Solar Thermochemical CO₂ Splitting Integrated with Supercritical CO₂ Cycle for Efficient Fuel and Power Generation

Abstract

Converting CO₂ into fuels via solar-driven thermochemical cycles of metal oxides is promising to address global climate change and energy crisis challenges simultaneously. However, it suffers from low energy conversion efficiency (${\eta }_{\mathrm{en}}$) due to high sensible heat losses when swinging between reduction and oxidation cycles, and a single product of fuels can hardly meet multiple kinds of energy demands. Here, we propose an alternative way to upsurge energy conversion efficiency by integrating solar thermochemical CO₂ splitting with a supercritical CO₂ thermodynamic cycle. When gas phase heat recovery (ε_gg) is equal to 0.9, the highest energy conversion efficiency of 20.4% is obtained at the optimal cycle high pressure of 260 bar. In stark contrast, the highest energy conversion efficiency is only 9.8% for conventional solar thermochemical CO₂ splitting without including a supercritical CO₂ cycle. The superior performance is attributed to efficient harvesting of waste heat and synergy of CO₂ splitting cycles with supercritical CO₂ cycles. This work provides alternative routes for promoting the development and deployment of solar thermochemical CO₂ splitting techniques.

1. Introduction

Concentrations of carbon dioxide in the atmosphere have been continuously increasing by 50% since the beginning of the industrial era and set a new record value of 421 ppm in 2022 [1]. Unprecedented CO₂ has led to severe climate change and global warming problems, which threatens the sustainable development of human beings. The dominant contribution of excess CO₂ emissions is related with massive utilization of fossil fuels. Employing sustainable energy to convert CO₂, the major products of carbon-containing fuels combustion, into fuels such as carbon monoxide (CO) is one of the most effective routes to reduce CO₂ concentrations [2]. On the other hand, CO is one of the main components of syngas, which can be further converted into liquid fuels through the Fischer-Tropsch process [3,4,5]. Therefore, converting CO₂ into fuels is promising to tackle both climate change problems by reducing CO₂ in the atmosphere and energy crisis challenges via providing sustainable carbon fuels.

Several methods of using solar energy to produce CO are on the list. Photocatalysis [5,6,7,8], electrolysis [9,10,11], and thermochemical CO₂ splitting [12,13,14] have been investigated extensively. Recently, thermochemical CO₂ splitting has attracted widespread attention due to its high theoretical energy conversion efficiency (${\eta }_{\mathrm{en}}$) due to the capability of utilizing the entire solar spectrum [15,16,17]. For one-step CO₂ decomposition, an extremely high temperature over 3000 K is required [18], and mixture gas (possible explosive) needs to be separated, which consumes extra energy. Two-step non-volatile metal oxide cycles, on the other hand, can reduce the required decomposition temperature down to 1773 K and produce O₂ and CO in separate steps [19], thus avoiding energy-consuming gas separation issues. Meanwhile, metal oxide cycles enable rather simple design and operation and can achieve high solar-to-fuel efficiency theoretically [20,21,22]. The process of two-step metal oxide cycles is shown as Equations (1)–(3),

$${\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{ox}}}\to {\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{red}}}+\raisebox{1ex}{$\Delta \delta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\mathrm{O}}_2$$

(1)

$${\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{red}}}+\Delta \delta {\mathrm{CO}}_2\to {\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{ox}}}+\Delta \delta \mathrm{CO}$$

(2)

$$\Delta \delta ={\delta }_{\mathrm{red}}-{\delta }_{\mathrm{ox}}$$

(3)

where ${\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{red}}}$ and ${\mathrm{M}}_x{\mathrm{O}}_{y-{\delta }_{\mathrm{ox}}}$ represent the reduced and oxidized metal oxides, respectively. $\Delta \delta ={\delta }_{\mathrm{red}}-{\delta }_{\mathrm{ox}}$ is the nonstoichiometric swing of the redox material between the reduced and oxidized states.

To achieve a high solar-to-fuel efficiency, developing new materials and optimizing cyclic systems have been extensively investigated in a parallel effort. Ceria has been investigated from a wide range of oxygen pressures and temperatures due to its rapid reaction kinetics at high temperatures [23]. On this basis, the transition metals such as Ca²⁺, Cr³⁺ and Zr⁴⁺ were doped into cerium dioxide to further increase the CO yield to 156, 251, and 315.4 μmol/g, respectively [24,25,26]. Recently, perovskite oxides have received much attention due to their lower reaction temperatures and high CO yield. Gao et al. reported a high CO yield of 595.6 μmol/g based on Sm_0.6Ca_0.4Mn_0.8Al_0.2O₃ [27]. Different reactor designs are also investigated to achieve high efficiencies. For example, researchers proposed a rotary-type reactor by using the reactive ceramics of ceria and Ni_0.5Mn0_.5Fe₂O₄ to produce CO continuously, and the highest average efficiency of 0.66% was obtained [28,29]. Marxer et al. designed a high-temperature solar reactor containing a reticulated porous ceramic, which was made of pure ceria, and obtained a maximum solar-to-fuel efficiency of 1.73% [30]. Haeussler et al. designed and tested a monolithic solar reactor using cerium dioxide foam with a peak solar fuel efficiency higher than 8% [2]. However, energy conversion efficiency based on traditional metal oxide cycles is still limited due to high sensible heat losses when switching between reduction and oxidation processes. Such heat losses can be harvested via a high-temperature particle-particle heat exchanger but suffer from low efficiencies due to a poor heat transfer coefficent between particles. In addition, the single product of fuels can hardly meet multiple kinds of energy demands for practical applications.

