Design and optimisation of alkaline water electrolysers depend on modelling equations. One of these equations relate to the gas hold-up, a key factor influencing performance of electrolysers. In electrolysis setups, a maximum gas hold-up is observed which affects the resulting gas hold-up. Gas hold-up prediction models adhere to this maximum gas hold-up, yet its exact nature remains open to discussion. Additionally, relations of slip velocities within the electrochemical multi-phase flows in electrolysis setups are not well understood yet. Several studies propose empirical models, but the mapping of gas hold-up and slip in terms of operating conditions is limited.
Accordingly, this study involves experimental measurements of gas hold-up across a broad range of operating conditions in terms of current densities and superficial liquid velocities. Gas hold-up prediction models are tested on their validity across these operating conditions. Both an explicit as well as an implicit 1D model are addressed and compared to the existing Coalescence Barrier Model. Validity ranges for specific slip and gas hold-up relations have been identified.
The explicit 1D model shows good agreement with flows that are dominated by liquid flow inertia and have relatively small slip. On another note, it was found that slip is pronounced intensely at higher current densities, which led to the proposal of a slip boosting factor. As its exact origin is unclear, it raises more questions on the validity of existing slip functions at higher current densities. A transition towards slug flow might explain this, but should be studied further.
Further results conclude a consistent and physically sensible maximum gas hold-up of ⟨ε⟩_max = 0.71 for the proposed implicit 1D models, compared to a rather arbitrary ⟨ε⟩_max = 0.49 for the Coalescence Barrier Model.
Additionally, slip functions have been assessed. Results over the assessed range of operating conditions indicate accurate gas hold-up predictions using an empirical hindrance factor of (1-⟨ε⟩)^2.54, which aligns closely with the theoretically derived Marrucci equation.

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. @en