Crude biogas upgrade is required in order to boost its industrial use as it contains impurities such as carbon dioxide, carbon monoxide, hydrogen sulphide and ammonia that limits its value. Renewable hydrogen is a clean, carbon-free energy resource that is obtainable from biogas upgrade via the reforming process. To increase hydrogen yield and CO conversion in reformate gas, the product of reforming, the water gas shift (WGS) reaction is required. The conduction of the WGS reaction in a membrane reactor (MR) is a process intensive technology that not only increases hydrogen yield and purity but also reduces costs due to lesser energy required and lesser number of process units required compared to the traditional WGS approach. The use of a novel catalyst that combats the limitations of the traditional WGS catalyst is necessary to further cut down costs and improve the overall process efficiency. Such a novel catalyst (3Ni5Cu/Ce0.5Zr0.33Ca0.17) was developed in a previous experimental study in our group. To gain insights into the interaction of 3Ni5Cu/Ce0.5Zr0.33Ca0.17 catalyst with fluid transport phenomena taking place inside the reactor, a comprehensive computational fluid dynamics (CFD) model has been developed in this study for WGS reaction of biogas reformate in a reactor with and without the presence of a membrane. The model is comprehensive, as it does not consider non-practical assumptions like isothermal condition, isobaric condition, adiabatic condition, constant fluid properties and ideal feed. The developed CFD model aligned with both literature and experimental results. An average absolute deviation (AAD) of 8.59% and 6.32% was obtained when the CFD model was validated with experimental fixed bed reactor (FBR) data and experimental MR data respectively. Comparison between operating the MR in counter-flow configuration versus co-flow configuration revealed that the counter-flow configuration is marginally better in terms of CO conversion. The advantage of the counter-flow configuration is however more evident with respect to decreasing the exothermic temperature rise within the catalyst bed. Increasing the wall heat transfer coefficient from 0 to 14.6 W/m2/K results in a rise in conversion of 8% and 5% for the MR and FBR respectively. Above 8.6 W/m2/K, the effect on conversion is negligible, amounting to only a 1% increase in conversion for both reactors. Conversion values comparable to equilibrium conversion was attained by increasing either the H2O/CO ratio to 3.4 or the catalyst weight time to 2.95 gcat.h/mol CO. Equilibrium conversion was exceeded when the catalyst weight time is increased to at least 2.04 gcat.h/mol CO and the H2O/CO ratio is as high as 3.4.