Physically? Eventually all the containers would be full, then the pipelines would back up, then the ships would be full and lack any place to unload, then the loading terminals at oil producing countries would be full, then their pipelines would be full, then finally any buffer at the well head would be full, and ultimately the well owners would be forced to stop pumping or else place the oil somewhere other than into the system (on the ground or into the sky by burning it).