Low carbon fuel production from combined solid oxide CO2 co-electrolysis and Fischer-Tropsch synthesis system_ A modelling study

CH4-assisted solid oxide electrolyzer cells (SOECs) can co-electrolyze H2O and CO2 effectively for simultaneous energy storage and CO2 utilization. Compared with conventional SOECs, CH4-assisted SOECs consume less electricity because CH4 in the anode provides part of the energy for electrolysis. As syngas (CO and H2 mixture) is generated from the co-electrolysis process, it is necessary to study its utilization through the subsequent processes, such as Fischer-Tropsch (F-T) synthesis to produce more value-added products. An F-T reactor can convert syngas into hydrocarbons, and thus it is very suitable for the utilization of syngas. In this paper, the combined CH4-assisted SOEC and F-T synthesis system is numerically studied. Validated 2D models for CH4assisted SOEC and F-T processes are adopted for parametric studies. It is found that the cathode inlet H2O/CO2 ratio in the SOEC significantly affects the production components through the F-T process. Other operating parameters such as the operating temperature and applied voltage of the SOEC are found to greatly affect the productions of the system. This model is important for understanding and design optimization of the combined fuel-assisted SOEC and F-T synthesis system to achieve economical hydrocarbon generation.


Introduction
With the growing attention on global warming, effective CO 2 utilization methods are urgently needed [1]. Solid oxide electrolyzer cells (SOECs) are high-temperature technologies [2], which are suitable to convert CO 2 into chemicals or fuels by utilizing the renewable energy or excessive electricity produced from renewable resources [3]. SOECs are solid-state device working quietly at high efficiency [4]. In the SOEC, a dense ion-conducting electrolyte is sandwiched between two porous electrodes [5]. Compared with low-temperature electrolyzers, SOECs consume less electrical energy as part of the input energy comes from heat [6]. The high operating temperature also allows the use of nonnoble catalysts in the SOEC, leading to a lower overall cost [7]. In addition, solid oxide cells are suitable components to be combined in the hybrid systems such as the combination with Stirling cycle [8], the Otto heat engine [9] and the Vacuum thermionic generator [10] for overall performance improvement. Recently, the concept of fuel-assisted SOECs has been proposed and demonstrated [11], where low-cost fuels (e.g. methane from biogas or natural gas) are supplied to the anode to reduce the operating potentials of the SOEC. Through experimental and numerical analysis [12], the CH 4 -assisted SOEC has been demonstrated to have a higher electrochemical performance compared with the ones using CO as the assistant fuel. In some operating conditions, the fuel-assisted SOECs can even electrolyze oxidants without consuming electricity, which means it is possible to convert CO 2 to fuels by only consuming low-cost fuels in the SOEC [13]. Therefore, using SOECs for CO 2 recycle is an attractive solution for emission reduction [14].
SOECs can co-electrolyze H 2 O and CO 2 and generate syngas (H 2 and CO mixture) [15], which is a feedstock for the production of synthetic hydrocarbons via Fischer-Tropsch (F-T) process [16]. As methane is usually less wanted from the F-T process [17], it is therefore suitable to recycle methane from F-T reactor as the assistant fuel in the SOEC [18].
A system consisting of a CH 4 -assisted SOEC and an F-T reactor can effectively convert CO 2 and generate desired hydrocarbons. Therefore, such a hybrid system is very promising for CO 2 utilization and hydrocarbon fuels generation. However, despite some preliminary studies on the combined SOEC and F-T systems through Techno-economic analysis  [19] and thermodynamic analysis [20], no detailed physicochemical, kinetics and thermofluids analysis on a combined fuel-assisted SOEC and F-T synthesis system has been conducted thus far.
To fill this research gap, in this work, 2D mathematical models are developed for a combined CH 4 -assisted SOEC and F-T synthesis system for H 2 O/CO 2 co-electrolysis and hydrocarbon fuels generation. The submodels for the CH 4 -assisted SOEC [21] and the F-T reactor [22] are validated in the previous studies. Parametric simulations are conducted to understand the characteristics of such a system and the interplay of different physical/chemical processes.

