We perform direct numerical simulation using a pore-scale fluid-fluid reactive transport model (Alhashmi et al. in J Contam Hydrol 179:171-181, 2015. doi:10.1016/j.jconhyd.2015.06.004) to investigate the impact of pore structure heterogeneity on the effective reaction rate in different porous media. We simulate flow, transport, and reaction in three pore-scale images: a beadpack, Bentheimer sandstone, and Doddington sandstone for a range of transport and reaction conditions. We compute the reaction rate, velocity distributions, and dispersion coefficient comparing them with the results for non-reactive transport. The rate of reaction is a subtle combination of the amount of mixing and spreading that cannot be predicted from the non-reactive dispersion coefficient. We demonstrate how the flow field heterogeneity affects the effective reaction rate. Dependent on the intrinsic flow field heterogeneity characteristic and the flow rate, reaction may: (a) occur throughout the zones where both resident and injected particles exist (for low P,clet number and a homogeneous flow field), (b) preferentially occur at the trailing edge of the plume (for high P,clet number and a homogeneous flow field), or (c) be disfavored in slow-moving zones (for high P,clet number and a heterogeneous flow field).