Electrolytic cell engineering and device optimization for electrosynthesis of e-biofuels via co-valorisation of bio-feedstocks and captured CO2

Utilizing CO2 in an electro-chemical process and synthesizing value-added chemicals are amongst the few viable and scalable pathways in carbon capture and utilization technologies. CO2 electro-reduction is also counted as one of the main options entailing less fossil fuel consumption and as a future electrical energy storage strategy. The current study aims at developing a new electrochemical platform to produce low-carbon e-biofuel through multifunctional electrosynthesis and integrated co-valorisation of biomass feedstocks with captured CO2. In this approach, CO2 is reduced at the cathode to produce drop-in fuels (e.g., methanol) while value-added chemicals (e.g., selective oxidation of alcohols, aldehydes, carboxylic acids and amines/amides) are produced at the anode. In this work, a numerical model of a continuous-flow design considering various anodic and cathodic reactions was built to determine the most techno-economically feasible configurations from the aspects of energy efficiency, environment impact and economical values. The reactor design was then optimized via parametric analysis.


Introduction
Research on electrochemical reduction of CO 2 has drawn intensive attention in recent years for the purpose of reducing the CO 2 emission, as well as energy storage of renewable electricity generated from solar and wind energy [1]. CO 2 electro-reduction technology is at its infancy stages especially from an industrial point of view. The main issue lies in its economic viability due to the high energy consumption and relatively low energy conversion efficiency. Moreover, long-term economic impacts and environmental issues are counted amongst the issues of this approach [2]. The energy and cost analyses based on techno-economic and environmental evaluation indicates that electrochemical systems can be sustainable only when electrolyser technology becomes more mature [3]. In this regard, formic acid electrosynthesis using CO 2 as raw material is one of the most commonly explored kinetics due to its simple charge transfer pathways and fast kinetics comparing with other conversion reactions [4]. The recent studies show exciting results of efficient formic acid electrochemical synthesis from CO 2 on low cost catalyst [5]. The selectivity of the formation of the formic acid with respect to the total CO 2 reduced product is around 95.73%. The performance can be further enhanced by electrode material enhancement and membrane improvement [6,7]. While solid oxide electrolysers show a promising alternative trend in CO 2 utilisation, due to high operational temperature, system optimization is still under investigation and requires further improvement [8][9][10][11][12].
As the other half electrochemical reaction associating with CO 2 reduction, oxygen evolution reaction (OER) at anode is another source contributing major part of energy loss within the electrolyzer. About 70% of the whole energy loss is caused by OER [13]. Moreover, in order to minimize the voltage loss of OER, catalysts based on noble metals are generally applied [14]. Unfortunately, although considerable energy along with the high cost catalyst is consumed, the byproduct (O 2 ) generated from anode brings little value.
Using biofuels or organic wastes as resources to synthesize high value-added chemicals under controllable electro oxidization is regarded as a promising and viable way to promote the economic viability of electrochemical approach for CO 2 mitigation [15]. However, this approach, known as 'e-biofuel' is still at its initial stage. The feasibility and technical potential of coupling it with CO 2 electrochemical reduction is less explored from an industrial point of view.
In this work, a numerical model of a continuous-flow design considering various anodic and cathodic reactions was built to investigate the products generation from the aspects of energy efficiency, environment impact and economical values. Numerical analyses on device optimization and device engineering in different economic and industrial scenarios were carried out as well. This study provides a comprehensive understanding on simultaneous electrochemical synthesis of high add-valued chemicals and CO 2 reduction.

Problem description
The first step in designing an electrolytic cell is deciding the reaction kinetics which is to take place at each electrode. The chosen kinetics greatly affects the reactor geometry, inlet liquid and gas flow velocities and electrode catalyst material. To identify the half-cell reactions with the desired performance properties, at least one reaction was chosen from each potential cathode and anode halfcell group (e.g., carboxylic acids, alcohols, aldehydes, etc.). Recent progress involving CO 2 electroreduction and biomass oxidation for fuel production were also extracted from literature and included in the reaction list. Herein, 20 anodic and 10 cathodic half-cell reactions are listed in Tables 1-3. Water is assumed to be the solvent for watersoluble reactants while dimethylformamide (DMF) is used where an organic solvent is required. The model schematic for e-biofuel reactor is shown in Fig. 1.

