In this thesis, analytical and computational models have been created for the electroreduction of CO2 in gas-diffusion electrodes. It initially covers the creation of a 1D analytical model of CO2 mass transport and reaction in a gas-diffusion electrode catalyst layer in an electrolyser with a flowing catholyte layer. This model balances the diffusion of CO2 through the porous media against the reaction of CO2. Both electrochemical conversion, with concentration dependent Tafel kinetics, and chemical reaction with OH- in the bicarbonate buffer system, rapidly consume CO2. It shows that the OH- produced in the reduction reaction and competing hydrogen evolution reaction lead to an alkalinity problem, in which large fractions CO2 are converted to bicarbonate and carbonate instead of the intended electroreduction product. This problem is pervasive in the catalyst layer environment, and the rising pH further causes significant increases in local carbonate concentrations, limiting the CO2 solubility through the salting-out effect. The carbonate concentrations can approach the solubility limit in the electrolyte and precipitate with cations into solid carbonate crystals in the pore structure.

Rudimentary optimisation is performed on this 1D system, and it determines that the effectiveness of a catalyst layer is governed to an extent by the Thiele modulus. Furthermore, a thick catalyst layer is usually underutilised when there is insufficient CO2 partial pressure in the gas feed or excessive cathode potential. In these cases, the regions of the catalyst furthest from the gas supply perform very little CO2 electroreduction, but still perform hydrogen evolution. This hydrogen evolution produces OH- ions that further consume CO2 and consumes electricity that would ideally instead be used to produce the more valuable products of CO2 reduction.

The 1D model necessarily used averaged values for components that depend on the perpendicular flow direction, namely the flowing catholyte channel and the reactant gas CO2 channel. We note that this treatment is insufficient to describe the whole electrolyser, as CO2 conversion to carbonate and OH- production create a developing concentration boundary layer. Similarly, the partial pressure of the gas channel CO2 will vary along the electrolyser as it reacts away.

To address these issues, the model is converted into a computational 2D system, solved in COMSOL Multiphysics. This also permits the inclusion of some of the more convoluted effects of ionic strength and temperature on the system. Homogeneous reaction rates, anodic and cathodic reaction rates, pH, and reaction equilibrium potentials and constants are all corrected in this way. This gives a more detailed representation of the physical processes, but given the complicated forms of the corrections it becomes far more difficult to interpret the interactions behind observed phenomena when compared to the analytical model. With some additional computational methods of domain decomposition and variable recasting, the model is applied to both a small lab-scale scenario and an upscaled metre-long channel, to demonstrate the scaling relations and limitations of a typical CO2 electrolyser with flowing catholyte. It shows that the reaction environment at the inlet is far more favourable than further down the stream, as the reactant partial pressure is higher, the local catalyst layer pH is lower, the local CO2 solubility is higher, the catholyte is purer, and the catholyte concentration boundary layer is thinner. The model allows us to see that the majority of reactant and current utilisation limitations come from unabated hydrogen evolution in the poorly utilised regions, similar to what was found in the perpendicular direction in the 1D model. We propose some methods to mitigate these limitations. One of these methods is the selective removal of catalyst in these poorly utilised areas, to ensure that limiting kinetics and limiting mass transport share similar values and hydrogen evolution only occurs where necessary.

With the rudimentary hypothesis of selective catalyst removal showing some promising results, we return to a readily optimisable 1D system in the flow-wise direction of both a simple flow-through reactor and a gas-diffusion electrode with flowing catholyte. We find that variable catalyst loading can act as a modifier of the dimensionless Damk\"{o}hler number that typically governs the performance of such a system. The effect is more profound in a gas-diffusion electrode however, so we create a numerical framework in which we can perform functional optimisation to find ideal loading profiles for a range of electrolyser setups and operational loads. We found that high single-pass conversion is associated with lower reaction selectivity, and subsequently constructed a more robust financial cost weighted metric. This metric reveals that many electrolyser setups can be improved by reducing the amount of catalyst used further down the channels, as the reduced cost of electricity spent on the hydrogen evolution reaction far outweighs the reduction in product yield and reactant utilisation. Furthermore, the optimisation process reveals that the most economically feasible setups for contemporary costs are categorically those that operate at minimal cell voltage and single-pass conversion, as
electrolysis cost is dominant, even in cells with optimised catalyst loading. This high electrolysis cost, exceeds reactant cost and separation costs, so a low single-pass conversion is preferable to maintain a high reactant availability for efficient electrolysis in the catalyst layer, even if this leads to higher product stream separation costs due to more unreacted CO2 in the outlet.
We conclude with a recommendation for a focus on minimising electrolysis cost and maximising long-term stability and scalability, with less of a focus on reactant utilisation and intensive upstream or downstream processing, as the former attributes are of greater financial significance. ... Read more

