We model the experimental results on waterflooding of fractured chalk block using a numerical simulator and demonstrate that the oil recovery depends nonlinearly on the applied differential pressure. We argue that for small flow velocities, the recovery is mostly affected by capillary forces, and for higher flow velocities–by viscous forces. This interplay is analysed using a sensitivity study for different values of the applied differential pressure. For the test cases considered, we obtain a range of boundary pressures which yield optimal waterflood efficiency. The results are presented for both brine and smart water, which is represented by a relative permeability function with reduced residual oil saturation.