Computational model
The maximum Reynold's number at the centre of the liquid channel is below 0.4. This leads to a laminar flow system that can be described by Naiver-Stocks and continuity equations: where is the liquid density, u is velocity, p refers to pressure, and I denotes the unit matrix in the proposed spatial dimension. The boundaries at the walls and the electrodes were assumed to be non-slip. The inlet gas was assumed to be at 20°C and 1.013Â10 5 Pa with the gas completely dissolving in the liquid phase. The gaseous byproducts are assumed to diffuse through the anode completely, hence the bubble mechanics are neglected in the computational fluid dynamics (CFD) model. The species mass balance is described by Eq. (3): where A is the area, V is the volume of the cell, F is the Faraday constant, n i denotes the number of transferred electrons, X i is the mass fraction, D i is the diffusivity, M i is the molar weight and j i is the partial current density for species i. Constant species mass fraction is assumed at the inlet while non-flux boundaries are set at the electrodes and zero diffusive flux at the outlet. Charge conservation is accounted for by Eq. (4): where is the electric conductivity and φ refers to the electric potential. A constant potential was assumed at the electrodes as a boundary condition for charge conservation equation.
The resulting system of equations combined with the electrode kinetics described in 2.3 was solved using Galerkin Finite Element Method in COMSOL Multiphysics ® [35]. A 2D geometry was created and the computational domain was described using 7692 tetrahedral mesh elements. The number of degrees of freedom solved was 36876, and the computational time was approximately 2 min for each case on a PC with quadcore Intel core i-7 CPU at 2.8 GHz and 16 GB RAM.

Electrode kinetics
Electrochemical reactions are assumed to occur at the electrode surfaces as listed in Tables 1-3. In cases where water is the solvent, the hydrogen evolution reaction (HER) is a side reaction at the cathode which can be shown as: At the anode, the oxidation reaction can be shown as: Electrode overpotential at each electrode is defined by: where η is the electrode overpotential, E is the electrode potential and E 0 is the equilibrium potential of each partial reaction. This value can then be calculated by using Tafel law: where R is universal gas constant, T is the temperature, z is the electron transfer number, j refers to the electrode current density, j 0 is the exchange current density and α is the charge transfer coefficient. For CO 2 reduction half-cell, a mass transfer constraint is imposed and Eq. (8) is rewritten as [36]: where C CO 2 is the local carbon dioxide concentration.
To incorporate the half-cell reactions in the model, a few factors need to be specified. The first factor is standard free 10 Gibbs energy of formation for each reactant and product species. This is to determine cell energy performance (e.g., energy efficiency and current efficiency) and to estimate cell equilibrium potential when experimental values are not available in the literature. Standard Gibbs free energy of formation was extracted from [37][38][39] and estimated by Joback method [40] in case of more structurally complicated organic compounds. Cell equilibrium potential can be estimated by: With the results being mostly accurate (error bellow 4%) when compared with experimental observations. Another important factor is the cell exchange current density used in Eqs. (8) and (9). This value was estimated by scaling cell exchange current density from available experimental observations through the following equation [41]: 16 18 19 a) The electrolyte conductivity was acquired from [27], physical properties from [28].
where x indicates the exchange current density to be scaled and 1 denotes the known exchange current density.

Model validation
The CFD model results are compared with experimental data as shown in Fig. 2. The computational model velocity field shows a good correlation with experimental data extracted from [42]. To further validate the computational model, electrode potential vs. current density is plotted for pH of 10 in a case where CO 2 is used at the cathode (reaction 21 in Table 3) and compared with experimental results from reference [43] as shown in Fig. 3. The input parameters used are listed in Table 4.

