Oil recovery from water‑wet, naturally fractured reservoirs subjected to waterflooding is governed by spontaneous imbibition of water from the fractures into the matrix rock due to capillary and gravity forces, which results in the displacement of the non‑wetting oil. Several parameters, such as wettability, boundary conditions, rock geometry, fluid properties, and IFT between oil and water affect the oil recovery. A three‑dimensional, two‑phase numerical simulator was developed to investigate both mechanisms of oil production and the parameters that influence recovery in water‑wet laboratory cores. The model was validated by a comparison of calculations to the numerical simulation of Blair (1964) and experimental data presented by Schechter et al. (1991) and Fischer & Morrow (2005). Agreement between model calculations and data was excellent. When capillary forces are negligible, gravity force causes displacement of the oil spontaneously due to density difference between the oil and water in cores mounted vertically. The effect of reducing the interfacial tension between water and oil on oil recovery by spontaneous imbibition was numerically investigated for a wide range of IFT's in cores oriented vertically and compared against experimental data. Capillary force is lowered when IFT is reduced through capillary pressure curve. The study showed that reducing the IFT between oil and water may decrease the rate of imbibition in low permeability cores. However, the ultimate recovery increases when compared to the same system with higher IFT. Comparison of the imbibition curves obtained for the same value of oil/water viscosity ratio revealed that oil recovery is lowest when the one‑end, open‑boundary condition was applied on the core. Ultimate recovery was almost the same in all other different boundary conditions.