The South Arne field presents an example of a North Sea chalk field with an oil distribution strongly affected by fluid dynamics, even at initial conditions. The oil-saturation variation in the South Arne field is effectively modeled with free-water-level (FWL) surfaces, the height above which defines the capillary pressure of oil vs. water. This FWL is in the shape of an elongated dome with a relief on the order of 200 m, corresponding to a smooth, lower-amplitude version of the field structure itself. Dip of the FWL exceeds 100 m/km locally. 2D geological time-scale reservoir simulation is successfully deployed to replicate observed oil-saturation distribution and geometry of the FWL surface. This modeling greatly improves the understanding of and ability to predict the saturation distribution. The anomalous doming of the FWL is thus shown to be because of anomalous lateral-pressure gradients mainly in the water phase, whereas pressure measurements show the oil phase to be without lateral-pressure gradients. The main doming occurs where the oil extends vertically down to a seal at the base of the reservoir. The strong FWL dip is thus maintained on geological time scales (but less than 5 million years) because of low relative permeability to water, whereas oil flows just as readily as in other chalk fields. Because the dip is controlled mainly by low relative mobility of the water, the dip tends to vanish in parts of the field where a water leg is present in permeable rock beneath the oil to allow dissipation of anomalous water pressures. Partial- to full-preproduction imbibition has been identified and modeled in some flank areas. This explains why these parts produce water while other areas at similar saturation and porosity levels flow oil owing to drainage conditions. Identification of degree of imbibition is thus of paramount importance for optimal well placement and prediction of performance. An additional anomaly is found on the northeast flank of the field, where oil in drainage conditions is found deeper than anywhere else in the field. This deep occurrence of oil owes its presence to an anomalously permeable sandy layer close to the northeast flank, stratigraphically above the reservoir. This layer partially drains overpressure, thereby allowing oil to move down the flank from the main field, again because of water-phase-pressure variation, possibly allowing oil to spill into the sandy layer.