In flow-by capacitive deionization (CDI) brackish water flows between two electrodes that capacitively remove salt. We assume low inlet concentrations so “salt shocks” appear in the electrodes and the process becomes diffusion-limited. For unit charge efficiency, a simplified model is derived consisting of two coupled partial differential equations. We obtain approximations, and exact solutions in terms of the Lambert W function, for the salt concentration as a function of time and space and for the equilibrium charge-voltage relation. These surprisingly simple solutions compare well with the results from comprehensive two-dimensional simulations. Useful analytical expressions are obtained for optimal geometrical and operational parameters that maximize the productivity and minimize the specific energy losses. By making cells much thinner the productivity can be increased an order of magnitude compared to typical values in the literature. The optimal electrode is found to be roughly six times thinner than the spacer. The associated pressure drop is around 0.4 bar per 1 mM of inlet salt concentration, making our recommendations practically feasible only for relatively low concentrations. The obtained model and analytical expressions provide useful guidance to strongly improve the design process. ... Read more

The electrochemical conversion of CO₂ is a promising method of carbon-neutral chemical production. However, commercial realisation in aqueous electrolytes is challenging, due to competition with the hydrogen evolution reaction (HER), and the propensity for CO₂ to participate in the carbonate equilibrium reactions. These two phenomena are linked through OH⁻ ions, as both the by-product of the catalytic reactions and the culprit behind the parasitic carbonate reactions. By reducing the local catalyst loading where the CO₂ concentration is low, the HER is decreased more than the reactions that are dependent on CO₂ as a reactant. Therefore, it is possible to improve reaction selectivity and reactant utilisation while reducing the capital cost of catalyst. We demonstrate this theory through an analytical solution of a 1D flow electrolyser model. We extend this to a comprehensive model of a contemporary gas-diffusion electrode (GDE) setup. We find that the operation costs are dominated by the electrolyser power consumption and, to a lesser degree, the cost of CO₂ and its recovery at the anode. We numerically obtain the catalyst loading profiles that maximise operating profit. The optimisation process reveals that profits are maximised for high gas flow rates, and consequently, low single pass conversions, where the CO₂ concentration is as high as possible. However, when lower gas flow rates are used for practical reasons, variable catalyst loadings are shown to lead to significant operational improvements, especially in the production of higher C products that require a greater number of electrons transferred. The model is made freely available in MATLAB and its use is encouraged in determining the applicability of variable catalyst loading to future experimental setups. ... Read more

The use of gas diffusion electrodes that supply gaseous CO₂ directly to the catalyst layer has greatly improved the performance of electrochemical CO₂ conversion. However, reports of high current densities and Faradaic efficiencies primarily come from small lab scale electrolysers. Such electrolysers typically have a geometric area of 5 cm², while an industrial electrolyser would require an area closer to 1 m². The difference in scales means that many limitations that manifest only for larger electrolysers are not captured in lab scale setups. We develop a 2D computational model of both a lab scale and upscaled CO₂ electrolyser to determine performance limitations at larger scales and how they compare to the performance limitations observed at the lab scale. We find that for the same current density larger electrolysers exhibit much greater reaction and local environment inhomogeneity. Increasing catalyst layer pH and widening concentration boundary layers of the KHCO₃ buffer in the electrolyte channel lead to higher activation overpotential and increased parasitic loss of reactant CO₂ to the electrolyte solution. We show that a variable catalyst loading along the direction of the flow channel may improve the economics of a large scale CO₂ electrolyser. ... Read more

The electrochemical reduction of CO₂ on planar electrodes is limited by its prohibitively low diffusivity and solubility in water. Gas-diffusion electrodes (GDEs) can be used to reduce these limitations, and facilitate current densities orders of magnitude higher than the limiting current densities of planar electrodes. These improvements are accompanied by increased variation in the local environment within the cathode, with significant effect on Faradaic efficiency. By developing a simple and freely available analytical model of a cathodic catalyst layer configured for the production of CO, we investigate the relationships between electrode reaction kinetics, cell operation conditions, catholyte composition and cell performance. Analytical methods allow us to cover parameter ranges that are intractable for numerical and experimental studies. We validate our findings against experimental and numerical results and provide a derivation and implementation of the analytical model. ... Read more