Utilization of MnFe₂O₄ Redox Ferrite for Solar Fuel Production via CO₂ Splitting: A Thermodynamic Study

Abstract

A thermodynamic efficiency analysis of $MnF{e}_2{O}_4$-based CO₂ splitting (CDS) cycle is reported. HSC Chemistry software is used for performing the calculations allied with the model developed. By maintaining the reduction nonstoichiometry equal to 0.1, variations in the thermal energy required to drive the cycle and solar-to-fuel energy conversion efficiency as a function of the ratio of the molar flow rate of inert sweep gas to the molar flow rate of Mn-ferrite, reduction temperature, and gas-to-gas heat recovery effectiveness are studied. This study confirms that the thermal reduction temperature needed to achieve reduction nonstoichiometry equal to 0.1 is reduced when the inert gas flow rate is increased. Conversely, due to the requirement of the additional energy to heat the inert gas, the thermal energy required to drive the cycle is upsurged considerably. As the solar-to-fuel energy conversion efficiency depends significantly on the thermal energy required to drive the cycle, a reduction in it is recorded. As the ratio of the molar flow rate of inert sweep gas to the molar flow rate of Mn-ferrite is increased from 10 to 100, the solar-to-fuel energy conversion efficiency is decreased from 14.9% to 9.9%. By incorporating gas-to-gas heat recovery, a drastic drop in the thermal energy required to drive the cycle is attained which further resulted in a rise in the solar-to-fuel energy conversion efficiency. The maximum solar-to-fuel energy conversion efficiency (17.5%) is achieved at the ratio of the molar flow rate of inert sweep gas to the molar flow rate of Mn-ferrite equal to 10 as well as 20 when 90% of gas-to-gas heat recovery is applied.

1. Introduction

The average atmospheric CO₂ concentration is equal to 422.52 ppm as of 7 July 2023, higher by 3.37 ppm when compared to 8 July 2022. This continuous increase in the atmospheric CO₂ concentration is considerably harmful as it helps global warming through the greenhouse effect [1]. For example, the 4th of July 2023 has been recorded as the hottest day on the planet in as many as 125,000 years. The hazardous effects associated with the ongoing emissions of CO₂ can be resolved by using technologies such as the solar thermochemical CO₂ splitting (CDS) cycle [2]. This cycle can split CO₂ into CO by using solar thermal power. The solar thermochemical community’s final aim is to produce solar syngas by combining CO from CDS and H₂ from H₂O splitting (WS) [3]. Various fuels can be manufactured using the catalytic Fischer Tropsch process using solar syngas.

In addition to electrocatalysis [4], the redox chemistry associated with the metal oxides (MOs) drives the solar thermochemical cycle. Several MOs redox systems have been investigated for both CDS and WS. The list includes ZnO/Zn [5,6], SnO₂/SnO/Sn [7,8], Fe₃O₄/FeO/Fe [9,10], ferrites [11,12], ceria [13,14], doped ceria [15,16], perovskites [17,18], and others [19,20]. Among all the MOs mentioned above, ferrites (doped iron oxides) were examined for WS application more than CDS. The ferrites investigated until now mainly includes NiFe₂O₄ [21], CoFe₂O₄ [22], ZnFe₂O₄ [23], Sn-ferrite [24], Mg-ferrite [25], Ni-Zn-ferrite [26], and Ni-Mg-ferrite [27].

Mn-ferrite ($MnF{e}_2{O}_4$) was also tested for H₂ generation via WS reactions. Mn-ferrite seems advantageous for the redox reactions associated with the thermochemical WS and CDS as it carries the unique combination of a Mn-based oxide (variable Mn valance in-between 3 and 4) and an Fe-based oxide (variable Fe valance is in-between 2 and 3). A redox system of Mn-ferrite/ZnO/H₂O was examined for WS application at 1273 K [28]. A total of 70% of the theoretical H₂ production is reported to be carried out by Mn-ferrite nanoparticles produced via ball milling [29]. Solid-state synthesized Mn-ferrite showed a five-times-lower H₂ production aptitude than the Mn-ferrite prepared using high-energy ball milling [30]. The rate of H₂ production via WS reaction was higher in the case of Mn-ferrite as compared to $ZnF{e}_2{O}_4$ and $F{e}_2{O}_3$ [31]. A powdered mixture of Mn-ferrite and CaO produced 0.4 to 0.9 mL of H₂/g in three WS cycles performed at 1273 K [32]. A study also reported that the Mn-ferrite became segregated during the WS reaction [33]. Sol–gel-derived Mn-ferrite nanoparticles were also tested for H₂ production via thermochemical WS reaction [34].

All the studies mentioned above are experimental investigations of the Mn-ferrite-based WS cycle. Besides experimentally determined fuel production capacity, estimation of the solar-to-fuel energy conversion efficiency (${ \eta }_{solar-to-fuel}$) is also essential for judging a MO’s suitability for solar thermochemical cycles. Recently, the ${ \eta }_{solar-to-fuel}$ of the Mn-ferrite-based WS cycle has been reported [35]. However, this study estimates the ${ \eta }_{solar-to-fuel}$ without considering the thermal energy requirements allied with the heating of inert sweeping gas and separation of gaseous components. Additionally, using Mn-ferrite-based redox reactions for CDS has not yet been studied. Hence, in this investigation, a theoretical model for the $MnF{e}_2{O}_4$-based CDS cycle is developed, and a detailed thermodynamic efficiency analysis is carried out. ${ \eta }_{solar-to-fuel}$ is calculated by considering the energy penalties associated with the heating of inert sweep gas and the separation of inert/O₂ and CO₂/CO gas mixtures.

