Solar Hydrogen Production via a Samarium Oxide-Based Thermochemical Water Splitting Cycle

The computational thermodynamic analysis of a samarium oxide-based two-step solar thermochemical water splitting cycle is reported. The analysis is performed using HSC chemistry software and databases. The first (solar-based) step drives the thermal reduction of Sm2O3 into Sm and O2. The second (non-solar) step corresponds to the production of H2 via a water splitting reaction and the oxidation of Sm to Sm2O3. The equilibrium thermodynamic compositions related to the thermal reduction and water splitting steps are determined. The effect of oxygen partial pressure in the inert flushing gas on the thermal reduction temperature (TH) is examined. An analysis based on the second law of thermodynamics is performed to determine the cycle efficiency (ηcycle) and solar-to-fuel energy conversion efficiency (ηsolar ́to ́fuel) attainable with and without heat recuperation. The results indicate that ηcycle and ηsolar ́to ́fuel both increase with decreasing TH, due to the reduction in oxygen partial pressure in the inert flushing gas. Furthermore, the recuperation of heat for the operation of the cycle significantly improves the solar reactor efficiency. For instance, in the case where TH = 2280 K, ηcycle = 24.4% and ηsolar ́to ́fuel = 29.5% (without heat recuperation), while ηcycle = 31.3% and ηsolar ́to ́fuel = 37.8% (with 40% heat recuperation).


Introduction
Two concerns in many countries are long-term shortages of fossil fuels and the need to secure fuel supplies.Carbon dioxide emissions constitute another significant issue concerning all societies, as such emissions are considered the main cause of global warming and climate change, for which the consequences are predicted to be melting of glaciers, a sea level rise, and increased weather extremes.The CO 2 emissions from fuel combustion were 32.1 Gt (billion metric tons) in 2015 [1].As a consequence, it is important for countries to invest in and shift towards clean energy technologies such as solar energy.
The conversion of solar energy to chemical energy in the form of an alternative fuel such as H 2 provides a promising future sustainable energy pathway.Hydrogen can be produced with solar thermal energy via water splitting reactions.Hydrogen used in this manner is an energy carrier.Its advantages include a high energy density (on a mass basis) and non-polluting nature.The metal oxide (MO)-based two-step solar thermochemical cycle is a potentially advantageous way to produce hydrogen via water splitting [2][3][4].The main reactions involved in the MO based two-step solar thermochemical water splitting cycle are as follows: Reaction 1: Solar thermal dissociation of MO: Reaction 2: Non-solar water splitting step: The MO-based two-step solar thermochemical water splitting cycle is beneficial because it avoids the formation of an explosive gaseous mixture of H 2 and O 2 (since both gases are produced in different steps).Furthermore, the MO can be used in multiple thermochemical cycles as it is not consumed during any of the steps involved.
In this paper, the thermodynamic feasibility of a novel samarium oxide-based two-step solar thermochemical water splitting (Sm-WS) cycle is investigated.This is, to the best of the authors' knowledge, the first time that a Sm-WS cycle has been investigated for use in solar H 2 production.Thermodynamic modeling of the Sm-WS cycle is performed (in two sections) using the commercial thermodynamic HSC Chemistry software and databases [33].In section one, the thermodynamic equilibrium compositions during the solar thermal reduction of Sm 2 O 3 and the oxidation of Sm via water splitting are determined.The effect of the oxygen partial pressure in the inert flushing gas used inside a solar reactor during thermal reduction of Sm 2 O 3 is examined.Also, the variation in the Gibbs free energy as a function of water splitting temperature (T L ) for the H 2 production step is estimated.In section two, energy and exergy analyses of the Sm-WS cycle are carried out.The solar reactor absorption efficiency, the required solar energy input, radiation heat losses, the rate of heat rejected by the quench unit and the water splitting reactor, and the solar-to-fuel conversion efficiency of the Sm-WS cycle are determined via computational thermodynamic modeling and the results are reported.A typical Sm-WS cycle is presented in Figure 1.
Energies 2016, 9, 316 2 of 14 thermal energy via water splitting reactions.Hydrogen used in this manner is an energy carrier.Its advantages include a high energy density (on a mass basis) and non-polluting nature.
The metal oxide (MO)-based two-step solar thermochemical cycle is a potentially advantageous way to produce hydrogen via water splitting [2][3][4].The main reactions involved in the MO based two-step solar thermochemical water splitting cycle are as follows: Reaction 1: Solar thermal dissociation of MO: Reaction 2: Non-solar water splitting step: The MO-based two-step solar thermochemical water splitting cycle is beneficial because it avoids the formation of an explosive gaseous mixture of H2 and O2 (since both gases are produced in different steps).Furthermore, the MO can be used in multiple thermochemical cycles as it is not consumed during any of the steps involved.
In this paper, the thermodynamic feasibility of a novel samarium oxide-based two-step solar thermochemical water splitting (Sm-WS) cycle is investigated.This is, to the best of the authors' knowledge, the first time that a Sm-WS cycle has been investigated for use in solar H2 production.Thermodynamic modeling of the Sm-WS cycle is performed (in two sections) using the commercial thermodynamic HSC Chemistry software and databases [33].In section one, the thermodynamic equilibrium compositions during the solar thermal reduction of Sm2O3 and the oxidation of Sm via water splitting are determined.The effect of the oxygen partial pressure in the inert flushing gas used inside a solar reactor during thermal reduction of Sm2O3 is examined.Also, the variation in the Gibbs free energy as a function of water splitting temperature (TL) for the H2 production step is estimated.In section two, energy and exergy analyses of the Sm-WS cycle are carried out.The solar reactor absorption efficiency, the required solar energy input, radiation heat losses, the rate of heat rejected by the quench unit and the water splitting reactor, and the solar-to-fuel conversion efficiency of the Sm-WS cycle are determined via computational thermodynamic modeling and the results are reported.A typical Sm-WS cycle is presented in Figure 1.To perform the thermodynamic calculations in a conventional way, we rely on the experimental or assessed data (which utilizes stability functions) published in thermodynamic books and scientific journals.This approach is time consuming due to the difficulty in locating the thermodynamic data in the published literature and also because the calculations involved are complicated.Furthermore, inconsistencies arising from the use of different standard and reference states make the final results uncomparable.HSC Chemistry software and its databases permit rapid and straightforward conventional thermodynamic calculations on personal computers.The software provides calculation procedures for investigating the influence of different variables on a chemical system at equilibrium.In addition to the thermodynamic calculations, with the help of HSC Chemistry software and its databases, heat and material balance calculations for processes can be carried out straightforwardly, especially compared to manual methods.The dissolution and corrosion behavior of materials can also be studied in an expedite way using the Eh-pH-diagrams available in HSC Chemistry software.One of the limitations associated with the software is its inability to solve all chemical problems as it does not take into account the kinetics of chemical reactions.Nevertheless, it can be used to determine the optimal reaction conditions and yields of experiments (without carrying out actual expensive experiments) in an economical and effective manner.The name of the software is based on the fact that it performs calculations utilizing thermochemical database related to enthalpy (H), entropy (S), and heat capacity (Cp), for more than 28,000 chemical species.Due to these features, HSC has been widely used for a range of applications in academia, industry and research.
With an average concentration of about 8 parts per million (ppm), samarium is the 40th most abundant element in the Earth's crust.It is the fifth most abundant lanthanide and is more common than elements such as tin.Samarium oxides are readily available from commercial suppliers such as Sigma Aldrich.It can be synthesized inexpensively in laboratories using various synthesis approaches, such as combustion synthesis, the sol-gel method and the co-precipitation method, as samarium precursors such as samarium nitrate are available at a low cost.Samarium does not pose a threat to environment, including plants and animals.The melting points for Sm 2 O 3 and Sm are 2608 and 1347 K, respectively.Similarly, the ∆H and ∆S values for the decomposition of Sm 2 O 3 (according the reaction chemistry mentioned in Figure 1) are equal to 2240.5 kJ and 0.527 kJ/K, respectively.

