With an alarming rise in carbon dioxide (CO2) emission from anthropogenic sources, CO2 sequestration has become an attractive choice to mitigate the emission. Some popular storage media for CO{sub 2} are oil reservoirs, deep coal-bed, and deep oceanic-beds. These have been used for the long term CO{sub 2} storage. Due to special lowering viscosity and surface tension property of CO{sub 2}, it has been widely used for enhanced oil recovery. The sites for CO{sub 2} sequestration or enhanced oil recovery mostly consist of porous rocks. Lack of knowledge of molecular mobility under confinement and molecule-surface interactions between CO2 and natural porous media results in generally governed by unpredictable absorption kinetics and total absorption capacity for injected fluids, and therefore, constitutes barriers to the deployment of this technology. Therefore, it is important to understand the flow dynamics of CO{sub 2} through the porous microstructures at the finest scale (pore-scale) to accurately predict the storage potential and long-term dynamics of the sequestered CO{sub 2}. This report discusses about pore-network flow modeling approach using variational method and analyzes simulated results this method simulations at pore-scales for idealized network and using Berea Sandstone CT scanned images. Variational method provides a promising way to study the kinetic behavior and storage potential at the pore scale in the presence of other phases. The current study validates variational solutions for single and two-phase Newtonian and single phase non-Newtonian flow through angular pores for special geometries whose analytical and/or empirical solutions are known. The hydraulic conductance for single phase flow through a triangular duct was also validated against empirical results derived from lubricant theory.