Mass transfer
Mass transfer throughout the cell plays a key role in determination of cell efficiency and overall performance. For the case study explained in section 2.4, CO 2 mass fraction decreases across the cathode. The CO 2 removal rate is only 24.4% in this case, which implies there is a great room for improvement by replacing the half-cell reaction and improving cell design. Since HER in this case is regarded as a parasitic reaction, which decreases the cell energy efficiency, the mass fraction of hydrogen as high as 0.7 at the outlet is another indication of cell poor performance. Formic acid is formed in the liquid phase across the cathode accumulating towards the outlet of the electrolytic cell. While OHis produced at the cathode according to Eq. (5), it is consumed at the anode according to Eq. (6), affecting the local pH profile in the system. The average pH may not show significant variation when measured experimentally at the cell outlet, however, the local pH becomes particularly important where the electrode surface and catalyst performance is influenced by the local pH of the system. Each cell kinetic scheme imposes specific limitations in terms of mass transfer in the system. Understanding the bottleneck in each case provides an insight to the overall contribution of each electrode where potentially removing the limitation can improve the cell efficiency. Table 5 shows the limiting factor in each reaction scheme. The limiting factor was characterised by calculating the availability of each reactant at the electrode surface towards the outlet of the cell. Once the reactant concentration drops below a threshold on the surface of one electrode, it is marked as the mass transfer limiting Fig. 2 (a) Velocity field of the gas and liquid (m/s); (b) dimensionless velocity profile across channel height at 6 mm from the entrance, model results vs. experimental measurements [42].
factor. Electrode diffusivity is specified as the limiting factor when neither the concentrations reach the threshold. To establish a valid benchmark for the reaction schemes, independent of the diffusion coefficient of the electrode, the porosity of the electrode was kept constant in all cases. As shown in Table 5, CO 2 at the cathode is the limiting factor for most of the organic-based solvents. This underlines the efficiency of the cell for CO 2 utilization in these cases where other factors of the cell can be improved to increase the cell efficiency.
Incorporating the discussed mass transfer results in choosing the highest performance configuration requires extra care as each reaction set will lead to a unique cell condition, solvent and catalyst determination. Cell performance design can be tailored from multiple points of view, depending on the industrial and economical requirements.
Here, we study cell kinetic configuration according to energy and current efficiencies (section 3.2), environmental (section 3.3) and economical (section 3.4) aspects.

Maximizing cell energy and current efficiencies
Cell energy efficiency is calculated by: Energy content of the products ðkJ=molÞ Â cell fuel production ðmol=sÞ V cell I cell ðkJ=sÞ , (12) where η e is the energy efficiency, V cell is the cell voltage and I cell is the electrical current consumed in the cell. As shown in Fig. 4(a), cell energy efficiency changes across a wide range depending on the reaction kinetics. Replacing the initial anodic half-cell mentioned in section 2.3 can result in up to~88.0% increase in cell energy efficiency. Another important factor that needs to be taken into consideration is cell current efficiency. This value demonstrates cell selectivity and is the current transferred to CO 2 divided by the total current consumed in the cell: η i ¼ Current transferred to the main reactant=product Current consumed in the cell : Figure 4(b) shows the current efficiency for various halfcell reactions. In general, higher current efficiency and hence, better cell selectivity is observed when organic solvents are used because of the lack of HER at the cathode. The reason behind higher current efficiencies in half-cell reactions 2 and 5 is that CO 2 is assumed to be the main reactant in these cases, however, CO 2 is also produced at the anode and hence the reactions show a higher current efficiency.

Environmental aspects
To get a step closer to completing CO 2 industrial cycle, one of the main requirements of the proposed electrolytic cell is higher CO 2 consumption rate in the proposed reaction scheme. CO 2 consumption rate can be defined as: Figure 5(a) shows the CO 2 consumption rate. Using organic solvents result in higher overall CO 2 removal rate, due to the lack of HER at the cathode (e.g., reactions 16- 20). Some reactions produce CO 2 which will result in negative values (e.g., reactions 3 & 4). This value can also become zero when using other materials at the cathode (e.g., reactions [25][26][27][28][29][30]. Replacing the anodic reactions can result in up to~50% increase in CO 2 removal rate compared to the initial cell reaction configuration discussed in section 2.3. Another important factor that needs to be accounted for during industrialization of the process is the amount of waste produced during the process. This can be quantified by calculating the E-factor of the process [44]: E-factor ¼ kgs of waste produced kgs of desired product : (15) Figure 5(b) shows the E-factor of the cell according to various incorporated half-cell kinetics. The overall E-factor is high due to the design of the studied continues-flow reactor. A large amount of solvent and reactant is flushed in the system leaving a large environmental carbon footprint. This issue can be mitigated by optimizing the cell and recycling the solvent.

