Capillary trapping plays a central role in the geological storage of CO2, oil recovery, and water soil infiltration. The key aim of this study is to investigate the impact of surface properties (wettability, roughness, heterogeneous mineral composition) on the dynamics of quasi-static fluid displacement process and capillary trapping efficiency in porous medium. We concluded that for homogeneous wet smooth glass beads surfaces, a transition in fluid displacement pattern occurs from a compact (for θ < 90°; imbibition process) to a fractal front-pattern (for θ > 90°; drainage process) leading to a crossover in capillary trapping efficiency from zero to maximum. The impact of surface roughness on capillary trapping efficiency was also studied, and an opposite trends in terms of wettability dependency was observed. Rough natural sands surfaces depicts a non-monotonous wettability dependency, i.e. a transition from maximal trapping (for θ < 90°) to no-trapping occurs (at θ = 90°), followed by an increase to medium trapping (for θ > 90°). For a fractional-wet media, the percolating cluster of hydrophobic sediments (connected hydrophobic pathways) characterize the fluid displacement pattern and trapping efficiency.