We focus on numerical simulation of low salinity waterflood on outcrop-based models, which are representative of North Sea fractured chalk reservoirs. To this end, we consider a 2D model of an outcrop at Lägerdorf quarry in northwest Germany, which reveals an extensive fracture network together with several major faults, see Koestler and Rekstein (1995). The model is populated with rock and fluid properties, representative for North Sea chalk reservoirs, see Graue and Bognø (1999). We discretize the domain using a Discrete Fracture Matrix (DFM) approach so that the fractures are represented as low-dimensional finite volumes, see Gläser et al. 2017. Low salinity waterflood is modelled as a two-phase oil-water immiscible displacement with oil being a single component incompressible liquid. The water phase is represented either with two components - high-salinity (HS) and low-salinity (LS) injection water, or with a variable number of chemical elements. In the latter case, the thermodynamic equilibrium for the water phase is achieved by coupling the transport solver to the reaction module PhreeqcRM of Parkhurst and Wissmeier (2015). This model was implemented in DuMuX, a free and open-source simulator for flow and transport processes in porous media, see Flemisch et al. 2011. We run a sensitivity study on the dependency of recovery rate on water injection rates for various fracture apertures and wettability distribution. The results demonstrate that for certain range of injection rates there is an optimal value in terms of recovery rate vs. number of pore volumes injected.