We apply a multi-component reactive transport lattice Boltzmann model developed in previous studies for modeling the injection of a CO2-saturated brine into various porous media structures at temperatures T = 25 and 80 degrees C. In the various cases considered the porous medium consists initially of calcite with varying grain size and shape. A chemical system consisting of Na+, Ca2+, Mg2+, H+, CO degrees 2 (aq), and Cl is considered. Flow and transport by advection and diffusion of aqueous species, combined with homogeneous reactions occurring in the bulk fluid, as well as the dissolution of calcite and precipitation of dolomite are simulated at the pore scale. The effects of the structure of the porous media on reactive transport are investigated. The results are compared with a continuum-scale model and the discrepancies between the pore- and continuum-scale models are discussed. This study sheds some light on the fundamental physics occurring at the pore scale for reactive transport involved in geologic CO2 sequestration.