Chemical Thermodynamic Equilibrium
The Sm-WS cycle mainly involves the following reactions: According to the reaction chemistry, three moles of H 2 can be produced in one complete thermochemical cycle including one thermal reduction and one water splitting step.This seems to be an advantage of the Sm-WS cycle over previously investigated thermochemical cycles, as they are capable of producing either 1 or less than 1 mole of H 2 in one complete thermochemical cycle.To perform the energy and exergy analyses, thermodynamic data for all the reactive species involved (as shown in Equations ( 3) and ( 4)) are taken from HSC and the analyses are performed assuming continuous operation of the solar reactor with an inlet molar flow rate of Sm 2 O 3 of 1 mol¨s ´1.
As reported in previous studies [14,19,29], the temperature required for the thermal reduction of MOs can be reduced using an inert flushing gas such as ultra-high purity Ar with an oxygen partial pressure in the range of 10 ´5 to 10 ´8 bar.From this viewpoint, the effect of the oxygen partial pressure in the inert flushing gas on the thermal reduction of Sm 2 O 3 is examined.According to Figure 2, as the oxygen partial pressure in the inert flushing gas is decreased, T H can be significantly reduced.For instance, at oxygen partial pressure of 10 ´5 bar, the complete thermal reduction of Sm 2 O 3 can be achieved at 3000 K.As the oxygen partial pressure is further lowered to 10 ´6, 10 ´7, and 10 ´8 bar, the required T H values decease to 2780, 2540, and 2280 K, respectively.The influence of oxygen partial pressure in the inert flushing gas on the equilibrium compositions associated with the thermal reduction of Sm2O3 is also studied.As per the results in Figures 3a-c, the slope of the decrease in the molar concentration of Sm2O3 and the increase in the molar concentration of Sm(g) and O2(g) both shift towards lower TH with a reduction in the oxygen partial pressure in the inert flushing gas.Because of the lower value of oxygen partial pressure in the inert flushing gas, the entropy of the product gases increases and hence thermal reduction is possible at lower temperatures.
The variation in the Gibbs free energy associated with the water splitting reaction (Figure 4) indicates that H2 generation via water splitting using Sm produced after the reduction of Sm2O3 is possible below 6800 K (for a pressure of 1 bar).For a decrease in TL from 6800 to 1900 K, Δ reduces by 1010 kJ•mol −1 .However, further lowering of TL from 1900 to 300 K does not affect Δ significantly.The influence of oxygen partial pressure in the inert flushing gas on the equilibrium compositions associated with the thermal reduction of Sm 2 O 3 is also studied.As per the results in Figure 3a-c, the slope of the decrease in the molar concentration of Sm 2 O 3 and the increase in the molar concentration of Sm(g) and O 2 (g) both shift towards lower T H with a reduction in the oxygen partial pressure in the inert flushing gas.Because of the lower value of oxygen partial pressure in the inert flushing gas, the entropy of the product gases increases and hence thermal reduction is possible at lower temperatures.
The variation in the Gibbs free energy associated with the water splitting reaction (Figure 4) indicates that H 2 generation via water splitting using Sm produced after the reduction of Sm 2 O 3 is possible below 6800 K (for a pressure of 1 bar).For a decrease in T L from 6800 to 1900 K, ∆G ws reduces by 1010 kJ¨mol ´1.However, further lowering of T L from 1900 to 300 K does not affect ∆G ws significantly.The influence of oxygen partial pressure in the inert flushing gas on the equilibrium compositions associated with the thermal reduction of Sm2O3 is also studied.As per the results in Figures 3a-c, the slope of the decrease in the molar concentration of Sm2O3 and the increase in the molar concentration of Sm(g) and O2(g) both shift towards lower TH with a reduction in the oxygen partial pressure in the inert flushing gas.Because of the lower value of oxygen partial pressure in the inert flushing gas, the entropy of the product gases increases and hence thermal reduction is possible at lower temperatures.
The variation in the Gibbs free energy associated with the water splitting reaction (Figure 4) indicates that H2 generation via water splitting using Sm produced after the reduction of Sm2O3 is possible below 6800 K (for a pressure of 1 bar).For a decrease in TL from 6800 to 1900 K, Δ reduces by 1010 kJ•mol −1 .However, further lowering of TL from 1900 to 300 K does not affect Δ significantly.