In this paper, we propose to combine thermochemical CO₂ splitting with a supercritical CO₂ Bryton cycle and to use cerium dioxide as an intermediate medium. The heat dissipated by cerium dioxide from a high reduction temperature down to a low oxidation temperature is used to heat the supercritical CO₂, which is then fed to the turbine to export power. Simultaneously, cerium dioxide is oxidized at low temperatures to produce CO, which can be used as solar fuel. This combined cycle enriches products of traditional thermochemical CO₂ splitting cycles and makes it possible to reach a higher overall energy efficiency of 20.4% compared with 9.8% otherwise. More detailed thermodynamic analysis and economic analysis, including the energy distribution of sub-systems and effects of different operating parameters on the system efficiency, are discussed.

2. Thermodynamic Model

The system of combining a solar thermochemical CO₂ splitting system [31,32] and a supercritical CO₂ Brayton cycle [33,34] is shown in Figure 1, in which ceria is used as intermediate medium to transport energy. Sunlight (I = 1 kW/m⁻²) shines directly on the heliostat which concentrates solar energy into the solar receiver via reflection. Cerium dioxide particles are irradiated directly by sunshine inside the solar receiver and are rapidly heated to reduction temperature to release O₂. The solar receiver is maintained at a low pressure using a vacuum pump to ensure that the cerium dioxide reduction reaction continues. O₂ cleaved from the fluorite phase is removed by the vacuum pump. Meanwhile, CO₂ enters the compressor at room temperature (T₀) and is compressed to circulating high pressure (P₇), passing through a heat exchanger at the turbine outlet to reach an intermediate temperature (T₈), and then flows into the reaction chamber. In the reaction chamber, CO₂ and ceria exchange heat and undergo an oxidation reaction, during which CO is produced. Therefore, the CO₂ flowing out of the reaction chamber also contains CO, which will be split up by the separator. The pure CO₂ leaves the separator and enters the turbine to expand and export power and then flows into the heat exchanger to recover the waste heat.

It is noted that the functions given require temperatures in Kelvin and pressures in bar for a uniform form of expression. We assume that the system operates in steady-state and thermodynamic equilibrium, meaning that all heat and mass fluxes are independent of time. This facilitates us to calculate the optimal energy conversion efficiency of the system, since the continuous production avoids the start-up and cooling process of the material, thus minimizing losses.

2.1. Thermodynamic Efficiency

We introduce thermodynamic efficiency (${\eta }_{\mathrm{th}}$) to calculate energy uniformly, which depends on the energy obtained by solar receiver (${\dot{Q}}_{\mathrm{rec}}$), radiation loss (${\dot{Q}}_{\mathrm{rad}}$), convection loss (${\dot{Q}}_{\mathrm{conv}}$), and reflected energy (${\dot{Q}}_{\mathrm{ref}}$). The energy analysis of the fixed heliostat field and the solar receiver is shown below. The design parameters are shown in

Table 1. Properties and values for the integrated system.

Property	Value(s)
C	3000
Fr	0.0757
Tred	1400–2100 K
Tox	700–1500 K
P0	1 bar
Pc,in	72–90 bar
Pt,in	180–300 bar
ηmech	0.1
ηO2-rem	0.15
ηsep	0.15
ρ	0.05

as well.

$${\dot{Q}}_{\mathrm{rec}}={\eta }_{\mathrm{h}}IC$$

(4)

where I is the direct normal solar irradiation intensity, C is the solar concentration ratio, and ${\eta }_{\mathrm{h}}$ is the optical efficiency. It is noted that optical efficiency varies widely depending on specific designs, taking values from 60% [35] to 90% [36,37]. Since the decrease in optical efficiency suppresses the overall system efficiency, we choose the upper value of the interval to maximize the energy conversion efficiency.

The radiation and convection loss rates of the solar receiver are represented by Equations (5) and (6), respectively [38,39],

$${\dot{Q}}_{\mathrm{rad}}=A_{\mathrm{ape}}\epsilon \sigma (T_{\mathrm{surf}}{}^4-T_0{}^4)$$

(5)

$${\dot{Q}}_{\mathrm{conv}}=h_{\mathrm{nc}}(T_{\mathrm{surf}}-T_0)A_{\mathrm{surf}}+h_{\mathrm{fc}}(T_{\mathrm{surf}}-T_0)A_{\mathrm{ape}}$$

(6)

where $A_{\mathrm{ape}}$ is the receiver aperture size, $A_{\mathrm{surf}}$ is the surface area of the receiver, ε is the average emissivity of the solar receiver (ε = 0.85), and σ is the Stefan–Boltzmann constant. The convection loss of the solar receiver is the sum of the forced convection loss and the natural convection loss. The forced convection loss comes from the flat plate and is related to the size of the aperture. The natural convection cavity is similar to the flat plate. Here, the wall temperature (T_surf) of the receiver is 20 K higher than the reduction temperature (T₁) [39,40]. We noted that there is a critical point for supercritical CO₂ (7.38 Mpa, 304 K), so here, we set T₀ to 305K [41].

Since the solar receiver reflectivity changes with surface temperature, the numerical simulation of reflection loss is difficult to implement. Therefore, we introduce the view factor with reflectance to simplify the calculation

$${\dot{Q}}_{\mathrm{ref}}={\dot{Q}}_{\mathrm{rec}}\rho F_{\mathrm{r}}$$

(7)

wherein $\rho$ is the reflectance and F_r is the view factor. The view factor is defined as the ratio of the solar receiver aperture area to the solar receiver surface area [42].

