Modelling of a hybrid system for on-site power generation from solar fuels

Solar fuels, as clean and sustainable fuels, are promising energy sources for future low carbon economy. In this work, a hybrid system consisting of a photoreactor and a solid oxide fuel cell (SOFC) is proposed for on-site power generation from solar fuels. 2D numerical models are developed for the hybrid system for the first time by coupling the mass/momentum transport with the charge (electrons/ions) transport and the electrochemical/ chemical reactions. A peak power density of 2162Wm is achieved from the SOFC at 1073 K operating temperature. However, a rapid drop of the power density is observed at large current density due to the fuel starvation in the anode. The inlet CO2 mole fraction is found to significantly affect the output power density of the SOFC and CO2 utilization rate of the photo reactor, where a CO2 mole fraction of 40% is the optimum value for the studied cases. The results offer insightful information on energy conversion from solar to fuel to power and provide new options for sustainable energy conversion devices.


Introduction
Development of low-carbon and sustainable energy technologies has raised widely interest due to recent concerns about climate change and environmental problems [1][2][3]. Renewable energy technology such as photovoltaics (PV) is promising for sustainable energy utilization [4][5][6]. However, with the solar radiation being intermittent and unstable, a more effective energy storage and smarter transportation system is required for reliable energy supply [7][8][9][10]. Limited by complex energy storage and smart grid technologies, solar-driven fuel generation has become a viable solution towards solar energy harnessing and is worthy of significant effort [11][12][13].
In the process of solar fuel generation, solar energy is harvested by semiconductors, such as titanium dioxide (TiO 2 ) in a photoreactor [14][15][16]. On the catalyst surface, photochemical reduction reactions are initiated when electron-hole pairs are generated by light radiations [17]. Through photochemical reduction reactions, CO 2 and H 2 O vapour can be reduced to CO, methane and other hydrocarbon fuels [18,19]. Since Fujishima & Honda first demonstrated the use of TiO 2 in photocatalytic H 2 O splitting [20], the route from solar to fuel has been widely investigated by researchers all over the world. With the development of catalysts, higher light absorption, large surface area and improved charge separation were achieved by Kim et al. [21], where a methane generation rate of approximately 12 times higher than that of using pure TiO 2 was observed. Recently, Sorcar et al. [22] also described an efficient, stable, and readily synthesized CO 2 -reduction photocatalyst, which produces a unprecedented high combined photocatalytic yield of ethane (2.7%) and methane (5.2%) over the 42 h test duration. In spite of significant progress in solar fuels synthesis, the direct utilization of product (the gas species mixture including hydrocarbons, CO, CO 2 , solar cells, the utilization of solar fuels offers a potential way of continuous and stable power supply [24,25]. Therefore, the utilization of solar energy can be simplified by combining photochemical synthesis reactor with a device that can effectively utilize the mixture gas of solar fuel, such as solid oxide fuel cells (SOFCs).
SOFCs are electrochemical devices for converting chemical energy into electricity with high efficiency (> 60%) [26][27][28]. They are whole solid-state devices working quietly, usually with a dense ion-conducting electrolyte sandwiched between two electrodes [29,30]. Using this sandwich structure, fuel and oxidant (air) are well separated and the emission can be controlled in a way that the outlet gas can be recycled for an efficient loop [31,32]. Besides, the high operating temperature (about 800°C) of SOFCs allows the use of non-noble catalyst (such as nickel) while keeping high electrochemical activity [33,34]. Fuel flexibility is another important advantage in SOFCs compared with low temperature fuel cells [35,36]. H 2 , ammonia, various hydrocarbon fuels, and even solid carbon can be utilized for power generation [37][38][39]. In particular, the direct utilization of low-cost fuels (such as methane) in SOFCs has attracted great attention, where novel electrolyte structures have been proposed [40][41][42]. Due to the maturing market for SOFCs and their excellent scalability, SOFC-combined systems have been widely studied for further performance improvement [43][44][45][46]. It has been proved by previous researchers that SOFCs are very suitable components of hybrid systems; however, so far no work has been done to investigate a hybrid system combing a SOFC with a photoreactor to achieve on-site solar-fuel-to-power process (Fig. 1). Since this hybrid system has potential to realize low-carbon economy, it is of great importance to understand the detailed chemical/physical processes of the system. To fill the above-mentioned research gap, a hybrid system containing an SOFC and a photoreactor is proposed and evaluated by a 2D mathematical model. The kinetics for the SOFC section are validated with the experimental data, whilst validated kinetics for the photoreactor section are adopted for model development.
Parametric simulations are performed to gain insights in the coupled physical/chemical processes in the hybrid system for further optimization.