Energy and Exergy Analyses
An exergy analysis of the Sm-WS cycle is carried out to provide a second law perspective.The process flow diagram for the Sm-WS cycle is shown in Figure 5.This cycle is comprised of a solar reactor, a quench unit, water splitting reactor, and a theoretical H2/O2 fuel cell.To perform the exergy analysis, the following assumptions are made:


The production of H2 is carried out at 1 bar and steady state conditions, with negligible viscous losses and changes in kinetic and potential energies.


The solar reactor is considered a perfectly insulated blackbody absorber.


The effective emissivity and absorptivity is both equal to unity. There are negligible convective/conductive heat losses. All reactions reach 100% completion.


All products separate naturally without expending any work. Heat exchangers required for recovering the sensible and latent heat are omitted.The exergy analysis is performed following the methodology and governing equations derived and used previously for other MO based solar thermochemical cycles [6,9,10].Thermodynamic properties are extracted from HSC software and databases and the analysis is normalized to a unit Sm2O3 molar flow rate (1 mol•s −1 ) entering the solar reactor.
As a first step in the exergy analysis, the absorption efficiency ( ), which is defined as the net rate at which energy is absorbed by the solar reactor divided by the solar energy input through the aperture, is determined as follows:

Energy and Exergy Analyses
An exergy analysis of the Sm-WS cycle is carried out to provide a second law perspective.The process flow diagram for the Sm-WS cycle is shown in Figure 5.This cycle is comprised of a solar reactor, a quench unit, water splitting reactor, and a theoretical H 2 /O 2 fuel cell.To perform the exergy analysis, the following assumptions are made:

‚
The production of H 2 is carried out at 1 bar and steady state conditions, with negligible viscous losses and changes in kinetic and potential energies.

‚
The solar reactor is considered a perfectly insulated blackbody absorber.

