Permeability decline during corefloods with varying water composition, especially with low salinity water, has been widely reported in the literature. It has often been explained by the lifting, migration and subsequent plugging of pores by fine particles, which has been observed in numerous core flood tests with altered water composition. In the present paper, we derive a new system of governing equations describing fines mobilisation, migration and subsequent permeability decline for 1-phase and 2-phase flows. In large scale approximation, the mathematical model for 2-phase flow with induced fines migration is equivalent to polymer flooding model. It allows taking advantage of the polymer flooding option for the Eclipse black oil simulator in order to model waterflood with low salinity water, where the induced fines migration and permeability damage can be considered to provide a relatively simple method for mobility control during waterflooding. The modelling showed that permeability decline in the water swept zone, caused by the alteration of the injected water composition and induced fines migration, may be able to improve waterflood performance by delaying water breakthrough and reducing the water cut.