Model description
The proposed hybrid system mainly consists of a photoreactor and an SOFC, as shown in Fig. 1. The SOFC and the photoreactor are physically separated (which can be realized through multi-layer insulation structure), and their working temperatures are separately controlled. Thus, their different operating temperature will not affect each other. CO 2 and H 2 O are introduced into the photoreactor, where they are reduced by solar energy to generate CH 4 , CO and O 2 . After O 2 separation, the mixed gas (containing CH 4 , CO, CO 2 and H 2 O) is supplied to the SOFC anode, where methane steam reforming (MSR) and water gas shift reaction (WGSR) take place and H 2 is generated through these reactions. In the anode, H 2 and CO are electrochemically oxidized to H 2 O and CO 2 by the oxygen ions (O 2− ), which is reduced from O 2 in the cathode and transported through the electrolyte. From the electrochemical oxidation reactions, the released electrons flow from the anode to cathode through the outer circuit and power is generated in this process.
In this study, 2D numerical models for the SOFC and the photoreactor are developed to simulate the characteristics of the hybrid system. Three sub-models are coupled, including SOFC sub-model, photoreactor sub-model and computational fluid dynamic (CFD) submodel. For model simplification, the following assumptions are adopted: 1. The electrochemical reactions occur on the triple phase boundaries (TPBs), which are distributed uniformly in the porous electrodes. 2. The electronic and ionic conducting phases are continuous and homogeneous in the porous electrodes. 3. All the gases are considered as ideal gases. 4. Temperature distribution is uniform in the reactors due to the small size. 5. Only methane and CO are the fuels generated from photoreactor as described by Eq. (23). 6. The oxygen separator works perfectly and there is no species loss in the transportation. 7. Only H 2 and CO are electrochemically oxidized in the anode. 8. Light intensity for photoreactor is stable and constant. 9. Reaction order of the photocatalytic reaction is not affected by the light intensity.

SOFC chemical/electrochemical sub-model
Chemical and electrochemical reactions significantly affect the conversion of different species and the generation of electricity in the SOFC. Understanding this complicated process is a key step to the optimization of the hybrid system. Here, the SOFC sub-model is used to calculate the chemical and electrochemical reaction in the cell at given operating conditions such as applied voltage, operating temperature and inlet gas components. In accordance with the experiments for model validation [47], SOFC has the thickness of its anode, electrolyte and cathode being 400 µm, 8 µm and 24 µm, respectively. The cell is made of Ni-yttrium stabilized zirconium (YSZ) composite anode, YSZ/ samaria-doped ceria (SDC) bilayer electrolyte and lanthanum strontium cobalt ferrite (LSCF) cathode. The properties of these materials including their conductivities, porosities and volume fractions can be found in Table 1.

Chemical reactions in the SOFC
The mixture of CH 4 , H 2 O, CO and CO 2 is supplied to the anode and air is supplied to the cathode (Fig. 1). In the porous anode, MSR and WGSR happen, as shown in Eqs. (1) and (2) (1) For the calculation of MSR rate (R MSR mol m −3 s −1 ) and WGSR rate (R WGSR mol m −3 s −1 ), the following widely validated expressions are adopted [48]:

