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During water injection in a reservoir at the secondary recovery phase, oil is replaced by salt water, producing different saturation zones in the formation containing this reservoir. This process could be optimized if the direction of the fluids is monitored. Since there are large contrasts in the electric conductivity between salt water and oil, geoelectrical methods could provide a water saturation map at any given moment of the production. The case we study here corresponds to a rather shallow reservoir (between 500 and 600 m in depth). As the wells are in production, electrodes for borehole measurements cannot be introduced. Hence, our objectives are to determine the possibilities of detecting the channelling direction of saline water between injection and producing wells, and applying the method of placing electrodes on the surface or even burying them, but at depths corresponding to shallow layers. We design an electrical model of the reservoir and then numerically simulate the geoelectrical response in order to determine the conditions under which the anomaly, i.e. the accumulation of brine in a reduced area, can be detected. We find that the channelling of the brine can be detected for the reservoir studied here if the electrodes are placed at 180 m depth. The Wenner configuration using 16 electrodes provides the best resolution. Therefore, monitoring the voltage at a number of electrodes embedded at rather shallow depths (from a technical-logistic point of view) could give information about the direction of the saline channelling even if a quantitative image of the subsoil cannot be obtained due to the reduced number of electrodes used in the study.