Geological carbon sequestration is a proven method of safely storing carbon dioxide in formations, thereby reducing atmospheric carbon imprint and mitigating global warming. The relative permeability to carbon dioxide versus brine/water in geological formations determines flow characteristics of one fluid in the presence of another. The objective of this research is to evaluate the relative permeability to carbon dioxide in both the gas phase and the supercritical state in the presence of water in a Vedder sandstone core sample. The sandstone sample used is medium- to fine-grain arkosic artenite containing primarily quartz, potassium feldspar, plagioclase, and biotite. The effect of the viscosity ratio between the non-wetting phase and the wetting phase, on the relative permeability to the non-wetting phase, is studied. Computational fluid dynamics (CFD) is used for this study. Results show that with the same amount of irreducible water fraction, the endpoint relative permeability to the non-wetting phase is approximately one order of magnitude lower for supercritical carbon dioxide than for gaseous carbon dioxide. The endpoint relative permeability does not change significantly with the change in inlet pressure for gaseous carbon dioxide. Additionally, the endpoint relative permeability to the non-wetting phase increases with an increase in the viscosity ratio. Results suggest that CFD can be effectively used to study relative permeability, precluding expensive experiments.