Depleted oil fields in the Gulf of Suez (Egypt) can serve as geothermal reservoirs for power production 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 modeling 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 illustrate the sensitivity of the pore-scale fluid-displacement and trapping processes on some key parameters (i.e. advancing contact angle, pore-body-to-throat aspect ratio, and initial wetting-phase saturation) and improve our understanding of the potential magnitude of capillary trapping in Nubian Sandstone.