Electrochemical reactions
In the cathode, O 2− ions are generated through the electrochemical In the anode, H 2 and CO are electrochemically oxidized by the O 2− ions transported from the cathode and electrons are released in this process as shown in Eqs. (11) and (12): During operation, the output voltage from the SOFC can be calculated by extracting activation overpotential (η act ) and ohmic overpotential (η ohmic ) from the equilibrium overpotential (E eq ) as shown in Eq. (13): It should be noted that the equilibrium overpotential is calculated based on local gas partial pressures, so that concentration overpotential is included.
2.1.2.1. Equilibrium potential. Equilibrium potential is related with thermodynamic. The calculation of equilibrium potentials for H 2 and CO electrochemical oxidization can be expressed by Eqs. (14) and (15): Here P H O Here, i 0 is the exchange current density (Am −2 ) and α is the transfer coefficient. These two parameters are tuning parameters in fitting the simulation results with experimental data. As both H 2 and CO can be electrochemically oxidized in the anode, the exchange current density of H 2 is set to be 2.2 times of CO according to previous study [49].
Here, ∅ l and ∅ s are the ionic and electronic potentials, respectively. In the typical composite electrodes, the effective conductivities (σ l eff and σ s eff ) can be further expressed as Eqs. (21) and (22), respectively.
Here, σ is the intrinsic conductivity, V is the volume fraction value and τ is the tortuosity value. Related parameter values of SOFC submodel can be found in Table 1.

Photoreactor reaction sub-model
The photoreactor model contains photochemical reaction and computational fluid dynamic (CFD) for the calculation of species      [50], a montmorillonite (MMT)/ TiO2 coated monolith photoreactor is adopted. The photochemical reaction rate directly affects the concentration of solar fuels and the subsequent power generation in the SOFC. Therefore, it is important to study the effects of given operating conditions on the photoreactor such as the inlet gas component and light intensity. Here, the photoreactor reaction sub-model is used to calculate the photo reduction reaction rates (R photo mol m −3 s −1 ) of CO 2 and H 2 O at given operating parameters. The kinetic model is based on the experimental results and numerically validated from Tahir et al. [50] as follows: Here, k is the rate constant, I is light intensity and α is reaction   Table 2.

Computational fluid dynamic (CFD) sub-model
The mass transport and momentum transport are important physical processes that affect the species distribution in both the photoreactor and SOFC. The CFD model is also coupled with the chemical/electrochemical model, thus affects the chemical electrochemical reactions rate in the SOFC and photoreactor. With the solar-fuels transporting from photoreactor to the SOFC in the hybrid system, the CFD sub-model connects the SOFC chemical/electrochemical sub-model and photoreactor reaction sub-model. In the CFD sub-model, mass transport of gas species is calculated by extended Fick's law as shown in Eq. (25).
Here, B 0 is the permeability, μ is the gas viscosity, Here, ε is the porosity, τ is the tortuosity factor, D im eff is the molecular diffusion coefficient and D ik eff is the Knudsen diffusion coefficient [51].
When coupled with chemical/electrochemical reactions, the mass conservation can be calculated by Eq. (27).
Here, c i is the gas molar concentration and r i is the mass source term of the gaseous species.
The momentum transport is calculated by Navier-Stokes equation with Darcy's term as shown in Eq. (28).
Here, ρ is the gas density and u is the velocity vector.

Boundary conditions
The electric potentials are specified at the outer boundaries of anode and cathode, respectively. Insulation condition is specified at the bottom and top of the SOFC. Inlet gas flow rate and mole fraction of the species are given at inlets of the photoreactor. The inlet gas of SOFC anode is the same with the outlet of photoreactor, while O 2 is excluded. Pressure conditions are specified for both SOFC and photoreactor, respectively. Specific boundary condition values can be found in Tables  2-6 for each parametric study. The numerical models are solved at given parameters using commercial software COMSOL MULTIPHYS-ICS®.

Model validation
In the SOFC sub-model, the same material and geometry are adopted in accordance with the experiments conducted by Xu et al. [47]. The kinetic parameters of the solid oxide cell are validated by comparing the current-voltage characteristic of simulation results and experimental data with good agreement, as shown in Fig. 2a. In the subsequent parametric study, the same cell structure and tuning parameters are used and the cell area is extended to 1 cm × 10 cm for the study of practical application.
In the photoreactor sub-model, the same operating temperature and pressure are used in accordance with the experiments. The experimental and simulation data of methane yield rate at different CO 2 partial pressures are compared for model validation. According to the testing and simulation results reported by Tahir et al. [50] (as shown in Fig. 2b), the validated Langmuir-Hinshelwood kinetic model is adopted. In the parametric study, the reaction area of photoreactor is set to be 10 cm × 10 m with a thickness of 2 μm to match the reaction rates of the SOFC.

