The increasing adoption of hydrogen in industrial applications is driven by its potential to decarbonize various industries. Among the various methods of hydrogen production, water electrolysis is considered one of the environmentally friendliest options. However, hydrogen produced from water electrolysis contains impurities such as oxygen and water vapour, and the required level of purity varies depending on the specific industrial application. To address this issue, catalytic recombination of hydrogen and oxygen into water is selected as a method for oxygen removal due to its high efficacy in completely converting oxygen. Subsequently, hydrogen drying is achieved using Pressure Swing Adsorption (PSA) following the catalytic recombination process. This thesis work primarily focuses on the modelling and sizing of adsorption columns within the PSA system. One-dimensional dynamic models describing the pressurization, adsorption, depressurization, and desorption steps of PSA are mathematically derived and developed in Python. The adsorption modelling approach is validated using experimental data from a scientific paper. Insightful information was obtained during the model validation process, shedding light on the consequences of the assumptions made to simplify the energy balance, as well as revealing the decrease in adsorption capacity during the pressurization process. The PSA system is designed to process 400 kg of hydrogen per day with the aim of reducing the water vapour content below 5 ppm. While pressure plays a central role in PSA control, it has been discovered that the primary design challenge relates to temperature control within the operating range. Therefore, adsorption column sizing is optimized, taking into account PSA performance and required energy input. A sensitivity analysis is conducted to identify the optimal adsorbent, considering zeolite 3A and silica gel. Based on the results, a column length of 2 meters and a diameter of 0.0914 meters are considered optimal for zeolite-packed adsorption columns, resulting in a productivity of 35.62 mol/hr/kg and requiring 50.21 kJ during the desorption step. The optimal size for silica gel-packed adsorption columns has not been determined due to a significant temperature drop during desorption, which could risk ice formation and subsequent flow blockage. Nevertheless, silica gel, with its higher adsorption capacity leading to a longer adsorption step, remains a viable option from an operational perspective and should not be disregarded as a potential choice.