Because of the high green-house gas emission, in the last decade there was an increased interest on underground disposal of carbon-dioxide (CO2) in underground geological formations. One example of those is deep saline aquifer, what has a wide availability around the world. As underground CO2 storage is a long-term commitment, the determination of the injected CO2 plume migration is essential. The displacement process of brine by CO2 at the early injection stages (when saturation equilibrium is already achieved), what is the objective of this study, can be described as two-phase immiscible flow dominated by primary drainage. As brine and CO2, even in supercritical state, has substantial density and viscosity contrast; instabilities, as viscous fingering and gravity override, are expected to occur. There are several petro-physical properties affecting the displacement front stability of CO2 plume, including relative permeability relationships and capillary saturation function. The stabilizing effect of capillary pressure as a function of different length scales and the effect of the parameter alteration of the extended Corey relative permeability model on the CO2 flood front stability had been studied extensively by means of numerical simulation. The scope of this research is to broaden the available results on the displacement stability of CO2-brine systems by performing a sequence of numerical simulations with a focus on the possible mitigation effect of micro-porosity (typical for carbonates) on gravity segregation, by the occupation of micro-pores. To obtain an extensive picture on the effect of micro-pores on displacement stability, series of numerical experiments were performed in 2D, under representative conditions for CO2 sequestration, with the systematic modification of length scales, capillary saturation functions representing typical rock types and the exponents of the extended Corey-model. Furthermore, the length-scale effect of gravity-override mitigation by micro-porosity was investigated. With the simulation results it was exemplified that with increasing length-scale (so increasing expected CO2 column) the micro-porosity gains substantial effect on the stabilization of gravity fingering.