Results and discussion
To investigate the effects of operating conditions on the system performance, parametric studies are conducted by varying the operating temperature, applied voltage and inlet CO 2 mole fraction. For the performance evaluation, CO 2 utilization rate is the main evaluation criterion in the photoreactor, while the output power density and CO 2 recovery rate are the main criteria in the SOFC section.

Effect of SOFC operating temperature
The operating temperature is a key parameter affecting the chemical and electrochemical kinetics in the SOFC. In this parametric study, the operating temperature is varied from 973 K to 1173 K, while other operating conditions are kept as constant, as shown in Table 3.
As found in Fig. 3a, the output current density at given applied voltage is significantly affected by the operating temperature. With the operating temperature increasing from 973 K to 1173 K, the output current density raises quickly from 1194 A m −2 to 4728 A m −2 , which shows a more than 3 times improvement. Meanwhile, there is no significant decrease of H 2 or CO mole fractions observed at anode with the increase of operating temperature, as shown in Fig. 3b. Although the high operating temperature results in a faster electrochemical consumption of H 2 and CO, the consumed H 2 and CO are recovered by the largely improved MSR rate at high operating temperature. As can be seen form Fig. 3c, the MSR rate increases from 0.5 mol m −3 s −1 at 973 K to 15.6 mol m −3 s −1 at 1173 K. The quick MSR rate also explains the significant decrease of CH 4 mole fraction at high temperature, as shown in Fig. 3b. Compared with the steady growth of MSR rate with the increase of operating temperature, the WGSR rate keeps negative and reaches a peak at 1113 K, which means H 2 and CO 2 are consumed to generate CO and H 2 O for the balance of gas species.

Effect of applied voltage
As the main product from the proposed system, output power is significantly affected not only by the operating temperature, but also by the applied voltage. In this parametric study, the applied voltage is varied from 0.2 V to 0.9 V at 973 K and 1073 K operating temperature, respectively. The other operating parameters are kept constant as shown in Table 4.
At both two operating temperatures, the current densities enjoy a quick increase while reach a limitation at ∼3200 A m −2 (973 K) and 5000 A m −2 (1073 K) as shown in Fig. 4a and b, respectively. In accordance with this, their power densities boost in the beginning and fall off quickly form the peak power density of 1092 W m −2 (973 K) and 2162 W m −2 (1073 K), respectively. This significant decline is mainly caused by fuel starvation, as can be found in Fig. 4c and d. With the decrease of applied voltage, a higher activation overpotential can be applied to the electrochemical reaction, which significantly increases the electrochemical reaction rate. Therefore, H 2 and CO are quickly consumed, and their mole fractions are significantly declined. When the cell works at 0.2 V applied voltage and 1073 K operating temperature, only 0.67% of H 2 and 0.71% of CO exist in the anode. It can also be found that the mole faction of CH 4 is much higher than H 2 and CO at low voltage, indicating a faster MSR rate can be helpful to ease the fuelstarvation phenomenon.