2. Thermodynamic Model and Equations

By considering the following assumptions, a thermodynamic model is developed for the determination of ${\eta }_{solar-to-fuel}$ and other process parameters of the $MnF{e}_2{O}_4$-based CDS cycle. The developed thermodynamic model is presented in Figure 1.

(1)

All processes operated at steady-state;

(2)

Ideal gas behavior;

(3)

Reduction, as well as oxidation chambers, are operated at isothermal conditions;

(4)

Chemical equilibrium between the $MnF{e}_2{O}_4$ and the gases;

(5)

The efficiency of an Ideal CO₂/CO fuel cell equal to 100%;

(6)

All reactions undergo complete conversion;

(7)

Kinetic/potential energy and viscous losses are not considered;

(8)

No side reactions;

(9)

20% of thermal energy losses from the reduction chamber;

(10)

All the calculations are standardized to ${\dot{n}}_{MnF}$ = 1 mol/s.

As shown in Figure 1, separate reaction chambers are installed to reduce and re-oxidize the Mn-ferrite, as per Equations (1) and (2). These two chambers are operated isothermally, i.e., the reduction chamber at a reduction temperature ($T_{red}$) and the re-oxidation chamber at oxidation temperature ($T_{oxd}$).

$$MnF{e}_2{O}_4\to MnF{e}_2{O}_{4-{\delta }_{red}}+\frac{{\delta }_{red}}{2}{O}_2$$

(1)

$$MnF{e}_2{O}_{4-{\delta }_{red}}+\left({\delta }_{red}\right){CO}_2\to MnF{e}_2{O}_4+\left({\delta }_{red}\right)CO$$

(2)

The equations listed above show that the reduction and re-oxidation of $MnF{e}_2{O}_4$ occurs in two separate steps. Step 1 deals with the release of O₂ due to the thermal reduction of $MnF{e}_2{O}_4$. On the other hand, re-oxidation of $MnF{e}_2{O}_{4-{\delta }_{red}}$ is carried out in step 2, which results in the production of CO via thermochemical CDS. All the calculations are performed by assuming ${\delta }_{red}$ = 0.1.

The inert sweeping gas method is applied to maintain the partial pressure of O₂ in the reduction chamber. The entrance of the inert sweep gas in the reduction chamber is located at the state ${red}_1$. Likewise, state ${red}_2$ indicates the exit of the inert sweep gas from the reduction chamber. $MnF{e}_2{O}_4$ is shuttled in the reduction chamber from the state ${red}_3$ to ${red}_4$. Estimation of the heat energy needed for the thermal reduction of $MnF{e}_2{O}_4$ is carried out by using the following equation.

$${\dot{Q}}_{MnF-red}={\dot{n}}_{MnF}∆{\left.H\right|}_{MnF{e}_2{O}_4\to MnF{e}_2{O}_{4-{\delta }_{red}}+\frac{{\delta }_{red}}{2}{O}_2}$$

(3)

By using Equation (4), the thermal energy needed for the heating of $MnF{e}_2{O}_4$ from $T_{oxd}$ to $T_{red}$ is calculated.

$${\dot{Q}}_{MnF-sens}={\dot{n}}_{MnF}∆{\left.H\right|}_{MnF{e}_2{O}_4@T_{oxd}\to MnF{e}_2{O}_4@T_{red}}$$

(4)

The thermal reduction of $MnF{e}_2{O}_4$ results in the release of O₂ from the ferrite crystal lattice. The released O₂ is further conveyed away from the reduction chamber with the help of inert sweep gas. After exiting the reduction chamber, the gas mixture containing inert sweep gas and O₂ is cooled down from $T_{red}$ to $T_{sep-1}$ by using HEX-2 (gas-to-gas heat exchanger). After cooling, the gas mixture is transported to separator-1 to separate O₂ from the inert sweep gas. Separator-1 is operated with an assumed efficiency (${\eta }_{sep-1}$) equal to 15% and as per the process described in the published literature [36]. The heat energy required for the separation of O₂ from inert sweep gas is calculated as per the following set of equations:

$${\dot{Q}}_{sep-1}={\dot{n}}_{MnF}\left[\frac{T_{sep-1}}{{\eta }_{sep-1}}(\mathsf{\Delta }{S}_{mix,{red}_2}-\mathsf{\Delta }{S}_{mix,{red}_1})\right]$$

(5)

$$\mathsf{\Delta }{S}_{mix,{red}_1}=-R\left\{n_{inert}\ln (1-y_{O_2,{red}_1})+n_{O_2,{red}_1}ln{y}_{O_2,{red}_1}\right\}$$

(6)

$$\mathsf{\Delta }{S}_{mix,{red}_2}=-R\left\{n_{inert}\ln (1-y_{O_2,{red}_2})+n_{O_2,{red}_2}ln{y}_{O_2,{red}_2}\right\}$$

(7)

HEX-3 (gas-to-gas heat exchanger) is placed in the model to reduce the temperature of O₂ separated from the inert sweep gas from $T_{sep-1}$ to $T_0$ = 298 K. O₂ is transferred to an ideal CO/O₂ fuel cell after cooling. The inert sweep gas, separated from the O₂, is heated from $T_{sep-1}$ to $T_{red}$ by going through three gas-to-gas heat exchangers (HEX-1, HEX-2, and HEX-3). If required, supplementary heat is provided with the help of auxiliary heater-1. The energy needed to heat the inert sweep gas is estimated as follows:

$${\dot{Q}}_{inert-heat}={\epsilon }_{gg}\left[{\dot{Q}}_{\left(inert+O_2\right)-cool}+{\dot{Q}}_{O_2-cool}+{\dot{Q}}_{{CO}_2-cool}\right]+{\dot{Q}}_{heater-1}$$

