The Korba aquifer is located in the east of the Cape Bon peninsula in Tunisia. A large groundwater depression has been created in the central part of the aquifer since the 1980s, due to intense groundwater pumping for irrigation. The data collected show that the situation continues to deteriorate. Consequently, seawater is continuing to invade a large part of the aquifer. To better understand the situation and try to forecast its evolution, a three dimensional (3D) transient density-dependent groundwater model has been developed. The model building process was difficult because of data required on groundwater discharge from thousands of unmonitored private wells. To circumvent that difficulty, indirect exhaustive information including remote sensing data and the physical parameters of the aquifer have been used in a multi-linear regression framework. The resulting 3D model shows that the aquifer is over-exploited. It also shows that after 50 years of exploitation, the time needed to turn back to the natural situation would be about 150 years if the authorities would ban all exploitation now. Such an asymmetry in the time scales required to contaminate or remediate an aquifer is an important characteristic of coastal aquifers that must be taken into account in their management.