‚
The effective emissivity and absorptivity is both equal to unity.

‚
There are negligible convective/conductive heat losses.

‚
All products separate naturally without expending any work.

‚
Heat exchangers required for recovering the sensible and latent heat are omitted.

Energy and Exergy Analyses
An exergy analysis of the Sm-WS cycle is carried out to provide a second law perspective.The process flow diagram for the Sm-WS cycle is shown in Figure 5.This cycle is comprised of a solar reactor, a quench unit, water splitting reactor, and a theoretical H2/O2 fuel cell.To perform the exergy analysis, the following assumptions are made:


The production of H2 is carried out at 1 bar and steady state conditions, with negligible viscous losses and changes in kinetic and potential energies.


The solar reactor is considered a perfectly insulated blackbody absorber.


The effective emissivity and absorptivity is both equal to unity. There are negligible convective/conductive heat losses.


All products separate naturally without expending any work.


Heat exchangers required for recovering the sensible and latent heat are omitted.The exergy analysis is performed following the methodology and governing equations derived and used previously for other MO based solar thermochemical cycles [6,9,10].Thermodynamic properties are extracted from HSC software and databases and the analysis is normalized to a unit Sm2O3 molar flow rate (1 mol•s −1 ) entering the solar reactor.
As a first step in the exergy analysis, the absorption efficiency ( ), which is defined as the net rate at which energy is absorbed by the solar reactor divided by the solar energy input through the aperture, is determined as follows: The exergy analysis is performed following the methodology and governing equations derived and used previously for other MO based solar thermochemical cycles [6,9,10].Thermodynamic properties are extracted from HSC software and databases and the analysis is normalized to a unit Sm 2 O 3 molar flow rate (1 mol¨s ´1) entering the solar reactor.As a first step in the exergy analysis, the absorption efficiency (η absorption ), which is defined as the net rate at which energy is absorbed by the solar reactor divided by the solar energy input through the aperture, is determined as follows: Here, I denotes the direct normal solar irradiance i.e., normal beam insolation (W/m), C denotes the solar flux concentration ratio (suns), T H denotes the solar reactor temperature required for the thermal reduction of Sm 2 O 3 and σ denotes the Stefan-Boltzmann constant (5.6705 ˆ10 ´8 W¨m ´2¨K ´4).
Values for η absorption calculated as a function of T H are presented in Figure 6a.The trends indicate that η absorption increases with decreasing T H .For instance, at T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar), η absorption is 54%.As oxygen partial pressure in the inert flushing gas is further reduced to 10 ´8 bar, the corresponding T H decreases by 720 K and η absorption rises to 84.7%.
The influence of C on η absorption (at constant T H = 2280 K and oxygen partial pressure = 10 ´8 bar in the inert flushing gas) is also examined.At C = 2000 suns, η absorption is 23.4%.The efficiency η absorption can be increased to 38.3, 51.1, 57.5, and 61.3% by raising C to 4000, 6000, 8000, and 10,000 suns, respectively (Figure 6b).To operate the Sm-WS cycle, solar energy is required 1) to heat the Sm2O3 from TL to TH and 2) for complete thermal reduction of Sm2O3 as per Equation (3).For comparison purposes, the heating of Ar is not included in this calculation as it was not considered in previous studies.The net solar energy absorbed by the solar reactor to perform the above mentioned tasks can be calculated as: (8) Ar is not included in this calculation as it was not considered in previous studies.The net solar energy absorbed by the solar reactor to perform the above mentioned tasks can be calculated as: n∆ H| Sm 2 O 3 @T H Ñ2Smpgq`1.5O 2 pgq@T H (8) As per Figure 7, at T H = 3000 K (when oxygen partial pressure = 10 ´5 bar in the inert flushing gas), Q reactor´net is 2583 kW.With a further decrease in oxygen partial pressure in the inert flushing gas, T H reduces and the corresponding Q reactor´net values also decline.The value of Q reactor´net decreases by 82.3 and 120 kW with a decline in T H to 2540 and 2280 K respectively as the oxygen pressure in the inert flushing gas is lowered to 10 ´7 and 10 ´8 bar.Based on the calculated values for and , the solar energy input required for the operation of Sm-WS cycle can be calculated as follows: (9) The variation in as a function of TH is shown in Figure 7.It is seen that the maximum value of (4777 kW) is needed at TH = 3000 K (oxygen partial pressure in the inert flushing gas = 10 −5 bar).Furthermore, the required value of decreases as TH reduces.For instance, at TH = 2780 K (oxygen partial pressure = 10 −6 bar in the inert flushing gas), is 3248 kW.An additional drop in TH to 2540 K (oxygen partial pressure = 10 −7 bar in the inert flushing gas) reduces to 3273 kW.The reason behind this lowering of is the increase in due to the decline in TH.Overall, as the oxygen partial pressure in the inert flushing gas decreases from 10 −5 to 10 −8 bar, TH declines by 720 K and by 39.1%.Due to operation at elevated temperatures, radiation heat losses from the solar reactor are inevitable.The radiation heat losses associated with the solar reactor installed for the Sm-WS cycle can be calculated as: (10) The values of reported in Table 1 indicate that radiation heat losses are greatest (2194 kW) when TH = 3000 K (oxygen partial pressure in the inert flushing gas = 10 −5 bar).A decrease in TH results in a significant reduction in .This is again due to the fact that is higher at lower values of TH.The quantity can be lowered by 1748 kW with a decrease in TH to 2280 K (oxygen partial pressure = 10 −8 bar in the inert flushing gas), which is a very significant reduction in input heat.Based on the calculated values for η absorption and Q reactor´net , the solar energy input required for the operation of Sm-WS cycle can be calculated as follows: The variation in Q solar as a function of T H is shown in Figure 7.It is seen that the maximum value of Q solar (4777 kW) is needed at T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar).Furthermore, the required value of Q solar decreases as T H reduces.For instance, at T H = 2780 K (oxygen partial pressure = 10 ´6 bar in the inert flushing gas), Q solar is 3248 kW.An additional drop in T H to 2540 K (oxygen partial pressure = 10 ´7 bar in the inert flushing gas) reduces Q solar to 3273 kW.The reason behind this lowering of Q solar is the increase in η absorption due to the decline in T H . Overall, as the oxygen partial pressure in the inert flushing gas decreases from 10 ´5 to 10 ´8 bar, T H declines by 720 K and Q solar by 39.1%.
