We study the impact of the neutron star binaries ’ ( NSBs ) natal kick distribution on the Galactic r-process enrichment . We model the growth of a Milky Way type halo based on N-body simulation results and its star formation history based on multi epoch abundance matching techniques . We consider the NSBs that merge well beyond the galaxy ’ s effective radius ( > 2 \times R _ { \mathrm { eff } } ) do not contribute to Galactic r-process enrichment . Assuming a power-law delay-time distribution ( DTD ) function ( \propto t ^ { -1 } ) with t _ { \mathrm { min } } = 30 Myr for binaries ’ coalescence timescales , and an exponential profile for their natal kick distribution with an average value of 180 km s ^ { -1 } , we show that up to \sim 40 % of all formed NSBs do not contribute to r-process enrichment by z = 0 , either because they merge far from the galaxy at a given redshift ( up to \sim 25 % ) or have not yet merged by today ( \sim 15 % ) . Our result is largely insensitive to the details of the DTD function . Assuming a constant coalescence timescale of 100 Myr well approximates the adopted DTD with 30 % of the NSBs not contributing to r-process enrichment . Our results , although rather dependent on the adopted natal kick distribution , represent a first step towards estimating the impact of natal kicks and DTD functions on r-process enrichment of galaxies that would need to be incorporated in the hydrodynamical simulations .