We present results from a new numerical model capable of simulating two-phase flow in a porous medium and the electrical potentials arising due to electrokinetic phenomena. We suggest that, during water-flood of an initially oil-filled reservoir, encroaching water causes changes in the electrokinetic potential at the production well which could be resolved above background electrical noise; indeed, water approaching the well could be detected several 10's to 100's of meters away. The magnitude of the measured potential depends upon the production rate, the coupling between fluid and electrical potentials, and the nature of the front between the displaced oil and the displacing water.