Due to operation at elevated temperatures, radiation heat losses from the solar reactor are inevitable.The radiation heat losses associated with the solar reactor installed for the Sm-WS cycle can be calculated as: The values of Q re´radiation reported in Table 1 indicate that radiation heat losses are greatest (2194 kW) when T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar).A decrease in T H results in a significant reduction in Q re´radiation .This is again due to the fact that η absorption is higher at lower values of T H .The quantity Q re´radiation can be lowered by 1748 kW with a decrease in T H to 2280 K (oxygen partial pressure = 10 ´8 bar in the inert flushing gas), which is a very significant reduction in input heat.Products of the thermal reduction of Sm 2 O 3 (i.e., Sm and O 2 ) leaving the solar reactor are in the gas phase and also at high T H .At such T H levels, these gaseous products have a tendency to recombine and convert to Sm 2 O 3 .To avoid the re-formation of Sm 2 O 3 , the gaseous products exiting the solar reactor at T H are rapidly cooled to T L using a quench unit.During quenching, it is assumed that the chemical compositions of the products remain unaltered.The latent and sensible heat rejected by the quench unit can be determined as follows: The thermal energy required for the separation of O 2 and the inert Ar (gas separation) is not considered for comparison purposes, as it was excluded in previous studies.
Table 1 reports the change in Q quench with respect to T H .It can be seen that, at higher T H , Q quench is also elevated.For instance, at T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar), Q quench is 756 kW.The data also confirm that the heat loss due to quenching can be reduced if the solar reactor is operated at a lower oxygen partial pressure in the inert flushing gas, which also results in a lower T H .For instance, at an oxygen partial pressure in the inert flushing gas of 10 ´8 bar, the required values are T H = 2280 K and Q quench = 636 kW.
Irreversibilities associated with the solar reactor and quench unit due to the non-reversible chemical transformations and re-radiation losses to the surroundings can be calculated as: Irr quench " ˆQquench 298 Similarly, Q solar and Q reactor´net , as well as Irr reactor and Irr quench , are also observed to be greatest at T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar).As shown in Figure 8, the HSC simulation results indicate an 85.1% decrease in Irr reactor for a reduction in T H from 3000 to 2280 K as the oxygen partial pressure in the inert flushing gas decreases to 10 ´8 bar.Correspondingly, Irr quench is also lowered by 0.5 kW¨K ´1 due to a similar decline in T H .These trends are in good agreement with the results reported in previous studies [9,10].
Solid Sm obtained after the quench unit (at 298 K) is transferred to the water splitting reactor (Sm oxidizer) and reacted with water at T L = 298 K producing solar H 2 .The rate of heat rejected to the surroundings by the water splitting reactor is estimated as 970 kW using the following equation and assuming 100% conversion: Solid Sm obtained after the quench unit (at 298 K) is transferred to the water splitting reactor (Sm oxidizer) and reacted with water at TL = 298 K producing solar H2.The rate of heat rejected to the surroundings by the water splitting reactor is estimated as 970 kW using the following equation and assuming 100% conversion: Also, the irreversibility associated with the water splitting reactor is observed to be 3.5 kW•K −1 using the following equation: Also, the irreversibility associated with the water splitting reactor is observed to be 3.5 kW¨K ´1 using the following equation: An ideal H 2 /O 2 fuel cell is added to the Sm-WS cycle to extract the maximum work from the net H 2 produced.In this study, the efficiency of the H 2 /O 2 fuel cell is considered as 100% and hence it is defined as an ideal fuel cell.The following two equations can be used to determine the theoretical rate of work performed (711 kW) and heat energy released (146 kW) by the H 2 /O 2 fuel cell: In the case of solar thermochemical cycles, the cycle efficiency (η cycle ) is defined as the ratio of theoretical work performed by the ideal fuel cell to the solar energy input: Similarly, the solar-to-fuel-conversion efficiency ( η solar´to´f uel ) can be defined as the ratio of higher heating value (HHV) of the H 2 produced to the solar energy input: Both η cycle and η solar´to´f uel of the Sm-WS cycle are estimated based on the HSC simulation results and given in Table 2.The values for η cycle and η solar´to´f uel increase as T H decreases.At T H = 3000 K (oxygen partial pressure in the inert flushing gas = 10 ´5 bar), η cycle is 14.9% and η solar´to´f uel is 17.9%.For a reduction in T H to 2280 K due to the decline in oxygen partial pressure in the inert flushing gas to 10 ´8 bar, both η cycle and η solar´to´f uel can be increased up to 24.5% and 29.5%, respectively.These efficiency values are comparable with other MO cycles such as the ZnO/Zn cycle (29%) [5], the SnO 2 /SnO cycle (29.8%)[33], the Fe 3 O 4 /FeO cycle (30%) [34] and the ceria cycle (20.2%)[29], which all were investigated previously employing similar operating conditions.By applying heat recuperation, η cycle and η solar´to´f uel for the Sm-WS cycle can be further enhanced [19,29,35].Heat rejected by the quench unit and the water