Model description
The proposed hybrid system consists of a CH 4 -assisted SOEC and an F-T reactor, as shown in Fig. 1. In the SOEC anode, CH 4 and H 2 O are supplied to anode with a ratio of 1:1.5 to avoid methane coking. CO 2 and H 2 O are supplied to the cathode, where they are electrolyzed to generate syngas. Syngas generated from the SOEC section is collected for F-T reactor, where hydrocarbons are generated through the synthesis process.
2D numerical models are developed to simulate the characteristics of the system, the model kinetics for both the CH 4 -assisted SOEC [21] and the F-T reactor [22] are validated by using prior published work. In accordance with the experimental work, the tubular SOEC adopted in the model has a length of 7 cm, an inner diameter of 0.3 cm and an outer diameter of 0.5 cm. It uses Ni-YSZ as anode support layer, Ni-ScSZ as anode active layer, ScSZ as electrolyte and Ni-ScSZ as cathode. The tubular F-T reactor has a length of 30 cm and an outer diameter of 1 cm. It uses Fe-based catalyst for the improvement of synthesis reaction rates. The material properties for the SOEC can be found in Table 1.
For model simplification and easier calculation, the following assumptions are adopted: 1. The triple phase boundaries are uniformly distributed in the porous electrodes as the ionic and electronic conducting materials are well mixed in the electrode preparing. 2. The electronic and ionic conducting phases are continuous and homogeneous in the porous electrodes as the electronic and ionic conducting materials are well mixed in the electrode preparing. 3. All the gases are considered as ideal gases because the effects of intermolecular forces and molecules sizes are less significant at high operating temperature. 4. Temperature distribution is uniform in the reactors due to the small size.

Sub-model of CH 4 -assisted SOEC for CO 2 and H 2 O co-electrolysis
As shown in Fig. 1, the gas mixture of H 2 O and CO 2 flows into the cathode channel, while the gas mixture of CH 4 and H 2 O flows into the anode channel. In the cathode, both H 2 O and CO 2 are reduced to generate H 2 and CO as shown in Eq. (1) and Eq. (2), respectively. (1) In the anode, the methane steam reforming (MSR) reaction happens to generate H 2 and CO, which are then electrochemically oxidized by the − O 2 ions transported from the cathode. The MSR reaction and electrochemical oxidations of H 2 and CO are listed as shown in Eqs.
Due to the existence of H 2 O and CO, water gas shift reaction (WGSR) occurs in both anode and cathode as shown in Eq. (6).
In operation, the required voltage applied to SOEC can be calculated by Eq. (7) as: where E is the equilibrium potential related with thermodynamics; η act is the activation overpotentials reflecting the electrochemical activities and η ohmic is the ohmic overpotential which can be calculated by the Ohmic law. The calculation of equilibrium potential is based on oxygen partial pressure [23] and calculated as: The activation overpotential is calculated by the Butler-Volmer equation as: where i 0 is the exchange current density and α is the electronic transfer coefficient. For H 2 O electrolysis, the exchange current density can be further expressed as: where β is the activity factor and E a is the activation energy. For CO 2 electrolysis, its exchange current density is 0.45 times of H 2 O electrolysis [24]. All the kinetics for above reactions can be found in Table 2.

Sub-model of F-T reactor
The F-T reactor uses Fe-HZSM5 as catalyst and works at 573 K and 2 MPa for syngas synthesis. The reactions in the F-T process are shown in Eqs. (13)- (20).
The reaction kinetics for above reactions can be expressed as shown in Eq. (21) [22].
Related kinetics for reactions (13) to (20) are list in Table 3.

CFD Sub-model
For both the SOEC and the F-T reactor, the mass transport of gas species is calculated by extended Fick's law as shown in Eq. (22).
Here B 0 is the material permeability, μ is the gas viscosity, y i and D i eff are the mole fraction and effective diffusion coefficient of component i, respectively. D i eff can be further determined by where 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 [25].
The mass conservation can be described by where c i is the gas molar concentration and r i is the mass source term of the gaseous species. Navier-Stokes equation with Darcy's term is adopted to calculate the momentum transport in both the SOEC and F-T reactor as shown in Eq. (25).
Here ρ is the gas density and u is the velocity vector.

