We present cosmological hydrodynamical simulations of galaxy clusters aimed at studying the process of metal enrichment of the intra-cluster medium (ICM). These simulations have been performed by implementing a detailed model of chemical evolution in the TREE-PM+SPMGADGET-2 code. This model allows us to follow the metal release from Type II supernovae (SNII), Type Ia supernovae (SNIa) and asymptotic giant branch (AGB) stars by properly accounting for the lifetimes of stars of different mass, as well as to change the stellar initial mass function (IMF), the lifetime function and the stellar yields. As such, our implementation of chemical evolution represents a powerful instrument to follow the cosmic history of metal production. The simulations presented here have been performed with the twofold aim of checking numerical effects, as well as the impact of changing the model of chemical evolution and the efficiency of stellar feedback. In general, we find that the distribution of metals produced by SNII is more clumpy than for the product of low-mass stars, as a consequence of the different time-scales over which they are released. Using a standard Salpeter IMF produces a radial profile of iron abundance which is in fairly good agreement with observations available out to ~=0.6R500. This result holds almost independent of the numerical scheme adopted to distribute metals around star-forming regions. The mean age of enrichment of the ICM corresponds to redshift z ~ 0.5, which progressively increases outside the virial region. Increasing resolution, we improve the description of a diffuse high-redshift enrichment of the inter-galactic medium (IGM). This turns into a progressively more efficient enrichment of the cluster outskirts, while having a smaller impact at R <~ 0.5R500. As for the effect of the model of chemical evolution, we find that changing the IMF has the strongest impact. Using an IMF, which is top-heavier than the Salpeter one, provides a larger iron abundance, possibly in excess of the observed level, also significantly increasing the [O/Fe] relative abundance. Our simulations always show an excess of low-redshift star formation and, therefore, of the abundance of oxygen in central cluster regions, at variance with observations. This problem is not significantly ameliorated by increasing the efficiency of the stellar feedback.