(8)

where,

$${\dot{Q}}_{inert-heat}={\dot{n}}_{inert}∆{\left.H\right|}_{inert@T_{sep-1}\to inert@T_{red}}$$

(9)

$${\dot{Q}}_{\left(inert+O_2\right)-cool}={\dot{n}}_{inert}∆{\left.H\right|}_{inert@T_{red}\to inert@T_{sep-1}}+{\dot{n}}_{O_2}∆{\left.H\right|}_{O_2@T_{red}\to O_2@T_{sep-1}}$$

(10)

$${\dot{Q}}_{O_2-cool}={\dot{n}}_{O_2}∆{\left.H\right|}_{O_2@T_{sep-1}\to O_2@T_0}$$

(11)

$${\dot{Q}}_{{CO}_2-cool}={\dot{n}}_{{CO}_2}∆{\left.H\right|}_{{CO}_2@T_{sep-2}\to {CO}_2@T_0}$$

(12)

To carry out the thermochemical CDC, CO₂ (in an excess amount, 10${\delta }_{red}$) enters the oxidation chamber at the state ${oxd}_3$. After completion of the CDC reaction, a gas mixture comprising unreacted CO₂ and produced CO leaves the oxidation chamber at the state ${oxd}_4$. Alternatively, $MnF{e}_2{O}_{4-{\delta }_{red}}$ is shuttled from states ${oxd}_3$ to ${oxd}_4$ in a counter-current fashion relative to the gases encountered. As the CDC reaction is carried out at $T_{oxd}$ = 1000 K, the temperature of $MnF{e}_2{O}_{4-{\delta }_{red}}$ is decreased from $T_{red}$ to $T_{oxd}$ with the help of HEX-1 (solid-to-solid heat exchanger). As the solid-to-solid heat recovery effectiveness (${\epsilon }_{ss}$) is assumed to be zero, the heat energy liberated during the cooling of $MnF{e}_2{O}_{4-{\delta }_{red}}$ is not reused for the heating of $MnF{e}_2{O}_4$. ${\dot{ Q}}_{MnF-oxd}$ is assumed to be rejected to the ambient. The heat dissipated during CO production via CDC is computed using the following equation.

$${\dot{ Q}}_{MnF-oxd}=-{\dot{n}}_{MnF}{\left.∆H\right|}_{MnF{e}_2{O}_{4-{\delta }_{red}}+\left(10{\delta }_{red}\right){CO}_2\to MnF{e}_2{O}_4+(10{\delta }_{red}-{\delta }_{red})C{O}_2+\left({\delta }_{red}\right)CO}$$

(13)

HEX-5 (gas-to-gas heat exchanger) and auxiliary heater-2 are installed in the model to pre-heat CO₂ from $T_0$ to $T_{oxd}$. Equation (14) calculates the heating energy in the case of CO₂.

$${\dot{Q}}_{{CO}_2-heat}={\epsilon }_{gg}\left[{\dot{Q}}_{\left({CO}_2+CO\right)-cool}\right]+{\dot{Q}}_{heater-2}$$

(14)

where,

$${\dot{Q}}_{{CO}_2-heat}={\dot{n}}_{{CO}_2}∆{\left.H\right|}_{{CO}_2@T_0\to {CO}_2@T_{oxd}}$$

(15)

$${\dot{Q}}_{\left({CO}_2+CO\right)-cool}={\dot{n}}_{{CO}_2}∆{\left.H\right|}_{{CO}_2@T_{oxd}\to {CO}_2@T_{sep-2}}+{\dot{n}}_{CO}∆{\left.H\right|}_{CO@T_{oxd}\to CO@T_{sep-2}}$$

(16)

The reuse of CO₂ is possible only if it is separated from CO, for which separator-2 is included. Separator-2 is operated at $T_{sep-2}$ = 400 K and its efficiency (${\eta }_{sep-2}$) equal to 15% [37]. As the CO₂/CO separation is carried out at 400 K, the CO₂/CO gas mixture temperature is reduced from $T_{oxd}$ to $T_{sep-2}$ by passing through HEX-5. The following three equations are used for determining ${\dot{Q}}_{sep-2}$ (heat energy needed for the separation).

$${\dot{Q}}_{sep-2}={\dot{n}}_{MnF}\left[\frac{T_{sep-2}}{{\eta }_{sep-2}}(\mathsf{\Delta }{S}_{mix,{oxd}_4}-\mathsf{\Delta }{S}_{mix,{oxd}_3})\right]$$

(17)

$$\mathsf{\Delta }{S}_{mix,{oxd}_3}=-R\left\{n_{C{O}_2}\ln (1-y_{CO,{oxd}_3})+n_{CO,{oxd}_3}ln{y}_{CO,{oxd}_3}\right\}$$

(18)

$$\mathsf{\Delta }{S}_{mix,{oxd}_4}=-R\left\{n_{C{O}_2}\ln (1-y_{CO,{oxd}_4})+n_{CO,{oxd}_4}ln{y}_{CO,{oxd}_4}\right\}$$

(19)

CO separated from the CO₂/CO gas mixture is further cooled down to $T_0$ with the help of auxiliary cooler-1 (heat rejected to the ambient). CO at 298 K is then transported to the fuel cell, which is installed in the model to complete the thermochemical $MnF{e}_2{O}_{4-{\delta }_{red}}$ based CDC cycle. The fuel cell’s outlet stream, CO₂ at 298 K, is mixed with the unreacted CO₂ (separated from the CO) and then transferred to the oxidation chamber through HEX-5 and heater-2.