Boundary conditions and model solution
Electric potentials are specified at the outer surface of two electrodes with the cell ends electrical insulated. Inlet gas flow rate and mole fraction of the species are given at inlets of the SOEC. The ratio of H 2 to CO for F-T reactor inlet is consistent with the ratio of H 2 to CO of SOEC cathode outlet. The numerical models are solved at given parameters using commercial software COMSOL MULTIPHYSICS® version 5.2.

Model validation
In the SOEC sub-model, the same material and geometry are adopted in accordance with the experiments conducted by Luo et al. [24]. The kinetic parameters of the SOEC are validated by comparing the current-voltage characteristic of simulation results and experimental data with good agreement as shown in Fig. 2. In the subsequent parametric studies, the same cell structure and tuning parameters are used. The detailed operating conditions for model validation are given in Table 4.
In the Fisher-Tropsch sub-model, the same catalyst, operating temperature and pressure are used in accordance with the experiments. According to the testing and simulation results reported by Rahimpour et al. [22], the well validated power law kinetic model is adopted.
For above models, proper mesh densities are adopted with mesh independence validations conducted as shown in Fig. 2c and Fig. 2d.

Parametric studies
As shown in Fig. 3, CO and H 2 are generated in the SOEC and their mole fractions increase continuously from the inlet to the outlet. While in the F-T reactor, CO and H 2 are consumed and their mole fractions are  decreasing continuously from the inlet to the outlet. As syngas is the key intermediate in this hybrid system, the power consumption for generating syngas and hydrocarbons generated from syngas are detailed studied in the following parametric studies. Both cathode inlet     gas species and applied voltage are studies for the understanding and optimization of operating parameters. The detailed operating parameters are listed in Table 5 and Table 6.

Effects on the syngas mole fractions and power consumption rate
As the intermediate product, syngas is generated from SOEC and consumed in the F-T reactor. It has been proved by previous studies [26] that the CO/H 2 ratio has great effects on the methane selectivity and chain growth probability. Besides, the power consumption should also be considered for the optimization of economic efficiency. Therefore, it is important to study the factors that affects the generation of syngas as well as the power consumption rate in the production of syngas.
As shown in Fig. 4, the mole factions of H 2 and CO at the SOEC cathode outlet are significantly affected by the CO 2 mole fraction at the inlet. With the increase of inlet CO 2 mole fraction, the mole fraction of produced CO rises quickly while the mole fraction of H 2 declines continuously. The CO/H 2 ratio is thus significantly improved with the increase of inlet CO 2 mole fraction, where the ratio is only 0.056 when CO 2 mole fraction at inlet is 0.2 while boosts to 4.6 when the CO 2 mole fraction at inlet increases to 0.8. This 80-times increasement proves that it is effective to control the CO/H 2 ratio at SOEC outlet by adjusting the inlet CO 2 /H 2 O mole ratio.
The CO/H 2 ratio is also affected by the applied voltage as shown in Fig. 5. In accordance with previous reports [21], the SOEC can work at a lower applied voltage with fuel assistance. In addition, a lower CO/H 2 ratio at SOEC outlet can be obtained with the decrease of applied voltage. For comparison, the CO/H 2 ratio at SOEC outlet is 0.76 at 0.7 V applied voltage while decreases to less than half (0.3) at 0.05 V applied voltage. Moreover, the input power density is significantly declined with the decrease of applied voltage, where the power density is 6258 W m −2 at 0.7 V while decreases to 17 W m −2 at 0.05 V. However, the conversion rate of both H 2 O and CO 2 also drop quickly with the decrease of applied voltage as shown in Fig. 6. At 0.7 V applied voltage, the conversion rate of H 2 O and CO 2 are 87% and 67%, respectively. While at 0.05 V applied voltage, the conversion rate of H 2 O and CO 2 drop to 5.5% and 1.7%, which is too low for practical application. The power consumption of electrolysis is also affected by the operating temperature of SOEC as shown in Fig. 7. At 2000 A m −2 operating current density, 0.57 V input voltage is required when the SOEC is working at 1023 K operating temperature. When the operating temperature increases to 1123 K, only 0.12 V input voltage is required, which means about 80% of power consumption can be saved in this case.