Economic factor
The overall economical added value during the process can be calculated as: added value ð£=molÞ ¼ value of products ð£=molÞvalue of reactants ð£=molÞ: As shown in Fig. 6, added value changes over a wide range and can reach up to~20000 £/mol if the product is purified to 99.9% or~1000 £/mol if the product is purified to 80%. However, some reactions lead to negative added value which are not economic viable.

Cell optimization and device engineering
The cathodic overpotential is among the largest sources of inefficiencies in current CO 2 electrolysers, followed by the anodic one [13]. Replacing the cathodic and anodic reactions can greatly improve cell performance by introducing new kinetics at each electrode. Various industrial scenarios can now be targeted with the proper reaction scheme identified based on the results discussed in section 3.2-3.4. Cell optimization can be performed by maximizing cell energy and current efficiencies, environmental aspects or economic factors.
From an efficiency point of view, anodic reaction 13 and cathodic reaction 22 were used as cell main kinetics (see Fig. 4). This is oxidizing glucose to gluconic acid at the anode while reducing CO 2 to ethanol at the cathode. The overall cell energy efficiency was increased to 340% as both products have high free Gibbs energy content. Other cell performance factors include CO 2 conversion rate of 69.3%, current efficiency of 56.7% and E-factor of 704. Another important performance factor can be optimized is the CO 2 conversion rate (see Fig. 5). DMF is assumed to be the solvent as the HER is omitted at the cathode. Any of the cathodic reactions 16-20 can be used as they demonstrate similar CO 2 conversion rate. In theory, it is possible to pick a water-based solvent at the anode and separate the two phases either by a proton exchange membrane or rely on the natural phase separation as the two phases become immiscible in the given cell dimensions. Reaction number 24 is chosen at the anode where CO 2 is reduced to CO.  Under these conditions the theoretical CO 2 conversion rate reaches~90% as the reaction is limited by the CO 2 diffusibility rather than cell kinetics. From an economical point of view, the added value of the product is not affected by altering the cathodic reaction. The results shown in Fig. 6 can be used to estimate the cell overall added value for various cell kinetics.
An indication of the cell performing at its optimized state is maximizing the current density across the electrodes in the direction of flow. Current density rises sharply at the cell entrance due to availability of the reactants. Moving in the stream direction, products begin to accumulate across the electrode surface, creating a resistive layer which occupies the catalyst active sites and slows down the electrode reaction. Due to extremely laminar flow throughout the system, the dominant mass transfer mechanism along the channel width and height is diffusion, which drives the resistive layer formation. The resistive layer formation rate depends on the reaction kinetics, reactant and product diffusivity in the solvent and stream velocity.
For the case study mentioned earlier where the cell efficiency is maximized, the reactor length was calculated 120 mm for 90% CO 2 conversion rate. This length was chosen because from this point, increasing the channel length does not increase the energy efficiency significantly as shown in Fig. 7(a). To determine other design parameters, energy conversion rate was considered as free Gibbs energy of the products divided by the energy consumed in the continuous flow reactor. Please note that this parameter can be greater than 100%, as the energy content of the final products may be higher than the energy used during the process. Other design parameters were determined from Figs. 7(b and c) as follows: Electrolyte flowrate 0.65 L/min, CO 2 inlet flowrate 4.5 SCCM and channel height 1.7 mm.

Conclusions
A continuous electrolytic cell was computationally modelled and verified. The model was then used with various cell kinetics to determine the most optimized cell configuration in different scenarios for the e-biofuel processes. The kinetics studied were chosen from a range of organic compounds where at least one reaction from each group (carboxylic acids, alcohols, aldehydes, etc.) was presented. Latest progresses in CO 2 electroreduction kinetics and biomass oxidation for fuel production was included in this study as well.
Using non-water solvent in general improves the cell efficiency as HER is omitted at the cathode. While the energy efficiency of the cell is mostly dictated by the energy content of the main products, the CO 2 conversion rate can be greatly improved by cleverly choosing the reactor kinetics. The overall environmental impact (E-factor) is high compared to other industrial processes. This is due to the high volume of the solvent compared to the product and can potentially be mitigated by re-circulating the solvent in the system. The economic added value of the cell is mostly determined by the products at the anode for the selected reaction scheme.  The guidelines provided in this study can be used to design economically and industrially viable continuous flow electrolytic cells and pave the way for future carbon utilization setups.