The total amount of heat energy essential for the operation of $MnF{e}_2{O}_4$-based CDS cycle is computed by using Equation (20).

$${\dot{Q}}_{TC}={\dot{Q}}_{MnF-red}+{\dot{Q}}_{MnF-sens}+{\dot{Q}}_{heater-1}+{\dot{Q}}_{heater-2}+{\dot{Q}}_{sep-1}+{\dot{Q}}_{sep-2}+{\dot{Q}}_{surf}$$

(20)

where,

$${\dot{Q}}_{surf}=0.2\times {\dot{Q}}_{MnF-red}$$

(21)

For the estimation of the solar-to-fuel energy conversion efficiency (${ \eta }_{solar-to-fuel}$) it is essential first to calculate the solar energy required to drive the cycle (${\dot{Q}}_{solar}$). Hence, ${\dot{Q}}_{solar}$ is determined by using the following set of equations.

$${\dot{Q}}_{solar}=\frac{{\dot{Q}}_{TC}}{{\eta }_{absoption}}$$

(22)

Here,

$${\eta }_{absorption}=1-\left(\frac{\sigma T_{red}^4}{IC}\right)$$

(23)

For the estimation of ${\eta }_{absorption}$, $\sigma$, I, and C are taken as 5.6705 × 10⁻⁸ W/m²·K⁴, 1000 W/m², and 3000 suns, respectively. Re-radiation losses from the model are also calculated by using Equation (24)

$${\dot{Q}}_{re-rad}={\eta }_{absorption}\times {\dot{Q}}_{solar}$$

(24)

Finally, ${ \eta }_{solar-to-fuel}$ is estimated as follows:

$${ \eta }_{solar-to-fuel}=\frac{{{\dot{n}}_{CO}\times HHV}_{CO}}{{\dot{Q}}_{solar}}$$

(25)

3. Results and Discussion

Reduction temperature ($T_{red}$) required to attain ${\delta }_{red}$ = 0.1 is estimated as a function of the ratio of the molar flow rates of inert sweep gas (${\dot{n}}_{inert}$) and $MnF{e}_2{O}_4$ (${\dot{n}}_{MnF}$), i.e., $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$. As per the data presented in Figure 2, the highest $T_{red}$ equal to 1405 K is recorded for $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ and is equal to 10. A further rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 100 reduces $T_{red}$ from 1405 K to 1265 K. Interestingly, the decrease in $T_{red}$ is higher (100 K) when $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ upturns from 10 to 50 as compared to a rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 50 to 100 ($T_{red}$ reduces by 40 K). These observations confirm that the effect of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on $T_{red}$ is less weighty during the increment in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 50 to 100.

The effect of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on the energy required for the reduction of $MnF{e}_2{O}_4$ into $MnF{e}_2{O}_{4-{\delta }_{red}}$ (${\delta }_{red}$ = 0.1) is explored, and the obtained results are presented in Figure 3. As the pre-heating of both inert sweep gas and $MnF{e}_2{O}_4$ are carried out separately (not in the reduction chamber), the heat energy needed for both pre-heating operations is not included in the computation of ${\dot{Q}}_{MnF-red}$. The presented results show that the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ results in a very minute change in ${\dot{Q}}_{MnF-red}$. As $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 100, although $T_{red}$ reduces by 140 K, ${\dot{Q}}_{MnF-red}$ upsurges only by a factor of 1.02.

Equation (4) is applied for the calculation of ${\dot{Q}}_{MnF-sens}$. As mentioned in Section 2, the heat energy dissipated during the cooling of $MnF{e}_2{O}_{4-{\delta }_{red}}$ is not recuperated for the pre-heating of $MnF{e}_2{O}_4$. Variations recorded in ${\dot{Q}}_{MnF-sens}$ due to the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ are presented in Figure 4. The reported trends show that the change in $T_{red}$ has a considerable effect on ${\dot{Q}}_{MnF-sens}$. As per the results, ${\dot{Q}}_{MnF-sens}$ reduces below 77.9 kW by 16.0%, 24.6%, 29.6%, and 33.3% as the $T_{red}$ decreases below 65 K, 100 K, 120 K, and 135 K due to the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 30, 50, 70, and 90, respectively. An overall increase in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{ZnF}$}\right.$ from 10 to 100 is responsible for the reduction in ${\dot{Q}}_{MnF-sens}$ from 77.9 kW to 51.0 kW, respectively.

As per the model presented in Figure 1, after completion of the reduction step, $MnF{e}_2{O}_{4-{\delta }_{red}}$ is transported to the oxidation chamber. In this chamber, the re-oxidation of $MnF{e}_2{O}_{4-{\delta }_{red}}$ is conducted at steady $T_{oxd}$ = 1000 K. As the molar compositions and reaction temperature stay unchanged, ${\dot{ Q}}_{MnF-oxd}$ remains stable at 0.3 kW. Therefore, this heat energy is not utilized and is rejected to the ambient.

O₂ released during the reduction of $MnF{e}_2{O}_4$ is mixed with the inert sweeping gas and moves out of the reduction chamber. To reuse inert sweep gas, the O₂ has to be separated for this gas mixture. As this gas mixture has a temperature higher than 1000 K, ion transport membrane technology (operating temperature range: 1050 to 1200 K) is used for the separation [38]. The operating temperature of separator-1 is assumed to be 1123 K. It is essential first to reduce the temperature of the gas mixture containing inert sweep gas and O₂ from $T_{red}$ to $T_{sep-1}$. This is achieved by passing this gas mixture through HEX-2.

