Depleted oil fields in the Gulf of Suez (Egypt) can serve as geothermal reservoirs for power generation using a CO₂-Plume Geothermal (CPG) system, while geologically sequestering CO₂. This entails the injection of a substantial amount of CO₂ into the highly permeable brine-saturated Nubian Sandstone. Numerical models of two-phase flow processes are indispensable for predicting the CO₂-plume migration at a representative geological scale. Such models require reliable constitutive relationships, including relative permeability and capillary pressure curves. In this study, quasi-static pore-network modelling has been used to simulate the equilibrium positions of fluid–fluid interfaces, and thus determine the capillary pressure and relative permeability curves. Three-dimensional images with a voxel size of 0.65 μm3 of a Nubian Sandstone rock sample have been obtained using Synchrotron Radiation X-ray Tomographic Microscopy. From the images, topological properties of pores/throats were constructed. Using a pore-network model, we performed a sequential primary drainage, main imbibition cycle of quasi-static invasion in order to quantify (1) the CO₂ and brine relative permeability curves, (2) the effect of initial wetting-phase saturation (i.e. the saturation at the point of reversal from drainage to imbibition) on the residual-trapping potential, and (3) study the relative permeability-saturation hysteresis. The results improve our understanding of the potential magnitude of capillary trapping in Nubian Sandstone, essential for future field-scale simulations.