Geological storage of CO₂ in deep saline reservoirs is being studied widely to reduce carbon emission from power plants. The physics of CO₂-brine flow at pore-scale is a key part of prediction of amount and fate of residual trapped CO₂. The description of this flow system in the form of pore-level flow models through pore-bodies and pore-throats of an extracted pore-network (PN) from micro-CT images of real rock is a practical approach to obtain important characteristic curves during a drainage-imbibition cycle. However, this description can be improved by more specific and accurate relations for CO₂-brine flow that can come from direct numerical simulation methods. This study presented a new set of pore-level flow models during pore-body filling and snap-off events of imbibition process in PN modeling of CO₂-brine flow. Lattice-Boltzmann simulations were carried out on several designed PN configurations and the threshold local capillary pressure was evaluated to develop modified equations of threshold capillary pressure as a function of shape factor. The modified equations of local capillary were incorporated in a quasi-static PN solver. This modified model resulted a new pattern of invasion during imbibition process due to a different order of competing pore-level events compare to the original model. We applied the modified model on extracted PN of a Berea sandstone sample to obtain relative permeabilities and saturation of residual trapped CO₂ after a drainage-imbibition cycle. The statistics of pore-level imbibition events changed by replacing the original model with the modified model. The occurrence of snap-off in pore-throats was reduced by about 10% which means more frontal displacement pattern across the sample. As a result, our modified model was in closer agreement than the original model based on the comparison of the residual trapped CO₂ with experimental data.