After attaining the separation temperature (1123 K), the inert sweep gas and O₂ gas mixture enters separator-1. Here, 99.9% of O₂ is separated from the inert sweeping gas. Equations (5)–(7) are applied for the determination of the heat energy required for the operation of separator-1 (${\dot{Q}}_{sep-1}$). All the calculations associated with the separator-1 are carried out based on the second law of thermodynamics $\left(\mathsf{\Delta }Q=T\mathsf{\Delta }S\right)$. Moreover, by estimating the entropy of mixing for each stream. As $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ upsurges from 10 to 100, ${\dot{Q}}_{sep-1}$ differs due to the variation in the mole fraction of O₂ at the states ${red}_1$ and ${red}_2$. As shown in Figure 5, the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 30, 50, 70, and 90 results in an upturn in ${\dot{Q}}_{sep-1}$ above 19.6 kW by 3.4 kW, 5.0 kW, 6.0 kW, and 6.8 kW, respectively.

The fuel cell is fed with the O_2, which is first separated from the inert sweep gas and then cooled to 298 K by passing through HEX-3. Alternatively, by going through HEX-2, HEX-3, HEX-4, and heater-1, the inert sweep gas is pre-heated from $T_{sep-1}$ to $T_{red}$.

Table 1. Effect of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on thermal energy required after each gas-to-gas heat exchanger (${\epsilon }_{gg}$ = 0.7) for the pre-heating of inert sweep gas (${\dot{Q}}_{inert-heat}$).

$\raisebox{1ex}{${\dot{\mathit{n}}}_{\mathit{i}\mathit{n}\mathit{e}\mathit{r}\mathit{t}}$}\!\left/ \!\raisebox{-1ex}{${\dot{\mathit{n}}}_{\mathit{M}\mathit{n}\mathit{F}}$}\right.$	${\mathit{T}}_{\mathit{r}\mathit{e}\mathit{d}}$ (K)	${\dot{\mathit{Q}}}_{\mathit{i}\mathit{n}\mathit{e}\mathit{r}\mathit{t}-\mathit{h}\mathit{e}\mathit{a}\mathit{t}}$ (kW)	${\dot{\mathit{Q}}}_{\mathit{i}\mathit{n}\mathit{e}\mathit{r}\mathit{t}-\mathit{h}\mathit{e}\mathit{a}\mathit{t}}$ Required
			After HEX-2 (kW)	After HEX-3 (kW)	After HEX-4 (kW)
10	1405	95.8	28.4	27.5	24.9
20	1365	164.1	48.9	48.0	45.5
30	1340	220.4	65.8	64.9	62.4
40	1320	266.4	79.7	78.7	76.2
50	1305	307.4	92.0	91.0	88.5
60	1295	348.4	104.3	103.3	100.8
70	1285	382.6	114.6	113.6	111.1
80	1275	409.9	122.8	121.8	119.3
90	1270	445.9	133.6	132.6	130.1
100	1265	478.4	143.3	142.4	139.9

reports the influence of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on ${\dot{Q}}_{inert-heat}$. Due to the increase in the $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$, as per the expectations, ${\dot{Q}}_{inert-heat}$ surges substantially. For instance, as $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{ZnF}$}\right.$ rises from 10 to 50 and then to 100, ${\dot{Q}}_{inert-heat}$ increase from 95.8 kW to 307.4 kW and 478.4 kW, respectively.

In HEX-2, heat energy released by inert/O₂ gas mixture during cooling from $T_{red}$ to $T_{sep-1}$ is utilized to pre-heat the inert sweep gas (${\epsilon }_{gg}$ = 0.7). ${\dot{Q}}_{inert-heat}$ considerably decreased when the inert sweep gas passes through the HEX-2. As an example, ${\dot{Q}}_{inert-heat}$ drops from 95.8 kW, 307.4 kW, and 478.4 kW to 28.4 kW, 92.0 kW, and 143.3 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10, 50, and 100, respectively. After HEX-2, the inert sweep gas is then passed through HEX-3 (${\epsilon }_{gg}$ = 0.7). The cooling stream is O_2, which came out of separator-2. In this gas-to-gas heat exchanger, ${\dot{Q}}_{inert-heat}$ decreases only by 0.9 kW for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$. The reason for this lower drop in ${\dot{Q}}_{inert-heat}$ is the lower molar flow rate of O₂. In HEX-4 (${\epsilon }_{gg}$ = 0.7), heat energy dissipated during the cooling of unreacted CO₂ is utilized to heat inert sweep gas. As the CO₂ molar flow rate is much higher than O₂, as compared to HEX-3, the employment of HEX-4 is responsible for a more significant reduction in ${\dot{Q}}_{inert-heat}$. For all values of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$, ${\dot{Q}}_{inert-heat}$ decreases by 2.5 kW.

As shown in Table 1, even though three gas-to-gas heat exchangers are installed, supplementary energy is still needed to heat inert sweep gas. Heater-1 provides the extra heat energy required. Due to the variation in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$, ${\dot{Q}}_{heater-1}$ also differs (Figure 6). For example, as $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 30, 50, 70, and 90, ${\dot{Q}}_{heater-1}$ rises from 24.9 kW to 62.4 kW, 88.5 kW, 111.1 kW, and 130.1 kW, respectively.

The laboratory-scale thermochemical CDS experiments are carried out using excess CO₂. Hence, in this thermodynamic study, a CO₂ molar flow rate equal to 10 times ${\delta }_{red}$ is used. After the completion of CDS, due to the excess supply of CO₂, the oxidation chamber’s exit gas composition contains unreacted CO₂ and CO produced. Unreacted CO₂ can be reutilized for the re-oxidation of $MnF{e}_2{O}_{4-{\delta }_{red}}$ (as shown in Figure 1). To do this, the separation of CO₂ from CO is necessary.

