In addition to the oxygen partial pressure in the inert flushing gas and   ,  also has a significant impact on  absorption .At oxygen partial pressure of 10 −8 atm and   of 2280 K, the lower values of  (2000 suns) yield  absorption of 23.4%.As the value of  increases up to 3000 to 5000 suns,  absorption 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: TbO 2 -heating = ṅ Δ| TbO 2 @  → TbO 2 @  (5) The variation in  reactor-net with respect to the change in   is presented in Figure 7. Presented results indicate that the required  reactor-net decreases with the drop in   and oxygen partial pressure in the inert flushing gas.As   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),  reactor-net is also lowered from 1543.0 kW to 1499.2 kW, respectively.By using the calculated  absorption and  reactor-net , total amount of solar energy required for the operation of the Tb-WS cycle can be estimated as The decrease in  solar as a function of reduction in   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 −5 atm (  = 2780 K).  solar is reduced to 1970.3 kW as the oxygen partial pressure in the inert flushing gas is lowered to 10 −7 atm (  = 2520 K).
As per the modeling conditions employed in this study, the minimum  solar (1770.5 kW) is possible at oxygen partial pressure in the inert flushing gas of 10 −8 atm (  = 2280 K).The reason behind this drop in  solar is the elevation in  absorption due to the fall in   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 The radiation heat losses associated with the Tb-WS cycle are presented in Figure 8(a).The plot shown indicates that, at   = 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   .For instance, at   = 2280 K, only 271.3 kW of reradiation losses is reported as per the thermodynamic modeling.This is again due to the fact that  absorption of the Tb-WS solar reactor is higher at lower   .Solar thermal reduction of TbO 2 yields Tb(g) and O 2 (g).As the operating temperatures are very high, these compounds will try to recombine and reform the TbO 2 .Therefore, it is highly essential to quench these compounds from   to   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 O 2 (g).Also, during quenching, latent and sensible heat will be lost to the surroundings from the quench unit which can be estimated as The data reported in Figure 8(b) indicates that higher amount of heat is lost due to quenching (571.4 kW) when   is 2780 K (oxygen partial pressure in the inert flushing gas is 10 −5 atm).
International Journal of Photoenergy However, as   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 + ṅ Δ| TbO 2 @  → Tb(g)+O 2 (g)@  (10) Irr quench = (  quench

)
+ ṅ Δ| Tb(g)+O 2 (g)@  → Tb(s)+O 2 (g)@  . ( Table 1 lists the Irr reactor and Irr quench values as a function of   .From the reported numbers, it can be seen that, in case of both the Tb-WS solar reactor and quench unit, Irr reactor and Irr quench values are maximum at higher   and decrease with the reduction in   .For instance, Irr reactor and Irr quench can be lowered by 73.8% and 7.8% due to the drop in   from 2780 to 2280 K. H 2 generation via water splitting reaction can be carried out at   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 Similarly, the irreversibility associated with the water splitting reaction is estimated (1.5 kW/K) by solving Irr Sm oxidation = (  Sm oxidation 298 ) Efficiency (%) To determine the maximum work that can be extracted from the H 2 generated, an ideal H 2 /O 2 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: The cycle ( cycle ) and solar-to-fuel conversion ( solar-to-fuel ) efficiency of the Tb-WS cycle can be defined as Variation in  cycle and  solar-to-fuel of the Tb-WS cycle as a function of   is presented in Figure 9.The data reported International Journal of Photoenergy   cycle and  solar-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 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 In case of   of 2280 K, Figure 10 shows that as the % heat recuperation increases,  recuperable enhances whereas  solar,with recuperation diminishes.At 10% heat recuperation,  solar,with recuperation 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%.According 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 all   ) confirms that  FC-Ideal =  solar − ( reradiation +  quench +  Sm oxidation +  FC-Ideal ) .

(22)
As an example, at   of 2280 K, (22) indicates  FC-Ideal of 473.9 kW which is equal to  FC-Ideal determined by (14).Furthermore, the maximum cycle efficiency is also calculated according to For all   , it was observed that  cycle,maximum is equal to the Carnot heat engine operating between hot and cold temperature reservoirs: For instance, at   of 2280 K and   of 298 K,  cycle,maximum is 86.9% which is equal to  carnot = 86.9%.

Summary and Conclusions
Solar reactor efficiency analysis of the Tb-WS cycle for the production of H 2 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 TbO 2 into Tb and O 2 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 that  absorption of the Tb-WS solar reactor can be increased by a factor of 1.28 due to the decrease in   from 2780 to 2280 K.It was also observed that  reactor-net and  solar can be reduced by 43.8 and 562.7 kW with the lowering of   from 2780 to 2280 K. Similarly, due to the similar fall in   , 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  absorption of the Tb-WS solar reactor improves with the decrease in   . cycle of 23.5% and  solar-to-fuel of 28.4% of Tb-WS cycle at   of 2280 K are observed to be comparable to the previously investigated MO cycles.Furthermore,  cycle and  solar-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.

𝐶:
Solar flux concentration ratio, suns HHV: Higher heating value : Normal beam solar insolation, W/m

Figure 1 :
Figure 1: Typical redox reactions involved in the Tb-WS cycle.

Figure 2 :
Figure 2: Influence of oxygen partial pressure in the inert flushing gas on   for Tb-WS cycle.

Figure 3 :Figure 4 :
Figure 3: Influence of oxygen partial pressure in the inert flushing gas on equilibrium compositions associated with the thermal reduction of TbO 2 .

Figure 5 :
Figure 5: Process flow diagram for H 2 production via Tb-WS cycle.

Figure 6 :
Figure 6: Effect of   on  absorption .

Figure 7 :
Figure 7: Effect of   on (a)  solar and (b)  reactor-net .

Figure 9 :
Figure 9:  cycle and  solar-to-fuel as a function of   .

Table 1 :
Irr reactor and Irr quench as a function of   for Tb-WS cycle. cycle of 20.3% and  solar-to-fuel of 24.5% at   of 2780 K.However, at lower   (2280 K), higher  cycle (26.8%)and  solar-to-fuel (32.3%) can be achieved. solar-to-fuel of the Tb-WS cycle at   of 2280 K is comparable to the efficiency values reported by previous investigators in case of ZnO/Zn cycle (29%), SnO 2 /SnO cycle (29.8%),Fe 3 O 4 /FeO cycle (30%), and ceria cycle (20.2%).

Table 2 :
cycle and  solar-to-fuel of Tb-WS cycle.After applying the heat recuperation,  cycle and  solar-to-fuel associated with the Tb-WS cycle can be calculated as

Table 2 reports
cycle and  solar-to-fuel of Tb-WS cycle for different   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  cycle and  solar-to-fuel of Tb-WS cycle are significantly improved.For instance, by applying International Journal of Photoenergy 7 20% heat recuperation at   of 2280 K,  cycle and  solar-to-fuel can be increased up to 23.5 and 28.4%.Likewise, at heat recuperation of 60% and   of 2280 K,  cycle and  solar-to-fuel can get enhanced up to 39.0 and 47.1%.