splitting reactor can be recycled and re-utilized to drive the Sm-WS cycle.The total amount of heat that can be recuperated is calculated as: With the inclusion of the heat recuperation, the solar energy required for the operation of the cycle can be reduced as follows: As an example, the alteration in Q solar, with recuperation and Q recuperable as a function of % heat recuperation for the case of T H = 2280 K (oxygen partial pressure in the inert flushing gas = 10 ´8 bar) is shown in Figure 9.The results indicate that, as the % heat recuperation increases, Q recuperable rises whereas Q solar, with recuperation declines.For instance, with no heat recuperation, Q solar, with recuperation = 2909 kW.But as heat recuperation increases to 50%, Q solar, with recuperation decreases to 2106 kW, with 803 kW of the thermal energy recycled from the quench unit and water splitting reactor to drive the Sm-WS cycle.The efficiencies and after heat recuperation can be determined as: The effects of heat recuperation on and for all TH values are provided in Table 3.Also, the increase in and due to heat recuperation for the case of TH = 2280 K (oxygen partial pressure in the inert flushing gas = 10 −8 bar) is presented in Figure 10.The data reported in Table 3 and Figure 10 confirm that, as heat recuperation is employed, both and increase significantly.For example, at TH = 2280 K, and (without heat recuperation) are 24.5% and 29.5%.However, if 60% heat recuperation is employed, both and can be raised further, to 36.5% and 44.1%, respectively.These efficiency values are much higher than for previously examined MO cycles (Table 4).The efficiencies η cycle and η solar´to´f uel after heat recuperation can be determined as: W FC´Ideal Q solar,with recuperation (22) η solar´to´f uel " HHV H 2 Q solar,with recuperation (23) The effects of heat recuperation on η cycle and η solar´to´f uel for all T H values are provided in Table 3.Also, the increase in η cycle and η solar´to´f uel due to heat recuperation for the case of T H = 2280 K (oxygen partial pressure in the inert flushing gas = 10 ´8 bar) is presented in Figure 10.The data reported in Table 3 and Figure 10 confirm that, as heat recuperation is employed, both η cycle and η solar´to´f uel increase significantly.For example, at T H = 2280 K, η cycle and η solar´to´f uel (without heat recuperation) are 24.5% and 29.5%.However, if 60% heat recuperation is employed, both η cycle and η solar´to´f uel can be raised further, to 36.5% and 44.1%, respectively.These efficiency values are much higher than for previously examined MO cycles (Table 4).The exergy analysis performed for the Sm-WS cycle can be verified by conducting an energy balance and evaluating the maximum achievable efficiency from the total available work and from the total solar power input.The energy balance (for all TH) confirms that: (24) At TH = 2540 K, the energy balance in Equation ( 24) indicates that = 712 kW which is equal to determined by Equation (16).Likewise, at TH = 2280 K, the energy balance indicates that = 712 kW which is again equal to the value of determined by Equation ( 16).The available work can be estimated as the addition of the work done by the fuel cell and the work lost due to the irreversibilities in the solar reactor, quench unit, and water splitting reactor.In case of the Sm-WS cycle, the maximum cycle efficiency can be calculated as: , For all values of TH, it is observed that , is equal to the efficiency of a Carnot heat engine operating between hot and cold temperature reservoirs: For instance, at TH = 2280 K and TL = 298 K, , = 86.9%which is equal to = 86.9%.Similarly, at TH = 2780 K and TL = 298 K, , = 89.3%which is again equal to = 89.3%.From the results obtained during this investigation (phase-1: thermodynamic analysis), we have realized that the temperatures required in case of Sm-WS cycle are significantly higher.To overcome this limitation, we are currently working towards improving the redox reactivity of Sm2O3 at lower temperatures by synthesizing doped Sm2O3.The host, i.e., Sm2O3, will be doped by suitable  The exergy analysis performed for the Sm-WS cycle can be verified by conducting an energy balance and evaluating the maximum achievable efficiency from the total available work and from the total solar power input.The energy balance (for all T H ) confirms that: At T H = 2540 K, the energy balance in Equation (24) indicates that W FC´Ideal = 712 kW which is equal to W FC´Ideal determined by Equation (16).Likewise, at T H = 2280 K, the energy balance indicates that W FC´Ideal = 712 kW which is again equal to the value of W FC´Ideal determined by Equation ( 16).The available work can be estimated as the addition of the work done by the fuel cell and the work lost due to the irreversibilities in the solar reactor, quench unit, and water splitting reactor.In case of the Sm-WS cycle, the maximum cycle efficiency can be calculated as: η cycle,maximum " W FC´Ideal `TL ´Irr reactor `Irr quench `Irr sm oxidation Qsolar (25) For all values of T H , it is observed that η cycle,maximum is equal to the efficiency of a Carnot heat engine operating between hot and cold temperature reservoirs: For instance, at T H = 2280 K and T L = 298 K, η cycle,maximum = 86.9%which is equal to η carnot = 86.9%.Similarly, at T H = 2780 K and T L = 298 K, η cycle,maximum = 89.3%which is again equal to η carnot = 89.3%.
From the results obtained during this investigation (phase-1: thermodynamic analysis), we have realized that the temperatures required in case of Sm-WS cycle are significantly higher.To overcome this limitation, we are currently working towards improving the redox reactivity of Sm 2 O 3 at lower temperatures by synthesizing doped Sm 2 O 3 .The host, i.e., Sm 2 O 3 , will be doped by suitable metal cations such as Ni, Mn, Co, Fe, Ce, and others using various synthesis approaches such as sol-gel, co-precipitation, combustion synthesis, etc.It is expected that in the case of doped Sm 2 O 3 , the temperatures required for thermal reduction will be lower as compared to pure Sm 2 O 3 .This second phase of this investigation is underway in our laboratories.