According to the first law of thermodynamics, the remaining absorbed heat can be computed as:

$${\dot{Q}}_{\mathrm{abs}}={\eta }_{\mathrm{h}}IC-{\dot{Q}}_{\mathrm{rad}}-{\dot{Q}}_{\mathrm{conv}}-{\dot{Q}}_{\mathrm{ref}}$$

(8)

The thermodynamic efficiency thus can be counted due to the analysis of heat loss from Equation (9).

$${\eta }_{\mathrm{th}}=\frac{{\eta }_{\mathrm{h}}IC-{\dot{Q}}_{\mathrm{rad}}-{\dot{Q}}_{\mathrm{conv}}-{\dot{Q}}_{\mathrm{ref}}}{IC}$$

(9)

2.2. Ceria’s Reduction and Heating

We set T₁ as the reduction temperature (T_red) and T₄ as the oxidation temperature (T_ox) to describe the loop conveniently. Equations (1) and (2) describe the cyclic reaction of cerium dioxide. Ceria is reduced in a low oxygen atmosphere at a temperature of T₁ and a partial pressure of oxygen, $P_{\mathrm{red}}$. ${\delta }_{\mathrm{red}}$ is the oxygen vacancy concentration after reduction reaction. Cerium dioxide is then oxidized in CO₂ at a pressure of $P_{\mathrm{ox}}$, where the oxygen vacancy concentration is ${\delta }_{\mathrm{ox}}$. The yield of each cycle is the difference in oxygen vacancy concentration $\Delta \delta$. For ease of understanding, $\delta$ is defined as a unitless measure:

$$\delta =\frac{[\mathrm{O}]}{[\mathrm{Ce}]}$$

(10)

where [O] is the concentration of oxygen vacancies and [Ce] is the concentration of cerium atoms.

Factors affecting the oxygen vacancy concentration of cerium dioxide have long been the subject of research [23,43]. After continuous exploration, it has been found that the oxygen vacancy concentration is only related to the temperature and the amount of oxygen pressure in the environment. The properties of cerium dioxide have also been investigated over a wide range of oxygen partial pressures (10⁻² to 10⁻⁸ bar) and temperatures (1273–2173 K) [44]. Bulfin et al. fitted the curve based on the accumulated experimental data and obtained Equation (11) [44].

$$(\frac{\delta }{0.35-\delta })=8700P_{{\mathrm{O}}_2}{}^{-0.217}\exp (\frac{-195.6{ \mathrm{kJ} \mathrm{mol}}^{-1}}{RT})$$

(11)

The units of temperature in Equation (11) are Kelvin and the units of partial pressure of oxygen are bar. We bring T₁ into Equation (11) with the adjusted oxygen partial pressure $P_{\mathrm{red}}$ in the solar receiver to calculate ${\delta }_{\mathrm{red}}$. For calculating ${\delta }_{\mathrm{ox}}$, the oxygen partial pressure in T₄ and 200 bar CO₂ is brought into Equation (11), where parameters used in the calculation of ${\delta }_{\mathrm{ox}}$ are computed via HSC.

Figure 2 shows the values of nonstoichiometric coefficient $\delta$ in a low oxygen partial pressure and a CO₂ atmosphere. The ${\delta }_{\mathrm{red}}$ and ${\delta }_{\mathrm{ox}}$ we calculate are consistent with previous thermodynamic studies [45]. Meanwhile, cerium dioxide requires energy ($\Delta H_{\mathrm{red}}$) to undergo reduction to remove the oxygen atoms from the lattice. The change in enthalpy has been found to only depend on the nonstoichiometric coefficient [23]. A polynomial curve of the enthalpy change was fitted.

$$\Delta H=(478-1158\delta +1790{\delta }^2+23368{\delta }^3-64929{\delta }^4{)10}^3$$

(12)

The heat required to reduce 1 mol of cerium dioxide from ${\delta }_{\mathrm{red}}$ to ${\delta }_{\mathrm{ox}}$ can be obtained via variable integration using Equation (12). However, oxidizing cerium dioxide to ${\delta }_{\mathrm{red}}$ requires an excess of oxidant. Therefore, we introduce a stopping point for the oxidation reaction:

$${\delta }_{\mathrm{ox}}(\alpha )={\delta }_{\mathrm{ox}}+(1-\alpha )\Delta \delta ,\hspace{1em}\hspace{1em} 0< \alpha <1$$

(13)

where $\alpha$ is the fraction of the reaction completed and is a number between 0 and 1. Based on a previous calculation [46,47], we take the value of $\alpha$ to be 0.95. Combining Equations (12) and (13), the energy required for the reduction of cerium dioxide can be counted.

$${\dot{Q}}_{\mathrm{red}}={\dot{n}}_{{\mathrm{CeO}}_2}{\displaystyle {\int }_{{\delta }_{\mathrm{ox}}\left(\alpha \right)}^{{\delta }_{\mathrm{red}}}\Delta H \mathrm{d}\delta }$$

(14)

Since the re-oxidation process of cerium dioxide involves the decomposition of CO₂ and the generation of CO, the energy (${\dot{Q}}_{\mathrm{HOX}}$) required for the oxidation of cerium dioxide can be obtained according to the empirical formula [22]

$${\dot{Q}}_{\mathrm{hox}}={\dot{n}}_{{\mathrm{CeO}}_2}(-\Delta H_{\mathrm{red}}-\Delta H_{{\mathrm{CO}}_2}^f+\Delta H_{\mathrm{CO}}^f)$$

(15)

where $\Delta H_{\mathrm{red}}$ represents the heat required for 1 mol of cerium dioxide to be reduced, and this can be calculated using Equations (12) and (13). The $\Delta H_{{\mathrm{CO}}_2}^f$ and $\Delta H_{\mathrm{CO}}^f$ are the mole heat of the formation of CO₂ and CO, respectively, which can be found from the NIST Chemistry Webbook.