Separator-2 is installed to separate the CO₂ and CO gas mixture. It is operated at $T_{sep-2}$ = 400 K and hence the CO₂/CO gas mixture, which exited the oxidation chamber at $T_{oxd}$ = 1000 K, is cooled by using HEX-5. After the reduction in the temperature, the CO₂/CO gas mixture enters separator-2 (${\eta }_{sep-2}$ = 15%). Like separator-1, 99.9% of CO is separated from the CO₂ stream. The heat energy required to achieve this separation (${\dot{Q}}_{sep-2}$) is calculated by solving Equations (17)–(19). The thermodynamic computations indicate that the mole fraction of CO remains stable at states ${oxd}_3$ and ${oxd}_4$, even though $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 100. Due to this, a stable value of 7.2 kW is recorded for ${\dot{Q}}_{sep-2}$ (for all values of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$).

Supplementary cooler-1 is installed in the model to reduce the temperature of CO (separated from the CO₂/CO gas mixture) from $T_{sep-2}$ to $T_0$. The heat energy dissipated during this cooling is assumed to be rejected to the ambient. As an essential step to close the cycle, CO is transported to the fuel cell and reacts with the O_2, producing CO₂.

CO₂ generated via the fuel cell reaction is mixed with the unreacted CO₂. Before entering into the oxidation chamber, the temperature of the CO₂ needs to be increased from 298 K up to $T_{oxd}$ = 1000 K. This is achieved by using HEX-5 and a supplementary heater-2. It is important to note that even though $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 100, the molar flow rate of CO₂ entering and exiting HEX-5 and heater-2 is steady. Hence, after passing through HEX-5, the additional heat needed for the heating, i.e., ${\dot{Q}}_{heater-2}$, remains unchanged at 13.6 kW.

As mentioned in Section 2 and as per the previously published work [39], it is assumed that 20% of the heat energy associated with the reduction chamber is lost to the ambient due to the issues related to the thermal insulation. By considering these surface heat losses and other necessary heat energy requirements, ${\dot{Q}}_{TC}$ needed to drive the cycle is estimated as per Equation (20). Figure 7 shows the effect of change in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on ${\dot{Q}}_{TC}$. It is visible from the plot that the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ yields into an increase in ${\dot{Q}}_{TC}$. For example, ${\dot{Q}}_{TC}$ mounts above 176.0 kW by 28.6 kW, 49.7 kW, 69.5 kW, and 86.5 kW due to the increment in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 30, 50, 70, and 90, respectively. The reason for the enhancement in ${\dot{Q}}_{TC}$ is the upsurge in ${\dot{Q}}_{heater-1}$ and ${\dot{Q}}_{sep-1}$ as a function of rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$.

After estimating ${\dot{Q}}_{TC}$, ${\dot{Q}}_{solar}$ and ${\dot{Q}}_{re-rad}$ are calculated by employing Equations (22) and (24). Figure 7 and Figure 8 present the divergences allied with both ${\dot{Q}}_{re-rad}$ and ${\dot{Q}}_{solar}$. Both ${\dot{Q}}_{solar}$ and ${\dot{Q}}_{re-rad}$ depends upon ${\eta }_{absorption}$, which in turn relies on $T_{red}$. ${\eta }_{absorption}$ of this cycle increases from 92.6% to 95.2% due to the drop in $T_{red}$ from 1405 K to 1265 K. This rise in ${\eta }_{absorption}$ indicates that a higher percentage of solar energy is absorbed and hence ${\dot{Q}}_{re-rad}$ losses are lower (Figure 7). On the other hand, as ${\eta }_{absorption}$ is less than 100%, ${\dot{Q}}_{solar}$ is recorded to be higher than ${\dot{Q}}_{TC}$ for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ values. For example, ${\dot{Q}}_{solar}$ is recorded to be higher than ${\dot{Q}}_{TC}$ by 14.0 kW, 13.3 kW, 13.1 kW, 13.3 kW, and 13.6 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10, 30, 50, 70, and 90, respectively.

Figure 8 shows the effect of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ on ${ \eta }_{solar-to-fuel}$. For the estimation of ${ \eta }_{solar–to–fuel}$, Equation (25) is used. In this equation, the numerator is steady as ${\dot{n}}_{CO}$ and $HH{V}_{CO}$ are stable at 0.1 and 283.24 kW, respectively. Enhancement in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ is responsible for a rise in ${\dot{Q}}_{solar}$ which in turn reduces ${ \eta }_{solar–to–fuel}$. For example, as $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 30, 50, 70, and 90, ${\dot{Q}}_{solar}$ also rises from 190.0 kW up to 217.8 kW, 238.8 kW, 258.9 kW, and 276.1 kW, respectively. This increment in ${\dot{Q}}_{solar}$ is responsible for the decrease in ${ \eta }_{solar–to–fuel}$ from 14.9% to 13.0%, 11.9%, 10.9%, and 10.3% when $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ upsurges from 10 to 30, 50, 70, and 90, respectively. The obtained results confirm that the maximum ${ \eta }_{solar–to–fuel}$ (14.9%) is attainable at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 ($T_{red}$ = 1405 K, $T_{oxd}$ = 1000 K, ${\epsilon }_{gg}$ = 0.7, and ${\epsilon }_{ss}$ = 0).

The results reported until now confirm that the prime reason for the increment in ${\dot{Q}}_{solar}$ and reduction in ${\eta }_{solar–to–fuel}$ is the rise in ${\dot{Q}}_{MnF-sens}$, ${\dot{Q}}_{heater-1}$, and ${\dot{Q}}_{{CO}_2-heat}$ as $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ upturns from 10 to 100. All the calculations are conducted by assuming ${\epsilon }_{ss}$ and ${\epsilon }_{gg}$ constant at 0.0 and 0.7, respectively. It is well-known that solids’ heat recovery to other solids is challenging and not often used. On the other hand, gas-to-gas heat recovery is commonly used with gas-to-gas heat exchangers. To explore this further, the effect of variation in ${\epsilon }_{gg}$ (from 0.0 to 0.9) on ${\dot{Q}}_{solar}$ and ${\eta }_{solar–to–fuel}$ is investigated here. A 100% gas-to-gas heat recovery (${\epsilon }_{gg}$ = 1) is not practical and hence not considered.