Effect of inlet CO 2 mole fraction
The mole fraction of inlet gas specie is an important parameter that affects both the photo reduction rate and gas utilization. In this parametric study, the inlet CO 2 mole fraction is varied from 0.1 to 0.9 at given SOFC operating temperatures, while other operating conditions are kept as constant, as shown in Table 5.
As shown in Fig. 5a, the current density is significantly affected by the inlet CO 2 mole fraction at all three given temperatures. In accordance with previous analysis in Section 3.1, the highest SOFC operating temperature (1173 K) provides the largest peak current density (4736 A m −2 ) and the lowest operating temperature (973 K) provides the smallest peak current density (1196 A m −2 ). However, along with the increase of inlet CO 2 mole fraction, the current densities rise in the beginning and decrease continuously until reach a very low value (about 100 A m −2 ) when the inlet CO 2 mole fraction is increased to 0.9. This huge difference can be explained by the similar tendency of mole fraction changes of the fuels at anode as shown in Fig. 5b. The mole fractions of H 2 , CO and CH 4 at anode all reach peak values, when the inlet CO 2 mole fraction is controlled at ∼0.4. The further explanation comes from the effects of inlet CO 2 mole fraction on the photo reduction rate, as shown in Fig. 5c, which also shows a peak photo reduction reaction rate at ∼0.4 inlet CO 2 mole fraction, while the rate quickly decreases with the further increase of inlet CO 2 mole fraction. In addition, a high inlet CO 2 mole fraction not only lowers down the current density, but also reduces the CO 2 utilization rate. As shown in Fig. 5d, the CO 2 utilization rate is close to 100% when the inlet CO 2 mole fraction is less than 0.4. However, it quickly decreases to less than 10% when the inlet CO 2 mole fraction is high than 0.66.

Effect of light intensity
Light intensity is an important factor that affects the photochemical reaction rate. In this parametric study, the light intensity is varied from 150 to 300 mW cm −2 (which is stronger than the light intensity given in Ref. [50]), while other operating conditions are kept constant, as shown in Table 6.
As shown in Fig. 6a, the current density is promoted from 1745 to 2462 A m −2 with the light intensity increasing from 150 to 300 mW cm −2 . Since the applied voltage is kept at 0.7 V, the increase of output current density also means the increase of output power density with the increase of light intensity. This significant improvement is mainly contributed by the improved CO 2 conversion rate as well as the solar-fuel concentration in the photoreactor as shown in Fig. 6b-d. With the increase of light intensity from 150 to 200, 250 and 300 mW cm −2 , the mole fraction of CO 2 continuously decreases from 0.25 to 0.19, 0.12 and 0.08 at the outlet of the photoreactor, respectively. Meanwhile, the mole factions of CH 4 and CO continuously increases from 0.07 to 0.09, 0.12 and 0.13 and from 0.13 to 0.18, 0.25 and 0.28 at the outlet of the photoreactor, respectively. Therefore, a stronger light intensity is very helpful to improve the performance of the hybrid system, which can be achieved by concentrating the sunlight to the photoreactor.

Conclusions
In summary, a novel strategy towards power generation from solar energy has been put forward in this work. With the reduction of CO 2 with H 2 O in the photoreactor, the outlet gas mixture can be directly utilized in the SOFC after O 2 separation. 2D numerical models are developed to investigate the detailed chemical/physical process in the hybrid system and parametric studies are conducted for performance optimization. The kinetics of SOFC sub-model and photoreactor submodel are validated by comparing experimental data with simulation results, where there are only 5% and 3% relative errors for each submodel, respectively.
Through numerical simulation, we observed that the opetating temperature of the SOFC, the applied voltage and the inlet gas component of the photoreactor have great influence on the output power density. In addition, the reaction rate of MSR plays an important role to prevent the fuel starvation in the electrochemical reactions of the SOFC. Considering the relative lower fuel concentration, a relative higher operating voltage is suggested. Adding an external fuel inlet for the SOFC anode can also help release the "fuel-starvation" problem, while its detailed effects on the overall system performance needs future study. A peak power density of 2162 W m −2 is obtained at 1073 K operating temperature of the SOFC. The stronger light intensity is also found to significantly improve the output current density and CO 2 conversion rate, thus concentrating the sunlight to the photoreactor is also suggested.
Although the preliminary results are promising, challenges need to be carefully addressed such as the low solar-to fuel efficiency (< 1%), low photochemical reduction rate, effective O 2 separation and fuel storage. More studies are needed to improve this hybrid system. For example, the development of an effective separator membrane, highly active photocatalyst, direct utilization of separated oxygen and advanced recycle design are needed. Overall, this photoreactor-SOFC hybrid system demonstrates a new design with promising preliminary performance for power generation from solar energy and build a solid foundation to undestand the chemical/physical mechanism of the system, and more importantly, offers a feasible and effective approach for achieving stable solar-to-power energy devices.