Ceria will be heated from T₄ to T₁ after entering the solar receiver. The heat capacity for ceria is taken to be 80 J/mol K [48], because the specific capacity heat of ceria dioxide has little change in the range of 1400–2100 K.

$${\dot{Q}}_{{\mathrm{CeO}}_2}={\dot{n}}_{{\mathrm{CeO}}_2}C{p}_{{\mathrm{CeO}}_2}(T_4-T_1)$$

(16)

The heat (${\dot{Q}}_{\mathrm{reco}}$) recovered from the reheater at the outlet of the turbine is used to heat more supercritical CO₂. Although this heat is not counted as solar energy, it is also one of the energy sources worth investigating.

$${\dot{Q}}_{\mathrm{reco}}={\dot{n}}_{{\mathrm{CO}}_2,\mathrm{t},\mathrm{out}}{\epsilon }_{\mathrm{gg}}(h_{11}-h_{12})={\dot{n}}_{{\mathrm{CO}}_2}(h_8-h_7)$$

(17)

The local heat capacity of supercritical CO₂ varies greatly, thus, the return heat exchanger is generally of segmented design [49], and discontinuous design allows for faster heat transfer [50]. For the convenience of calculation, we use ${\epsilon }_{\mathrm{gg}}$ to denote the heat transfer efficiency of the return heater.

2.3. Storage Tank and Reaction Chamber

Cerium dioxide pellets are transported to a hot tank for storage and subsequently enter the reaction chamber to exchange heat with CO₂ and react. Both components have heat losses to the environment, so we discuss them together. The main sources of energy loss in a particle storage facility are convection from the surrounding environment and conduction from the bin walls [51], which can be expressed by Equation (18).

$${\dot{Q}}_{\mathrm{loss},\tan \mathrm{k}}={\dot{Q}}_{\mathrm{foundation}}+{\displaystyle {\int }_0^{l}ph(T_{\tan \mathrm{k}}-T_0) \mathrm{d}x+{\dot{Q}}_{\mathrm{top}}}$$

(18)

$${\dot{Q}}_{\mathrm{loss},\tan \mathrm{k}}={\dot{n}}_{{\mathrm{CeO}}_2}C{p}_{{\mathrm{CeO}}_2}(T_2-T_3)$$

(19)

where ${\dot{Q}}_{\mathrm{foundation}}$ and ${\dot{Q}}_{\mathrm{top}}$ are the heat loss at the bottom and top of the heat storage tank, respectively. The perimeter p is for a round silo to $2\sqrt{\pi A}$, and A is the silo cross sectional area. The heat loss of the silo is integrated along the silo height l. According to the second law of thermodynamics, the outlet temperature of the heat storage tank can be easily calculated using Equation (19).

In the reaction chamber, cerium dioxide reacts with CO₂ in an oxidation process and heat exchange takes place. This can be achieved using either a fluidized bed or a cyclone heat exchanger [52,53]. In order to facilitate the calculations, the pressure drop in the reaction chamber is ignored and the forced heat balance is reached at the outlet.

$${\dot{Q}}_{\mathrm{loss},\mathrm{camber}}+{\dot{n}}_{{\mathrm{CeO}}_2}(h_3-h_4)+{\dot{Q}}_{\mathrm{hox}}={\dot{n}}_{{\mathrm{CO}}_2}(h_9-h_8)+{\dot{n}}_{\mathrm{CO}}HHV$$

(20)

The energy that can be released by the fuel is expressed in terms of the high heat value (HHV), because CO is gaseous and there is no latent heat of vaporization. Thus, here, the HHV is equal to the value of the low heat value (i.e., heat of combustion).

2.4. Auxiliary Energy

In exception to chemical reactions that require heat to complete the reaction, the system requires additional energy to complete the cycle, including removal of oxygen from the solar receiver (${\dot{Q}}_{\mathrm{pump}}$), transport of cerium dioxide between cold/hot tanks (${\dot{Q}}_{\mathrm{mech}}$), compression of supercritical CO₂ from low to high pressure in the cycle (${\dot{W}}_{\mathrm{c}}$), and separation of the mixture of CO₂ and CO (${\dot{Q}}_{\mathrm{sep}}$).

Other methods such as inert gas sweeping and chemical removal can remove the generated oxygen [54]; here, we use a vacuum pump to remove the excess oxygen in the solar receiver for convenience of calculation and give the formula

$${\dot{Q}}_{\mathrm{pump}}={\dot{n}}_{{\mathrm{O}}_2}R{T}_0\ln (\frac{P_0}{P_{\mathrm{red}}}) \frac{1}{{\eta }_{\mathrm{pump}}}$$

(21)

wherein the value of $P_{\mathrm{red}}$ is equal to the partial pressure of oxygen at point 1 and the pumping efficiency (${\eta }_{\mathrm{pump}}$) is as shown in Table 1.

The particles in the thermochemical CO₂ splitting system need to be transported to the solar receiver and sent to the thermal storage tank for cycling. We assume that the transport height H for one cycle is 10 m. The mechanical work is obtained by dividing the gravitational potential energy by the mechanical efficiency (${\eta }_{\mathrm{mech}}$). The energy share of ${\dot{Q}}_{\mathrm{mech}}$ in the system is very low (less than 1%) and almost negligible.

$${\dot{Q}}_{\mathrm{mech}}={\dot{n}}_{{\mathrm{CeO}}_2}\frac{M\times g\times H}{{\eta }_{\mathrm{mech}}}$$

(22)

In a supercritical CO₂ Brayton cycle, the compressor works on the same principle as a turbine, in which CO₂ is compressed or expanded, resulting in a change in enthalpy that can be calculated as power. The flow rate in the compressor and the turbine is not the same due to the fact that the CO₂ flows through the separator and into the turbine.

