Abstract Chalk fields in the North Sea have seen recent large increases in recovery factors and a lowered limit on the effective permeability of reservoirs that can be developed. For example, the Halfdan Field in Denmark has an effective permeability of 0.5 mD. As a result the industry expects to recover significantly more hydrocarbons from most Chalk fields but, in addition, there is an additional source of upside in existing fields, which is the dynamic trap. Due to the low permeability of the Chalk, hydrocarbon migration and re-equilibration occurs over geological time-scales. Examples of these types of traps are the Halfdan and South Arne fields in the Danish sector and, possibly, the Joanne Field in the UK. All these fields have strongly tilted free-water levels (FWLs). The implications are that reserves downflank of discoveries may be overlooked, as was the case with the South Arne Field, developed 30 years after discovery following the drilling of better reservoir downflank and tilted FWLs. Another example is the Halfdan Field, which was discovered in 1999. The oil legs in the Halfdan and Dan fields are connected, but Halfdan was not discovered until 1998, although Dan has been producing since 1972. Dynamic trapping mechanisms also suggest enormous additional exploration potential in the North Sea Chalk if the location of migrating hydrocarbons can be predicted. A new type of trap — the constriction trap — is discussed, which is caused by a permeability reduction in the migration direction causing ‘banking’ of hydrocarbons due to the greater influx of hydrocarbons than outflow over geological time. The thickness of post intra-Chalk unconformity Chalk in the Danish sector is used to predict these traps in the Chalk: lateral thinning of the relatively high permeability Tor can potentially create a trap if all the other elements of the petroleum system are in place.