Conclusions
The thermodynamic feasibility of a Sm-WS cycle for the production of solar hydrogen is investigated.HSC simulation results indicate that the temperature (T H ) required for complete thermal reduction of Sm 2 O 3 can be significantly decreased with a reduction in the oxygen partial pressure in the inert flushing gas used inside the reactor.For instance, at oxygen partial pressure in the inert flushing gas = 10 ´5 bar, T H is 3000 K.As the oxygen partial pressure in the inert flushing gas decreases to 10 ´8 bar, T H can be lowered to 2280 K. Thermodynamic calculations confirm that the water splitting reaction via Sm oxidation is feasible below 6800 K.
The exergy analysis of the Sm-WS cycle indicates that η absorption can be increased by 30.61% due to the decrease in T H from 3000 to 2280 K as the oxygen partial pressure in the inert flushing gas reduces from 10 ´5 to 10 ´8 bar.In contrast, η absorption can be reduced by 61.3% with a decrease in the value of C from 10,000 to 2000 suns (at T H = 2280 K).The quantities Q reactor´net and Q solar can also be lowered by 4.6 and 39.1% as T H falls from 3000 to 2280 K. Correspondingly, the heat losses due to quenching and re-radiation can be reduced by 120 and 1748 kW for a similar reduction in T H .The lower solar energy input requirements and heat losses during quenching and re-radiation are possible as η absorption increases with decreasing T H .The maximum efficiencies, η cycle = 24.5% and η solar´to´f uel = 29.5%, are observed at lower values of T H = 2280 K and oxygen partial pressure in the inert flushing gas = 10 ´8 bar (with no heat recuperation).These efficiency values can be further enhanced by recycling the heat recuperated from the quench unit and water splitting reactor to drive the cycle.For instance, at heat recuperation levels of 20%, 40% and 60%, η solar´to´f uel can be increased by a factor of 1.12, 1.28, and 1.49, respectively.

