Carbon dioxide geological storage has the potential to reduce the atmospheric carbon dioxide concentration and limit climate change. In this method, carbon dioxide is injected into underground geological formations to permanently reside in the capillary networks of reservoir rocks. Due to the physical mechanism of capillary trapping, carbon dioxide is immobilized inside the rock's pore channels. We deploy computational models that describe a rock's pore space as a network of connected capillaries with spatially varying radii in which fluids flow in the laminar regime. The network-based representation is extracted from x-ray microtomography images of representative rock samples, providing the geometric boundaries for single- and multi-phase flow simulations. In this contribution, we map the parameter space by assessing the effects of fluid properties such as viscosity, interfacial tension and contact angle on the amount of carbon dioxide that can be trapped inside the capillary network. In order to decrease the computational cost, we employ a novel network simplification technique that preserves the original network's geometrical and topological properties. We demonstrate how the choice of parameters determines the trapping efficiency of supercritical carbon dioxide in digital representations of sandstone rock samples at elevated pressures and temperatures.