$${\dot{W}}_{\mathrm{c}}={\dot{n}}_{{\mathrm{CO}}_2}(h_7-h_6)$$

(23)

$${\dot{W}}_{\mathrm{t}}={\dot{n}}_{{\mathrm{CO}}_2,\mathrm{t},\mathrm{in}}(h_{10}-h_{11})$$

(24)

The energy required for the separator can be determined using the second law of thermodynamics with the entropy of the separated gas divided by the separation efficiency (${\eta }_{\mathrm{sep}}$) to derive Equation (25). Here, ${\dot{n}}_{\mathrm{mix}}$ and $\Delta S_{\mathrm{mix}}$ correspond to the flow rate and the entropy of the unseparated gas mixture at state 9, respectively. We assume that the value of $T_{\mathrm{sep}}$ is equal to the oxidation temperature.

$${\dot{Q}}_{\mathrm{sep}}=\frac{\Delta S_{\mathrm{unmix}}{T}_{\mathrm{sep}}}{{\eta }_{\mathrm{sep}}}=T_{\mathrm{sep}}({\dot{n}}_{\mathrm{CO}}\Delta S_{14}+{\dot{n}}_{{\mathrm{CO}}_2,\mathrm{sep},\mathrm{out}}\Delta S_{10}-{\dot{n}}_{\mathrm{mix}}\Delta S_{\mathrm{mix}})\frac{1}{{\eta }_{\mathrm{sep}}}$$

(25)

2.5. System Efficiency

The total amount of energy essential for the operation of a ceria-based thermochemical CO₂ splitting system integrating supercritical CO₂ is computed via Equation (26).

$${\dot{Q}}_{\mathrm{tc}}={\dot{Q}}_{{\mathrm{CeO}}_2}+{\dot{Q}}_{\mathrm{red}}+{\dot{Q}}_{\mathrm{pump}}+{\dot{Q}}_{\mathrm{mech}}+{\dot{Q}}_{\mathrm{sep}}+{\dot{W}}_{\mathrm{c}}$$

(26)

Based on our calculated thermodynamic efficiency, we can work out the solar energy needed for the system.

$${\dot{Q}}_{\mathrm{solar}}=\frac{{\dot{Q}}_{\mathrm{tc}}}{{\eta }_{\mathrm{th}}}$$

(27)

The total energy losses of the system are also computed using Equation (28).

$${\dot{Q}}_{\mathrm{loss}}={\dot{Q}}_{\mathrm{solar}}(1-{\eta }_{\mathrm{th}})$$

(28)

The system fuel efficiency (${\eta }_{\mathrm{fuel}}$) of the process is defined as the ratio of the high heating value of the production fuel to the solar energy needed to drive the cycle. Analogously, the system’s turbine efficiency (${\eta }_{W_{\mathrm{t}}}$) can be defined as the ratio of power exported by the turbine to the total solar energy.

$${\eta }_{\mathrm{fuel}}=\frac{{\dot{n}}_{\mathrm{CO}}HHV}{{\dot{Q}}_{\mathrm{solar}}}$$

(29)

$${\eta }_{W_{\mathrm{t}}}=\frac{{\dot{W}}_{\mathrm{t}}}{{\dot{Q}}_{\mathrm{solar}}}$$

(30)

To count the energy conversion of the system, we write Equation (31) by adding the values of ${\eta }_{\mathrm{fuel}}$ and ${\eta }_{W_{\mathrm{t}}}$.

$${\eta }_{\mathrm{en}}=\frac{{\dot{n}}_{\mathrm{CO}}HHV+{\dot{W}}_{\mathrm{t}}}{{\dot{Q}}_{\mathrm{solar}}}$$

(31)

3. Results

3.1. Oxygen Partial Pressure during Reduction

In terms of the degree of ${\delta }_{\mathrm{red}}$ created in the ceria crystal structure, Figure 3a reports the amount of O₂ released during reduction conducted at different T_red (from 1400–2100 K) and P_red (from 10⁻³–10⁻⁵ bar). The results presented show that, at all T_red, the ${\delta }_{\mathrm{red}}$ upsurged with the reduction in the P_red. For instance, the ${\delta }_{\mathrm{red}}$ was increased by 0.077, 0.037, 0.009, and 0.001 at 2100 K, 1900 K, 1700 K, and 1500 K, respectively, when the P_red was decreased from 10⁻³–10⁻⁵ bar. Simultaneously, the growth in the T_red was beneficial towards improving the capacity of O₂ released during reduction. In terms of values, the δ_red was increased by 0.12, 0.16, and 0.21 when the T_red was enhanced from 1400–2100 K at stable P_red = 10⁻³ bar, P_red = 10⁻⁴ bar, and P_red = 10⁻⁵ bar, separately.

