The evolution of the residual oil saturation as a function of the trapping number (capillary number plus Bond number), is generally known as the capillary desaturation curve (CDC) and constitutes an important input parameter in chemical enhanced oil recovery flooding. However, less importance has been paid to the investigation of the influence of oil ganglia evacuation on relative permeabilities. We report on an experimental investigation dealing with the effect of flooding parameters, fluid interfacial properties and rock structure on the CDC and on the water relative permeability. Experiments were performed on a set of water-wet sandstone plugs with different petrophysical properties, and X-ray computed tomography (CT-scan) imaging was used to accurately measure the local oil saturation. Oil ganglia size distribution as well as pore scale geometrical properties was also quantified at the scale of the micrometer using high-resolution micro-computed tomography (MCT). Results showed that the CDC depends on the pore structure and specifically on the average throat radius and the inverse of the relative permeability. Oil ganglia size distribution obtained by MCT follows a typical power law as suggested by percolation theory. We also showed that CDC obtained from macroscopic measurements can be predicted from the measured oil ganglia size distribution and rock structure geometrical parameters. In parallel, we observed that for low trapping numbers, water relative permeability is independent of the trapping number. However, for intermediate trapping numbers, a strong dependence of the water relative permeability on the latter can be noticed. In this range, we showed that water relative permeability has a specific scaling with the trapping number.