Effects on the distribution of fuels at F-T outlet
Considering the conversion from CO 2 to carbon-contained fuels, the proportions of C atoms among the carbon-contained fuels (including CH 4 (C 1 ), C 2 H 4 , C 2 H 6 (C 2 ), C 3 H 8 (C 3 ), i-C 4 H 10 , n-C 4 H 10 , C 6.05 H 12.36 (C 5+ ) and CO) are calculated. The proportion of C atoms in each fuel is calculated as = P C C i total , where C i is the amount of C atoms contained in one specific fuel and C total is the amount of C atoms contained in all the fuels.
As shown in Fig. 8, when the CO 2 mole fraction at inlet is 0.5, the largest part of C atoms (30%) is contained in CH 4 among all the fuels, while only 20% C atoms are contained in C 5+ , and there are still 9% CO not fully used. With the increase of inlet CO 2 mole fraction, the C atoms contained in CH 4 continuously decreases, where there are only 16%, 9% and even 4% C atoms contained in CH 4 at 0.55, 0.6 and 0.65 inlet CO 2 mole fractions, respectively. On the other hand, the C atoms contained in CO increases quickly with the increase of CO 2 mole fractions at inlet, where 26%, 41% and 53% C atoms are contained in CO at 0.55, 0.6 and 0.65 inlet CO 2 mole fractions, respectively. The proportion of C atoms contained in C 5+ is relatively stable with the change of inlet CO 2 mole fraction, which only varies between 22% and 18% at given operating parameters. As CH 4 can be recycled to be utilized in the SOEC section and a high CO conversion rate is preferred, a lower inlet CO 2 mole fraction is thus suggested through above analysis.
The proportion of C atoms contained in hydrocarbons (C n H m ) and CO 2 conversion rate is also given as shown in Fig. 9. Although the proportion of C n H m continuously decreases (from 90% to 26%) with the increase of inlet CO 2 mole fraction, the significant increase of CO 2 conversion rate (from 46% to 74%) is still attractive in the utilization of CO 2 .

Conclusions
In this paper, the first 2D model combining a CH 4 -assisted solid oxide co-electrolysis and Fischer-Tropsch synthesis system for CO 2 utilization and hydrocarbon generation is developed. The kinetics of the model are validated by using previous studies. CO 2 and H 2 O are used as the feedstock to produce low-carbon fuel through the F-T reactor. Through parametric studies, the effects of CO 2 (H 2 O) mole fraction on the production of syngas is studies. It is found that it is effective to control the CO/H 2 ratio of the syngas by adjusting the CO 2 /H 2 O ratio at  the SOEC inlet. Besides, the applied voltage is also varied for the parametric study, where the applied voltage and operating temperature are found to significantly affect the power consumption rate as well as the CO 2 and H 2 O conversion rate. Finally, the distribution of carboncontained fuels generated by the F-T reactor is studied. The proportions of C atoms among different fuels are compared, where it is found that the inlet CO 2 (H 2 O) mole fraction significantly affects the proportion of fuels, particularly CH 4 and CO in the F-T outlet. In general, the mole fractions of hydrocarbons from C 1 to C 5+ generated by the F-T reactor can be controlled by adjusting the inlet H 2 O/CO 2 ratio in the electrolysis process. This study builds a solid foundation for the understanding and optimization of a combined fuel-assisted SOEC and F-T reactor system. Based on this preliminary work, a higher-level model is still needed, which can give a detailed analysis on the integration of this low-carbon fuel generation technology with other energy conversionstorage hubs.