Our results indicate that ${\dot{Q}}_{MnF-red}$ and ${\dot{Q}}_{MnF-sens}$ remain unaltered due to the variation in ${\epsilon }_{gg}$. Conversely, ${\dot{Q}}_{heater-1}$ and ${\dot{Q}}_{heater-2}$ are recorded to be varied considerably when ${\epsilon }_{gg}$ increases from 0.0 to 0.9. As per the trends reported in Figure 9, at steady $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$, a rise in ${\epsilon }_{gg}$ yields a significant reduction in ${\dot{Q}}_{heater-1}$. For example, at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ = 10, ${\dot{Q}}_{heater-1}$ decreases by 91.2 kW when ${\epsilon }_{gg}$ surges from 0.0 to 0.9. Due to the similar upturn in ${\epsilon }_{gg}$, ${\dot{Q}}_{heater-1}$ diminishes by 435.5 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 100.

The influence of ${\epsilon }_{gg}$ on ${\dot{Q}}_{heater-2}$ is reported in

Table 2. Effect of gas-to-gas heat recovery effectiveness (${\epsilon }_{gg}$) on the thermal energy provided by heater-2 (${\dot{Q}}_{heater-2}$) for the pre-heating of CO₂ (for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$).

${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$	${\dot{\mathit{Q}}}_{\mathit{h}\mathit{e}\mathit{a}\mathit{t}\mathit{e}\mathit{r}-2}$ (kW)
0.0	33.4
0.1	30.6
0.3	24.9
0.5	19.2
0.7	13.6
0.9	7.9

. It is already understood that the rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 100 does not affect ${\dot{Q}}_{heater-2}$. Opposite to this, an increment in ${\epsilon }_{gg}$ decreases ${\dot{Q}}_{heater-2}$. The values reported in Table 2 show that ${\dot{Q}}_{heater-2}$ declines below 33.4 kW by 8.4%, 25.4%, 42.5%, 59.3%, and 76.3% due to the rise in ${\epsilon }_{gg}$ from 0.1 to 0.3, 0.5, 0.7, and 0.9, respectively (for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$).

Figure 10 shows that the rise in ${\epsilon }_{gg}$ reduces ${\dot{Q}}_{TC}$ for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$. As per the reported trends, ${\dot{Q}}_{TC}$ decreases by 116.7 kW, 228.7 kW, 306.9 kW, 374.5 kW, and 431.5 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{ZnF}$}\right.$ equal to 10, 30, 40, 50, and 90, respectively, due to the increment in ${\epsilon }_{gg}$ from 0.0 to 0.9. It is also understood that the enhancement in ${\epsilon }_{gg}$ from 0.0 to 0.9 is responsible for the reduction in the difference between ${\dot{Q}}_{TC}$ at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 and 100. For example, the difference between ${\dot{Q}}_{TC}$ at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 and 100 decreases from 363.3 kW (at ${\epsilon }_{gg}$ = 0.0) to 172.1 kW (at ${\epsilon }_{gg}$ = 0.5) and 19.2 kW (at ${\epsilon }_{gg}$ = 0.9).

Table 3. Effect of $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ and gas-to-gas heat recovery effectiveness (${\epsilon }_{gg}$) on the solar energy required to operate $MnF{e}_2{O}_4$-based CO₂ splitting cycle (${\dot{Q}}_{solar}$).

$\raisebox{1ex}{${\dot{\mathit{n}}}_{\mathit{i}\mathit{n}\mathit{e}\mathit{r}\mathit{t}}$}\!\left/ \!\raisebox{-1ex}{${\dot{\mathit{n}}}_{\mathit{M}\mathit{n}\mathit{F}}$}\right.$	${\mathit{T}}_{\mathit{r}\mathit{e}\mathit{d}}$ (K)	${\dot{\mathit{Q}}}_{\mathit{s}\mathit{o}\mathit{l}\mathit{a}\mathit{r}}$ (kW)
		${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.0	${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.1	${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.3	${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.5	${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.7	${\mathit{\epsilon }}_{\mathit{g}\mathit{g}}$ = 0.9
10	1405	288.0	274.0	246.0	218.0	190.0	162.0
20	1365	352.7	331.6	289.2	246.9	204.5	162.2
30	1340	407.2	380.2	326.1	272.0	217.8	163.7
40	1320	451.5	419.7	356.0	292.3	228.7	165.0
50	1305	491.4	455.3	383.1	311.0	238.8	166.6
60	1295	532.4	492.0	411.3	330.6	250.0	169.3
70	1285	566.0	522.1	434.4	346.6	258.9	171.1
80	1275	592.3	545.6	452.3	358.9	265.6	172.2
90	1270	629.0	578.6	477.8	376.9	276.1	175.2
100	1265	662.1	608.3	500.7	393.1	285.5	177.9

