Due to the fracturing fluid imbibition and primary water, oil-water two-phase fluids generally exist in shale nanoporous media. The effects of water phase on shale oil recovery and geological carbon sequestration via CO2 huff-n-puff is non-negligible. Meanwhile, oil-CO2 miscibility after CO2 huff-n-puff also has an important effect on oil-water two-phase flow behaviors. In this work, by considering the oil-CO2 competitive adsorption behaviors and the effects of oil-CO2 miscibility on water wettability, an improved multicomponent and multiphase lattice Boltzmann method is proposed to study the effects of water phase on CO2 huff-n-puff. Additionally, the effects of oil-CO2 miscibility on oil-water flow behaviors and relative permeability are also discussed. The results show that due to Jamin's effect of water droplets in oil-wetting pores and the capillary resistance of bridge-like water phase in water-wetting pores, CO2 can hardly diffuse into the oil phase, causing a large amount of remaining oil. As water saturation increases, Jamin's effect and the capillary resistance become more pronounced, and the CO2 storage mass gradually decreases. Then, based on the results from molecular dynamics simulations, the influences of oil-CO2 miscibility on oil-water relative permeability in calcite nanoporous media are studied, and as the oil mass percentage in the oil-CO2 miscible system decreases, the oil/water relative permeability decreases/increases. The improved lattice Boltzmann model can be readily extended to quantitatively calculate geological CO2 storage mass considering water saturation and calculate the accurate oil-water relative permeability based on the real 3D digital core.