The effect of T_red on ${\dot{n}}_{{\mathrm{CO}}_2}$, ${\dot{n}}_{{\mathrm{CO}}_2,\mathrm{sep},\mathrm{out}}$, and ${\dot{n}}_{\mathrm{CO},\mathrm{sep},\mathrm{out}}$ is shown in Figure 3b. The ${\dot{n}}_{{\mathrm{CO}}_2}$ and the ${\dot{n}}_{{\mathrm{CO}}_2,\mathrm{sep},\mathrm{out}}$ were reduced due to the increment in the ${\dot{Q}}_{\mathrm{loss}}$. For example, as the T_red was upsurged from 1400–2100 K, the ${\dot{n}}_{{\mathrm{CO}}_2}$ and ${\dot{n}}_{{\mathrm{CO}}_2,\mathrm{sep},\mathrm{out}}$ decreased by 16.7 mol/s and 17.9 mol/s, respectively. On the contrary, the ${\dot{n}}_{\mathrm{CO},\mathrm{sep},\mathrm{out}}$ rose by 1.3 mol/s due to the escalation in the T_red from 1400–2100 K. The variations in the ${\dot{W}}_{\mathrm{t}}$, ${\dot{n}}_{\mathrm{CO}}HHV$, and ${\dot{Q}}_{\mathrm{solar}}$ due to the decrease of P_red are presented in Figure 3c. As the released O₂ was increased due to the decreased P_red from 10⁻³ to 10⁻⁵ bar, a greater quantity of CO was produced during the oxidation reaction, i.e., the ${\dot{n}}_{\mathrm{CO}}HHV$ rose from 307.6–508.9 kW at 1900 K. In contrast, the ${\dot{W}}_{\mathrm{t}}$ decreased from 138.1–107.0 kW due to the upsurged CO when the P_red decreased from 10⁻³–10⁻⁵ bar. In terms of numbers, the value and growth of ${\dot{n}}_{\mathrm{CO}}HHV$ far exceeds that of ${\dot{W}}_{\mathrm{t}}$. Simultaneously, the ${\dot{Q}}_{\mathrm{solar}}$ was increased from 3680.4–4048.6 kW due to the increment in the P_red from 10⁻³ to 10⁻⁵ bar.

The efficiency analysis was initiated by exploring the effect of oxygen partial pressure (P_red) on the various process parameters at constant T_ox = 1300 K, P_c,in = 75 bar, and P_t,in = 200 bar. By using Equation (31), the ${\eta }_{\mathrm{en}}$ was computed. As shown in Figure 3d, the numbers obtained indicated that each curve of ${\eta }_{\mathrm{en}}$ had a peak at high temperatures at all P_red as the T_ox, P_c,in, and P_t,in were kept constant. All these peak values were observed to be increased with the increased P_red. In terms of numerical values, the value of the peak escalated from 12.2–15.2%, and the peak temperatures went down from 1950–1850 K due to the decrease in the P_red from 10⁻³–10⁻⁵ bar.

3.2. Reduction Temperature

In this part, the effect of oscillation in the T_red from 1400–2100 K at constant P_red = 10⁻⁴ bar and T_ox = 1300 K on the energy distribution of the cycle was examined. Firstly, the values associated with ${\eta }_{\mathrm{th}}$ were computed using Equation (9). As the T_ox was steady at 1300 K, the ${\eta }_{\mathrm{th}}$ was reduced by 33% due to the rise in the T_red from 1400–2100 K.

Figure 4b shows the percentage of energy required for each part of the system. The heat losses due to radiation, convection, and reflection were estimated as Equations (5)–(7). As expected according to the principles of heat transfer, ${\dot{Q}}_{\mathrm{loss}}$ was observed to be increased with the rise in T_red. For instance, as the T_red rose from 1400–2100 K, the percentage of ${\dot{Q}}_{\mathrm{loss}}$ upsurged from 0.26–0.59. Meanwhile, with the increase of T_red, a higher quantity of O₂ was released. Thus, as the ${\delta }_{\mathrm{red}}$ upsurged, the energy needed to drive the reduction reaction also increased considerably. In terms of ratios, when the ${\dot{Q}}_{\mathrm{rec}}$ was constant and the T_red was increased from 1400–2100 K, the proportion of ${\dot{Q}}_{{\mathrm{CeO}}_2}$ decreased from 0.67–0.16 because of the increased ${\dot{Q}}_{\mathrm{loss}}$ and ${\dot{Q}}_{\mathrm{red}}$.In contrast, the ratio of ${\dot{Q}}_{\mathrm{red}}$ increased from 0.03–0.18 when T_red upsurged from 1400–2000 K, due to the rise in the conversion rate, and decreased by 0.02 as T_red was 2100 K because of the increment of ${\dot{Q}}_{\mathrm{loss}}$. The summary of ${\dot{Q}}_{\mathrm{mech}}$, ${\dot{Q}}_{\mathrm{pump}}$, ${\dot{Q}}_{\mathrm{sep}}$, and ${\dot{W}}_{\mathrm{c}}$ accounted for 0.04 of ${\dot{Q}}_{\mathrm{solar}}$ when the T_red was 1400 K, and the proportion rose to 0.09 as the T_red reached 2100 K. The change in proportion in this process was tiny enough to be ignored.

The effect of ascension in the T_red on the ${\eta }_{\mathrm{fuel}}$, ${\eta }_{W_{\mathrm{t}}}$, and ${\eta }_{\mathrm{en}}$ of the system are presented in Figure 4a. Based on the substantial loss in the ${\dot{Q}}_{\mathrm{solar}}$ and the increment in the conversion rate, the trend of ${\eta }_{\mathrm{fuel}}$ was similar to that of ${\dot{Q}}_{\mathrm{red}}$. In terms of numbers, the highest ${\eta }_{\mathrm{fuel}}$ = 11% in the cycle was obtained at T_red = 2000 K. Due to the ascension of the conversion rate, a higher quantity of CO was released during the oxidation reaction, reducing the amount of CO₂ which was delivered into the turbine. The ${\eta }_{W_{\mathrm{t}}}$, thus, dropped from 7.8% to 1.9% when T_red upsurged from 1400–2100 K. According to Equation (31), the ${\eta }_{\mathrm{en}}$ rose to 13.8%, as T_red increased from 1400–1900 K and decreased by 1.4% when T_red rose to 2100 K.