shows the effect of ${\epsilon }_{gg}$ on ${\dot{Q}}_{solar}$ for all $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ values. Similar to ${\dot{Q}}_{TC}$, ${\dot{Q}}_{solar}$ also decreases as a function of ${\epsilon }_{gg}$. Even though there is no influence of ${\epsilon }_{gg}$ on ${\eta }_{absorption}$, the increment in ${\epsilon }_{gg}$ from 0.0 to 0.9 is responsible for lessening ${\dot{Q}}_{solar}$ by 126.0 kW, 243.5 kW, 324.8 kW, 394.9 kW, and 453.8 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10, 30, 50, 70, and 90, respectively. Alike ${\dot{Q}}_{TC}$, the increase in ${\epsilon }_{gg}$ also helps to decline the difference between ${\dot{Q}}_{solar}$ at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 and 100. For example, the difference between ${\dot{Q}}_{solar}$ at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 and 100 decreases from 374.1 kW to 334.3 kW, 254.7 kW, 175.1 kW, 95.5 kW, and 15.9 kW due to the upsurge in ${\epsilon }_{gg}$ from 0.0 to 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. Similar to ${\dot{Q}}_{solar}$, ${\dot{Q}}_{re-rad}$ also drops considerably when ${\epsilon }_{gg}$ increases. In terms of numbers, the increment in ${\epsilon }_{gg}$ from 0.0 to 0.9 is responsible for a reduction in ${\dot{Q}}_{re-rad}$ by 9.3 kW, 14.8 kW, 17.8 kW, 20.4 kW, and 22.3 kW at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10, 30, 50, 70, and 90, respectively.

Due to the significant decrease in ${\dot{Q}}_{solar}$, ${\dot{Q}}_{TC}$, and ${\dot{Q}}_{re-rad}$, ${ \eta }_{solar–to–fuel}$ of the $MnF{e}_2{O}_4$-based CDS cycle increases when ${\epsilon }_{gg}$ enhances from 0.0 to 0.9. The trends reported in Figure 11 show that as ${\epsilon }_{gg}$ increments from 0.0 to 0.9, ${ \eta }_{solar-to-fuel}$ improves from 9.8% to 17.5%, 5.8% to 17.0%, and 4.3% to 15.9% at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10, 50, and 90, respectively. It is also understood that when the $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ increases from 10 to 100, the drop in ${ \eta }_{solar–to–fuel}$ is in the range of 5% to 6% for ${\epsilon }_{gg}$ equal to 0.1 to 0.7. However, in the case of ${\epsilon }_{gg}$ = 0.9, as ${\dot{Q}}_{solar}$ ranges from 162.0 kW to 177.9 kW, ${ \eta }_{solar–to–fuel}$ decreases by a lower amount (1.6%) when $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ enhances from 10 to 100. In the end, by applying ${\epsilon }_{gg}$ = 0.9, a maximum ${ \eta }_{solar–to–fuel}$ of 17.5% can be achieved by using $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ equal to 10 as well as 20.

The results obtained in case of Mn-ferrite are compared with the Zn-ferrite [40] redox system, recently investigated by us. At a common ratio of the inert gas flow rate to the ferrite flow rate equal to 20 and gas-to-gas heat recovery effectiveness equal to 0.7, the $T_{red}$ required for the 10% reduction of the Mn-ferrite redox system (1365 K) is recorded to be lower than the Zn-ferrite redox system (1385 K). At these operating conditions, ${\dot{Q}}_{solar}$ in the case of the Mn-ferrite redox system is equal to 204.5 kW whereas for the Zn-ferrite redox system it is equal to 213.8 kW. As with the ${\dot{Q}}_{solar}$ trend, the ${ \eta }_{solar-to-fuel}$ is recorded to be higher for the Mn-ferrite redox system (13.8%) than that of the Zn-ferrite redox system (13.2%).

4. Conclusions

A thermodynamic model for a high-temperature solar thermochemical CDS cycle driven by $MnF{e}_2{O}_4$ is developed and used for the estimation of thermodynamics process parameters. An increase in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 100 is responsible for the decrease in $T_{red}$ from 1405 K to 1265 K. The initial calculations performed at ${\epsilon }_{gg}$ = 0.7 confirm a slight enhancement in ${\dot{Q}}_{MnF-red}$ (0.4 kW) even though the $T_{red}$ reduces by 140 K. Conversely, ${\dot{Q}}_{MnF-sens}$ decreases by 26.9 kW due to the drop in $T_{red}$ from 1405 K to 1265 K. The amount of heat energy required for the separation of inert gas from the inert/O₂ gas mixture increases by 7.2 kW as $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ enhances from 10 to 100. Opposite to this, due to the unchanged molar flow rates of CO₂ and CO, the heat energy needed to separate CO from the CO₂/CO gas mixture remains steady. The rise in $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ from 10 to 100 is also responsible for the increase in ${\dot{Q}}_{heater-1}$ from 24.9 kW to 139.9 kW, respectively. This rise in the thermal energy required for the heating of inert sweep gas results in an enhancement in ${\dot{Q}}_{solar}$ from 190.0 kW to 285.5 kW, which further decreases ${ \eta }_{solar-to-fuel}$ by ~5%. To improve ${ \eta }_{solar–to–fuel}$, ${\epsilon }_{gg}$ is enhanced from 0.7 to 0.9, which significantly reduces ${\dot{Q}}_{TC}$ and ${\dot{Q}}_{solar}$. At ${\epsilon }_{gg}$ equal to 0.9, ${\dot{Q}}_{TC}$ and ${\dot{Q}}_{solar}$ attains lowest values, i.e., 150.1 kW and 162.0 kW (at $\raisebox{1ex}{${\dot{n}}_{inert}$}\!\left/ \!\raisebox{-1ex}{${\dot{n}}_{MnF}$}\right.$ = 10). The reduction in both ${\dot{Q}}_{TC}$ and ${\dot{Q}}_{solar}$ helps the $MnF{e}_2{O}_4$-based CDC cycle to accomplish an ${ \eta }_{solar-to-fuel}$ equal to 17.5%.