We present a numerical model to simulate reactive transport involving homogeneous (fluid-fluid) and heterogeneous reactions (fluid-solid) in porous media. The model includes mass transport, homogeneous reaction, heterogeneous reaction and solid modification. The model is validated by comparing reactive flow in simple geometries with analytical solutions and previously published experimental results. Fluid flow, solute transport, and chemical reactions are simulated directly on 3D images of carbonates. The concentration profiles are analysed for comparison of homogeneous and homogeneous heterogeneous reactions. A large discrepancy is observed between the concentration profiles of reactants due to the mineral dissolution. The simulation results are also compared with the predictions of reactive transport model with only heterogeneous reactions. In such regimes, mineral dissolution occurs near the inlet. However, with addition of homogeneous reaction, more uniform dissolution is observed in the carbonate. Rock mechanical properties including Young's modulus and Poisson's ratio are also compared between the two reaction conditions. The results show that the homogeneous-heterogeneous reaction leads to pore geometries with higher mechanical strength. This work investigates the complex process of chemical reactions in carbonates and improves the understanding of reactive transport in porous media. (C) 2017 Elsevier Ltd. All rights reserved.