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Abstract Low salinity waterflooding is an emerging EOR technique in which the salinity of the injected water is controlled to improve oil recovery over conventional higher salinity waterflooding. Corefloods and single well chemical tracer tests have shown that low salinity waterflooding can improve basic waterflood performance by 5 to 38%. This paper describes a model of low salinity flooding that can be used to evaluate projects, shows the implications of that model, demonstrates its use to represent corefloods and single well tests as well as field scale simulations, and gives insight into the reservoir engineering of low salinity floods. The model represents low salinity flooding using salinity dependent oil/water relative permeability functions resulting from wettability change. This is similar to other EOR modelling and conventional fractional flow theory can be adapted to describe the process in one dimension for secondary and tertiary low salinity waterflooding. This simple analysis shows that while some degree of connate water banking occurs it need not hinder the process. Because mixing of injected water with in situ water delays the attainment of low salinity, potentially preventing attainment of low salinity all together if very small slugs of low salinity water are used, care must be taken in representing mixing appropriately in interpreting data and in constructing models. The use of numerical dispersion to represent physical dispersion in 1D, radial and pattern simulations of this process is demonstrated, i.e. coarse simulations are shown to give the same result as fine grid simulations with appropriately large physical dispersion. In many applications, the fine grid simulation necessary to represent appropriate levels of dispersion is not practical and pseudoization is necessary. We demonstrate that this can be done by changing the salinity dependence and shapes of relative permeability curves.