3.3. Oxidation Temperature

After investigating the influence of T_red, this part further explores the consequence of a rise in T_ox from 700–1500 K on energy distribution associated with the cycle. The energy trend of each part is reported in Figure 5b at constant T_red = 1900 K and ε_gg = 0.9 (at stable P_red = 10⁻⁴ bar). According to Equation (9), the ${\eta }_{\mathrm{th}}$ was stable when T_red was a constant.

Namely, the percentage of ${\dot{Q}}_{\mathrm{loss}}$ was maintained at 0.46 due to the fixed thermodynamic efficiency. In the case of the solar receiver, the inlet and outlet of ceria was T_ox and T_red, individually. Thus, while the T_ox was increased, the temperature gap between the inlet and outlet ceria temperature was diminished. This decrease in the temperature gap resulted in an upturn in the ${\dot{Q}}_{\mathrm{red}}$, as a higher quantity of cerium dioxide can be heated to the reduction temperature. Conversely, the ratio of the ${\dot{Q}}_{{\mathrm{CeO}}_2}$ diminished from 1220–828.3 kW when the T_ox increased from 700–1500 K. This consequence was caused by the upsurged ${\dot{Q}}_{\mathrm{pump}}$ and ${\dot{Q}}_{\mathrm{sep}}$ because more O₂ and CO was released with the increase of the ceria. For instance, the proportion of ${\dot{Q}}_{\mathrm{pump}}$ and ${\dot{Q}}_{\mathrm{sep}}$ rose by 0.01 and 0.07, respectively, due to the upsurge in the T_ox from 700 to 1500 K.

The ${\eta }_{\mathrm{fuel}}$, ${\eta }_{W_{\mathrm{t}}}$, and ${\eta }_{\mathrm{en}}$ were calculated as functions of T_ox, meanwhile, the results are presented in Figure 5a. The finding shown in the figure indicates that the ${\eta }_{\mathrm{fuel}}$ had a continuous growth due to the increased ${\dot{Q}}_{\mathrm{red}}$. In terms of numbers, the ${\eta }_{\mathrm{fuel}}$ rose from 6.9–11.6% when the T_ox increased from 700–1500 K. The upturned ${\dot{Q}}_{\mathrm{red}}$ resulted in the reduction of ${\dot{Q}}_{{\mathrm{CeO}}_2}$, diminishing the quantity of CO₂ imported into the turbine. The ${\eta }_{W_{\mathrm{t}}}$, thus, reduced from 11.1–7.4%, as the T_ox upsurged from 760–1500 K. It should be noted that there was an ascension of the ${\eta }_{W_{\mathrm{t}}}$ with the increment of T_ox because the enthalpy of CO₂ increases rapidly during this period. The trend of ${\eta }_{\mathrm{en}}$ about T_red is similar to that about T_ox. The highest ${\eta }_{\mathrm{en}}$ = 19.05% in this case was obtained at T_ox = 1300 K, and the ${\eta }_{\mathrm{en}}$ upsurged from 18.95–18.87% with the increment of the T_ox from 1460–1500 K due to the considerable rise in the ${\eta }_{\mathrm{fuel}}$.

3.4. Heat Recovery

At T_red = 1900 K and T_ox = 1300 K, the effect of variation in the ε_gg from 0 to 1 on the ${\eta }_{\mathrm{en}}$ was investigated. In case of the heat exchanger, as the ε_gg was increased, the ${\dot{Q}}_{\mathrm{reco}}$ and the quantity of CO₂ upsurged due to the constant ${\dot{Q}}_{\mathrm{rec}}$. Figure 6a indicates that the ${\dot{Q}}_{\mathrm{reco}}$ had an ascension from 0 to 2140 kW when the ε_gg increased from 0 to 1. The consequence of the increment in the ε_gg for the ${\dot{Q}}_{\mathrm{sep}}$ and ${\dot{Q}}_{\mathrm{solar}}$ was explored using Equations (25) and (27), respectively. With the increment in the ε_gg from 0 to 1, the ${\dot{Q}}_{\mathrm{sep}}$ was enhanced from 333.6–470.3 kW. This ascension in the ${\dot{Q}}_{\mathrm{sep}}$ reflected an increase in the ${\dot{Q}}_{\mathrm{solar}}$ from 3870–4210 kW.

Figure 6b represents the variation associated with the ${\eta }_{\mathrm{fuel}}$, ${\eta }_{W_{\mathrm{t}}}$, and ${\eta }_{\mathrm{en}}$ as a function of ε_gg. Because the ${\dot{Q}}_{\mathrm{rec}}$ was at a constant and the ceria can be converted completely, the value of ${\dot{n}}_{\mathrm{CO}}HHV$ was kept at 406.9 kW. As previously studied, the ${\dot{Q}}_{\mathrm{solar}}$ was escalated with the increment in the ε_gg. The ${\eta }_{\mathrm{fuel}}$, thus, diminished from 10.5–9.7% when the ε_gg increased from 0 to 1. In contrast, the ${\eta }_{W_{\mathrm{t}}}$ upsurged from 3.2–11.6%, as a larger amount of CO₂ was fed into the turbine. Overall, the ${\eta }_{\mathrm{en}}$ improved by 7.5%, as calculated via Equation (31).

3.5. Cycle High Pressure

The effect of upswing in the cycle high pressure (i.e., P_t,in) on the ${\dot{n}}_{{\mathrm{CO}}_2}$ and ${\dot{W}}_{\mathrm{t}}$ of the cycle is presented in Figure 7b, when T_red = 1900 K, T_ox = 1300 K, and ε_gg = 0.9.