Figure 2 .
Figure 2. Effect of oxygen partial pressure in the inert flushing gas on TH.

Figure 3 .
Figure 3.Effect of oxygen partial pressure in the inert flushing gas on equilibrium compositions related to the thermal reduction of Sm2O3.Change in the molar concentration of (a): Sm2O3; (b): Sm(g); (c): O2(g).

Figure 2 .
Figure 2. Effect of oxygen partial pressure in the inert flushing gas on T H .

Figure 2 .
Figure 2. Effect of oxygen partial pressure in the inert flushing gas on TH.

Figure 3 .
Figure 3.Effect of oxygen partial pressure in the inert flushing gas on equilibrium compositions related to the thermal reduction of Sm2O3.Change in the molar concentration of (a): Sm2O3; (b): Sm(g); (c): O2(g).

Figure 3 .
Figure 3.Effect of oxygen partial pressure in the inert flushing gas on equilibrium compositions related to the thermal reduction of Sm 2 O 3 .Change in the molar concentration of (a): Sm 2 O 3 ; (b): Sm(g); (c): O 2 (g).

Figure 4 .
Figure 4. Variation in Δ as a function of TL during H2 production step.

Figure 5 .
Figure 5. Process configuration for H2 production via Sm-WS cycle.

Figure 4 .
Figure 4. Variation in ∆G ws as a function of T L during H 2 production step.

Figure 4 .
Figure 4. Variation in Δ as a function of TL during H2 production step.

Figure 5 .
Figure 5. Process configuration for H2 production via Sm-WS cycle.

Figure 5 .
Figure 5. Process configuration for H 2 production via Sm-WS cycle.
denotes the direct normal solar irradiance i.e., normal beam insolation (W/m), C denotes the solar flux concentration ratio (suns), TH denotes the solar reactor temperature required for the thermal reduction of Sm2O3 and denotes the Stefan-Boltzmann constant (5.6705 10 W•m −2 •K −4 ).Values for calculated as a function of TH are presented in Figure 6a.The trends indicate that increases with decreasing TH.For instance, at TH = 3000 K (oxygen partial pressure in the inert flushing gas = 10 −5 bar), is 54%.As oxygen partial pressure in the inert flushing gas is further reduced to 10 −8 bar, the corresponding TH decreases by 720 K and rises to 84.7%.The influence of C on (at constant TH = 2280 K and oxygen partial pressure = 10 −8 bar in the inert flushing gas) is also examined.At C = 2000 suns, is 23.4%.The efficiency can be increased to 38.3, 51.1, 57.5, and 61.3% by raising C to 4000, 6000, 8000, and 10,000 suns, respectively (Figure 6b).

Figure 6 .
Figure 6.Effect of (a) TH at C = 10,000 suns; and (b) C on at TH = 2280 K.

Figure 6 .
Figure 6.Effect of (a) T H at C = 10,000 suns; and (b) C on η absorption at T H = 2280 K.
7, at TH = 3000 K (when oxygen partial pressure = 10 −5 bar in the inert flushing gas), is 2583 kW.With a further decrease in oxygen partial pressure in the inert flushing gas, TH reduces and the corresponding values also decline.The value of decreases by 82.3 and 120 kW with a decline in TH to 2540 and 2280 K respectively as the oxygen partial pressure in the inert flushing gas is lowered to 10 −7 and 10 −8 bar.

Figure 7 .
Figure 7. Effect of TH on and .

Figure 7 .
Figure 7. Effect of T H on Q solar and Q reactor´net .

Figure 8 .
Figure 8.Effect of TH on and .

Figure 8 .
Figure 8.Effect of T H on Irr reactor andIrr quench .

Figure 9 .
Figure 9.Effect of % heat recuperation on

Figure 9 .
Figure 9.Effect of % heat recuperation on Q solar, with recuperation and Q recuperable (T H = 2280 K).

Figure 10 .
Figure 10.Effect of % heat recuperation on η cycle and η solar´to´f uel (T H = 2280 K).

Table 1 .
Variation in and as a function of TH.

Table 1 .
Variation in Q quench and Q re´radiation as a function of T H .

Table 2 .
Values for η cycle and η solar´to´f uel as a function of T H .

Table 4 .
Comparison between Sm-WS cycle and previously investigated metal oxide based cycles in terms of .Cycle (%)

Table 3 .
η cycle and η solar´to´f uel for Sm-WS cycle.

Table 4 .
Comparison between Sm-WS cycle and previously investigated metal oxide based cycles in terms of η solar´to´f uel .