Oil can be displaced from preferentially oil-wet low permeability chalk by spontaneous imbibition of seawater containing a cationic surfactant, C12TAB, as wettability modifier. In the presence of the cationic surfactant, the capillary forces are decreased due to lowering of the IFT, but at the same time, the capillary forces are also increased due to increased water wetness. The relative impact of capillary and gravity forces on the fluid flow is experimentally studied by comparing the fractional oil production rate per area unit from the top surface and the other core surfaces. The cores used had a dimension of height approximate to 5 cm and diameter approximate to 3.5 cm. For IFT values in the range of 1.10 mN/m, the displacement of oil was dominated mainly by capillary forces at the start, but a crossover to gravity dominated flow was observed at a later stage. The impact of gravity forces decreased as the height of the core decreased. For IFT values below 0.63 mN/m, the oil displacement was mainly dominated by gravity forces (i.e., the oil was recovered mostly from the top surface of the core). In a fractured carbonate reservoir with significant capillary continuity in vertical direction, it is therefore expected that the oil displacement using the cationic surfactant is totally dominated by gravity forces.