In case of the compressor, the inlet and the outlet pressure of CO₂ was 75 bar and P_t,in, respectively. Hence, as the P_t,in was increased, the pressure gap between the inlet and the outlet of the compressor upsurged. Thus, the outlet temperature of the compressor rose accordingly by about a dozen degrees, reducing the temperature increase required for CO₂. However, Figure 8 indicates that the average heat capacity of CO₂ was increased due to the increment in the P_t,in. Thus, the ${\dot{n}}_{{\mathrm{CO}}_2}$ had a decrease with the upturned P_t,in. In terms of numbers, the ${\dot{n}}_{{\mathrm{CO}}_2}$ diminished from 45.5–33.9 mol/s, as the P_t,in improved from 180–260 bar. In addition, the h_t,in can be reduced due to the ascension in the P_t,in, making it possible for the turbine to export more power under a limited flow rate. Thence, the highest ${\dot{W}}_{\mathrm{t}}$ = 437.9 kJ/s in case of the cycle was obtained at P_t,in = 260 bar, reaching to the maximum value, which was 10.6%, and then diminished in the range of 260–300 bar. Opposite to this consequence, the ${\eta }_{\mathrm{fuel}}$ remained at about 9.8% due to the stable CO generation and ${\dot{Q}}_{\mathrm{solar}}$. Overall, it seems that the oscillation of the system high pressure mainly impacted the ${\eta }_{\mathrm{en}}$ when T_red and T_ox were constant, as the trend of ${\eta }_{\mathrm{en}}$ was similar to that of ${\eta }_{{\mathrm{W}}_{\mathrm{t}}}$. In terms of values, the maximum ${\eta }_{\mathrm{en}}$ = 20.4% was attained at P_t,in = 260 bar.

3.6. Cycle Low Pressure

Figure 9a presents the effect of cycle low pressure (i.e., P_c,in) on system performance. It can be seen that the increasing cycle low pressure was profitless in terms of both ${\eta }_{{\mathrm{W}}_{\mathrm{t}}}$ and ${\eta }_{\mathrm{en}}$ in the range of 75–87 bar, but the ${\eta }_{\mathrm{fuel}}$ was maintained at 9.9%, as the increase in cycle low pressure caused the compressor outlet temperature to decrease. However, unlike the cycle high pressure, the increase in cycle low pressure from 72 bar to 90 bar will decrease the compressor outlet temperature by 50 degrees. Near the critical point of supercritical CO₂, a temperature difference of a few tens of degrees will cause a wide range of fluctuations in the heat capacity of supercritical CO₂. In addition, the average heat capacity of supercritical CO₂ was upsurged with the increment in cycle low pressure. Therefore, as shown in Figure 9b, our calculated CO₂ flow rate and ${\dot{W}}_{\mathrm{t}}$ are not regular with the change of cycle low pressure.

3.7. Economic Analysis

The economic evaluation can derive the production cost of solar thermal chemical CO production and electricity generation [55,56]. This cost takes into account the time value cost of money and calculates the total cost of the system over its life cycle [57,58]. Using the annual rate method to derive annualized values, the total life cycle cost (TLCC) can be used to derive the cost per kilogram of CO. TLCC is computed by Equation (32), wherein V denotes the investments, M the tax rate, PV_DEP the present value of the series of occurring depreciation, and PV_O&M the present value of operation and maintenance costs. And the present value of reducing recurring U over a time period is found with Equation (33). In case of constant annual payments, the equation can be simplified using the annuity factor $N=i {(1- {(1+i)}^{-b})}^{-1}$, wherein i is the interest rate and b is the lifetime of the system.

$$TLCC=\frac{V- (M\ast P{V}_{\mathrm{DEP}})+(1-M) P{V}_{O\&M}}{1-M}$$

(32)

$$P{V}_x=\{\mathrm{DEP},\mathrm{O}\&\mathrm{M}\}={\displaystyle \sum _{j=1}^{U_j}\frac{U_j}{{\left(1+i\right)}^j}=U_j\ast N}$$

(33)

The production costs, or levelized costs per kilogram of CO (LCO), can then be determined by dividing the TLCC by the annual factor times the annual production rate Q (kg CO per year): $LCO=\frac{TLCC}{Q\ast N}$. Finally, Equation (32) can be simplified to $TLCC=V+P{V}_{O\&M}$, when the project is supported by the government and no taxes have to be paid.

Regardless of weather changes and the intensity of light, the system’s working time is set to 12 h a day, and a year is 365 days. At the highest energy conversion efficiency, the value of the annual output of CO is 634,819.68 kg, while the annual output of electricity is 76,734.97 kWh. The lifetime of the system is 25 years, the average interest rate is 6%, and other parameters are obtained from the previous literature [59,60]. According to Equations (32) and (33), the unit cost of solar fuel is $ 5.86/kg, which is lower than the average market price of CO. The unit cost further decreases to $ 5.62/kg when economic benefits of electricity generation are deducted. The electricity produced by the supercritical CO₂ cycle reduces the cost of the conventional thermochemical cycle by 4%, improving the economics of the system.

4. Conclusions

In summary, we proposed an alternative way to upsurge energy conversion efficiency by integrating solar thermochemical CO₂ splitting with a supercritical CO₂ thermodynamic cycle. For a traditional thermochemical CO₂ splitting cycle, the optimal reduction temperature is around 1900 K at a partial pressure of oxygen of 10⁻⁴ bar, where the highest energy conversion efficiency is 11%. For an integrated system, the optimal reduction and oxidation temperatures were found to be 1900 and 1300 K, respectively. Simultaneously, the fuel efficiency was constant at 9.8% and the energy efficiency was upturned to 20.4% under the cycle high pressure of 260 bar. The superior performance is attributed to efficient harvesting of waste heat and synergy of CO₂ splitting cycles with supercritical CO₂ cycles. This work provides alternative routes for improving low efficiency of traditional solar thermochemical CO₂ splitting cycles while also enriching products beyond single fuels.