Reactive flow is imperative in a wide range of chemical sciences, hydrogeological and environmental applications. A parallel numerical framework is presented for modelling the dissolution of a carbonate rock at the pore scale. Mass transport, chemical reactions, solid updates and migration are included in the model which are solved by the combination of lattice Boltzmann and finite volume methods. For calculation of the flow field, the incompressible Stokes equation is solved by applying an efficient lattice Boltzmann method with the D3Q19scheme. The solid-fluid interaction is computed with the finite volume method. The numerical method includes the migration of solid particles released due to dissolution within the porous medium. The solid migration is realised by the cluster analysis and local movement. We validate this model by comparing against published dynamic micro-CT imaging experiments for dissolution of a Ketton carbonate. To measure the local dissolution, the porosity profiles are compared with the published experimental observations. The increases in permeability and porosity are investigated and a power law is derived to describe their relationship. Then, the significance of capturing the migration of solid particles released due to dissolution on hydrological properties of rocks is explored. The numerical approach is able to perform parallel simulation on large high-resolution micro-CT images. We show the importance of simulation directly on micro-CT images without reducing the resolution of rock micro-CT images. Further simulations are performed at Peclet regimes similar to sub-surface flow and the effect of flow rate on reactive transport is studied. This study illustrates the effect of inclusion of solid migration and the capability of simulation of reactive transport directly on high-resolution images and helps understand the reactive transport at the pore scale. (C) 2016 Elsevier Ltd. All rights reserved.